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Tutorial on Biological Vision- 1

1. The last 500 Million Years of Evolution

Taxonomists have struggled mightily in organizing the animal kingdom by familiar traits [1.2]. They have usually considered about 12 different traits as important. By selecting these traits in different order, they have constructed many family trees representing the evolution of all animals from a single cell ancestor. A sequence that has been useful and widely published is: + Type of body symmetry + Presence or absence of a coelom, an intestinal tract + Presence or absence of a digestive system + Type of skeleton This sequence has led to the widely recognized dichotomies, vertebrates versus invertebrates OR chordates versus non chordates OR internal versus external skeletons. It has also generated the much more formal dichotomy dividing all animals into Protostomia and Deuterostomia, which also conform approximately to non-chordates and chordates respectively. These formal names have led to the formal Diphyletic Theory of Phylogeny. This theory is not well suited to describing animal vision. Figure 1.1.1-1 provides a more detailed phylogenic tree describing the bilaterally symmetrical animals. It is based on two traits. First, it is based on the form of the eyes used in the animal kingdom. It is also based on an unusual second trait. This second trait is based on the molecular form of a s116pecific retinoid found in the animals. The retinoids are a large group of organic chemicals based on the structure of Vitamin A. The name retinoid is derived from the common name for Vitamin A, retinal. This vitamin has had a close association with vision since its discovery in the early 1900's. The figure includes a bottom row to help orient the reader. With the recent discovery of the hyperthermophiles (primarily tube worms at the bottom of the ocean near hot water vents), the most recent classification of life contains three branches. The first and possibly oldest is Archaea. It is a eukaryote system, (including the hyperthermophiles), that does not rely upon oxygen in its metabolism. The second branch contains the oxygen loving prokaryotes, the Bacteria. The third branch includes the eukaryotes that include the plant and animals. In this arrangement, the Algae and Fungi are considered plants. Protozoa remain grouped with the animals. Many primitive animals placed between the protozoa and the first animal of interest in vision continue to live to this day. These animals divide into two fundamental groups. Group I includes animals that lack a symmetry with respect to their features or exhibit a point symmetry. This symmetry is found in cylindrical animals and starfish. Many animals in this group, such as the round worms, lack any obvious structural symmetry. Group II animals generally exhibit a bilateral symmetry. It begins with the very simple flat worms. They are assigned to the Phylum, Annelida. The first animal to exhibit a primitive vision capability was an early bilaterally symmetrical flat worm known as Annelida Planaria.

2 Guide to Processes in Biological Vision The bilateral feature seems to have been the key to success in evolution. Annelida soon evolved into three additional phyla that form the cornerstones of animal life today. These additional phyla exhibit substantially different forms based on their skeletons. Mollusca includes a wide range of essentially skeleton-free, soft bodied animals. Most of these animals are aquatic. Arthropoda include a similarly wide range of animals with an exterior shell-like skeleton. The insects, spiders and many other classes and families are members of this phylum. Chordata include animals with well-defined internal skeletons, although the skeletons need not be completely calcified. The internal skeleton allows the animal to grow larger without needing to shed its skeleton. On the other hand, many members of Chordata display a keratinoid-based external structure providing some protection found in an external skeleton. These structures are usually localized and do not impede growth. Many animals within Chordata belong to the class, Vertebrata. Vertebrata is also known by the name Craniata indicative of the hard skeletal case enclosing the central nervous system, the brain. Using the name Vertebrata as a synonym for Chordata is misleading when discussing vision. It leads to the dichotic classification of all other animals as invertebrates. As will be developed in the next section, the bilateral animal kingdom is best described by a triphyletic theory, based on the unique eyes found in Mollusca, Arthropoda and Chordata. This organization leaves the phylum Annelida, and the point symmetrical phylum known as Radiata in null positions. The members of these phyla do not have eyes by the definition to be developed below. In this work, the word Chordata will be used rather than Vertebrata because of its greater scope. While all vertebrates are chordates, the opposite is not true. No time will be wasted discussing whether sharks, and other animals with non-calcified spines, are vertebrates. They are clearly chordates. Figure 1.1.1-1 Phylogenic relationships tracing the presence of Vitamin A in various families and species. Note the presence of Vitamin A2 and A3 but the predominance of Vitamin A1. The form of the vitamin used appears to depend on the environment. The chart varies considerably from that of other investigators. Several authors use the horizontal dashed line to separate vertebrates from invertebrates . Only the phylum Chordata is reasonably completely documented.

The figure has been annotated with letter subscripts describing the type of Vitamin A found in a variety of species. The interesting fact is that the type of Vitamin A found in the circulation of an animal depends more on its environment than anything else. An even more interesting fact to this author is the discovery of a third fundamental form of Vitamin A.

Two forms of Vitamin A have been known previously. The form found in all marine animals, and animals living on land but derived from marine animals, is known as Vitamin A1. The form found in all freshwater-based animals is known as Vitamin A2. Recently, a third fundamental form, Vitamin A3 has been defined based on animals, primarily insects, who feed on decaying plant matter. Although many Orders of Insecta use Vitamin A3, the largest Order is known as Diptera. The three forms of Vitamin A differ in the state of oxidation of part of the retinal molecule known as

Tutorial on Biological Vision- 3 the ionone ring. Note carefully the anadromous and catadromous fish. These animals begin life based on one form of Vitamin A but change to a second form during their lifetime. The change depends on their migratory pattern. Salmon are considered anadromous based on their birth in freshwater followed by their migration to the sea. It is interesting to consider whether their systems would become based on Vitamin A2 again if they lived after their return to their native riverbed to spawn. Figure 1.1.1-2 provides a more concise mapping of the evolution of animals from the sea into two major and one minor “niches.” The map is incomplete but establishes some important guidelines. All of the marine-based families, including the bulk of the terrestrial mammals, have saline-based blood and use Vitamin A1. The figure includes several notes concerning the spectral capability of the different groups. However, the field is far from completely explored. The photochemistry used by all animals provides four distinct spectral absorption bands. Thus, all animals are theoretically capable of tetrachromatic vision. Some may not employ the full tetrachromatic visual spectrum. Many members of Arthropoda, particularly among the insects, are unable to use the long wavelength (L or red) portion of the spectrum. The condition appears related to the temperature of the hive before their birth. It is well established that they can use the ultraviolet (UV), short (S) and Mid (M) wavelength chromophores of animal vision. They can be considered “short-wavelength” trichromats. Among Chordata, most animals sense light in all four spectral regions and are tetrachromats (at least during part of their lifetime). The controlling factors are the size of the animal and its environment. Large terrestrial animals (like man) are particularly susceptible to the loss of ultraviolet performance. As they grow larger, the thickness of the lens of their eye grows proportionally thicker. As a result, the absorption of their lens at wavelengths shorter than 400 nm in the ultraviolet becomes greater. This absorption restricts, but does not eliminate, the operation of the ultraviolet spectral channel of vision. Animals in this category can be considered blocked tetrachromats. They are recognized by the label 3.5 in the figure. Blocked tetrachromats (such as man) are typically labeled trichromats. A particularly large open question remains concerning how many spectral channels are employed by Mollusca. While many members of the phylum display color vision capabilities, the number of spectral channels may vary by species and family. When migrating to freshwater aquatic environments, the families retain their spectral capability but now employ Vitamin A2 in growth and vision. As mentioned above, carrion feeders among Arthropoda are now known to Figure 1.1.1-2 Mapping of phylogenic families by environment. employ Vitamin A3 in their Key considerations involve the salinity of the environment, the bodily functions. The shift in food supply and the index of refraction of the visual medium. the secondary structure of the retinoid causes no significant effect on the spectral response of these animal.

4 Guide to Processes in Biological Vision The literature contains an interesting dichotomy right now concerning the highly inferential science matching genetics to the features expressed by the genetic code in various animals (including humans). Several groups have sought and identified three putative genes responsible for the putative trichromatic vision of humans. However, equally good data is available showing that the human retina is sensitive to the complete visual spectrum, including the ultraviolet. This performance clearly requires the isolation of four genes not three. If the geneticist is correct and he has isolated the genes responsible for color vision in humans, and that spectral data is correct that human vision employs four chromophores, why are there only three genes? Figure 1.1.1-3 expands on the above phylogenic trees and will form a convenient reference. The tree is abbreviated, but remains based on the sequences discussed above. It explicitly recognizes the skeletal types associate with each phylum and shows a parallel between skeletal type and eye type. The species named in the top line are those exhibiting unique characteristics that will be touched upon in this tutorial. Several appear frequently as subjects in the laboratory literature.

Figure 1.1.1-3 An abbreviated Phylogenic Tree focused on the visual aspects of taxonomy. All of the animals shown are bilaterally symmetrical. Planaria can be considered the simplest of the bilaterals. All of the animals to the right of Planaria have a coelom. As indicated by the subtitles within the phylum boxes, each phylum has a different body structure and each phylum has evolved a functionally and structurally different visual system. Planaria, Copilia and Limulus evolved in ancient times but are still available for study. Also noted are the names of other species that have played a major role in the literature of vision. Copilia and Araneae are the only known eyes where the photoreceptors scan separately from, and behind, the lens. Each major phylum has adopted a fundamentally different form of eyes. The details of these will be developed below. Overall, the fundamental eye type is phylum-specific. However, there appears to be some overlap. The literature suggests that some species of Mollusca employ a few compound eyes along with their complex eyes. This would suggest that they carried forward compound eyes from an earlier evolutionary period or they evolved this type of eye independently (a process called evolutionary convergence). Whether members of Mollusca exhibit actual compound eyes may be a

Tutorial on Biological Vision- 5 matter of precision in definition. Alternately, it may be an evolutionary issue. No examples of evolutionary borrowing or significant convergence have been reported among Chordata. However, experimentation with unique variations upon the fundamental eye configurations is found in all phyla. Striking examples of mechanical scanning of the eyes or eye components are found in all phyla. Mechanical scanning is particularly important among the higher primates. Limulus, also known in the vernacular as the horseshoe crab or king crab, illustrates the difficulty of forming a phylogenic tree. Limulus has existed for so long, it affects the development of any chronologically based phylogenic tree. Limulus is not a crab (Subphylum Mandibulata, Order Decapoda). It belongs to a distinctly different subphylum of Arthropoda called chelicerata. Though it exhibits a prominent hard mantle, it is clearly not a member of Mollusca. Turning the animal over displays its exoskeleton. The mantle is unusual in having two compound eyes embedded in it. While modified in interesting ways, these are the eyes of Arthropoda. The Limulus literature is particularly inconsistent regarding its eyes. Some researchers have counted light-sensitive photospots (defined below) located within vascular tissue as eyes. Others have provided descriptions of eyes that can be interpreted as either compound or complex.

6 Guide to Processes in Biological Vision


2. The Variation among Eyes is Enormous

Most multi-celled animals are light sensitive [1.7]. As one ascends the evolutionary tree, the simplest animals begin to exhibit specialized cells sensitive to light. They invariably respond to light by attempting to move away from it. The round worms frequently exhibit light-sensitive cells on the surface of their “leading end.” These patches will be defined as photospots because they have no lens assembly. Early in the development of the flat worms, a bilaterally symmetrical species appeared known as planaria. Planaria developed a pair of ridges that can be considered the first “eyebrows.” These ridges acted as light stops. As a result, the photospots are placed in shadow when the animal is oriented properly with respect to the light source. Thus, the animal gained a greater degree of discrimination with respect to the direction of the light. Because of the precise orientation of these “eyebrows,” Planaria has earned the descriptor, “cross-eyed.” A second evolutionary feature was to recognize that the photospots were cells located on the animals exterior surface. They were sensitive to light from any direction. By forming ridges that enclosed three of the four sides of such cells, additional directional capability was achieved. Through additional evolution, two configurations of photospots emerged. The first could only be illuminated by light passing through the neural portion of the cell (labeled inverse photo spots). The second could only be illuminated by light not passing through the neural tissue (labeled direct photospots). This difference becomes a fundamental difference between the eyes of Mollusca and Chordata. The next two evolutionary developments occurred essentially in parallel and their statistical combination resulted in a great variety of eyes. Here the term lens must be replaced with the term aperture for reasons that will become obvious. If a photospot near the “leading end” of an animal could be enclosed by a ridge on three sides, it was not too difficult to evolve further. By revolving this structure about the axis through the photospot and the open area, a “camera” was created. The basic definition of a camera is an enclosed space with only one (entry) aperture. This definition is frequently associated with a secure luggage room at a railway station in Europe, Russia, etc. It was only through the efforts of George Eastman that the term was broadened to include a photographically sensitive material on the side of the chamber opposite the aperture. Simultaneous with the evolution of the camera structure, the photosensitive cell, or cells, began to proliferate and to evolve into four spectrally selective types. Some of these spectrally selective types also evolved into unique physical orientations, relative to the line between the cell location and the aperture, that provided polarization selective information. The resulting minimal groups of spectrally, and polarization, selective types are now found in the capsules of Arthropoda eyes. However, in Mollusca and Chordata, these minimal groups replicated into spatially extensive retinas. While Mollusca included the polarization sensitive photoreceptors in its minimal groups, Chordata did not. Where needed, Chordata introduced different mechanisms to sense polarization of the incident light.

8 Guide to Processes in Biological Vision Figure 2.1.1-1 is a caricature of the eye of Nautilus. It shows each feature discussed above. It is the basic pinhole camera. The figure also shows that the photoreceptors remain exposed to the outside environment. Such systems can give surprisingly good spatial image quality if the diameter of the pinhole is small. However, a small pinhole restricts the number of photons falling on a specific photoreceptor. The system lacks sensitivity. Nautilus discovered this very early. It also encountered another problem. Extraneous material could enter the camera. The obvious solution to these problems was to secrete a material that essentially sealed the camera to everything but light. If this material had a different index of refraction than the environment, and was formed into a spherical shape, it would exhibit the properties of a lens. This lens allowed a larger aperture while insuring that light from a given point in external (object) space fell only on the appropriate photoreceptor in image space. The result was the first complex eye, a camera containing a single lens and an extended retina. As defined above, this retina was of the direct type. Light impinging on the chromophores sensitive to light did not pass through any neural or metabolic material associated with the photoreceptor cell first. The mucous secreted by Nautilus soon became a more substantial proteinbased material forming the corneal layer in the typical eye of Mollusca.

2.1 Each Phylum has a distinctive eye architecture Various investigators have prepared artistic renditions describing different eyes found within the animal kingdom. They have frequently been unable to see the forests for the trees. This work will take a narrower and hopefully more precise position concerning evolution to focus on the main trends. Figure 2.1.1-2 shows a possible evolutionary path from the simple photospots of Planaria to the compound and complex eyes of the most advanced animals. Each of the different eyes is seen to evolve based on the replication of certain parts of the primitive photosensitive system. The top row contains two principal variants of the photospots that evolve into two major groups of eyes, those with direct and those with reverse retinas. The direct photospots, can evolve in two distinct Figure 2.1.1-1 Eye of the primitive mollusc, ways. First, a small group of seven to 25 Nautilus. The most well known pin-hole camera individual photospots can group together, with the epidermal layer surrounding them folding to in the Animal kingdom. The tissue forming the aperture has the potential to secrete material to the left in the figure to form a tube. Typically, form a lens. the end of the tube becomes sealed by a transparent material that forms a lens. This lens focuses light on the small group of cells called a retinula. In the most common case, two refracting elements or lenses have evolved. The resulting assembly (A) is known as an ommatidium. It can also be described as a converse ommatidium to distinguish it from a similar assembly formed from a group of inverse photospots. The inverse photospots can form an inverse ommatidium (not shown). Then, a neuron would be found in the optical path associated with the spectrally photosensitive material.

Tutorial on Biological Vision- 9 The photospots do not form real images of the scene around them. The second row shows two primitive eyes. These eyes do not form images of the scene either. The evolution of the ommatidium from a simple camera is clear. It has not replicated the minimal photoreceptor group. This group is called a rhabdome or retinula by various authors. These elements contain multiple individual photoreceptors and are frequently described as capsules to highlight this feature. The ommatidium has introduced two separate lenses in the aperture. In many members of arthropoda, the outer lens is used primarily as a tough protective element. In other species, it appears to have become a large lens supporting multiple groups of elements behind it. These groups, of a rhabdome and a lens (L2), can be considered an ommatidium based on their geometry. These two variants show the beginning of the evolutionary ramifications available in the basic design of eyes. The performance of the more complex ocellus cannot be discussed in detail without a knowledge of the focal lengths of the two types of lens. However, these eyes do not form an optical image. The only mapping of object space occurs within the neural processing system. The ommatidium (a simple eye) and the compound eye illustrate the forms found in Arthropoda. However, some variants may be hard to reconcile with the simple geometries shown. Copillia is an example. It employs two simple eyes. However, the rhabdome behind each lens performs a raster scanning motion similar to that of early television cameras. The result is a neural mapping of a significant area in object space by each eye using only one lens, one photoreceptor capsule and muscle power.


Figure 2.1.1-2 Evolution of the simple photospot into fundamental eye types by phylum. Top row; the direct and indirectly illuminated eye spots of the simplest bilateral animals. A; the fundamental ommatidium of Arthropoda showing the two lenses, the gel cone and the rhabdom. B; the ocellus or simple eye showing the rhabdom separated into its individual rhabdomin and rhabdomere (horizontal ellipses). C; the compound eye of Arthropoda, a replication of the ommatidium with the rhabdom forming a retina in the common plane of focus (not necessarily planar). D; the eye of Mollusca showing the directly illuminated retina body-mounted to the animal. E; the eye of Chordata showing the reverse illuminated retina mounted within a spherical eye ball able to rotate over a significant angle relative to the animal. The general plan is to have two distinct lenses in front of each type of retina, although the morphological names may vary. See text for details. The third row shows the eyes of the more advanced visual systems. Two eyes are shown on the right that obviously form optical images of the external scene. As with the ocellus, the compound eye does not form a continuous optical image. Each lens only focuses a small field in object space onto its individual rhabdome. Any mapping of object space occurs within the neural processing system. These eyes cannot scan like those in Coppilia. These compound eyes usually cover a large area of the head of the animal and interrogate a large volume in object space. When desiring to interrogate a

Tutorial on Biological Vision- 11 different optical volume in object space, the head is usually rotated through a large and obvious angle. The eyes of Mollusca have not been well characterized with respect to their geometry or their spectral performance. The higher members of Mollusca employ complex eyes with direct retinas. These appear to have evolved from the eye of Nautilus discussed above. Two lenses appear to have evolved in these eyes along with an outer covering that is not movable. In some of these animals, an iris has also developed that appears to be between the outer covering and the lens group. Some of these irises have highly tailored and unusual shapes. In lower members of Mollusca, a similar eye has developed. Its geometry appears to be of the ocellus type. The literature is not clear whether the more primitive eyes of Mollusca are simpler versions of the complex eye with a direct retina or whether they share an origin with the compound eye of Arthropoda. The eyes to the left of the vertical line all involve direct retinas. Those on the right employ reverse retinas. All of the known eyes of Chordata employ the complex eye with a reverse retina. This configuration introduces a significant set of problems but also provides for the development of the human eye. The most obvious problem is the existence of the blood vessels and other structures supporting the retina in the optical path of the incident light. Worse, these elements are found very close to the image plane where they are very near to being in focus. To achieve the high rotational flexibility of the chordate eye, the number of neurons in the optical nerve has been greatly reduced compared with eyes in Mollusca and Chordata with similar numbers of photoreceptors. This has required that more signal processing be accomplished within the ocular. The only potential location for the required neural circuitry in the reverse retina eye is in the path of the incident light. To achieve rotational flexibility, the eye of chordate has further complicated the optimization required to achieve high acuity. The next section will show how the chordate has overcome the problems with this configuration to achieve unprecedented performance in acuity over a large field of view. Chordata has taken a different approach than Arthropoda and Mollusca to the protection of the eyes. Instead of a single hard outer covering for physical protection, the basic chordate eye has evolved two distinctly separate flexible and movable eye lids. This redundant feature has evolved in a variety of directions. Complex eyes (D) and (E) also exhibit important mounting arrangements that are critical to their operation. These features will be discussed in the following section.

2.2 The chordate eye and the significance of the reverse retina Figure 2.2.1-1 provides details of the anatomy of the human eye as representative of the phylum Chordata [2.4]. It is important to note however, most chordate eyes are not round. The human eye is remarkable in this respect. This feature allows it to rotate much more freely than other chordate eyes. The figure differs from other similar figures in several respects. First, the area of the foveola is shown explicitly as the area of 1.2 degrees diameter at the very center of the larger fovea. Stereopsis, or precision imaging in three dimensions, is only achieved within this area [7.4.4]. The precision of depth perception falls by more than two orders of magnitude outside the 1.2 degree field shown. Spatial resolution also decreases precipitously outside this region. The larger fovea has a diameter of 6.5 degrees in image space (8.7 degrees in object space). Noting that light rays do not pass straight through the optics of the eye on the way to the retina, as shown

12 Guide to Processes in Biological Vision by most authors, is important. Because of the difference in index of refraction of the air outside the eye and the anterior and vitreous humors, the rays are bent significantly according to Snell’s Law. The foveola is not found exactly on the optical axis. It is displaced about 5.5 degrees as referred to object space by the typical optometrist or ophthalmologist. Measured from the back focal point of the


Figure 2.2.1-1 The Generic Chordate Eye as represented by Homo Sapien. The figure has been modified from a similar earlier one. The corneal epithelium has been separated from the conjunctiva. The photoreceptors of the sensory layer of retina (coarse hatched lines) point toward the 2nd principal point, not the so-called 2nd nodal point of Gaussian (small field angle and thin lens) optics. The small area of maximum resolution and depth perception (stereopsis) is also shown. This 1.2 degree diameter area is associated with the center of the fovea, the foveola. Compare to Torrey’s (1991). lens, the angle would be about 4.1 degrees. Optometrist and Ophthalmologists like to use the paraxial approximation first introduced by Newton but now known under the name Gaussian Optics. It simplifies the mathematics of the lens considerably but only applies to rays approaching the eye from within one degree of the optical axis. The 1.2 degree diameter of the foveola in object space is only 0.9 degrees in image space. Although slightly off-axis, its features and performance can be described using the paraxial approximation.

14 Guide to Processes in Biological Vision The paraxial approximation defines a nodal point along the optical axis at a distance from the retina of 75% of the back focal distance. This point is near the center of the ocular globe. This location has caused many authors to show all of the photoreceptors of the retina pointing toward this nodal point. However, this is a major error. All of the photoreceptors point toward the back focal point (along the optical axis near the back surface of the lens). This back focal point is also known as the 2nd principal point. For photoreceptors pointing elsewhere, performance is degraded significantly and the subject has a pathological problem. Finally, this eye is not typical of Chordata because it only exhibits one bilateral eyelid. Many chordates possess two eyelids. The second is a nictating eyelid that consists of only a single membrane. When extended, this eyelid completely covers the cornea. It is used for a variety of protective and adaptive purposes. The most striking is its use by diving birds, and other animals living at the air-water interface. They use the nictating eyelid as an auxiliary lens to compensate for the change in the index of refraction between air and water. When under water, they see as clearly as they do in the air. While not commonly stressed in the literature, it is not the “lens” but the cornea that is the most powerful lens in the human visual system. The cornea has a nominal power of 43 diopters while the power of the lens varies between 15 and 25 diopters in its autofocus role. A further correction regards the cornea. The cornea is not of uniform thickness. The inner radius is shorter than the outer radius. This causes the cornea to be thinner on-axis than at its edge. As a result, the cornea is a negative meniscus lens, a key feature of all wide angle optical systems. The optical power of the outer surface is nominally 49 diopters and the inner surface has a nominal power of – 6 diopters. The dashed line shows the effect of the autofocus lens and the meniscus lens of the cornea acting together. An optical ray approaching the eye at 70 degrees from the optical axis, leaves the autofocus lens at 45 degrees.


3. The Eyes are only part of a Visual System

Unfortunately, static figures describing the morphology of the human eye fail to suggest how the eye actually works. It will be shown that the familiar analogy to a camera fails when applied to vision. The retinas are not made up of integrating imaging elements like photographic film. The individual photoreceptors are continuously active change detectors. The consequences of this will become apparent in Section 8.3. The photoreceptors are not sampled at a regular interval like in a television camera. Thus, the concept of a frame time is different in vision. Such a concept is related more directly to the “flicker or fusion frequency” of the signal processing within the brain than that within the eyes. Without including the details of signal processing in both the retina and the rest of the brain, and also the motor-neuron system, understanding the operation of the eye is hindered considerably. What is initially sensed and eventually perceived by the animal is much more complicated than the notion of taking a picture. While crucial components of the visual system, the eyes are relatively simple parts of the overall visual system [2.8]. The sophistication of the overall system is in its feature extraction capability and its ability to recognize fine details related to those features. The visual system reaches its pinnacle of sophistication among only a few of the higher primates. In Man, it is epitomized by his ability to read. Understanding the operation of the visual system is simplified by defining a series of operating modes. These include the awareness, alarm, analytical, volition, and command modes. While the names were chosen to suggest their function, the details related to these modes will be introduced incrementally in the following discussion. They will be summarized in Figure 3.4.1-1. The signal processing system is designed to recognize the limited optical performance of the eye’s optics. The spatial performance of the optics of the eye falls very rapidly with field angle. The eye is only able to maintain high performance over a small portion of the fovea centered near the point of fixation and the foveola. To maximize performance, the visual system uses two parallel signal processing paths. The coarse path is associated with the awareness and alarm modes of perception. This path involves most the photoreceptors in all visual systems and corresponds to the full field of view of the animal. Many species also employ a precision path associated with the analytical mode of vision. This mode invariably involves a narrower field of view and a subset of the photoreceptors available (the foveola). Additional signal paths associated with the volition mode (involving the will of an animal) will be developed later in this work. The method of implementing the coarse and precision paths of the visual system vary considerably among species. The precision, or analytical path, is seldom implemented among Arthropoda. However, the spiders form the glaring exception. Their multiple eyes are tailored to meet the

16 Guide to Processes in Biological Vision objectives of coarse and precision performance. Typically having eight eyes, it is possible to describe the outer pair as providing coarse peripheral vision associated with the awareness and alarm modes of operation. Two of the forward facing eyes operate as a pair to provide binocular vision over a relatively wide field of view, generally extending to the peripheral area observed by the previously defined pair. These eyes also support the awareness and alarm mode. The inner pair of eyes is unique in that they can observe a small area within the field of view of the binocular pair. By limiting their field to a small region, they are able to observe that area at higher spatial resolution. This higher spatial resolution provides them the analytical capability they need to perform higher precision activities (such as jumping onto their prey from a distance). By distorting the tube connecting the photoreceptor capsules of these eyes with their lenses, the spider can cause the precision field of view of these eyes to scan within the binocular field of the earlier defined pair. Chordata has taken a different path in implementing both an awareness and alarm mode capability, and a separate analytical mode capability. Each of the two eyes exhibits a wide field of view with a limited spatial resolution. This limit is imposed primarily by the limited performance of their wideangle optical system. This capability provides them a significant field of view as required to satisfy the requirements of the awareness and alarm modes. In the more advanced species, an analytical capability has been implemented. This has been achieved by exploiting the limited high resolution capability of the particular wide angle lens system used in the eye. This capability only covers a field of view of a few degrees in object space. It occurs very near the optical axis of the lens. This corresponds to the area known as the foveola in Chordata. To achieve the variable pointing capability, like that of the jumping spider with only one pair of eyes, Chordata has adopted the rotating ocular approach. This capability requires a very flexible optic nerve connecting the oculars to the central nervous system. This flexibility is achieved by reducing the number of neurons leaving the ocular. Such a reduction is dependent on the reverse retina configuration and the enhanced signal processing associated with it Mollusca has generally followed the approach of Arthropoda. In some cases, hundreds of ocelli decorate one or more ridge lines of their exterior anatomy. For the more predatory, and therefore more advanced, members of Mollusca, a complex eye with a direct retina has been used to advantage. This configuration provides much the same capability as found in Chordata, except the ocular is more solidly mounted to the body. Even here, the squid and octopus have attempted to introduce tremor. The tremor mechanism is critical to the performance of the eyes of higher members of Chordata. This critical capability will be discussed in Section 8.2. Until recently, exploring and understanding the complete visual system has been difficult because of its packaging. Critical elements of the system were hidden deep within the central nervous system and surrounded by the skull. Recently, magnetic resonance imaging techniques have provided new avenues of exploration that have overcome these physical barriers. Unfortunately, these techniques are generally slow. Even the new functional magnetic resonance technique (fMRI) is unable to provide information about changes occurring within a few milliseconds within the neural pathways. A technique known as visual evoked potential (VEP) can provide much more temporally precise data than the magnetic imaging techniques. Combining the results from these techniques should soon provide unprecedented clarity on how the visual system works.

3.1 The Building Block Architecture of the Chordate Visual System While the basic organization of the visual system of all animals is the same, the complexity increases rapidly with position in the phylogenic tree. Speaking of the brain in the vernacular is common in the vision literature. Following the common

Tutorial on Biological Vision- 17 human proclivity, expressing ideas using a dichotomy is also common. Terms such as fore brain and midbrain are paired, regardless of the species being discussed. This nomenclature frequently overlooks the critical importance of the thalamus of Chordata. This morphological structure is occasionally associated with the forebrain. More often, it is associated with the midbrain. Its importance requires a more precise description. Figure 3.1.1-1 provides a clearer description of the morphological evolution of the brain using more scientific nomenclature. With sophistication comes complexity. In progressing from the simpler two-part anatomy of the brain to the five-part anatomy associated with the higher chordates, greater precision is required. The transition from the nomenclature of the three-part anatomy has been tortuous. Whereas the mesencephalon continues to correspond to the midbrain of classic morphology, and the telencephalon has become known as the forebrain, the diencephalon has struggled with multiple labels. The common appearance of “between-brain” or “interbrain” to describe the diencephalon suggests the problem. It suggests why it is frequently confused with or associated with the midbrain. The prefix of the technical name for the forebrain, tele- or distant, should suggest the telecephalon and the diencephalon are not closely related. This is particularly true from the physiological perspective. The mesencephalon, or midbrain is highly involved in motor activities. The telencephalon is the center of cognitive activities. It is the diencephalon that is the seat of sensory activity. These activities are concentrated in the thalamus. It is also the control center for the motor activities of the higher primate brain. These activities are shared between the thalamus and the cerebellum (not shown in this figure). As shown in the illustration, no sharp dividing lines appear related to the functional aspect of the neural system. This makes precise location of various functional elements difficult. To be clear, this work will separate the diencephalon and mesencephalon into the following series of distinct functional elements (proceeding from rostral to caudal). The series begins with the diencephalon elements, the thalamus, the pulvinar, and then the thalamic reticular nucleus (including the ventral tier thalamic nuclei, MGN, LGN & PGN). The series ends with the mesencephalon elements, the pretectum and the tectum (superior colliculus). The optic nerve interfaces with at least three of these elements. It interfaces with the LGN’s, the PGN’s and the superior colliculus.


Figure 3.1.1-1 Morphogenesis of the brain in the higher chordates showing evolution from a two-part to a five part anatomy. The precise point of junction between portions of the optic nerve and the functional elements of the old brain, A, B & C, are difficult to define precisely. Morphological markers do not always relate to functional borders. As will be developed in Section 8, the thalamus is divided into several critically important and physiologically distinct regions. When discussing the operation of the visual system, a more physiologically oriented framework is required. Figure 3.1.1-2 presents the visual system expressed in a more general top level block diagram form compatible with the rest of the neural system. While generally relatable to morphology, it is more functionally oriented. The following discussion will focus on the principal signal paths of the visual system. Many other unique paths associated with the alarm mode are present. Their purpose is to bypass some time consuming signal processing engines when necessary. Six major functional stages can be defined based on the physiology of the visual system. These same stages are found in any sensory system of an advanced chordate. The stages of the visual system are defined at:

Tutorial on Biological Vision- 19 #1. the Signal detection stage. #2. the signal manipulation stage (within the retina). #3. the signal projection stage (connecting any two engines of the neural system). #4. the signal perception stage (within the diencephalon). #5. the signal cognition and high-level response stage. #6. the motor/secretory response stage. Several other non-signaling stages are defined in this work using letters.

Figure 3.1.1-2 Top level block diagram of the neural system focused on the visual subsystem of Chordata. The stages defined in the text are shown. All of the projection neurons of stage 3 (employing action potentials) are shown by the arrows. Each of the boxes shown (except the lower left box) contain at least one million active analog devices. The role of the thalamic reticular nucleus, TRN, as a “gatekeeper” is highlighted by shading. The parallel roles of the LGN/occipital couple and the PGN/pulvinar couple is highlighted by hatching. The superior colliculus/cerebellum couple is highlighted by cross hatching. Noting that all of the above stages, except stage 3, involve analog signal processing is crucial to the understanding of vision. Only about 10% of the neural signals within the system involve pulse signaling (action potentials). The other 90% of all signals are analog (electrotonic) in character. Each of the signal processing engines represented by a box (except the oculomotor functions represented by the lower left box) contain at least a few million analog neural circuits. Each box also typically contains 1000 ganglion cells generating action potentials (and found near the tail of each arrow). The heads of each arrow represent a similar 1000 stellate cells converting the action potentials back to analog signals for processing within an engine. To complicate matters further, most of the signals projected between the engines of the central nervous system are projected in bit-parallel word format. Within the CNS, most of the information involves complex packets of information transmitted in vector format. This means that no one neural fiber carries an entire message. Multiple individual fibers carry different parts of the same

20 Guide to Processes in Biological Vision vectorized message. In the laboratory, multiple neural fibers must be observed at the same time to discern the meaning of any message transmitted within the CNS. A similar situation is found with respect to at least the aural and visual sensory systems. Their information is also transmitted in a bit-parallel format, although the bits may be skewed in time and position for purposes of computational convenience. This subject is discussed in Section 8. The two afferent boxes at upper left and the oculomotor box are within, or found next to, the ocular globes in Chordata. The signal processing of stage 2 is not found within the eyes in Arthropoda and Mollusca. It is found in a separate structure or consolidated with the brain. Stage 2 signal processing is found within the retina of Chordata. The two boxes at the far right, and the occipital box are located within the cerebral hemispheres (the telencephalon). The LGN, PGN, pulvinar and TRN are located within the diencephalon [15.6.2]. The superior colliculus and cerebellum are usually associated with the mesencephalon. Two of the stage 4 circuit couples, the LGN/occipital couple and the PGN/pulvinar couple, are each physically separated by stage 3 projection circuits. Both deliver their output to the stage 4 circuits of the parietal lobe. VEP data exists to show the output of the PGN/pulvinar couple travels directly to the parietal lobe without passing through the occipital lobe. VEP and morphological data also exists that suggests that most signals from the LGN/occipital couple pass back through the TRN before proceeding to the parietal lobe. It is the TRN that makes the final decision on the importance of information passing through it. Thus, the name “primary visual cortex” may not be appropriate for the rear section of the occipital lobe (Brodmann area 17). It is only primary with respect to the coarse signal path of vision. Understanding these signaling paths is an area of active current research. Because of the difficulty of accessing the thalamus in the laboratory, knowledge of the physiology of the pulvinar and the thalamic reticular nucleus is very limited. Understanding the complete role of the pulvinar and the TRN are also areas of active research. Clearly, the level of development of the PGN, pulvinar and TRN determine the visual capability of the higher primates. By combining their psychophysical performance and the model presented here, these species can be ranked. Only the great apes of the family Pongidae are competitive with humans. In descending order of ability, these are the chimpanzee, Pan, the Orangutan, Simia, and the Gorilla, Gorilla. When studying reading and the analysis of fine detail, the lesser apes and monkeys are not homologous with humans. In many cases, only the chimpanzee can be considered an adequate surrogate for humans in the laboratory. [1.2.1.5] The retinotopic character of the afferent signals is continuously degraded as the signals move to the right. They are entirely abstract and in vector form beyond the output of the pulvinar and occipital lobes. The vector map known as the saliency map has not been located morphologically or physiologically. It is shown under the label #4/#5 to show it receives information from stage 4 circuits and is accessible by stage 5 circuits of the anterior lobe.

3.1.1 The signal processing within the retina of man The interface between Stage 1 and Stage 2 circuitry in Chordata is shown in Figure 3.1.1-3 along with the lens of the physiological optics, Stage B. [17.2-17.4]. Three crucial situations are illustrated. First, the formation of multiple signaling channels at the output of the photoreceptor cells is described. Three chrominance channels, one luminance channel, and one appearance channel are described. The calculations performed in and the resulting performance of the appearance channel are unique. They will be described in Section 3.2. Second, the subdivision of the photoreceptor cells

Tutorial on Biological Vision- 21 into their functional elements is shown. Finally, a graphic representation of the signals carried by the individual channels at the location of the S-plane of the retina is presented. This figure shows that the theory presented here is an extension of the earlier zone theory. It expands the old YoungHelmholtz theory by adding the ultraviolet channel (ultraviolet light was unknown in Young’s time and largely a curiosity in Helmholtz’s time). It also introduces a series of color difference channels reminiscent of Hering. However, the difference channels are derived from the spectral channels and are defined in terms of the UV–, S–, M– and L–channel peak wavelengths rather than some other arbitrary colors. The differencing results in three “opponent channels” rather than the two of the Hering school. They are labeled the O–, P– and Q–channels as shown. These are the chrominance channels of chordate vision. There is also a summing channel, labeled the R–channel. This is the luminance channel of chordate vision. Note carefully, there is no achromatic (or rod) sensor channel in this configuration. All of the necessary information is acquired from the spectrally selective sensor channels. This figure shows a familial resemblance to many other figures in the literature (except for the addition of the ultraviolet channel). The functional difference will be discussed after discussing the elements of the photoreceptor cell.

Figure 3.1.1-3 (Color) The luminance, chrominance and appearance channels of the eye of tetrachromats and aphakic humans. The spectral response in the O-, P- and Q- channels are shown as sinusoidal for illustration. The UV photoreceptor cells are known to be functional in humans of all ages. Research is ongoing to determine if the signal in the O-channel of the aphakic human is typical of tetrachromats. If it is, an aphakic human will be able to tell us what “color” other animals perceive in the ultraviolet.

22 Guide to Processes in Biological Vision The ultraviolet spectral channel is an intrinsic component of all biological vision. It supports the fundamental tetrachromatic performance of biological vision. The absence of one or more of the spectral channels from the eye of a specific species is worthy of study in its own right. In the case of Chordata, the four spectral channels have been found in sufficient numbers of families (birds, fish, mammals, etc) to suggest they are present in all families. The fact that ultraviolet photoreceptors are present in humans is well documented. Much of the work has been done by a researcher that lacks a lens in one eye due to an accident. His research has demonstrated a spectral sensitivity in the ultraviolet comparable with that in the S– and M–channels of normal vision. It may be higher than in the typical S–channel. [17.2.2] The ultraviolet channel is important in vision because of its broad absorption compared to the absorption of the lens in Chordata. Even in large members of Chordata, the lens does not absorb significantly at wavelengths longer than 400 nm. However, the spectral absorption of the UV channel is still significant at wavelengths in the 400-475 nm region. As a result, the O–signal channel is operational and significant in humans. It plays a significant role in the development of the New Physiologically Based Chromaticity Diagram to be discussed in Section 9.1.3 [17.3.3]. Each photoreceptor of the eye is shown to consist of four distinctly separate physiological entities. The chromophores of the disk stack (the outer segment) is one entity. Two separate signal amplifiers form two more distinct entities. The final entity is the electrical load, marked (4). This entity is associated with the pedicle of each photoreceptor. It plays a critical role in converting the current derived from the incident photons into a voltage. It is this voltage that can be passed to the subsequent signal processing circuits without attenuation. The conversion is not linear. The conversion is logarithmic. The load associated with the pedicle is the fundamental element that negates the linearity laws, of Grassman and others, so frequently cited in the literature. It forces these laws into a category that only relate to “small signals.” This logarithmic conversion is also one of the principal features establishing the very large dynamic range of the visual system. The adaptation amplifier of each photoreceptor is critically important to the operation of the eye. This amplifier introduces a large amount of negative feedback. The level of feedback varies with temporal frequency. It is 100% at very low temporal frequencies. The low frequency half-amplitude point is between 0.3 and 0.5 Hz in most members of Chordata. The performance of the amplifier is also reduced at high frequencies. The upper half-amplitude point of the amplifier alone is between 812 Hz. This frequency varies with the health of the vascular system of the eye (and may vary with position within the chordate retina). The performance parameters of the photoreceptor cell are critical in determining the overall performance of the visual system. Because of the zero at zero frequency in the transfer characteristic of the adaptation amplifier, the eye of Chordata is fundamentally blind to stationary objects that do not change rapidly in lightness. This feature is commonly observed in reptiles and can be observed in humans. At least the mammals, and probably the fish and birds have introduced an additional mechanism to overcome this difficulty. They employ tremor to encode the imagery from a scene and bypass the limited performance of the adaptation amplifier [12.6-12.7]. Some mammals, particularly the cats appear to be able to turn this mechanism on and off to meet their predatory needs. Because the adaptation amplifiers of the retina operate independently, they introduce the concept of “color constancy” into the visual system. Over a local region, all of the adaptation amplifier associated with a particular spectral channel tend to receive the same signal level from their chromophores. They tend to adjust their amplification factor, or gain, in response to this level. As a result, all of the adaptation amplifiers associated with a particular spectral channel change their gain as a group. The effect is to adjust the gain of each spectral channel of vision to compensate for

Tutorial on Biological Vision- 23 major changes in lightness applied to that channel compared to the other channels. This is the essence of color constancy [17.3.6]. As noted above, the electrical load element associated with each pedicle performs a logarithmic conversion of current to voltage. As a result, the differencing circuits of the chrominance channels, O–, P– and Q– calculate the difference of logarithms. Such a calculation is equivalent to taking the logarithm of a ratio. This conversion plays a major role in stabilizing the color perceived by the brain. A similar calculation occurs in the luminance channel, R– . Here the luminance signal is the sum of the logarithms of the spectral inputs. This calculation introduces artifacts into the perceived brightness at wavelengths near 494 and 575 nm that have frequently been confused with primary spectral responses. This has been a particular problem in psychophysically isolating the L–channel response of human vision. The signature of these spectral frequencies are associated with the Bezold-Brucke and Purkinje Effects. Efforts to limit the intensity of light presented to the eye in the laboratory have frequently resulted in the peak at 575 nm being confused with the true long wavelength peak at 625 nm. The details of the human visual spectrum are discussed in Section 6. The signals generated by the various signaling channels are shown at the right in the figure. They are shown for both normal humans and aphakic eyes (eyes lacking a lens that absorbs the ultraviolet). These are the signals that can be recorded at the so-called S-Plane of the retina (named in honor of Svaetichin). It can be shown that the physiologically measured signals at the S-Plane of the retina are in excellent agreement with the psychophysically perceived signals in humans [17.3.3]. The agreement strongly suggests they are the same.

3.2 The major role played by the Diencephalon The information concerning the morphology of the diencephalon is frequently inconsistent. This situation is less due to conflict between investigators and more due to extrapolation from limited findings related to different physical areas. However, the data on the physical appearance of different portions of the diencephalon and the traffic analysis available allows many conclusions to be drawn [15.6]. The highly protected location of the diencephalon makes it very difficult to study in-vivo. Most of the available physiological data is inferred from psychophysical data following strokes or major injuries to the brain. While the recent development of magnetic resonance techniques offers new possibilities, these techniques are still limited. They do not explore the actual electrophysiology of the diencephalon. Instead they sense the presence, and change in concentration, of certain conditions related to reactants involved in respiration. Currently, these are blood flow and changes in hemoglobin content. Unfortunately, these are not the primary reactants supporting the signaling operation of the neural system. The primary chemical process is the conversion of glutamate (glutamic acid) to GABA (gamma amino-butyric acid) in an electrostenolytic process associated with every neural plasma. This process does not directly involve either the glucose level or the oxygen level of the blood and tissue. Most of the available data concerning the diencephalon is from detailed morphological examination and the study of the physical interconnections of the neurons of the brain. The study of these interconnections (a form of traffic analysis in the language of the cryptographer) has become sufficiently sophisticated to determine the direction of signal flow. Defining multiple terminations for the same neuron is also frequently possible. However, the chemical-based trail is interrupted by the presence of a synapse. The diencephalon is found between the mesencephalon (midbrain) and the telencephalon (the cerebral cortex). Its major constituents are the thalamus and the hypothalamus. The thalamus is

24 Guide to Processes in Biological Vision the element of principal interest in vision. It is a single structure of unusually construction. Instead of a thin corrugated shell, as found in many parts of the brain, it contains several solid threedimensional parts. The primary part is the large pulvinar. It also can be divided into several solid portions. During evolution, the brain of man has grown significantly. His mental and intellectual capacity is often judged by this fact. It is useful to note that the area of the thin corrugated shell associated with the cerebral cortex has increase about four times as the radius of the brain has doubled, the volume of the thalamus has increased by eight times. Until recently, several surface features of the thalamus were thought to be integral parts of the pulvinar. In many species, this is probably true. However, recent work on humans has shown that the pulvinar is enshrouded by a very important shell. This shell is called the thalamic reticular nucleus, TRN. It encloses more than two thirds of the human pulvinar and includes the geniculate nuclei. The lateral and medial geniculate nuclei are shared with many higher primates. However, it is the perigeniculate nuclei, found adjacent to the lateral geniculate nuclei, and the gross expansion of the pulvinar in humans that are of major interest. These features appear to distinguish the human visual system from all others, including the other great apes. The perigeniculate nuclei appear to have recently evolved from the lateral geniculate nuclei. Unless carefully instructed, most medical artists do not distinguish between these structures. Where the artists do not distinguish, neither do the textbooks [15.6]. Unlike the pulvinar it encloses, the TRN is a shell more typical of most brain tissue. It can be divided into several parts based on its surface structure and one other fact. A major part of the TRN is striated. A second part is pierced by a multitude of axons proceeding through the TRN shell. Some of these axons branch and support local terminations within the shell. Other neurons traversing the shell may accept synapse inputs from neurons originating within the shell. Finally, the parts forming the various geniculate nuclei appear to form significant feature extraction engines on their own [15.6.2 & 15.6.3]. While much of the TRN is bilateral, like most of the rest of the organism, the pulvinar appears to be different. The pulvinar and the cerebellum are two parts of the chordate body that are not bilateral. The striated portion of the TRN has an appearance reminiscent of the early man-made magnetic core memories for computers. The key features of these devices were a series of orthogonal electrical wire (conduits) interwoven with a series of sensing conduits. The orthogonal wires were used to introduce particular states of magnetization in the cores located at their junctions. The sensing wires allowed that state of magnetization of individual cores to be sensed without affecting that state. It appears the striated portion of the TRN serves this same functional role. The striated portion of the TRN appears to operate as a two-dimensional associative correlator under the control of an adjacent unstriated portion. The two bilateral striated portions will be labeled the perigeniculate nuclei, PGN. The capability of the 2-D associative correlator will be discussed further in Section 8.3 The perigeniculate nuclei differ from the lateral geniculate nuclei in one major characteristic. While the LGN’s accept input from their respective halves of the retina, they do not receive significant signals from the foveola. The signals from the foveola are directed to the perigeniculate nuclei. Whereas the outputs of the LGN proceed to the occipital lobe of the cerebral cortex, the outputs of the PGN are passed to the pulvinar.

Tutorial on Biological Vision- 25 The outputs of the two PGN correlators are passed to the “non-bilateral” posterior pulvinar. This configuration would suggest that the sensing circuits of the two PGN’s might be shared in order to form a single composite output that could be passed to the pulvinar. This concept supports the hypothesis that the pulvinar forms a very large lookup table that can accept the outputs of the PGN correlators and issue an output describing the input in terms of similar patterns found in its memory.

3.2.1 The operation of the TRN as the gatekeeper of sensory inputs and muscular/skeletal responses The performance of the non-striated portion of the thalamic reticular nucleus and its strategic location suggest that it is the seat of control (but not cognition) within the neural system. It is able to evaluate all sensory inputs passing through it. It is also able to inhibit or redirect all autonomous and volition mode instructions directed toward the musculature/skeletal system . This subject will be explored more completely in the supporting compendium [15.6.6]. The non-striated portion of the TRN is also optimally positioned to control the operation of the Precision Optical System (POS). Th POS forms a major closed loop servomechanism that supports a variety of visual functions [7.3]. These include pointing (version), convergence (vergence), focus, and analysis (interpretation and perception). It also contains and controls the tremor generator and the inertial reference signals provided by the vestibular nuclei frequently associated with the “inner ears” of the auditory system. Physically, the POS consists of the eyes, major parts of the thalamus, the oculomotor subsystem (and the skeletal motor system as required) and the neural nodes formerly known as the auxiliary optical system. This servomechanism is able to respond to alarm mode, analytical mode and volition mode instructions. Generating a variety of largely autonomous responses is also possible.

3.2.2 The operation of the PGN/pulvinar couple Based on the description discussed above, it is proposed that the PGN/pulvinar couple plays a critical role in human vision that is not achieved in any other species. This role involves the interpretation and perception of scenes presented to the foveola of the eyes. The extent of this capability is controlled largely by the size of the posterior portion of the pulvinar.

3.2.3 The Precision Optical System Time delay plays a major part in the operation of the nervous system of any animal. As will be shown in Section 4.3, action potentials associated with stage 3 signal projection move at less than 4 millimeters per millisecond (group velocity) in endothermic (warm blooded) animals. They move even slower in exothermic animals. For animals the size of humans, it requires several milliseconds for signals to travel from the retinas to the midbrain. It takes many more milliseconds to travel on to the cerebral cortex. This is the principal reason that the POS does not include the cerebral cortex. To achieve maximum performance, the design seeks to minimize the time delay within the POS servomechanism loop. All of the functional elements of the servomechanism are grouped in the space immediately behind and between the eyes. This provides optimum ability to rotate the eyes (and close the eyelids) in response to alarm signals. Where necessary to control the pointing of the head, a time penalty is accepted. An additional time penalty is accepted when controlling the movements of the skeleton is necessary. The operation of the precision optical system is summarized in Figure 3.2.1-1 [7.3]. Only the operation in the horizontal plane is shown. The servo mechanism loop contains several circuit elements. These include the the photoreceptors at the center of the foveola (associated with the line of fixation), the perigeniculate nucleus, the neurons of the auxiliary optical system (marked LTN, etc.) and the muscles that control the previously mentioned line of fixation. The medial and lateral muscles operate in opposition to each other. They cause each eye to rotate within its individual

26 Guide to Processes in Biological Vision socket.

Figure 3.2.1-1 The Precision Optical System highlighting the vergence subsystem. Note the separation of each muscle into its tonal and twitch component. All of the signals passing through the shaded area are under the supervision of, and subject to override by, the TRN. Note that each muscle is divided into two separate components. These are the tonal component with a bandwidth of up to only 5 Hz, and the twitch component with a bandwidth up to 130 Hz. The amplitude capability of each portion of the muscles is inversely proportional to their bandwidth. As a result, each globe can be rotated over large angles relatively slowly and over very small angles very rapidly. The rotation of the ocular globes at rates up to five Hz is controlled by the tonic portion of each muscle. These tonic muscle fibers are used for pointing and convergence. When driven in phase with each other, the eyes change their gross pointing direction (their vergence). When driven differentially, the eyes converge or diverge relative to each other. These actions can be caused by the POS operating on its own via the PGN (but under the ultimate control of the TRN). Alternately, they can be caused in response to alarm and volition mode instructions received via the superior colliculus. These instructions are converted to implementable commands by the superior colliculus (that is also under the ultimate control of the TRN). The TRN is in a position to supervise and override any signals passing through the shaded box in the figure. It has both an autonomous capability (based on previous instructions stored in memory) and can accept guidance from the higher cognitive centers (an expression of the will). The twitch portions of the muscles are used for greatly different functions. They are used for two functions. They are used to generate the motion necessary to change the spatial domain information presented to the retinas into the temporal domain information that can be processed by the neural

Tutorial on Biological Vision- 27 system. As noted earlier, the adaptation amplifiers of each photoreceptor have zero gain at zero temporal frequency. Because of this, no signal appears at the pedicle of a photoreceptor in the absence of some change in the image projected onto these photoreceptors. It is this change in the temporal signal due to the fine motion of the eyes that is perceived by the visual system. In fact, the signals from the retina generated during coarse motion caused by the tonic muscles are blanked out within the signal processing of the visual system. This avoids performing signal processing on hopelessly smeared information. As above, the twitch portion of the muscles can be independently driven by the PGN. However, an additional capability is introduced to support the analysis of fine detail and reading. The vertical and horizontal direction of motion of the eyes can be controlled separately. This allows the eyes to perform a small raster scan. The result of this scanning pattern is to provide information to the PGN/pulvinar couple that can be analyzed to detect (the term used in the literature is interpret) fine detail within the image projected on the foveola. This small raster scan is generated by the tremor generator and can be detected in the laboratory with sufficiently precise instrumentation. The amplitude of the tremor is normally only a few arc seconds in amplitude (about the angular size of one or two photoreceptors of 2 micron diameter).

3.3 Plan and profile views of the human visual system The discussion presented above leads to a significantly different view of the operation of the visual system than appears in texts more than a few years old. The pace of learning in physiology is similar to that in computer sciences. The ground rule is “Do not buy a text book with a copyright date earlier than two years ago.” Figure 3.3.1-1 provides a plan view, from below, of the visual pathways in the human brain external to the cerebral cortex. More important elements can be seen from below. Pathways within the cerebral cortex are discussed in detail in Chapter 15 of the supporting work referenced in the introduction. Many authors have provided a simpler figure omitting the fields of view of the eyes. The left portion of the figure shows a caricature of the visual fields of the eyes. The wide wedges drawn from each eye show the binocular field of view shared by the two eyes. The two shaded wedges show the fields of view of the two eyes shared in object space. Signals from these areas are overlaid and processed only by the contralateral portions of the visual system. The short dashed lines, “labeled extreme ray,” are only suggesting the maximum temporal extent of the field of view of each eye. The maximum temporal field of view extends to about 104 degrees from the line of fixation. The fields of view of the two foveola are not easily shown at this scale. They are only 1.2 degrees wide and are represented by the long dashed lines along the optical axis of each eye. Signals from each foveola are sent directly to the contralateral perigeniculate nucleus (PGN) of the thalamus just as the neurons from the peripheral retina pass to the contralateral lateral geniculate nucleus.


Because of the limited performance of the wide-angle optical system of the eye, the signals related to the foveola and processed by the PGN/pulvinar couple are of much higher spatial quality than those

Figure 3.3.1-1 Plan view of the human visual system as seen from BELOW. The retina projects to the lateral geniculate nuclei and the perigeniculate nuclei. Signals originate in the superior colliculus. The figure is similar to one by Daw (1995). The optical rays are redrawn to illustrate both the stereo viewing field and the maximum viewing field. Note the fact that the rays do not follow straight lines as they enter the eyes due to the immersion mode of the optics in terrestrial animals. The optic nerves are shown bifurcated. Note how they are rearranged at the chiasm so that all signals from the left field of vision proceed to the right side of the brain. Axons from nasal retina cross in the chiasm, and axons from temporal retina do not. Note also the additional bifurcation in the optical tracts with neurons proceeding to both the lateral geniculate nucleus, LGN, and the PGN. Neurons controlling the iris and lens originate in the superior colliculus. Additional neurons are shown leaving the LGN and proceeding to the striated cortex, Area 17, as the optic radiation. Note the presence of Meyer’s Loop. Additional neurons also leave the PGN and proceed (out of the plane of the paper) directly to Area 7 of the cortex via the Pulvinar Pathway. processed by the LGN/occipital couple. Note the off-axis optical rays shown are not straight lines. They bend as they pass through the cornea of the eye. This is due to Snell’s Law. Optical rays passing from air into a medium of higher index of refraction are bent toward the normal to the surface traversed. The dashed axial rays are shown converging on a distant object. It is only within the overlapping field of these two dashed rays that man achieves his highest degree of stereoscopic performance. The common and potential

Tutorial on Biological Vision- 29 stereographic field of the eyes is shown along with Two extreme rays are also shown. As mentioned above, the extreme rays are more than 90 degrees from the axial ray. The optical field of each eye is shown bifurcated and this arrangement is also found in the optic nerve. Upon reaching the optic Chiasm, these bifurcated bundles of nerves are rearranged into the bundles shown within the optic tracts. All of the nerves associated with the left fields of view go to the right half of the brain and vice versa. The secondary divisions in the optic tracts after this Chiasm are very important. They separate the signals related to the foveola from the main neural path. These signals are routed to the perigeniculate nucleus and the superior colliculus. Afferent signals from the retina are routed to the PGN. The signals related to the superior colliculus are efferent signals returning to the eyes and the associated eye muscles. Several investigators have reacted with surprise to their findings concerning the constituents of the optic nerve [3.2.2 & 15.1.1]. They found that no neurons from the foveola went to the LGN. About 10% of all neurons went directly to the PGN. As many as 80% of the neurons going to the LGN represent chrominance channels. Artistic license has been used in the figure for clarity. The two LGN’s and the two PGN’s are much smaller than the pulvinar. Morphologically, they are generally seen as protuberances on the surface of the posterior pulvinar. While two perigeniculate nuclei are shown, only one pulvinar is shown. The signals from the two halves of the two peripheral retinas are merged in one of the LGN’s. The merged data is then processed further in the associated halves of the occipital lobe of the cerebral cortex. However, the left and right fields are processed entirely separately. The signals from the two halves of the foveola are treated differently. While the left and right halves of the images from the two eyes are merged in separate PGN’s, the output of these two PGN’s is combined into a single channel. This channel is delivered to a single posterior pulvinar for further processing. From the pulvinar on, the signal processing associated with vision is no longer bilateral in character. The signals from the pulvinar are passed to area 7 of the parietal lobe in totally abstract form. This fact contributes to the hypothesis that signals from the two symmetrical regions of the occipital lobe are returned to the thalamus for merging before transmission to area 7. Evidence is growing that as many neural paths go from the occipital lobe to the thalamus as there are going from the LGN’s to the occipital lobes. This would suggest that the thalamus merges the signals into their final abstract form before delivery to the parietal areas. Under this interpretation, the PGN’s and posterior pulvinar act as one processing couple associated with fine detail in the analytical channel of vision. Similarly, the LGN’s and the Occipital lobe act as one processing couple associated with the coarse data in the awareness channel of vision. The output of these two couples is directed to the parietal lobe and used to populate a single saliency map. This totally abstract map is then accessed by the higher cognitive centers. The signal paths from the occipital lobes back to the thalamus may not be as circuitous as those shown going from the LGN’s to the occipital lobe. Meyer’s loops play a very important role in the visual system that has not been described previously. They will be discussed in Section 8.1. Figure 3.3.1-2 shows the visual pathways of the human visual system in profile. This figure is similar to earlier versions found in the literature except its explicit detailing of two important pathways [15.6.4]. The signal radiation along the Pulvinar Pathway to Area 7 of the cerebral cortex is shown explicitly. The signal paths from the thalamus back to the oculomotor system and the eyes are also shown explicitly (see inset). The figure stresses the role of the old brain as a communications hub. Various areas of the thalamus and the midbrain are shown playing important roles in both vision and the response to visual stimulation. Although not shown explicitly, signals from area 17 move forward through area 18, 19 etc. until they reach the parieto-occipital sulcus. Their travels from that point are not adequately documented. They may be able to proceed to the parietal lobe

30 Guide to Processes in Biological Vision directly or they may not. They may be routed back through the thalamus and then along the pulvinar pathway. The inset shows the separation between the diencephalon and the midbrain (mesencephalon). The structure of the LGN is shown in caricature. Many elements of the POS are shown adjacent to the circular symbol describing the POS. Historically, some of these elements have been labeled the auxiliary optical system. The location of the POS symbol in the inset stresses the critical location and the critical role played by the POS as the primary servomechanism associated with the acquisition of all precision signals related to vision. In this figure, the superior colliculus is shown as under the control of the TRN. It receives abstract instructions via the TRN and converts these into detailed commands for controlling the three motor muscle groups of the eyes (along with the signals controlling the focus mechanism). Also shown is the interconnection between the vestibular system and the TRN. This connection provides inertial orientation for the information sent to Area 7. It also supports the calculation of the appropriate oculomotor commands in the presence of other motions of the skeletal system. Data concerning Area 7 is difficult to obtain in the laboratory due to its abstract character. Most of the data is obtained by traffic analysis, instead of by actually reading and understanding the signals

Figure 3.3.1-2 Profile view of the human visual system. Signals from the optic tract separate at the secondary optic chiasm and proceed to the LGN and the PGN. These signals are arranged according their source. Upon reaching the LGN, the luminance signals enter the Magnocellular region. The chrominance signal enter the Parvocellular region. After processing, these signals proceed to Area 17 of the cerebral cortex along the calcerine fissure via the Parvocellular and Magnocellular pathways. The signals from the foveola proceed to Area 7 of the cerebral cortex after processing in the PGN/pulvinar via the Pulvinar pathway. Efferent signals from Area 7a return to the superior colliculus via this same pathway.

Tutorial on Biological Vision- 31 recorded. The inset shows command signals returning from layer 5 of Area 7a to the TRN and other elements of the thalamus before transmission to the superior colliculus. At this time different authors are correlating the cognitive visual engines of the anterior lobe of the brain with both areas 5 and 7, and a poorly defined area 7a, of the parietal lobe. This inconsistency may be partly due to lack of morphological repeatability in the folds of the cortex of different individuals. The correlation is also difficult due to the abstract nature of the signals. The inset also shows the separation in the signal paths between the foveola and non-foveola portions of the retina. As discussed in Chapter 15, recent experiments have shown that the visual signals from the foveola appear in area 7 before similar data appears in area 17. This demonstrates that important parts of the visual signals do not pass through area 17, 18 & 19. It is hoped that future experiments will provide more detailed and precise information concerning the time of appearance of signals within the thalamus compared with their appearance in either area 17 or area 7. Figure 3.3.1-3 shows the trunk diagram for the sensory portion of the visual system as it might be described by a telephone system engineer. The main constraint on the overall system is the requirement introduced into Chordata to provide a high degree of angular freedom between the eyes and the head. This requirement calls for a minimum size trunk (optic nerve) between the eyes and the head. The entire signaling architecture of the chordate visual system is determined by this requirement. As many as 108 photoreceptors are found in each retina. Probably 109 signal processing neurons are found in the remainder of the retina, and probably more than 1010 neurons are found in the cortex. However, only about one million nerves are found in each optic nerve. Each of these numbers are ballpark figures taken from the literature. The cortex value is probably low by one or two orders of magnitude since it is based on light microscopy and does not consider pairs of axon segments and Nodes of Ranvier as separate neural circuits.


Figure 3.3.1-3 Fundamental signaling architecture of the human visual system. Sophisticated encoding algorithms are employed to allow the optic nerve to be minimized in diameter and mechanical stiffness while allowing the recovery of all of the required information from the photoreceptors in the cortex. Numbers indicate the ballpark estimate of the number of nerves passing through each trunk. 75% of the signals in the awareness channel may represent chrominance information. While the ultraviolet photoreceptors do not contribute totally to the perception of brightness, they are significant in the creation of the O–chrominance channel signal. This signal plays a significant role in human vision (see Section 9.1.3). The figure shows why the analytical channel has been largely overlooked in the past. It is represented by less than a few percent of the neurons in the optic nerve. The thalamic reticular nucleus (TRN) is shown supervising the operations of the elements within the thalamus. This supervision includes the power to override many signals and establish precedence among the various signals received by the thalamus. The figure highlights the bidirectional nature of the pulvinar pathway.

3.4 Functional signal pathways within the visual system The earlier discussion provides a foundation for Figure 3.4.1-1. While complex, this newly revised Functional Diagram of human vision illustrates many functional paths of vision and their interrelationships. It is discussed in detail in Sections 15.2.3 & 15.2.6 of the supporting volume. Only

Tutorial on Biological Vision- 33 a brief overview will be provided here. The subject of a complete commissurotomy on visual performance will be discussed in Sections 3.4.1. The first order signal (FO) paths, for both the auditory and visual modalities, are shown as wide hollow lines. The letter S at the beginning of the visual channel is meant to signify the S-plane of the retina. Considerable signal processing has occurred before this point in order to generate the O–,P–,Q–, R– and G’– channel signals of vision. This processing has not introduced significant time delays. Thus, the symbol also indicates spatial coherence, or a high degree of retinotopicity. The signals at this point are spatially and temporally coherent with respect to the image projected onto the retina. The letters S–T in a circle along the awareness path describe areas where the signals are no longer temporally coherent and are being rearranged geometrically for purposes of anatomical computation. The mechanism is called computation anatomy [15.6.5]. It provides several spatial and temporal transforms of the data without requiring any specialized neural circuits. It plays a major role in interpreting the signals associated with the awareness signal path. This mechanism also allows the neural system to perform several complex signal transformations without requiring the introduction of any transcendental mathematical calculations. Significant time delays are shown in each of the subsequent signal paths. These delays are associated with the various signal projection paths of stage 3. At a group velocity averaging 4 mm per millisecond and path lengths of about 13 mm, these delays are typically about 3.3 ms in humans. Such delays further support the reason that the autonomous operation of the POS servomechanism does not include elements of the cerebral cortex. The recognition, in 2002, of the roles of computational anatomy and time delay within the brain suggest a reinterpretation of the previously described LGN/occipital couple. The LGN appears to play a more distinct role than suggested by the label LGN/occipital couple. Similarly, the roles of the striate cortex (area 17 or V1) and the non-striated portions of the occipital lobe (areas 18, 19, 20, etc.) appear to emulate the functional roles played within the PGN/pulvinar couple. Areas 18, 19, 20, etc. are also known by the functional labels V2, V3 & V4. It is suggested that future discussions employ a slightly different nomenclature. In this nomenclature, a striate/V>2 couple would be described as functionally equivalent to the PGN/pulvinar couple. This couple could also be described as the V1/V>2 couple. The combination of Reyem’s loop, the LGN and Meyer’s loop would be recognized as a significant functional grouping. The double bar at one end of each delay symbol locates the ganglion cell associated with that circuit. Some of these paths are afferent and some are efferent. The awareness paths are shown along the upper quarter of the figure. The analytical, information and volition paths are found in the middle of the figure. The information path is used to describe the totally abstract signals passing over the pulvinar pathway. The command paths, along with several important notes, are shown at the bottom of the figure. The path between area 18-19 and the parietal lobe is shown dashed based on earlier discussions. The very important alarm mode signal paths are shown by the vertical triplicates of lines converging on the thalamic reticular nucleus. Upon receiving an alarm mode signal, the TRN can exercise its authority to reconfigure the neural system and command immediate response as required. A specific example of this is shown at the lower left. An override signal is shown going from the TRN directly to a group of neurons placed very near the eyes. This signal path is well documented but its purpose is poorly understood. It is proposed that this signal path and node are used to reduce the response time of the oculomotor system under alarm conditions. Many signal paths between the thalamus and the cerebral cortex are large enough to be called

34 Guide to Processes in Biological Vision commissure. The commissure crossing from one side of the bilateral cerebral cortex to the other and many of those from the thalamus to the cerebral cortex are grouped into the corpus callosum. Another group traversing from one side of the thalamus to the other is largely buried within the diencephalon. This group is labeled the corpus principia. Elements of this group are known as the internal capsule of the thalamus, the corona radiata and the ventral thalamic peduncle. The importance of these two groups, which are shown shaded, will be discussed in Section 3.4.1.


Figure 3.4.1-1 A revised Functional Diagram of human vision, ca 2002, introducing the TRN, in its role as the central control point of vision, and the relationship between the left and right hemispheres of the cortex. The diagram shows the nominal resolution signal path via the LGN to the striate/V>2 couple of the occipital lobe and the high resolution signal path from the foveola to the PGN/pulvinar couple. The diagram is compatible with dual mechanisms of depth perception and shows only abstract command signals being transmitted to the SC/cerebellum for implementation. It also shows two distinct major commissure between the left and right portions of the brain. See text.

3.4.1 Effect of a “total commissurotomy” of the corpus callosum Trevarthen & Sperry reported the results of complete commissurotomies on most of their patients through 19731. Their report was presented based on the conventional wisdom of that time. That wisdom assumed the only signaling path between the two sides of the cerebral hemispheres was via the corpus callosum. They noted the observed performance of their patients was not compatible with

36 Guide to Processes in Biological Vision this framework. However, the performance is compatible with the Top Level Schematic presented above. The performance of their patient highlights two situations. A path between the two halves of the cerebral hemispheres independent of the corpus callosum clearly exists. This path was not interrupted surgically. This path is the corpus principia. It consists primarily of the internal capsule connecting the two halves of the thalamus, and the two halves of the TRN. While not as large as the corpus callosum, it is clearly as important or more important. Additional paths may also exist that pass between the two sides of the thalamus. These paths were only discussed in concept in Trevanthen & Sperry. The subjects were asked to report their visual capability using their voice. Reporting involves the generation of an instruction in the anterior lobe that can be converted into a set of commands within the superior colliculus/cerebellum couple under TRN control. The resulting report may be verbal, a grunt or a motion. It may also be reflexive based on an alarm signal and prior commands stored within the superior colliculus. Thus, a patient may be able to report a response from any sensory system without relying upon the corpus callosum. However, this does not insure he can report verbally. His ability to report verbally may require cooperation between the two hemispheres. The main role of the corpus callosum in vision may be to aid in the merging of the peripheral images from the left and right halves of the peripheral visual field. With training, a subject may regain nearly normal visual facility after a complete commissurotomy, except for the ability to merge extrafoveal images that cross the medial line dividing his visual field vertically. Based on the 2002 model of this work, a total commissurotomy is probably not an appropriate name for the procedure of Trevarthen & Sperry. It would be better to speak of a total corpus callosumotomy. The emerging model provides a more comprehensive explanation for the performance of the subjects of Trevarthen & Sperry both before and following their operation. The medical implications are discussed briefly in Section 18.8.6.

3.4.2 Agnosia as a function of location or of feature extraction engine Agnosia is the inability to perceive objects through otherwise normally functioning sensory channels. It includes alexia, the inability to read complex character groups and symbols. Alexia varies in degree from the inability to read multiple symbol syllables to global alexia, the inability to recognize individual numbers, letters and symbols. Global anterograde amnesia is a condition where the subject is no longer able to recognize people, places, facts etc. These conditions are frequently associated with problems in either the thalamus or the parietal lobe of the neo-cortex. This association is compatible with the analytical mode of vision described above. Kandel, Schwartz & Jessell2 have provided a table of visual agnosia by area of cortical lesions. Unfortunately it is dated 1980 and it can be assumed that better data is becoming available almost daily. Their synopsis concerning the blind painter on pp. 586-587 is important and touching. Discussions of this author with a clinical patient have also suggested the results of agnosia near area 7. The discussions concerned the merging of the vector data (abstract signals) from the PGN/pulvinar couple (related to the foveola of the retina) and the vector data received from the LGN/occipital couple (related to the non-foveola retina). He reported a shimmering area consisting of a wheel with a diameter of about 2-3 degrees and five or six equally spaced spokes radiating from the wheel. Whether these features were directly associated with the conformal transformation presented at the striate cortex could not be determined. However, the number of spokes and possible

Tutorial on Biological Vision- 37 damage involving the low resolution image of the fovea, found in the striate cortex, could explain these symptoms. They are compatible with the two-channel visual process described above. This subject appears to be suffering from an inability to merge the information from the analytical and awareness channels into a composite saliency map.

3.5 The thalamic reticular nucleus (TRN) as the gate keeper of vision Recent empirical and theoretical work has shown clearly that the so-called “primary visual cortex” is not a dominant element in the visual system. While physically easy to investigate, its importance is eclipsed by the diencephalon, with particular emphasis on the perigeniculate nucleus/pulvinar couple in humans. Furthermore, it is the shroud enclosing much of the thalamus, the thalamic reticular nucleus, that is the primary operational center of both the nervous system and the visual system. The typical chordate can survive and see adequately with the primary visual cortex completely destroyed or removed. The typical chordate can survive with the frontal lobes destroyed or removed. However, significant damage to the TRN leads quickly to the death of the organism. In this context, severing the corpus principia, within the diencephalon, is much more serious than severing the corpus callosum between the two lobes of the cerebral cortex. Among other effects, this action causes agnosia Within the context of the TRN as the most important element of the nervous system, describing the roles of the subservient elements more clearly is possible. The TRN receives, supervises and processes signals from all of the sensory systems. The location of many neural engines is determined by their operational importance and the time delay involved in transmitting and receiving information between them and the TRN. Time delay, related to the propagation of stage 3 (phasic) signals within the neural system, is a very important parameter of many signaling paths. In this context, the PGN/pulvinar couple is much more important than the LGN/occipital couple because of its role within the POS servomechanism. In addition, it appears a special neural complex, the ganglia nucleus is designed specifically to eliminate one source of delay. It is found along the oculomotor neural path from the AOS to the oculomotor muscles. When necessary to protect the organism, the TRN can command the muscles via this nucleus. Thus, coarse signals from the TRN to the oculomotor muscles can bypass the SC/cerebellum couple and the other nuclei associated with the oculomotor neural paths when a crisis arises.

3.6 Summary of overall visual operation In humans, the visual system is highly redundant. The critical aspects of the image forming physiological optics are duplicated in the two eyes. The retina of each eye consists of four sets of photoreceptors. It normally operates with the UV sensitive photoreceptors only partly operational. The signals from the four sets of photoreceptors are multiplexed in several ways. Those from the general retina are multiplexed into separate luminance and (3) chrominance channels. These signals are extended and processed in tandem as far as the striated area of the occipital lobe (area 17) of the cerebral cortex. These signals are used in the awareness mode of chordate vision. Simultaneously, the subset of the photoreceptors forming the foveola is processed in a separate channel, generally defined historically as the Y-channel in cats. This analytical channel is processed at a higher resolution. It provides signals to both the higher cognitive centers and to the POS. While the awareness mode signals are not processed synchronously when they reach the LGN, the analytical mode signals are processed synchronously within the loop of the POS servomechanism. Thus, processing within the PGN is accomplished synchronously. The information presented to the LGN is not temporally synchronous. Reyem’s loops are an element of computational anatomy. They introduce a time delay into the neural signals from the peripheral

38 Guide to Processes in Biological Vision retina that is proportional to their distance from the line of fixation. The two LGN’s have a major responsibility to recover this temporal information. The information is directly related to the position of sources of change in the visual field. Such information is a critical part of the operation of the alarm mode of vision. Following the LGN, the signals of the optic radiation going to the occipital lobe encounter Meyer’s loops. One of the functions of Meyer’s loops is to restore the temporal coherence of the neural signals by again employing computational anatomy. While the LGN/occipital couple extracts information from the peripheral retina describing the external environment of the organism, the information is of relatively coarse resolution. The precise information is extracted from near the point of fixation by the PGN/pulvinar couple. Both couples return most their information to the TRN, in abstract (non-visuotopic) form, for subsequent transmission to area 7 of the parietal lobe as messages compatible with the saliency map. This map is maintained within the parietal-occipital-temporal (P-O-T) area of the cerebral cortex. It is made available to the higher cognitive processing engines within the anterior lobe. These engines create instructions that are returned to the TRN via the P-O-T area, primarily via area 6 (sometimes labeled 7a). The TRN routinely routes these abstract volition commands to the superior colliculus/cerebellum couple for decoding, elaboration and implementation. The TRN operates semiautonomously based on prior learning and stored instructions from the engines of the anterior lobe. However, it has great flexibility and can often reroute signals when necessary (or learn new methods of operation). The lateral geniculate nuclei perform as more than relays. They are responsible for generating alarm mode signals at the earliest possible time (the primary reason the LGN’s are located within the diencephalon). These signals are used by the TRN to control blinking and other reflexive actions. The LGN’s also provide a coarse stereoptic error signal to the POS. A more precise stereopsis signal is provided to the parietal lobe by the PGN/pulvinar couple. The superior colliculus/cerebellum couple serves to convert all of the abstract volition and alarm signals processed through the TRN into action commands that the oculomotor and skeletal motor systems can accept. It does this for all of the efferent neural signals whatever the originating sensor modality. While neurons can be located in the superior colliculus/cerebellum couple that exhibit a receptive field in object space of vision, the relationship is not one-to-one. All of the signals have passed through an abstract phase before reaching this couple. Figure 3.6.1-1 summarizes the above discussion without showing all of the delay elements in the system. It also shows an expanded responsibility for the left and right portions of the pulvinar in support of the left and right lateral geniculate nuclei. If appropriate, this modification would redistribute the memory function within the awareness channels and further limit the role of the occipital lobe. To achieve the performance required, the oculomotor plant is of two-stage design. The tonal portions of the oculomotor muscles respond to the majority of signals calling for saccades. However, in the more advanced chordates, the twitch portions of the oculomotor muscles respond to higher frequency commands and create the tremor motion required to achieve fine detail analysis and reading. The stage 3 (phasic signaling) neural circuits associated with tremor, including the “Y-channel” circuits of the retina exhibit a much higher maximum frequency than do most sensory or efferent neural channels. The top frequency is near 150 Hz. Within the POS, and particularly within the PGN/pulvinar, there appear to be electrotonic signal processing circuits operating at significantly higher maximum frequencies. Some stage 3 circuits in this area can propagate signals approaching 500 Hz.


Figure 3.6.1-1 A simplified Functional Diagram of human vision, ca 2003, showing the TRN, in its role as the central control point of vision, and the relationship between the left and right hemispheres of the cortex. The many delay elements in the system are not shown. An expanded role for the pulvinar is shown. Among others, it exhibits three important subdivisions, the posterior, left lateral and right lateral portions. While the signaling code used in the eye and optic nerve is well understood, the machine language (neural code) used within the CNS is unknown at this time. Decoding it will be difficult because it appears many messages are transmitted in “word parallel format.” Each word is transmitted using multiple bits transmitted over separate parallel neural paths. This method results in the very complex “burst patterns” reported on individual neural paths in current research. Even to capture these words requires more sophisticated electronic data recording than usually used in vision research.



4. Neurons are the electrolytic equivalent of man-made electrical circuits

Many of the relationships and hypotheses presented above cannot be addressed without a detailed understanding of how the neuron works. Such an understanding is not available under the chemically based “neuron doctrine” or “neurotransmitter dogma” still taught within neuroscience programs. An electrolytically based description of the neuron and the synapse is needed to understand the detailed functional relationships of the neuron and the neural system. This section will provide an overview of that understanding. The primary point (that will be justified below) is that the electrolytic circuitry found within and between neurons is directly analogous to man-made electronic circuits. For the reader versed in electronics, the Activa™ of the neuron is a PNP type junction device operating at very low voltages (maximum collector potential of -154 mV). It is the electrolytic equivalent of a solid-state transistor. The man-made equivalent to the electrolytic Activa™ is protected by United States Patent #5,946,185. All of the neural circuits are direct coupled. However, a variety of techniques are used to avoid the problems inherent in direct coupled circuits. The introduction of phasic signaling (generation of action potentials) is a key method of decoupling the direct coupled circuits. Each neuron is supported by a number of individual electrolytic power sources. These sources use a unique battery concept similar to that found in a fuel cell.

4.1 The electrolytic versus ionic argument of neuron operation From the mid 1800's until about 1960, the neuron had been considered an electrical device of mysterious character. At the time of Hodgkin & Huxley, the argument turned to the neuron as a chemically controlled device. Three reasons are apparent for this change. First, most of the investigators were biologically oriented based on their early training in chemistry. Second, Hodgkin & Huxley had difficulty explaining how the electrical potential internal to an axon changed during their experiments. Lacking an alternative, they described the axolemma as an active tissue with two significantly different time related characteristics. It could transfer ions slowly from one side of the membrane to the other by an undefined metabolic mechanism they called an ion-pump. This provided the necessary bias potential. In addition, they described an action potential as consisting of two nominally exponential current functions opposing each other. By assuming two different time constants, they could generate current waveforms that resembled the responses they recorded from their test set. They then sought the potential sources of such currents. They looked at the concentration of different ions found on each side of the membrane. The conclusion was reached that sodium ions were more abundant on one side of the membrane than the other. Similarly, potassium

42 Guide to Processes in Biological Vision ions exhibited the opposite abundance characteristic. Based on these observations, they proceeded to conceptualize two separate conduction paths for ions of these types. These paths were variable in conductance and supported by opposing independent electrical batteries that only affected the individual conductance paths. Using this technique, they could explain to the biological audience of that day why two collections of different positive ions went in opposite directions relative to the bias across the membrane. Unfortunately, no explanation for the mechanism controlling the variable conductances was ever given, although they were obviously linked. Third, the technology of semiconductor physics was maturing simultaneously in a different field. It was a field where most biologists felt uncomfortable. The decision of the community at that time was to select ionic currents as the dominant source and mechanism of neuron activity. This decision became a strong suppressant to activity by investigators in the field. To be published, they had to accept what became the neurotransmitter dogma. Between the 1960's and the present, semiconductor physics has caused the greatest advancements in man’s knowledge, and standard of living, ever known. Meanwhile, the concept of the neuron has remained largely stagnant in the literature over the same period. To this day, most neuroscientists are unaware of the other mechanisms of charge transport provided by semiconductor physics and overlooked by Hodgkin & Huxley. Proving the motion of any ions across the membrane as part of an action potential is also extremely difficult. A typical current of 25 pA for 10 milliseconds amounts to only 2.6 micro-micro-micro moles of a mono-charged ion. Even with the latest instrumentation, this is a small number. Finally, the ideas offered by Hodgkin & Huxley only applied to neurons generating action potentials. Less than 10% of the neurons in the brain and less than 4% of the neurons in the retina generate action potentials. What is the conceptual explanation, based on chemistry, for the operation of the other 90% of the neurons?

4.2 Semiconductor physics applied to the neuron Early in the development of semiconductor physics, an unusual effect was isolated using the Hall Effect. This Effect showed clearly that two different kinds of charge were being transported through crystalline semiconductor materials. They appeared to be of opposite charge and to move in opposite directions within a single electrical field. They could be isolated by applying an orthogonal magnetic field. The result was the recognition of a negative charge carrier as the electron and an equivalent positive charge carrier called a “hole.” The hole is in fact an electron jumping from one electrically unbalanced location in the crystal lattice to another. This motion exhibits a significantly different mobility than does the motion of the electrons associated with the conduction band. Ample data is now available concerning the ability of liquid crystalline organic materials to transmit currents as either electrons or “holes.” In fact the field of organic semiconductors is now a major field of research leading to light-emitting diodes. The application of semiconductor physics to the liquid crystalline structures known as plasma membranes leads to an entirely different explanation of how a neuron works. This application will be explored below. It provides the answer to how a neuron works and also how it is powered. Section 4.3.2 will be shown that the long sought ion-pump is in fact an electron/hole pump based on an electrostenolytic chemical process.

4.2.1 The plasma membrane as an electrolytic component The fundamental molecular structure of the bilayer membrane forming the plasmalemma of a biological cell is well known [4.1]. However, the variations in that structure related specifically to the

Tutorial on Biological Vision- 43 neuron are not. The bilayer membrane is made up of two liquid crystalline layers of triphospholipids with their hydrophobic terminals facing each other. Their hydrophilic terminals face the water-based plasmas on each side of the membrane. The controlling feature of the membrane with respect to neural operation is the symmetry of the molecular layers. If the two liquid crystalline layers are symmetrical at the molecular level, the membrane is a very high quality insulator electrically. If however, the two liquid crystalline layers are asymmetrical, the membrane exhibits the electrical characteristic of a very high quality diode. A typical plasma membrane may have distinct zones consisting of symmetrical and asymmetrical layers. The asymmetrical zones are the keys to the operation of the neural system. Figure 4.2.1-1 illustrates the molecular structure of a typical bilayer membrane. It also defines the electrical characteristics of individual zones of the membrane from an electrical perspective. Additional labels are provided along the top to help orient the reader. Water-based solutions are shown on both sides of this membrane. In this simple example, one solution is associated with the intercellular space and one is associated with the intracellular space of the cell. These solutions are electrically conductive. The long-chain lipid portions of the molecules are labeled p-type below the figure. This is the term used in semiconductor physics to designate a material exhibiting a deficit of electrons (relative to a neutral condition) within its crystalline structure. Similarly, the phosphorylated portion of the molecules are labeled n-type material. This material is found to exhibit an excess of electrons relative to a neutral condition. These labels are consistent with the polarization of a molecule defined by a chemist. For membranes consisting of bilayers that are symmetrical at the molecular level, the net polarization across the membrane would be zero. The material would act as an excellent insulator. However if the molecular layers are asymmetrical, the net polarization represents an electrical diode. While this configuration has a very limited conduction band, and remains nearly an insulator, it is a semiconductor due to the charge transport associated with its valence band. Conduction via modifications to the valence band is a quantum-mechanical process that can be reviewed in any entry level semiconductor physics text. The layers marked 1, 2 & 3 exhibit different charge densities than the surrounding material marked 0 and 4. These layers of a bilayer membrane are observable using an electron microscope.

Figure 4.2.1-1 The juxtaposition of two asymmetrical triphosphoglycerides monolayer membranes to form a bilayer membrane (BLM) as well as an electrically definable diode junction.

4.2.2 The juxtaposition of two asymmetrical plasma membranes–the ACTIVA The solid state transistor was discovered empirically in the late 1940's. It took about five years after that to discover and understand the underlying mechanism generating electrical signal amplification in that device. The Hall Effect discussed above was a critically important tool in that analysis. The analysis opened an entirely new area of semiconductor physics to active exploration. Efforts to

44 Guide to Processes in Biological Vision discover an equivalent organic transistor have been under way for a long time. These efforts have been concentrated in the non-biological areas, except for the realization that bilayer membranes offered substantial research possibilities. In a sense, the investigators have not seen the forest because of all of the trees. Every neuron contains at least one active electrolytic semiconductor device equivalent to the transistor. These biological transistors are called Activas. This section develops the fundamental structure and elementary theory of the Activa. The complete theory requires more background in semiconductor (and quantum) physics. To provide a preview, this section will describe the operating fundamentals applicable to three morphologically defined areas. Two have been described in considerable morphological detail (although not in adequate electrolytic detail). These are the synapse and the Node of Ranvier. The third is only known indirectly by its character. It is the Conexus found within the hillock of every neuron. The conexus consists of an Activa and its associated electrolytic circuit elements. The presence of the conexus within the hillock has only been recognized in ganglion cells because of its generation of action potentials. However, the conexus is also found in electrotonic neurons as well. As noted elsewhere, the vast majority of neurons (>90%) are electrotonic in character. The previous section discussed the asymmetrical bilayer membrane as an electrolytic diode. The individual diode is a two-terminal device. The essence of a man-made transistor is two electrical diodes placed “back-to-back” and biased appropriately electrically. It must be noted that the two diodes must share a base region at the quantum-mechanical level. The thickness of this base region must be extremely small to qualify as a “common-base” region. As a rule, this base region must be electrically accessible for biasing purposes. As a result, the typical Activa is a three terminal device. It has an input, an output and a base terminal. The additional capability of the Activa as a three terminal device will be developed below. If two asymmetrical bilayer membranes are brought into juxtaposition (at the quantum-mechanical level) they can be described at the molecular level by Figure 4.2.2-1. The nomenclature of this figure follows that used above. The two solutes are labeled the dendroplasm and the axoplasm. The numbers 1 through 7 are those assigned by a cytologist to a seven-layer junction between two bilayer membrane walls. Note they usually see layers 1, 3, 5 & 7 as dark lines and assign 2, 4 & 6 to the light spaces between these lines. It is seen from this figure that the characters of these spaces are different. Whereas 2 & 6 appear empty, 4 has a distinct character. In fact, the material represented by 4 is critical to the operation of the neurons. A similar material that is performing a different function is found between layers 1 & 7 and their respective solutions. It would be advisable to number these regions 0 & 8 when speaking of the functional performance of such a sandwich.


Figure 4.2.2-1 The molecular structure of the Activa within the hillock of a neuron. In operation, the configuration consists of two asymmetrical bilayer membranes (BLM) in close proximity and appropriate voltages applied between the dendroplasm, the axoplasm and the material in the junction area between the two bilayers (the podaplasm). The lattices in the junction area and on the extreme left and right surfaces are hydronium. Note the complex molecular structure at the interface between each plasma (0 or 8) and the adjacent leaflet (1 or 7). This area is described in terms of hydronium ions. The structure in the junction area (4) is also described in terms of hydronium. In these cases, the material constitutes a hydronium crystal. There is no physical movement of heavy ions within this overall structure. This is true even under the influence of external voltages. Additional material related to the electrical topology of this sevenlayer junction will be found in Chapter 8 of the supporting work. The area marked 4 becomes the common base area of the Activa. It has a nominal width of less than 10 nanometers. Because of its small size (comparable to that of many molecules), units of Angstrom remain common when discussing this region. The gap is frequently described as less than 100 Angstrom wide. A value of 80 Angstrom can be considered typical for a “gap junction.” Under the above definition of an Activa, two different forms of “gap junction” are evident. The first merely meets the criteria of physical spacing between the two membranes. This condition is easily observed using the electron microscope. The second form is an “active gap junction,” (a-gap). It meets the additional criteria that it is electrically asymmetrical at the molecular level and is properly biased electrically. This form can also be recognized using the electron microscope. However, greater degrees of observation skill and experience are required. After physical juxtaposition, the electrical environment must be established that will support “transistor action.” This requires that the input diode be biased to encourage current flow from the input to the base. Simultaneously, the output diode must be biased to discourage current flow from the output to the base. Under these conditions, a remarkable result is achieved. A current equivalent to that injected at the input appears at the output terminal. It is as though the input current failed to make a turn to exit through the base and went on directly to the output terminal despite the opposing electrical bias of the output circuit. This effect is known as “transistor action.” In the figure, current introduced at terminal 0 will appear at terminal 8 under the appropriate bias

46 Guide to Processes in Biological Vision conditions. Theoretically, no net current need flow through terminal 4 under these conditions. However, a current through terminal 4 of between 0.1 and 1.0 percent of the output current is typically observed. Many researchers have noted the apparently small forward impedance between the input and output plasmas of neurons. They have also noted the high electrical impedance for current flowing in the opposite direction. This is a basic characteristic of an Activa with its input terminal forward biased and its output terminal reverse biased (as required to achieve the transistor effect). A simple operational Activa looks like an electrical diode connected between the appropriate input plasma and the appropriate output plasma. Using the electron microscope, the active electrolytic semiconducting device, the Activa, is easily identified. It is usually described cytologically as a seven-layer structure. The fourth layer is formed by the base region. Areas marked 0 and 8 are usually not considered part of the structure but indicative of the background environment formed by the associated plasmas. The two diodes exhibit a capacitance between their terminals. When properly biased for operation, these two capacitances within the Activa become charged electrically. If care is taken in specimen preparation, the presence of these charges can be seen using an appropriate electron microscope. These charges contribute to a more complex picture than that of an unbiased gap junction. The charges frequently bend the beam of the electron microscope sufficiently to obscure one or more individual layers of the junction. [4.3.6]. Additional material related to the electrical topology of this seven-layer junction will be found in Chapters 4 and 8 of the compendium.

4.2.3 The Electrostenolytic Process defines/replaces the ion-pump The source of the electrical bias across the plasma membrane of every cell has been sought a very long time. Based on their experiments, Hodgkin & Huxley hypothesized an ion-pump as a component of a neuron. This putative ion-pump could transfer ions across a membrane for purposes of biasing the cell. Because of their other hypotheses, two ion-pumps were required, one for moving sodium ions into the neuron and another one for moving potassium ions out of the neuron. These pumps necessarily moved one ion in opposition to the existing electrical bias. While many researchers have sought this ion-pump, no actual, or even plausible, cytological explanation of such a mechanism has appeared during the last 50 years. An asymmetrical bilayer membrane is an electrolytic diode. It can transport charge across the membrane under proper bias conditions. In this configuration, it can participate in an additional mechanism that is critical to the operation of all neurons. This is the electrostenolytic process, an obscure although well-documented process of physical chemistry. The electrostenolytic process involves a chemical reaction that is stereochemically dependent on a substrate. Substrate is used here in a physical as well as an enzymatic context. The reaction will not take place unless the potential reactant(s) is in a specific stereochemical relationship with the substrate. The electrostenolytic process of interest in neuroscience is the conversion of an unusual amino-acid in exchange for the release of CO2 and an electron. The specific reaction is shown in Figure 4.2.2-2. Glutamic acid (glutamate) can become attached to the surface of an asymmetrical bilayer membrane by sharing a hydrogen bond (shown by the dashed line) with that surface that is part of a carboxyl radical. The glutamate can then release a second carbon dioxide group along with an electron. This electron can then pass to the inside of the membrane. This charge movement causes a net negative

Tutorial on Biological Vision- 47 charge on the capacitor associated with the membrane. The inside of the associated cell (or a conduit of the cell) is thereby biased negatively with respect to the surrounding interneuron matrix. The underlying mechanism can be explained based on earlier descriptions. It uses the polarization of the asymmetrical bilayer and requires the characteristics of a gap junction formed by two asymmetrical bilayers. Here, the single asymmetrical bilayer exhibits a net polarization. The glutamate molecule also exhibits a net polarization. The net polarization of the two constituents causes the electron to move to the interior side of the membrane. Following, or simultaneous with, that action, the CO2 group is released. The remainder of the reactant is now described as gammaamino butyric acid (GABA). It could just as easily be described as alpha-amino-butyric acid except for the accepted rules for naming chemicals. This name would show its similarity to alpha-aminoglutaric acid, an alternate name for glutamate. Glutamate has about 15,000 more calories of stored energy than GABA. This is the energy that is available to force the electron to move to the interior of the cell. The potential associated with this force is approximately 150-154 mV at endothermic body temperature. This is also the cutoff potential associated with individual axoplasms of the neural system. The above reaction defines the role of glutamate as the primary neuro-facilitator (a more specific term than neurotransmitter) of the neural system. Simultaneously, it defines GABA as the primary neuro-inhibitor of the neural system. As found in pharmacology, the application of glutamate to the surface of a neuron tends to increase neural activity. The application of GABA to the surface of a neuron tends to decrease neural activity. As will become clear in subsequent discussion, the words tends, excite, and inhibit must be used with caution. The observed responses to the application of glutamate and GABA to a neuron depend on where they are applied. To complete this section, discussing other potential neuro-facilitators and neuroinhibitors is useful. Only two simple amino acids exist that are acidic. Interestingly, they are both considered nutritionally nonessential amino acids. The reason for this designation is simple. They can both be fabricated within the body. Of even more interest, they can both be fabricated within the blood-brain-barrier protecting the brain. They are both dicarboxylic and both exhibit a net negative charge (polarization). These are glutamic acid and aspartic acid (aspartate). Figure 4.2.2-2 The fundamental electrostenolytic process powering the neural system. Glutamic It is the net charge and specific stereoacid becomes associated with the cell membrane in chemistry of these two materials that make a highly selective stereo chemical relationship them unique participants in the (dashed vertical lines). A reduction then occurs. electrostenolytic reaction. Aspartate can The process releases carbon dioxide as shown. It participate in the proposed electrostenolytic also injects a free electron into the plasma on the reaction. However, the reaction product is a other side of the cell membrane. GABA is then simpler material, alanine. A drawback exists released from the stereo-chemical bond. The in relying on this backup capability. GABA is symbology in the center of the figure suggests the easily converted back to glutamate. The steps in the process. reconstituted glutamate can be reused without the consumption of additional material from either the glycolysis process or the tri-carboxylic-acid (Krebs) cycle. The process is more difficult for alanine.

48 Guide to Processes in Biological Vision The effect of both aspartate and alanine on the functioning of neurons is well documented. Using the above definitions, aspartate can be considered a secondary neuro-facilitator, backing up the primary neuro-facilitator glutamate. Similarly, alanine can be considered a secondary neuro-inhibitor due to its structural similarity to GABA. Based on the above discussion, seeing how other materials might affect the operation of neurons is easy. Two basic methods are available. One is to affect the access of glutamate to the electrostenolytic site and/or the removal of GABA from the site. The second is to affect the availability of glutamate regardless of access. The steps in providing glutamate to the neurons are many. Any chemical that interferes with the process of providing glutamate in nominal quantities can be considered a neuro-inhibitor. Any action that increases the concentration of glutamate at the electrostenolytic site can be considered a neuro-facilitator. Long lists of agents have been prepared based on these qualifications. They have previously been lumped under the designation “neurotransmitters.” However, it is critically important to note these materials are completely unrelated to signal transmission in a neuron. The symbol in the figure is drawn to suggest that glutamate reacts to form GABA while releasing CO2 on one side of the membrane and an electron on the other. It suggests the reaction occurs on the outside of the cell membrane. More study is required of this reaction. The reaction may occur within the cell The reaction of glutamate to form GABA has long been associated with the operation of neurons. By associating the reaction with the electrical biasing of the plasma associated with the process, the explanation of the putative ion-pump is provided. Noting that the ion-pump is really a charge-pump is important. Either electrons, or if the reader prefers, holes are the form of charge moved (pumped) across the membrane. There is no need for heavy ions to be transported (pumped) across the membrane as part of the neural mechanism.

4.3 The operation of the electrolytic neuron 4.3.1 The application of the ACTIVA and electrostenolysis to the synapse The above discussion can be applied directly to the synapse between two neurons. Only the names change. Within the synaptic region, the presynaptic terminal is now formed by the axolemma and axoplasm of the preceding neuron and the post synaptic terminal is now formed by the dendrolemma and dendroplasm of the orthodromic neuron. The base terminal is now at an electrical potential that is close to that of the interneuron matrix, except for any potential related to the impedance due to the very narrow passage connecting to the base region. This impedance can be significant. The synaptic region is so narrow that all large molecules are forced out of this region by Brownian motion. As a result, the remaining small molecules (water) form a liquid crystalline structure called hydronium. This small crystal has frequently been observed by electron microscopists (who have always considered it an unwelcome artifact). The electrostenolytic processes powering both the axoplasm and the dendroplasm are frequently found near the synaptic junction. However, they do not involve a juxtaposition of two membranes and need not be in any part of the synaptic gap. In fact the chemical reaction associated with electrostenolysis is enhanced by easy access to the surrounding interneuron matrix. Figure 4.3.1-1(A) provides a caricature of a synapse showing both the signaling and support areas.

Tutorial on Biological Vision- 49 This caricature is compatible with the electron microscope images in the literature. However, it differs in interpretation. The synapse can be divided into two major areas, the area associated with signaling and the area associated with support activities. These areas are frequently crowded together for two reasons. The presence of myelination on the axon restricts the diffusion of chemicals to the immediate area of the synapse. The size of the post synaptic structure is usually quite small. Keeping this component small assures adequate electrical conduit bandwidth in the absence of myelination. The support area also consists of two areas. The first area supports the metabolism of the cells. Many chemicals can be captured by vesicles and transferred into the two conduits as required. Similarly, waste products unable to diffuse through the cell membranes can be expired via vesicles. The second area provides the substrate for the electrostenolytic process. The process is shown here as releasing CO2 into the interneuron matrix. The very narrowest part of the synapse, the active gap junction is frequently obscured (appears fuzzy) in electron micrographs due to the concentration of charge in the area. The same fuzziness is frequently observed associated with the electrostenolytic processes shown along the top edge of both the pre and post synaptic junction. The more open area of the synapse is usually imaged with greater clarity. However, this clarity is not usually at sufficient magnification to show the vesicles clearly. In any case, the electron micrograph is an image in time. It does not show the dynamic character of the vesicles as they breach the membrane. The two electrostenolytic processes are the primary modes of biasing the active gap junction of the synapse. However, the impedance between the interneuron matrix and the base area of the Activa can also create a bias potential due to the current flowing through it. The resulting situation is shown in (B) from an electrical perspective. The active gap junction forms a conventional electrolytic semiconductor device, an Activa. The Activa is an analog device. A current injected into the pre synaptic circuit results in a nearly identical current in the post synaptic circuit. This fact is illustrated by the simplified symbol used in (C). The exposed active gap junction, or synapse is normally an electrotonic circuit characterized by its low forward impedance. However, as many investigators have found, making a synapse begin to generate action potentials is easy. The capacitance of the test probe is adequate to cause this action. The generation of action potentials will be discussed in Section 4.3.3.

Figure 4.3.1-1 A simple caricature of the morphology of a synapse with equivalent electrolytic symbols. A; the signaling space (between the two membranes in the lower half of the frame) does not contain any mobile ions or chemicals. Metabolic support to the synapse is via the adjacent support space. B; the electrical equivalent of the synapse showing the Activa. C; the simplified electrical equivalent when the instantaneous axoplasm potential is more positive than the instantaneous dendroplasm.

50 Guide to Processes in Biological Vision 4.3.2 The synapse in a morphological and functional context Figure 4.3.2-1 expands on the above figure to show the synapse in a larger morphological and functional context. The upper frame shows the morphological situation. Terminal 1 suggests the input of a current from the Activa found within a cell and to be discussed below. This occurs at a region of the axolemma that is molecularly asymmetrical. Most of the remainder of the axolemma is an insulator due to the presence of symmetrical bilayers. However, electrostenolysis occurs in the area labeled power source and the transfer of current from the axoplasm to the dendroplasm occurs via the active gap junction. The dendrolemma is designed like the axolemma. The membrane is inherently insulating except in regions where the bilayer is asymmetrical at the molecular level. These regions act analogously to those described above.

Figure 4.3.2-1 The topology, circuit and four terminal network of the synapse. (a); the complete electrical topology supporting the junction between the axoplasm and dendroplasm. (b); the circuit diagram of the synapse and its associated axon and dendrite elements. (c); the details of the Activa within the circuit of (b). This level of detail is only required when modeling the Activa at a very detailed electrical level. The lower portion of the figure shows two electronic (electrolytic) equivalent circuits. The figure on

Tutorial on Biological Vision- 51 the left shows the circuit as a conventional three-terminal Activa circuit. The impedance in the synapse associated with the base of the Activa is labeled the poda impedance. The three-terminal equivalent circuit can be expanded to a four-terminal network as shown on the right for purposes of circuit analysis. The element Z2 is typically the capacitance between the axoplasm and the dendroplasm. The two diodes are shown with a common base (dashed line). The batteries are small potentials associated with the quantum-mechanical states of the diodes. If a signal is applied from the left sufficient to cause current to flow through diode D1, an equal current will be found to flow from diode D2 into the axoplasm. As shown, this circuit remains an analog circuit. It can faithfully reproduce any waveform applied to the input terminal as long as the appropriate biases are maintained.

4.3.3 The application of the ACTIVA and electrostenolysis to the Node of Ranvier The operation of the Node of Ranvier has puzzled neuroscientists for a very long time. Each Node generally has a small pulse applied to its input terminal and produces a much larger pulse at its output. The circuit is clearly sensitive to the magnitude of the input pulse. The fact that there is a significant delay between these two events is frequently overlooked.

4.3.3.1 The Nodes of Ranvier within a single neuron While the neuron is clearly the basic unit of the neurological system from a morphological and metabolic perspective, the case is not so clear from an electrical and signaling perspective. Figure 4.3.3-1 shows a single more complex neuron within its normal interneuron matrix environment. It is supported by a glia cell that is not important in this discussion. The important features of this figure are the multiple Activas (shown by the solid black boxes) found between individual electrolytic conduits. The two conduits on the left of the nucleus represent the two input terminals of a complete neuron. The conventional dendrite (a neurite) forms the non inverting terminal of the neuron. It operates as described above. The podite terminal is also formed by a neurite. These two neurites are frequently identified when discussing neurons as separate bi-stratified neurite structures. They are frequently labeled bi-stratified dendritic structures when their differences in electrolytic properties have not been recognized.


Figure 4.3.3-1 The first-order hydraulic plan of the brain using a ganglion cell as an example. The axon is shown unmyelinated. The dendrite, podite, axon and interaxons are all supported metabolically by the nucleus within the soma. Additional amounts of lactate are probably supplied to the Interaxons by the Glia. The myelination of the Interaxons physically restricts such metabolic supply to the areas near the Nodes of Ranvier. In a properly biased neuron, introducing a differential current into the dendroplasm will cause an equal differential current in the axoplasm . As an alternative, a differential charge can be introduced into the podaplasm. However, this current will cause the output current to the axoplasm to be of equal magnitude but opposite in sign. The podite terminal is the inverting input to a neuron. The figure shows three conduit segments following the Conexus (Activa) embedded in the hillock of the cell body (soma). All of the neurite conduits and axon conduits are supplied metabolically from the soma of the neuron. In this sense, only one cell is present. However, multiple distinct axons and active devices are present. The biological neuron consists of multiple building blocks of several different types. In this sense, a single neuron is not a basic electrolytic entity. For purposes of signaling, a single Activa and its supporting conduits and bias supplies form the basic neurological element. These combinations are known as a conexus, a synapse or a Node of Ranvier based on their morphological location. Whether a conexus is supplied metabolically from the parent soma or via diffusion from the adjacent glia is largely immaterial. Using the above concept as a baseline, differentiating between the first axon and later axons is necessary. The first axon always connects to a dendrite via the Activa embedded in the hillock. The later axons do not. They connect between an axon, or an axon like structure, and the dendrite of an orthodromic neuron, OR another axon like structure. Here, the axon like structure looks like a dendrite or podite electrolytically. These intermediate structures will be labeled interaxons. From an electrolytic perspective, they are at the potential and have the properties of a dendrite at their antidromic end. At their orthodromic end, they are at the potential and have the properties of an axon. Within this overall configuration, each Node of Ranvier looks the same. It is an Activa found

Tutorial on Biological Vision- 53 between two conduits and it is not embedded in the hillock of the parent neuron. Either or both conduits may be myelinated. In the retina, axon segments are not myelinated until they enter the optic nerve.

4.3.3.2 The morphology/cytology of a Node of Ranvier Describing the morphology of a Node of Ranvier in detail is difficult, based on individual electron micrographs. The image portrayed in an electron micrograph only shows one plane, generally including the axis, of a tubular or rod like structure. While the electrolytic conduits associated with both sides of the Node are usually easily recognized, many other details are difficult to portray. When examining the tissue surrounding the Node of Ranvier, the metabolic tissue provided by the supporting soma may or may not be symmetrical with respect to the chosen slice. Similarly, the tissue associated with the glia may appear asymmetrically in the micrograph. These conditions complicate the analysis of the micrograph. The active gap junction is frequently so small, the microtome slice chosen for examination does not contain it. In this case, the investigator frequently suggests the two plasma membranes are not in intimate contact. Occasionally, the sample will contain the area immediately adjacent to the active gap junction but not the junction itself. Here, the investigator generally claims the two membranes are in intimate physical contact. Typically, the magnification of the microscope is not adequate to support this claim. A similar situation occurs when a cross section view of the Node is wanted. In this case, the microtome slice may not include the active gap junction. The investigator generally describes the area near the active gap junction as uniform. Alternately, the microtome slice may include the active gap junction. Here, the investigator frequently removes the hydronium crystal mechanically. He does this because the presence of water molecules seriously disrupts the vacuum pumping system associated with the microscope.

4.3.3.3 The Node of Ranvier alone The Node of Ranvier is fundamentally different from the synapse in at least three ways. First, the Node of Ranvier may be embedded within a neuron. If not totally embedded, it is frequently more completely surrounded by associated structures than the typical synapse. Second, the output circuit associated with a Node of Ranvier is not the dendrite of an orthodromic neuron. Finally, the circuit is designed as a monopulse oscillator. It is not electrotonic. It generates action potentials at the output terminal of the Activa. A series of Nodes of Ranvier may be found within one neuron. To understand how a Node of Ranvier can generate an action potential, it is necessary to understand the operation of a simple Activa when combined with an appropriate size capacitor. This capacitor can be found connecting any two terminals of the three-terminal device. This work will not dwell on the specific circuit configuration. Figure 4.3.3-2 (A) shows two capacitors in a typical Node of Ranvier circuit. One is connected between the emitter (input) terminal and the base. The second is connected between the collector (output) terminal and the base. Depending on their size, either one is adequate to cause oscillation [10.8.4].

54 Guide to Processes in Biological Vision There are three phases to the generation of an action potential. They are shown in frame (B) of the figure. After the biases are established in a Node of Ranvier, the circuit enters a quiescent mode. No current flows through the device and the output circuit potential is near electrical cutoff. This potential is typically –150 mV relative to the interneuron matrix. If a small input is applied to the emitter terminal, nothing will happen until the amplitude of that input exceeds a threshold value. At that point, current will begin to flow through the Activa. If the time constants of the emitter and collector circuits are appropriate, the net current through the poditic impedance will maintain the voltage difference between the emitter and the base until the collector (axoplasm) potential approaches a low voltage. This voltage is typically near -20 mV. At that point, the current through the Activa will cease. The input and output circuits will then recharge to their initial values. The various currents are shown by dashed lines in the frame. The output (axoplasm) potential is shown by the curved solid lines. Note the rising potential exhibits one time constant and the falling potential exhibits another. This feature and the discontinuity near the peak positive value of the waveform are characteristic of a Node of Ranvier action potential.

Figure 4.3.3-2 Functional operation of a Node of Ranvier. A; During discharge, the Activa “acts” as a short circuit between the emitter and collector circuits. During recharging, it is an open switch. The circuits recharge independently. B; details of the current flow during an action potential. C; current flow into and out of the INM during an action potential.

Frame C shows the net currents and voltages frequently recorded by investigators. The shape of these waveforms is consistent with the waveforms defined in frame B. The loop current shown can be predicted precisely if the limited travel velocity of electrolytic currents along the axon segment is accounted for. Figure 4.3.3-3 shows a theoretical action potential based on this model. It has been fit to a variety of measured action potentials [10.8.3]. The time constant of the rising waveform is 0.18 msec. The time constant of the nominal falling waveform (solid line) is 0.8 msec. Note that switching occurred at 0.6 msec after a voltage change of 62 mV. In the absence of switching, the rising waveform would have followed the dotted line. In the particular case shown, the dashed line shows the effect of superfusing the neuron with 4-aminopyridine. The effect has been to increase the time constant of only the falling waveform to 1.4 msec. The chemical did not affect the rising waveform or the switching point. This change suggests 4-aminopyridine interfered with the site of the electrostenolytic process providing power (current) to the neuron.

Tutorial on Biological Vision- 55 The action potential waveform is the result of a switching process related to the gain characteristic of the Activa and the impedance of the other electrolytic elements in the Node of Ranvier circuit. This is the switching mechanism that biochemists have been seeking ever since Hodgkin & Huxley proposed their ionic theory of the action potential during the 1950's. Note the fact that the action potential involves a true switching mechanism. Section 9.1.1 will show the waveform of the photoexcitation/de-excitation mechanism is fundamentally different. This so-called generator potential involves the difference between two exponential processes competing continuously against each other.

4.3.4 The application of the ACTIVA and electrostenolysis to a ganglion cell

Figure 4.3.3-3 The theoretical action potential for an endothermic animal. The solid curve represents the nominal response. The dashed curve represents the response after pharmacological intervention. While both the rising and falling waveforms are affected by temperature, only the falling waveform is affected by pharmacology. Note the abrupt switching transition at 0.0006 seconds.

Figure 4.3.3-2 (A) can also be used to describe the operation of any ganglion cell [14]. A ganglion cell is like a Node of Ranvier with respect to capacitance. However, two different types of ganglion cells exist based on their bias conditions [14.2]. If the Activa within the hillock is biased like the Node of Ranvier, the circuit will operate like a Node of Ranvier. It will generate an individual action potential upon the application of any waveform sufficient to start current flowing in the Activa. This monopulse will look exactly like the action potential of the typical Node of Ranvier unless the time constants are different. If the input waveform is held above the threshold for an extended interval, the circuit will generate a series of action potentials of essentially equal spacing (after the first pulse pair) until the input goes below threshold. The first pulse pair may exhibit a slightly different spacing because of the parameters of the circuit. This circuit action is that associated with the ganglion cells of the luminance channel (the R–channel) of biological vision. This type of ganglion cell is frequently associated with the magnocellular pathway of vision. It is also the type of signal observed in the G’–channel of vision. These cells are frequently labeled midget ganglion cells and exhibit an “intermittent” output. If the bias applied to the above ganglion cell is appropriate to cause a continuous current to flow in the Activa, a different action is observed. As in the previous case, the gain of the circuit will cause the Activa to begin to switch states and the axoplasm potential will fall. When the axoplasm reaches its minimum potential, the current through the Activa will cease and recharging of the input and output circuits will begin. However, the input circuit will reach a point where current will begin to flow through the Activa. As a result, the cycle will repeat itself. A continuous series of action potentials will be generated. This is the type of signal generated in the chrominance channels (O–, P– and Q–channels) of biological vision. It is frequently associated with the parvocellular pathway of vision. These cells are frequently labeled parasol ganglion cells and exhibit a “sustained” output. If an additional signal is applied to the input of a parasol ganglion cell, the interval between the action potentials will vary as a function of this input signal. This is the method used to encode electrotonic chrominance signals into phasic action potentials. The input signal can be of either

56 Guide to Processes in Biological Vision polarity or change polarities. The spacing between the action potentials will follow the prescribed waveform. Note that all action potentials exhibit a discontinuity near the peak positive excursion of the pulse. This feature is a characteristic of a switching type oscillator. It is seen in all recordings of action potentials if adequate care is taken.

4.3.5 The application of the Activa to a bipolar or lateral cell The above discussion of the ganglion cell provides the backdrop for understanding the operation of the bipolar and lateral cell types [13]. The bipolar and lateral cells do not contain the necessary capacitance to oscillate and generate action potentials. These cell types are electrotonic amplifiers. Their output is proportional to the difference between their input signals as long as their bias potentials are appropriate to allow some current to pass through the Activa. The lateral cells include the horizontal cell and a variety of amercine cells. The bipolar cell only uses the dendritic signal input and generates an output of the same polarity as the input. The lateral cells use both the dendritic and poditic inputs to generate an output that is the algebraic difference between the two inputs. While the output may be at a different absolute potential than the inputs, the output waveform will faithfully represent the electrotonic difference between the two input waveforms. The output of the lateral cells are frequently described as inverting cells. However, inversion only applies to the poditic input signal. The analyses provided above describe the exact potentials measured in the laboratory for the various classes of neurons.

4.3.6 The stellate cell recovers the encoded signals After the ganglion cells encode visual signal information, and propagation neurons deliver the signal information to the various feature extraction engines of the brain, an electrolytic circuit is needed to recover the encoded information [14]. This area has not been discussed previously in the literature. Examining the signal paths entering these engines, based on morphology, it appears the stellate cells perform this decoding function. Decoding of time-interval encoded streams of action potentials, like those found in the luminance channel, are quite easy from an electrical perspective. A circuit consisting of a series diode connected to a long time-constant parallel resistor-capacitor combination will accept a stream of pulses and provide an output waveform that is the time averaged equivalent of the input. As discussed above, the transfer characteristic between the input and output of the Activa within a typical neuron looks like a diode when properly biased. Decoding the chrominance channel signals is slightly more difficult. However, the same circuit can be used. Since the action potential stream is continuous here, an average output voltage will be generated in the absence of any signal. Where the pulses are more widely spaced, the output will be reduced. Where the pulses are closer together, the output will rise. Thus, the recovered output signal consists of a constant potential added to a faithful reconstruction of the encoded information. [14.5.4] The capacitance required in the resistor-capacitor network of the stellate cell is much larger than required for oscillation in the propagation neurons.

4.3.7 Signal propagation by a neuron Figure 4.3.7-1 illustrates the vastly different signal propagation velocities found in neural systems [14]. The velocity associated with the method of electromagnetic propagation is shown above the

Tutorial on Biological Vision- 57 graphic. The rate associated with the more commonly discussed diffusion method is shown below the graphic. The graphic shows multiple dendritic trees converging on the soma of the cell and one poditic tree. The Activa is shown by the crosshatched area. The size of the hillock is related to the size of the capacitors associated with the Activa. For propagation neurons, the hillock is large compared with the rest of the soma. Two Nodes of Ranvier are shown. The myelinated areas of the axon and interaxons are shown by the dark wrapping. Several distinctly different propagation modes are used within the neural system. The simplest to envision is that discussed in the neural literature. It involves the diffusion of ions through an electrolytic medium. This is the propagation mode used within electrotonic neurons. This method is quite slow. However, the method is adequate where distances of less than a few millimeters are involved. However, a much faster mode is needed for distances measured in centimeters to meters.

Figure 4.3.7-1 Summary of the signal propagation velocities in neural systems. Three distinct modes of propagation are shown within one neuron. Electromagnetic signal transport (using action potentials) is much faster than electrolytic transport (by ions). The electrolytic transport velocity shown above from Carpenter & Sutin appears excessively slow. See text. The dimensions of the dendritic tree are very small compared to the length of the axon. As a result, the dendritic tree plays a negligible role in the overall group velocity of the signals. Action potentials have electrical characteristics that allow them to be propagated like radio waves (electromagnetic waves). This mode of transmission does not involve the physical transport of any ions. It is about one thousand times faster than propagation by diffusion. The diffusion of ions through an electrolyte involves two important parameters. The first is the physical transport velocity of such ions in the presence of very low electrical fields. The electrical potential between the two ends of a neural conduit is measured in millivolts. Over distances of a millimeter, the result is a potential field of a few volts per meter. This is quite low and constrains the velocity of the ions significantly. Reported axoplasmic ion transport velocities are typically below 0.01 meters per second. The second problem involves the parameter known as phase distortion. If an

58 Guide to Processes in Biological Vision attempt is made to transmit two sinewave signals of different frequency through a diffusion medium, they will arrive at the output terminal at different times. The ion transport velocity of an electrolyte is a function of the frequency of the signal being transmitted. When transmitting narrow pulses, this distortion can be a major problem. This variation in velocity is associated with the high electrical capacitance across the extremely thin lemma of the conduit. Because of these parameters, diffusion is only used to transmit neural signals over distances of less than a few millimeters. A different method of neural signal transmission must be used for greater distances. The answer to the slow transport of electrotonic signals through an electrolyte by diffusion is the development of the phasic signaling method that uses action potentials.

4.3.7.1 A coaxial axon is not a Herman Cable The biological community has long discussed signal transmission within the neural system based on the simple concept of a continuous series of resistor-capacitor networks as defined by Herman in the mid 1800's. This was shortly after the invention of the telegraph and before the invention of the telephone. Soon after the invention of the telephone, it was discovered that wide bandwidth signals could not be sent any appreciable distance over a telephone line consisting of only resistors and capacitors. The phase distortion was so high, the voice signal could not be understood. Furthermore, the attenuation was excessive. Two solutions were devised. The earliest solution was to introduce large inductors periodically along the line to compensate for the effect of capacitance. A more satisfactory solution came later. It was found that coaxial cables did not suffer from the same phase distortion. Any coaxial cable exhibits an intrinsic inductance plus an intrinsic capacitance. In fact, the intrinsic capacitance and inductance of a coaxial cable are far more important than the resistance of the cable. They determine two properties of the cable, the input impedance and the propagation velocity of the circuit. A theoretical coaxial cable containing no resistance will still exhibit an input impedance that is resistive. It will also exhibit a propagation velocity given by the square root of the inductance per unit length divided by the capacitance per unit length (and independent of the resistance per unit length). These are the properties of importance in propagation of action potentials within neurons. To understand the electromagnetic propagation of action potentials, recognizing and understanding the electrical characteristics of an axon are important. Electrically, an axon is a coaxial cable. It consists of a conducting material, the plasma surrounded by a cylindrical insulating material, the lemma. The lemma is in turn surrounded by a second conducting material, the interneuron matrix. The fact that the interneuron matrix may be of great extent outside the axon is largely irrelevant. However, whether the axon is myelinated or not is highly relevant. The myelin exhibits a very low dielectric constant. Its presence greatly reduces the capacitance per unit length of the axon. This change increases the propagation velocity of the axon greatly. The Herman Cable has been an archaic concept since 1890 or earlier. More recent discussions based on the Herman Cable are largely irrelevant to the propagation of action potentials. Their only relevance is to the diffusion of electrotonic signals over distances of less than a few millimeters.

4.3.7.2 Understanding the group velocity, and other signal velocities within a neuron The literature frequently discusses the velocity of neural signals without clear definition of the velocities involved. The easiest velocity to define is the group velocity of a signal (an action potential) propagating within a stage 3 neuron. This is the average velocity of the signal measured by the time

Tutorial on Biological Vision- 59 for it to travel between two points separated by at least one cm. The longer the separation distance, the more accurate the measurement. Such a measurement will include multiple axon segments and multiple Nodes of Ranvier. A mixture of ion transport and electromagnetic propagation modes will also be involved. The resulting group velocity can be dissected into its components. These include the diffusion velocity of the signal during ion transport, the phase velocity of the signal during electromagnetic propagation and a fixed time delay during the regeneration cycle at each Activa. The easiest way to calculate the group velocity is to calculate the time delay associated with each segment of the propagation path. The group velocity is then given by the total distance divided by the total time delay. This allows the time delay associated with the regeneration process to fit seamlessly into the calculation. The phase velocity of a signal within a conduit is a function of the dimensions of the conduit. Because of their complex shape, computing the precise phase velocity within a neurite is difficult (even as a function of position along the dendritic tree). In addition, the high capacitance per unit length of the neurolemma reduces the achievable velocity. Values of 0.01 meters per second down to 4.6 x 10–6 meters per second appear in the literature. A typical diffusion velocity is near 7 x 10–3 meters per second based on ERG data [11.1.6 & 17.5.6]. The task is much easier for an axon or interaxon. These have relatively constant diameters over significant distances. The phase velocity for the typical myelinated neuron is about 4400 meters per second. While this velocity cannot be sustained over a long distance, it is much faster than any potential diffusion velocity. The time delay associated with regenerating an action potential is typically 0.6 ms in endothermic animals. The delay is much higher in exothermic animals. It can be as large as 500 ms at 20 degrees centigrade. Such a value explains the lethargy of many terrestrial exothermic animals before the sun warms them. After combining the above delays and velocities, a typical group velocity for the propagation of action potentials is between one and 120 meters per second. Values above five meters per second are only found in specialized circuits (mostly within the POS of the CNS). Even at an average group velocity of five meters per second, electromagnetic propagation is 1000 times faster than ion diffusion transport. The electrolyte within an axon plays no role in electromagnetic signal propagation. Any conductive electrolyte will serve as the inner conductor of the coaxial cable. The signal involves only electrical charges constrained to the surfaces of the lemma.

4.3.7.3 The marriage of the Node of Ranvier, electrostenolysis and the coaxial axon Figure 4.3.7-2 combines all of the principles discussed earlier into the morphological and electrolytic description of an axon. The signal, Ve is delivered to the Activa within the soma of the neuron by diffusion. The signal is used to cause the generation of an action potential at the output terminal of the Activa. The Activa circuit consists of a group of morphological and electrical components extending over a distance shown by the dimension x. These are called lumped components. Signals are transported by diffusion in this area at a velocity of less than 0.01 meters per second. Within the myelinated portion of the axon (labeled y), the electrical properties of the axon are described using distributed components described by their inductance, capacitance, etc. per unit length. The myelination of the axon greatly reduces its capacitance per unit length. As a result the propagation velocity is greatly increased. The signal is propagated by electromagnetic means at a nominal 4400

60 Guide to Processes in Biological Vision meters per sec. Attenuation of the signal is quite low in this region. The signal can be transmitted centimeters without being reduced below 10% of its original amplitude. At the termination of the myelination, the signal is returned to transport by diffusion. When it reaches the Node of Ranvier, it causes the Node to regenerate the action potential to its nominal amplitude. The process is repeated. The signal is returned to electromagnetic propagation until it approaches the next Node or a synapse. The drawback to the mixed mode of operation just described is the finite delay (0.6 ms for endothermic animals) introduced at each regeneration point. This delay becomes the tradeoff point between diffusion and electromagnetic propagation of neural signals. Once the electromagnetic propagation mode is adopted, it becomes important to minimize the distance related to the diffusion mode within the overall neuron. This is the reason why the myelination extends into the Node of Ranvier space so significantly. Any electrostenolytic and metabolic activity must occur as close to the junction of the Node as possible to minimize overall circuit delay.

4.4 Metabolic support to the neuron The metabolism of the neuron can be divided into two distinct parts, the metabolism required to maintain the homoeostasis of the cell and the metabolism required to support the signaling function of the cell. Maintaining homoeostasis involves the movement of many reactants and waste products through the walls of the cell. Precisely how this movement is accomplished for many different materials remains unclear after many years of study. Clearly, glycogen can move from the blood stream, through even the blood-brain-barrier and into any cell of the neural system with ease. This section will review the highlights of the process required to power the signaling function within a neuron.

Figure 4.3.7-2 The overall signal transmission environment for the propagation of action potentials. Top; the morphological situation with electrolytic symbols as an overlay. Bottom; the electrolytic situation stressing the relevant lumped components and the distributed nature of the myelinated portion of the axon. Resistance plays no role in the operation of the interaxon (over the distance y). The letters in the boxes refer to the complex impedances of the electrostenolytic supplies. P = podite or base. C = collector. E = emitter.

4.4.1 Introductory electrostatics The biology community has generally adopted a narrow philosophy regarding the electrostatics of a cell. They have assumed that it requires separating the ions of an ionizable material by a membrane to create an electrical potential across that membrane. Another method exists for achieving the same

Tutorial on Biological Vision- 61 potential. If the purest of deionized water (pH =7.000) is placed on each side of a closed insulating membrane and a battery is used to inject free electrons into the interior of the membrane, the same result will be obtained. The interior of the membrane will assume a negative electrical potential with respect to the outside fluid. The potential will be precisely equal to the charge injected times the capacitance of the membrane. If the experiment is repeated using a solution of neutral saltwater on each side of the membrane, the same result will be obtained. The fact that all of the salt in the water is fully ionized is immaterial. The above experiment shows that transferring ions through the membrane of a cell to achieve a negative electrical potential inside the cell is not necessary. Any mechanism that will transfer electrons to the interior of the membrane will generate such a negative potential. The simplest method of providing this potential has been described in Section 4.2.3. Electrostenolysis of glutamate on the surface of a locally asymmetric plasma membrane will inject electrons into the interior of the membrane and cause a negative potential to be observed. The free charge will spread out evenly over the interior of the closed membrane (assuming it is spherical) just as it would on the surface of any capacitor. The charge cannot escape through the membrane because of the insulating properties of the membrane with respect to negative charges attempting to move out through it. Chemically, the results of the electrostenolytic process are the release of a molecule of CO2 and the formation of a molecule of GABA.

4.4.2 Metabolic processes related to the operation of the neuron The generation and delivery of glutamate (glutamic acid) to the site of electrostenolysis, and the removal of the waste products, are key to the polarization of all living cells. Only small quantities of electrons are required per unit time in the typical cell. The transport of unbalanced charges through the membrane by metabolism is unusual. However, electrostenolysis plays a more important role in the dynamics of the neuron because of the use of electrons in signaling. Therefore, understanding the source of glutamate is more important in the study of the neuron. Glycogen is the primary source of energy for the cell. The complete degradation of a single molecule of glucose, the basic unit of the glycogen polymer, to CO2 and H2O releases a great deal of energy (686 kcalories). The energy associated with glucose and the quantized method of its release are key to the efficient operation of the neuron. The energy is usually released in units of 7.3 kcal through reactions involving ATP and other enzymes. The reaction of interest here, the electrostenolysis of glutamate to CO2 and GABA involves an energy change of about 14.6 kcal. This value generates a maximum negative potential of 154 mV across the lemma of a cell (or a conduit). To obtain glutamate from glucose involves the glycolysis of glucose to either pyruvate or lactate followed by two additional steps. The first involves the tri-carboxylic-acid (Krebs) cycle (abbreviated TCA) and the creation of alpha-ketoglutarate. This material can be readily converted into glutamate by amination. The process is carried out in the glutamate shunt to the TCA cycle. The reason both pyruvate and lactate are mentioned is because of their different properties. While they are easily interconverted, lactate moves easily through cell walls whereas pyruvate does not. There are suggestions in the literature that some neurons have limited capacity to prepare pyruvate and deliver it to the point of use along the axon. It is suggested that glia may generate excess lactate that can easily be transferred through the necessary cell walls to support the interaxons found far from the soma of a propagation neuron. In large animals like humans, individual stage 3 neurons may be one to a few meters long. Supplying of lactate by glia cells could substantially reduce the axoplasmic transport of pyruvate and other materials from the soma to the remote interaxons of the neuron.

62 Guide to Processes in Biological Vision Figure 4.3.3-1 provided a gross view of the stage 3 signal propagation neuron within the capillary bed and supported by the vascular system [10.8]. The location of the blood-brain-barrier was also shown symbolically. Figure 4.4.1-1 shows an expanded view of the area including the Activa embedded within the soma (the solid black box on the left) and the next Node of Ranvier (the solid black box on the right). The metabolic steps of primary interest in neuron signaling, discussed above, are illustrated in this figure.

Figure 4.4.1-1 Details of the metabolism and hydraulic flow related to the neuron. It is highly likely that the glia supply lactate to the remote sites of glutamate production (TCA2 and TCA3). Waste product removal is represented by the dashed arrow. The transport of glycogen, GABA and CO2 through the capillary bed and INM can be affected by many neuro-facilitators and neuro-inhibitors.

The solid arrows show the absorption of glycogen from the bloodstream by a neuron and a glial cell. Glycolysis is shown taking place in both cells. The process proceeds to pyruvate in the soma of the neuron. This material is transferred within the cell to the ribosomes. The ribosomes use the TCA cycle to prepare glutamate that can be used to support the electrical power generating electrostenolytic process. These ribosomes are found near or within every electrolytic conduit of the neuron. To reduce the need to transport pyruvate along the length of the axon, glia cells are shown preparing lactate that can be diffused into the capillary bed and across into the neural cell. Once

Tutorial on Biological Vision- 63 within the cell, this lactate can participate in the TCA cycle wherever ribosomes are located and contribute additional glutamate to the electrostenolytic process. The electrostenolytic process will seek to maintain a constant electrical potential within the conduit it is supporting compared with the outside of the conduit. In this process, the electrostenolytic circuit appears as an electrical load to the collector of nearby Activas. Electrostenolysis of glutamate produces CO2 and GABA. These materials must be removed from the immediate vicinity of the electrostenolytic process to avoid interfering with the ongoing process. The CO2 is diffused to the venule system as part of the respiration process. GABA may be removed in a similar way. However, GABA can be transaminated into succinic acid and then converted back to glutamate by the TCA cycle.

5. The unique neuro-secretory photoreceptor cell

The mechanical, metabolic and chromophoric dynamics associated with the photoreceptor cell makes it very difficult to discuss the cell in isolation. To understand the operation of the photoreceptor cell in chordates, reviewing the morphogenesis of the complex eye with a reversed retina described earlier is necessary. Conversely, appreciating the operation of the PC/IPM/RPE interface without a detailed appreciation of the operation of the photoreceptor cell is difficult. Once the genesis of the photoreceptor cells (PC’s) is understood, understanding their homoeostatic operation in the interphotoreceptor matrix (IPM) is easier. This IPM is a closed volume formed between the outer limiting membrane (OLM) of the retina and the retinal pigmented epithelium (RPE). The following material will discuss the photoreceptor cell in detail. Section 6 will discuss the spectral capability of the chromophores in detail and then Section 7 will blend these discussions into an overall discussion that will lead to Section 8 & 9. Beyond that related to metabolism, the internal structure of the photoreceptor cell has not received significant attention in recent years. This is particularly true with respect to the outer segment. Clearly, the outer segment is truly outer. It is external to the plasma membrane of the cell and interconnected with it electrolytically by the microtubules (dendrites) passing through the colax (or ciliary transport or ciliary collar). As discussed in greater detail in Section 7.3, the conceptual difference between rods and cones is largely historical. The upper left portion of Figure 5.1.1-1 will serve as a typical caricature of any chordate photoreceptor [4.3]. The figure bares a family resemblance to several figures appearing in the literature from 1975 through 1985. An exception is the clear absence of a membrane surrounding the disk stack. The plasma membrane of the inner segment is shown terminating at the calyx. The disks are shown as physically independent except for their intimate relationship with the microtubules in their fissures. The photoreceptor cell is one of the most complex cells within the

64 Guide to Processes in Biological Vision neural system. Like many other cells associated with the neural system (and particularly the vibrissal cells forming whiskers) it is neuro-secretory. Because of the complexity of the figure, an exploded view of the same cell will be presented later in this section. This caricature will be further developed into a block diagram and then further into a schematic diagram as the discussion below develops. The drawing has labeled three distortions. The outer segment has a typical length divided by width (L/D), or aspect ratio, of 25:1. It is long and fragile. Similarly, the distance between the nucleus and the pedicle and the distance between the nucleus and the inner segment can both be much longer than the entire inner segment. The caricature does not display the narrow neck between the Outer and Inner Segments that has become an icon based on an original caricature that appeared in 1967. The caricature was prepared by a medical illustrator and was apparently based on only a few images acquired with a light microscope, or limited verbal consultation. This narrow neck does not correspond to our current knowledge [4.3]. This caricature showed only the colax connecting the inner and outer segments. It also showed a very complex relationship between a putative membrane surrounding (and interconnecting with) the disks and connecting to the inner segment. The caricature would probably have been considerably different if based on higher magnification electron microscope imagery. Unfortunately the putative asymmetrically located neck between the inner and outer segment has produced an instantly recognizable icon of the photoreceptor cell. Interpreting the functional roles of components within the photoreceptor cell is complicate by its asymmetry. Individual micrographs do not represent the structure of the cell well. Images chosen to show the colax in detail frequently do not show the circularly symmetrical calyx area equally well. More recent electron micrographs, and autoradiographic data have defined the role of the colax, and the larger calyx more clearly [4.6.2]. No nutritional or metabolic functions have been associated with the colax. It is clearly the collar through which neural components pass from within the inner segment to interface with the disk stack. Similarly, the larger calyx can be identified as the source of the disks formed into the outer segment. It acts as an extrusion dye to form the disks from the protein material secreted by the inner segment.


Figure 5.1.1-1 Caricature of a photoreceptor cell with RPE interface and Outer Limiting Membrane. A complete cell is shown at upper left. Individual functional groups are shown on the right. Note the length to diameter ratios given for several elements, and the presence of the Activa and the poditic terminal on the left of the inner segment. Note also the calyx (extrusion cup) and the colax (ciliary transport) formed by the cellular membrane of the inner segment. The colax provides passage of the dendrites from the Activa to the disk stack of the outer segment. Compare to Fliesler & Anderson (1983) and Miller & Newman (1998). The neural elements within the photoreceptor cell have not been defined previously in the literature. Similarly, the analogous features of the photoreceptor cell and the somatosensory cells have not been described. Both cell types continuously secrete a similar protein material. In one case, the secretion is formed into a continuous structure (a hair). In the other the secreted material is broken into short segments and transformed into disks. In both cases, a single dendrite-like element has subdivided

66 Guide to Processes in Biological Vision into a group of microtubules. These microtubules are arranged to surround the protein material. In both cases, the continuous secretion of protein causes a continuous movement of the material away from the secretion area. Since the photoreceptor cell is found in a closed volume of finite size, the extruded protein material must eventually be disposed of. This is achieved by phagocytosis at the RPE interface. Disks are typically engulfed in groups of 20-50. Their digestion is well documented. It appears the protein material is broken down into amino acids and returned to the blood stream. The chromophores are isolated and stored in pigment granules before being redeployed to new disks.

5.1 Functional divisions of the photoreceptor cell The right portion of Figure 5.1.1-1 shows the photoreceptor cell and RPE separated into functional components using an exploded view format. The extracellular Outer Segment (the disk stack) is shown in the center of the figure. The glandular portion of the cell (part of the inner segment) is shown in the lower right along with the nucleus. A major function of this portion is the production of opsin by the Golgi Apparatus, mitochondria and ribosomes. This material is then secreted into the extrusion barrel where it is formed into furrowed disks by the calyx. The neural portion of the cell is shown in the lower left. The photoreceptor cell is one of the most complex neurons of the nervous system. It contains a host of individual Activa providing both signal processing (adaptation) and signal distribution. The reticulum (the conductor within the morphologically designated axon) connects the distribution amplifier to the pedicle of the cell. In this view, the (typically) nine microtubules of the neuron exit the cell at the colax (the basal body of the cilium) and fan out around the Outer Segment before being placed in the furrows of the disk stack. Microtubules are specialized forms of dendrites. Below the cilium, the dendrites merge into a single connection to the distribution amplifier, or Activa, shown. The poditic terminal of this Activa is shown explicitly. This terminal has been successfully documented with the electron microscope. [4.3.1] Full details of the elements of the photoreceptor cell are described in Chapter 12 of the supporting work. The individual structures associated with these portions of the cell can only be imaged at 120,000x or higher.

5.2 Electrical configuration of the photoreceptor cell 5.2.1 Unique dendritic structure of the neuron Like other initial neurons in an afferent neural signal path, the photoreceptor cell is highly specialized. It may contain the most complex neural circuitry in the organism. To achieve its function, the neuron has significantly modified the dendritic structure associated with one Activa. The main dendrite has ramified into nine individual dendrites (typical in humans but up to 25 in other species). These have been grouped into a small bundle before their passing out of the soma of the cell through the area morphologically labeled the colax. Beyond the colax, the individual dendrites change their character. The inner membrane, the reticulum, becomes very close to the outer lemma and becomes a bilayer. Simultaneously, the dendrolemma reverses the asymmetry of its bilayer. As a result, the dendrite forms what appears to be a continuous Activa along its surface. In actuality, an Activa is only formed periodically where the microtubule is in quantum-mechanical contact with a disk. This modified structure is labeled a microtubule in the morphology of the photoreceptor cell. In modifying the morphology of the dendrites as described, a significant change in performance has been achieved. The outer lemma of the microtubule has become the collector terminal of an Activa. The reticulum has become the emitter terminal and the hydronium liquid crystal formed between the two bilayers forms the base region. No electrical connection is provided to the base region. The

Tutorial on Biological Vision- 67 plasma within the reticulum remains in contact with the input terminal of the original Activa. The configuration of the Activas within the microtubules is fundamentally different from most other Activas of the neural system. The Activas of the microtubules are in the common-emitter configuration. The common-emitter configuration can provide significant current (or charge) gain between the charge introduced at the base terminal and the charge produced at the collector and emitter terminals. This gain would be typically 200:1 in a similar man-made transistor. However, an additional specialization is included that will be discussed below. The open-base common-emitter configuration is commonly found in man-made photosensitive transistors.

5.2.2 The unique adaptation amplifier formed within the microtubules In the early days of man-made transistor development, another feature was introduced to the commonly used open-base common-emitter photosensitive transistors. It was found that an additional gain mechanism could be achieved by making the collector region very thin and operating the device with a very high collector to emitter potential. Charges moving through the collector region under the initial control of the charges in the base region gained sufficient speed to cause a chain reaction effect among fixed charges within the crystalline structure. This chain reaction could be controlled and resulted in very high overall device gain. The mechanism became known as avalanche gain. This mechanism is also found within the microtubules. The resulting total circuit gain is typically in the region of 3500:1. A problem arises when using high values of avalanche gain in situations where the input signal may be high. The total current generated may be sufficient to destroy the device by resistive heating (thermal destruction). The typical solution to this problem is to limit the current supplying capability of the power supply. In this situation, the current (or charge) gain of the device can be made inversely proportional to the input signal. An essentially constant output signal is provided despite macro changes in the input signal. While this circuit essentially removes the direct current component of the signal, it also removes the alternating component as well. However by using a capacitor to “bypass” the current limiting feature in the power supply, a more desirable result is achieved. The gain for slowly changing input levels goes to zero while the gain for rapidly changing signals remains very high. This is the configuration found in the adaptation amplifier of the photoreceptor cell. The adaptation amplifier Activas cannot be identified in currently available electron micrographs. However, it is clear what features should be looked for in future investigations. Areas of the microtubules showing large charge concentrations are likely to represent the adaptation amplifiers of the visual system.

5.2.3 The quantum-mechanical interface between the disks and the microtubules The quantum-mechanical configuration between the disks and the base of the microtubules is defined in Section 6. Like man-made photodetectors, the quanta (excitons in this case) are able to fracture the bond between an electron-hole pair in the base region of the Activa into separate free charges. The difference in the mobility of these charges defines the net current within the base region. This small current is algebraically equal to the difference between the collector and emitter currents, which are individually much larger. The ratio of either of these larger currents to the initial current describes the gain of the circuit (before the avalanche gain contribution).

68 Guide to Processes in Biological Vision 5.2.4 The overall electrolytic configuration of the photoreceptor cell The overall electrolytic circuit of the photoreceptor cell is shown in Figure 5.2.4-1, along with certain morphological and physiological annotations [12.5]. The jagged line surrounding the cell represents the resistive character of the IPM and INM surrounding the photoreceptor cells. Note the insulating nature of the OLM that the photoreceptor cell penetrates. This insulating barrier plays a significant role in the formation of the signal recorded by an electroretinograph (ERG). The sources of the a-wave and a part of the b-wave of the ERG are shown. The delay between the generation of the a-wave and subsequent b-wave is significant [11.1.5]. The supporting document introduces a new and more explicit set of waveform classes to aid in understanding ERG waveforms. As developed earlier, photons cause excitons within the liquid crystalline chromophore coating on the protein-based disks. This charge-based energy moves to the edges of the disks by mutual repulsion. There, the excitons can de-excite while simultaneously exciting electron-hole pairs in the base region of the Activa shown on the left. The barred symbol in the collector lead of the device indicates avalanche gain within the device. The collector current passing through the electrostenolytic power source (1) passes into the resistive impedance of the IPM and can be measured as the a-wave of the common ERG. Simultaneously, the emitter current passes into the dendroplasm connecting to the emitter terminal of the distribution amplifier. The output current of this amplifier passes into the axoplasm of the neuron. As this current passes through the load (4), it creates an axoplasm potential that is logarithmically related to the current because of the diode characteristic of the load. The adaptation capability of the first amplifier, and the logarithmic conversion of the current into a voltage at the pedicle of the second amplifier, are key functions within the operation of the visual system. They account for most of the wide range in sensitivity associated with the visual system.

5.3 Secretory functions of the photoreceptor cell The secretory function of the photoreceptor cell is completely analogous to the secretory function in somatosensory sensors. Exactly how the large molecular weight protein passes through the plasmalemma of the inner segment into the IPM is still a subject of study. The material is constituted into a ribbon within the calyx of the inner segment and then broken and formed into circular disks. Figure 5.2.4-1 The principal signal waveforms of the These disks are then extruded photoreceptor cell. The Class A waveform is represented by the as a stack. The extruded jagged arrow and the word “excitons” in the figure. The Class B protein material is polar in waveform is measurable only at the open base connection of the character. This causes the left Activa. The Class C and Class D waveforms are in phase hydrophobic surfaces of the opposition and sum to a constant (neglecting the delay). See text. liquid crystalline protein material to associate with each other in a bilayer configuration. The result is an exterior surface that is hydrophilic. This exterior

Tutorial on Biological Vision- 69 surface appears to be quite compatible with the liquid crystalline structure of the chromophores. While in the region of the calyx, the disks are coated with the chromophore material delivered from the RPE by diffusion through the IPM. The last step of the extrusion process is the formation of the fissures along the outer edge of the disks. Once the individual microtubules are introduced into these fissures, the new disks are fully operational.

5.4 Growth within the individual photoreceptor space It is a little known but well documented fact that the disks of the outer segment are replaced at the nominal, and prodigious, rate of ten disks per hour. Every disk is replaced after one week of operation. The reason for this routine replacement is unknown. It may relate to the normal damage associated with cosmic rays and other high energy irradiation. Replacement does not appear to occur in members of Arthropoda and Mollusca. This may be related to their shorter lifespan of most Arthropoda and the nearly totally aquatic environments of Mollusca. The continual replacement of the disks of chordates makes the study of individual images of a cell in the absence of a time-context, inadequate. Figure 5.4.1-1 caricatures the overall growth of a photoreceptor cell. The process involves two totally separate processes. The first involves the generation and replacement of the disks on the schedule described above. The second involves the coating of the disks with chromophore followed by the recovering of the chromophore and their reuse.

5.4.1 The life cycle of a rhodopsin based disk The protein used in the disks is created by normal metabolic processes within the nucleus and inner segment of the cell. The completed protein is known as rhodopsin. Its amino acid sequence has been defined completely, except different investigators have found a variety of differences in their listings [5.1]. These variations may represent natural variants or a less developed sequencing technique than many have presumed. Each protein molecule appears to include one molecule of retinol associated with a lysine at position 296. The current techniques of amino acid sequencing do not identify the putative retinol molecule explicitly. Further, only a few amino acids occur in the sequence that can form a Schiff-base interface with another ligand. Therefore, certain inferences have been made in assigning the location of the putative Schiff-base.

Figure 5.4.1-1 Outer segment replacement in the photoreceptor cell. The disks are continuously replaced through the secretion of rhodopsin by the inner segment of the photoreceptor cell and phagocytosis by the RPE cells. The chromophore material, Rhodonine, is replaced using a shorter chromophore loop as shown. This material does not pass through the photoreceptor cells.

Conformal reconstructions of the putative rhodopsin molecule show the retinol ligand buried deep within the protein. Several investigators have questioned how this ligand could be effective as a chromophore. 1; it fails to exhibit a polar resonant structure. 2; it exhibits a small physical cross section to the absorption of light (relative to the cross section of the

70 Guide to Processes in Biological Vision complete molecule). 3; it has few options with which to communicate with the exterior surface of the membrane. 4; it clearly cannot be physically replaced on a frequent basis following its stereochemical conversion to a different form of retinol. The role of the retinol ligand within the rhodopsin molecule is exclusively metabolic. At the end of the disks life, it is phagocytized by the RPE cells and the individual amino acids are returned to the bloodstream where they are available for reuse. The S-shaped arrow in the figure describes the protein loop followed by the amino acids within the larger context of the retina and the bloodstream. Current estimates are that less than 4% of the retinoids present in the retina are found in the photoreceptor cells. About 87% is found in the RPE cells with the remainder in the IPM (including the disk coatings).

5.4.2 The life cycle of a molecule of a chromophore The vast majority of the retinoids found within the IPM are funneled through the RPE cells. The flow of these retinoids within the organism is well understood [7.1]. They are initially available in the liver as retinol. While being transported through the bloodstream to the RPE cells, the retinol is converted into one of four dicarboxylic acids of the retinol family, known as the Rhodonine™ family. These materials are stored within the RPE cells in highly colored vesicles observable with a light microscope. When required, they are moved through the IPM to their point of deposition as a liquid crystalline film covering the hydrophilic surface of the individual disks. The movement is aided by a special retinal binding protein (IRBP) found only within the IPM. While only one molecular layer thick, this material covers the disk with a very dense layer of chromophore [4.3.5]. In the absence of any liquid crystalline properties, each molecule of the layer would exhibit an absorption cross section equal to its own diameter (about 5 Angstrom or 0.5 nm). However, due to the liquid crystalline properties of the layer, the absorption is described by the same laws as for other electromagnetic absorbers (antennas). The absorption cross section of each molecule is equal to the area represented by the diameter of the full disk (about 2 microns). This extremely large effective absorption cross section is achieved at the expense of isotropic absorption. Only light traveling along the axis of the disk stack is absorbed with this efficiency. Since the chromophores of Rhodonine are excited by light but not stereochemically altered, each molecule can absorb light whenever it is unexcited. Once excited, it cannot absorb another photon until it has been de-excited as part of the photoexcitation/de-excitation process. This process is addressed in Section 9.1.1. At typical light levels, an individual molecule is de-excited within 10-20 ms of excitation. Under this operating scenario, an individual molecule can be excited and de-excited millions of times during the life of its associated disk. Replacing a stereochemically altered retinoid every time it is excited by light is not necessary. The recovery of the retinoids during disk phagocytosis is less well understood. However, it is a simple matter for the various RBP’s found within the RPE cells to bind to the chromophores freed during digestion. Once bound, the chromophores can be moved to the chromophore storage vesicles (pigment granules) or provided to the IRBP’s for redeployment to new disks.


6. The Tetrachromatic Capability of the Typical Photoreceptor Group

The material in this section is excerpted from several locations in the underlying work. Chapter 5 provides the bulk of the background. Other locations will be annotated with brackets as usual. The effect of absorption by oil droplets, found in the inner segments of many species (particularly birds) can affect the overall absorption of the eye. This absorption is not considered here. The typical biological photoreceptor group (retina in Mollusca and Chordata) exhibits significant spectral absorption over the range from 300 nm to 675 nm. This absorption is achieved by using four distinct spectral channels supported by four distinct chromophores. As noted in Section 1 and demonstrated in Section 9, the overall performance of the human eye, along with that of other large chordates, is restricted by the spectral absorption of the lens. The lens absorbs maximally in the 300–400 nm region of the spectrum. However, its absorption is related exponentially to its thickness. Smaller members of Chordata exhibit excellent vision in the 300-400 nm region [1.7.2]. Performance in this region falls exponentially with the size of the larger animals, since the eyes are nominally related to overall size. Because of this effect, the human eye can be characterized scientifically as that of a blocked tetrachromat. In the vernacular, the human is a trichromat. However, this designation obscures the fact that the ultraviolet spectral channel of the human eye plays a significant role when viewing colors with a peak intensity in the 400-437 nm region. A variety of technical barriers have restricted research into the nature of the chromophores of biological vision. The most limiting physical constraint has been the failure of the community to recognize that the photoreceptors of biological vision are quantum-mechanical detectors, rather than thermal detectors. Researchers have continued to investigate spectral absorption since the 1910's using light sources that were grossly deficient in the blue and purple region of the spectrum. From these measurements, they concluded the performance of the human eye was poor in these same regions. Another has been due to the claimed relationship between the chromophores of vision and the protein substrate, opsin, found in the disks of the outer segment of the chordate eye. In the 1930's, it was claimed that the putative marriage of the chromophore and the protein substrate deserved to claim the earlier conceptual name for the chromophore(s) of vision, rhodopsin. After many decades, the community has not shown how the putative rhodopsin achieved the required spectral absorption of the chordate retina. To understand the true nature and operation of the choromophores of vision requires a knowledge of liquid crystal semiconductor physics not available before the 1960's (although similar materials had

72 Guide to Processes in Biological Vision been used in commercial color photography since the late 1930's). The actual characteristics of the chromophores can be defined in detail based on conventional chemistry combined with knowledge of liquid crystal chemistry obtained from the photographic film industry. The four chromophores of biological vision are called Rhodonine™ based on their chemical composition. The liquid crystalline state of matter required to observe the spectral absorption of the chromophores (the Rhodonines) is routinely destroyed using the laboratory protocols designed to isolate rhodopsin. When the liquid crystalline material is separated from its de-excitation mechanism, it remains highly absorptive until it is excited by light. It then becomes transparent. When in solution, the low molecular weight chromophores are also transparent. The chromophores are generally discarded with the supernatant liquid following centrifugation. During the 1970's, excellent data was obtained showing that the source of the chromophores used in vision was not the photoreceptor cells themselves but the retinal pigment epithelial (RPE) cells. The photoreceptor cells only provided the protein substrate used to manufacture the disks. This knowledge, combined with the new data on quantum chemistry of the liquid crystal has provided a new understanding of the chromophores of vision. The new understanding described above has provided a new level of precision. The spectral performance of the visual system of any organism can now be calculated with an accuracy of better than 10%. With respect to the spectral bandwidth of each spectral absorber, it can be calculated to within 2 nm in 500 nm or 0.4 %. This capability will be proved in Section 9. These levels far exceed the accuracy of present day empirical laboratory techniques (usually about +/– 50%). Quantum physics explains the unique character of the long wavelength spectral absorber. It is this characteristic that explains why the biological eye loses sensitivity in the red portion of the spectrum as the illumination level is decreased (See Section 6.6.1).

6.1 The eyes are quantum detectors, not energy detectors Two great classes of photodetectors exist in science, the thermal absorbers and the quantum absorbers. Einstein defined the characteristics of the quantum absorbers in his famous paper of 1904 defining the photoelectric effect. The photochemistry of biological vision employs quantummechanical absorption. This has been amply shown by many analyses of the signal-to-noise performance of human vision. The signal-to-noise ratio follows Poisson statistics as a function of illumination intensity. To properly evaluate the spectral performance of a quantum-mechanical sensor system, it is critically important that an adequate test source be used. The test source should deliver the same number of quanta per unit wavelength to the specimen under test at any wavelength. To achieve a uniform photon flux over the spectrum of interest in vision, a source with a color temperature of 7053 degrees Kelvin is optimum [2.1.1]. This spectrum appears to provide an excess of energy, in watts, in the short wavelength region. Note however, energy in watts is applicable to thermal detectors, not the detectors of vision. A brief look at the spectral content of a blackbody (based on quantum flux) will show that “North Sky” daylight is an excellent source of broadband radiation for vision testing. However, the radiant intensity of daylight varies depending on local atmospheric conditions between a low of about 5000 and a high of about 20,000 Kelvin. Spectrally, daylight is not as uniform as a simple blackbody at 7053 Kelvin, D70. Unfortunately, the illumination community has chosen to define such radiation in terms of a “coordinated color temperature,” D65, of 6500 Kelvin. They have done this using a convoluted procedure that is difficult to use. To escape from this dilemma, the International

Tutorial on Biological Vision- 73 Standards Organization and the CIE do not offer a standard source at their recommended color temperature. Traditionally, laboratory investigators have used a light source as low as 2000 Kelvin (in the early part of the last century) to 3600 Kelvin. Only a rare investigator has used a 6500 Kelvin source. At source temperatures below 3600 Kelvin, the radiant flux at 400 nm is typically an order of magnitude less than at the peak wavelength. Using a low source temperature introduces needless requirements to perform correction calculations. It also introduces errors due to differences in signal-to-noise ratio within the measurements on a spectrally selective basis. Most of the psychophysical experiments of the last half century have suggested the “blue” spectral channel plays a lesser role in color vision than the “green” or “red” channels. This finding has been due largely to the color temperature of their sources.

6.2 Liquid crystal quantum physics is key to understanding spectral absorption The quantum physics of the chromophores of vision follows the same rules as that of the chromophores of photographic color chemistry [5]. All good absorbers of visible light share several characteristics. Each molecule contains two polar atoms of either oxygen or nitrogen. These atoms exhibit unpaired electrons even when part of a larger molecule. These polar atoms are connected by a conjugated carbon backbone. The straighter this backbone, the higher the peak spectral absorption. The unpaired electrons and the conjugated backbone result in a resonance condition at the molecular level. This resonance condition exhibits a “resonance” spectral absorption band separate from the normal molecular absorption spectrum of the material. This separate spectral absorption band is accentuated if like molecules form a liquid crystalline structure based on their stereochemical form. Figure 6.2.1-1 provides a summary of the quantum-mechanical energy band structure of different organic molecules. The vertical scale is in energy (usually electron-volts). The width of the individual bands shows the population of electrons free to transition to a different energy state or the empty quantum-mechanical states available to accept an excited electron (those levels with an asterisk). The horizontal scale can be ignored. It relates to the lattice spacing of the material. The bands shown have horizontal edges except near the edge of any crystalline structure present. Simple organic molecules are invariably transparent. They do exhibit a narrow absorption at a very specific wavelength given precisely by the difference in their energy levels. These absorptions are typically in the ultraviolet. Note the appearance of the n-band in frame (c). It describes the energy level of the unpaired electrons associated with the polar atoms. The importance of the liquid-crystalline structure to spectral absorption is seen in the right frame. Due to the Pauli Exclusion Principle, a single crystal cannot have multiple electrons (or empty states) in precisely the same electronic state. Therefore, the energy bands are broadened in proportion to the size of the aggregate structure. As a result, the efficient chromophore exhibits a minimum energy change (long-wavelength absorption edge) given by the energy level difference (a). The maximum energy change (short-wavelength absorption edge) is given by (c). Although not clearly defined using simple mathematics, the peak absorption occurs at a wavelength near the energy difference given by (b).


Figure 6.2.1-1 Energy Band structure for organic molecules. See text for details. Not shown in the above figure is the fact that the π* energy band becomes closer to the n-band as the conjugation distance between the two polar atoms grows. By using chromophores of different conjugation length, a family of spectral absorbers is obtained. The change in peak wavelength with conjugation level is nominally 95-100 nm in a wide range of industrially and biologically useful chromophores. A chromophore of the character described above will aggregate into liquid crystalline particles when the concentration of the solution it is part of is raised. The separate spectral absorption band is then easily measured. The separate spectral absorption will appear isotropic, like all of its other absorption bands because of the random orientation of the aggregates in the solution. However, if the material is allowed to precipitate onto an appropriate surface, all of the chromophore molecules will arrange themselves in a sheet with their long axis (their resonant axis) parallel. While the molecular absorption of common chromophores is isotropic, the resonance absorption of a molecule containing two polar atoms is anisotropic. This anisotropic absorption exhibits a peak for photons arriving on a trajectory that is parallel to the resonant axis of the chromophore. This characteristic is used effectively among Arthropoda to provide polarization sensitivity with respect to the incident light [1.7.2] The retina of Chordata does not use this property of the chromophores.

6.3 The four chromophores of biological vision The fact that the chromophores of vision were closely related to Vitamin A (retinol) was established in the 1930's. However, the specific form of the chromophore was not defined successfully. Great effort has been expended attempting to show that retinol joined to a protein by a Schiff-base would give the desired spectral absorption. The typical hypothesis has been that distorting the stereochemical structure of the Schiff-base material can account for the shift in absorption wavelength. Although many attempts to show the desired absorption have been made, these have routinely failed. While early researchers were correct that the protein material secreted by the photoreceptors to form the disks used in photodetection contain a ligand based on retinol, these molecules are not the chromophores of vision. The chromophores of biological vision are coated onto the disk substrate as a liquid crystal.

Tutorial on Biological Vision- 75 The chromophores of biological vision are manufactured, stored secreted, and recovered by the RPE cells (the name used for these cells in Chordata). While nitrogen is the polar atom of choice in commercial photography (because of the better storage properties of these materials), the polar atom of choice in biological vision appears to be oxygen. Based on this hypothesis, Figure 6.3.1-1 illustrates the four chromophores of Rhodonine based on Vitamin A1. The stereo-chemistry of these four chromophores is almost identical. They are each able to aggregate into a liquid crystal–and may be able to intermix in a single liquid crystal. For the moment, it will be assumed that they do not normally intermix on a given surface. As in many organic molecules, they will seek out their own kind as they aggregate on a surface. The Rhodonines are all derived from retinol through a simple process of oxidation. This process is carried out at the interface between the bloodstream and the RPE cells. It involves a series of unique stereochemical steps involving a set of retinol binding proteins (RBP’s). One RBP is found in the bloodstream and is known as SRBP for serum retinol binding protein. Others are found within the RPE cells and are labeled cellular retinol binding proteins (CRBP’s). For completeness, it will be noted that only one interphotoreceptor matrix retinol binding protein (IRBP) is known. It is used to transport the chromophores of vision from the RPE cells to their deposition point on the disks [7.1]. The bars shown under each chromophore show the peak wavelength of each molecule relative to the others. These peak wavelengths occur at 342, 437, 532 & 625 nm in endothermic organisms. These wavelengths vary with absolute temperature. Within the normal biological range, they do not vary significantly. The Rhodonines do not belong to a single simple family based on the standard methods of naming molecules. In two cases, a methyl group has been removed to form the molecule. In two other cases, a hydrogen has been removed. Thus, the four Rhodonines share two different molecular weights. The pairs with the same molecular weight have different stereo-chemistries. The Rhodonines are stored in separate vesicles within the RPE cells prior to their use in vision. The vesicles are sufficiently large that they have been photographed under the microscope [4.6.2]. Of course, the vesicles storing the ultraviolet sensitive chromophores usually appear transparent because of the limitations of the film and microscopes used.


Figure 6.3.1-1 The proposed chromophores of animal vision, the Rhodonines, based on Vitamin A1. Retinol (Vitamin A1) is shown for reference. Each chromophore is shown in its ionic form. The oxygen atoms are shown in red. The conjugation critical to absorption in the visual region of the spectrum is shown by the dashed bond. The horizontal line below each molecule shows the relative length of its resonant structure. These lengths also represent the relative peak absorptions of the molecules.

Tutorial on Biological Vision- 77 The spectral characteristics of the above chromophores, when present in nominal human eyes can be defined using the following table. The half-amplitude wavelengths given below are nominal for a human subject. They vary with the length of the outer segments and the area of the retina stimulated. The lengths vary with position within a retina. The half-amplitude values vary within a few nanometers among individuals. These variations are measurable psychophysically.

Transducer

Rhodonine (5) Rhodonine(7) Rhodonine(9) Rhodonine(11) [UV]

Resonant chain length

5 4 3 2 **

8l :

8m :

8h :

Q

0.595 0.500 0.400 0.300

0.625 0.532 0.437 0.342

0.655 0.565 0.475 0.385

10.4 8.2 5.8 4.0

where l, m and h indicate the low half-amplitude point, the mid wavelength point and the high halfamplitude point. The mean wavelengths have no electrophysiological meaning. They are the calculated mean of the low and high values because the function is so broad that the center point is ill defined. The value of Q given in the last column is a measure of the distance between the two halfamplitude values compared to the mean. The bands are separated by 0.095 +/-0.005 microns which is a typical spacing for these homologs. **The UV photoreceptors of the human eye are effectively shielded by the limited transmission of the optical system. They do influence the spectral discrimination capability of the eye in the region between 400 nm. and 437 nm.

6.4 Non-spectral variants between chromophores due to their Vitamin A base As noted in Section 1, the animal kingdom has come to rely on three different forms of Vitamin A [5.3.3]. These forms differ in the hydroxylation state of the β-ionone ring shown on the left of each Rhodonine. The differences in this ring do not affect the anisotropic absorption spectra of the Rhodonines significantly. While a difference on the order of 1-2 nm is possible at a given temperature, such differences have only occasionally been reported in the experimental record. The isotropic absorption spectra of the Vitamin A’s, which are not involved in the visual response, show greater deviation in peak wavelength. One recent report suggests the difference in the peak wavelength of molecular absorption was ten nm between Vitamin A1 and Vitamin A2. The data was based on a less than ideal protocol. The temperature was not specified [5.5.10].

6.5 Isotropic and anisotropic absorption of the liquid crystalline chromophores 6.5.1 Empirical verification of the isotropic and anisotropic spectra During the 1980's, a micropipette technique was used to measure the absorption spectrum of selected photoreceptors. The technique called for the isolation of a completely functional in-vivo photoreceptor and the drawing of the outer segment (and frequently part of the inner segment) of the cell into a pipette without damage. Light was then projected through the pipette and cell orthogonally to the axis of the cell. Cells were selected that were believed to be either “red cones” or

78 Guide to Processes in Biological Vision “green cones.” However, the recorded spectra invariably showed the molecular absorption characteristic of the cell and chromophore. This spectrum peaked near 500 nm. Investigators using an equal energy source usually report the value as higher, in the 500-505 nm range. Investigators using an equal photon flux source usually report the value as 495-500 nm.

6.6 The spectral characteristics of the in-vivo chromophores of biological vision The spectral absorption of a single photoreceptor cell exhibits a spectrally specific anisotropic absorption optimized to be maximum for light impinging parallel to its long axis. It also exhibits an isotropic absorption spectrum with a much lower peak absorption per unit angle. The width of the spectral peak of the anisotropic absorption of an individual photoreceptor depends on two physical quantities. First, it depends on the diameter of the disk stack. This diameter determines the spectral bandwidth of the liquid crystalline chromophore associated with each individual disk. This spectral broadening is based on the Pauli Exclusion Principle discussed above. Second, it depends on the number of chromophore-coated disks through which the photon flux passes. Each disk is optically and quantum-mechanically isolated from each other. Under this condition, each incident photon has a finite chance of being absorbed by each disk (until it is absorbed). With a nominal disk stack of 2000 disks, and a very efficient chromophore, the photons at the wavelength of peak absorption have a 100% chance of absorption. The photons at nearby wavelengths also have a very high chance of absorption. Even photons at a wavelength equal the half-amplitude point for the spectrum of a single disk have a very high chance of absorption before reaching the last disk in the stack. The absorption spectrum of the photoreceptor, due to its isotropic absorption, is also multiplied by the number of disks in the disk stack. However, the cumulative absorption is always less than that of the anisotropic absorption. This is due to the higher peak absorption per disk of the latter. Thus, the molecular absorption spectrum is not significant in normal human vision. Note that efforts to assess the spectral absorption spectrum of a photoreceptor using the suction pipette technique and transverse illumination are limited. The technique does not take advantage of the cumulative absorption provided by the multi-disk stack. When transverse illumination is used, this technique will routinely measure the isotropic spectrum of the chromophore of interest. Only an artifact of the anisotropic spectrum can be expected in the measured data. Axial illumination is required to measure the anisotropic (functional) absorption of a cell. Because of the above two-step broadening of the absorption spectrum of each chromophore, the effective spectrum of each chromophore can only be described based on empirical evidence. Figure 9.1.2-1 [17.2] below presents the best available data based on both the theory and the empirical measurements.

6.6.1 The unique character of the long wavelength spectral channel While the above spectra are those frequently obtained by micro-spectrometry in a variety of species, they are not the spectra that are always obtained using psychophysical methods. This is true for two reasons. First, the logarithmic signal processing of stage 2 introduces the previously described artifacts near 490 nm and 575 nm. Second, the long wavelength absorption spectrum exhibits a large variation in absorptance as a function of light intensity. This variation is due to a critical design feature of the interface between the chromophores and the neural system.

Tutorial on Biological Vision- 79 Figure 6.6.1-1 illustrates the quantum-mechanical model of the transduction process for a specific chromophore to transfer the energy of an incident photon to the dendrites of the inner segment for further manipulation. The energy bands on the left were discussed above. It was noted that the energy difference between the n-band and the π*-band varied among the chromophores. It varies in proportion to their level of conjugation between the polar atoms. The right side of this figure represents the energy band structure for the microtubules (dendrites) of the photoreceptor cell in contact with each disk. Note the change in horizontal scale between the left and right halves of the figure. The large distances on the left will be important in the development of the photoexcitation/deexcitation equation (P/D equation) in Section 9.1.1. On the right, the important energy bands are those of a conventional semiconductor. To excite a valence band electron into the conduction band requires a minimum energy, ε. For the endothermic biological system, this energy is not less than 2.2 electron-volts (or a maximum wavelength of 565 nm). This value is sufficiently high to insure excellent signal-to-(internal noise) within the visual system. However, it introduces a significant problem regarding the long wavelength spectral channel. The long wavelength spectral channel involves photons with energies ranging from 2.08 eV at the short wavelength half-amplitude point to 1.89 eV at the long wavelength half-amplitude point. These energy levels by themselves are not sufficient to excite the neural system. However, it is well known that the human spectral response extends beyond 1.0 microns for light of sufficient intensity. The dilemma is solved by using a two-exciton mechanism (and possibly a three-exciton mechanism at very long wavelengths). The excitation of the Activa formed by the Figure 6.6.1-1 The quantum-mechanical interface microtubules can be accomplished through the simultaneous de-excitation of multiple excitons between a specific liquid crystalline chromophore [12.5.2]. However, this mechanism converts the and the associated liquid crystalline transfer function from the linear function semiconductor device found within the associated with the UV–, S– & M– channels to a microtubules. See text for terminology. square law function. As a result, the efficiency of transduction from the chromophores to the electrical circuits of the neuron decreases as the intensity of photon-excitation is reduced. The result of this phenomenon is that, unlike the other channels, the effective sensitivity of the long wavelength spectral channel falls as the broad spectral band light level is reduced. The visual system transitions smoothly from a photopic capability to a scotopic capability due to the gradual loss of long wavelength spectral channel sensitivity. This transition will be presented graphically in Section 9.1.2. No change in class of photoreceptor is involved. The above two-exciton mechanism should not be confused with a two-photon mechanism. In the latter, the two photons must arrive nearly simultaneously. In the two-exciton mechanism, the excitons derived from oxygen have a very long half life. They will remain excited until they have an opportunity to transfer their energy to another molecule or another electronic media.



7. The Unique Photoreceptor/IPM/ RPE environment

As suggested in Section 5.4, the PC/IPM/RPE interface is a particularly complex one. It deserved separate analyses based on the electrical, metabolic, chromophore transfer, and disk growth aspects of overall performance. How this configuration protects the chromophores of vision from attack by oxygen is also worth study. The first order requirement appears to be protection of the chromophores from chemical attack.

7.1 Morphogenesis of the human eye An initial understanding of the dynamics of the PC/IPM/RPE interface can be obtained by examining the morphogenesis of the eye. The eyes are formed from a budding of the diencephalon of the brain. The budding first forms the optic nerve. This nerve elaborates into a terminal structure frequently portrayed as a tulip-shaped cup. Caricatures in the literature frequently begin with this cup as a basic structure. However, the actual embryology is much more complex [4.5]. Figure 7.1.1-1 provides a cross-sectional view of the eye during morphogenesis. The key is to recognize the continuous nature of the ectodermal surface forming the eye cup. This outer layer is an extension of the outer surface of the optic nerve. Two nested cups are actually formed from this continuous layer. Part of the outer surface of the inner cup (heavy lines) differentiates into the neuro-dermal layer associated with the photosensitive part of the retina. Part of the inner surface of the outer cup (heavy dotted lines) differentiates into a digestive layer of RPE cells. By merging the neuro-dermal layer and the digestive layer near the maximum diameter of the neuro-dermal layer, a totally enclosed volume is created. When filled, this volume becomes the interphotoreceptor matrix, IPM.

82 Guide to Processes in Biological Vision Whether the lens is formed by a merging of the two edges of the outer cup shown or from a distinctly separate layer of ectoderm is incidental to this discussion. However, a separate origin does not appear consistent with the operational nature of the system. No tissue arising from, and metabolically supported by, a source other than the optic stalk is normally associated with the optical globe. The neuro-dermal layer shares many features with any other portion of the ectodermis. The analogy is particularly close when one notes the similarity between a photoreceptor cell and a conventional hair generating cell. The analogy is most comprehensive when related to the facial whisker of a cat or other animal. The level of neural activity is prominent in both cases. For the PC, the extruded protein material is formed into a disk stack rather than a single continuous shaft. In both cases, the protein material is surrounded by a series of microtubules that are sensitive to the quantummechanical packets of energy. This energy has been given a variety of names, excitons, phonons, etc., depending on the circumstances. The digestive layer formed by the RPE cells shares many functions with any other digestive layer. It secretes a variety of complex materials. The dominant material found within the IPM is the retinol binding protein, IRBP. The literature is not completely clear whether the measured data refers to the apo-IRBP or the complete IRBP-chromophore complex. In either case, the IRBP provides the transport mechanism required to present the chromophores to the disks as they are formed within the calyx of the PC. Instead of attempting to digest the protein of the disks, the chromophores form a continuous liquid crystalline coating covering the disks. This coating becomes photosensitive following its quantum-mechanical interface with the microtubules along the edges of the disks. Disks are continuously formed by the PC. Like a hair, the disk stack moves away from the inner segment of the PC at a continuous rate. This rate is a nominal 350 nm per hour in a human. Similar rates can be expected in other endothermic animals. For an outer segment that is nominally 50 microns long, the lifetime of a 25 nm thick disk under these conditions is about one week.

Figure 7.1.1-1 Morphogenesis of the chordate eye. The structure is formed with one continuous ectodermal surface. A cul-de-sac, the Interphotoreceptor Matrix, IPM, is formed between the Interneural Matrix, INM, and the Choroidal Matrix. This IPM is extra-dermal and does not support any metabolic functions. When the Choroid surface closes at the top to form the pupil, the cul-de-sac is sealed off at the apex of the INM by contact with the choroidal structure.

The continuous secretion of protein material and the formation of disks obviously cannot continue in a closed space. When the disk stack begins to impinge on the RPE cells, the RPE cells partially invaginate and partially engulf the disks. They are then digested by the RPE cells in a process usually labeled phagocytosis. As discussed in Section 5.4, both the chromophore material and the protein material are salvaged for reuse.

7.2 The complete mature PC/IPM/RPE complex

Tutorial on Biological Vision- 83 This photoreceptor/IPM/RPE complex both provides and maintains the chromophores of vision. It also supports the electrical performance of the operating system. Figure 7.2.1-1 provides a composite view of this interface showing a variety of cells. It attempts to highlight a variety of conditions found within this complex. These conditions will be discussed individually by reference to the cell number along the left margin. A critically important feature of this figure is its dynamic character. As indicated at the bottom, the disks move continually toward the RPE cells at a rate of about 300 nm/hr. With a disk pitch of about 250 Angstrom (25 nm), this rate suggests a disk generation rate of ten disks per hour per disk. At this rate, each disk stack is completely replaced weekly in humans. The generation of new disks at a rate of ten per hour per cell suggests a prodigious manufacturing capability for each photoreceptor cell. Similarly, it suggests a prodigious phagocytotic capability for the RPE cells. The RPE cells on the right are shown storing a variety of chromophores in so-called color granules. The granules marked U represent stores of the ultraviolet chromophore, Rhodonine(11). The other granules represent the observed color of the granules. The observed color is the complement of the absorption spectra of the individual chromophores. The disks of the outer segment continue to be shown without an enclosing membrane. Several recent micrographs confirming this condition, by independent investigators, are provided in the supporting document [4.3.5]. Some of these micrographs provide details confirming the functional independence of the colax and the calyx. Bruch’s membrane is shown explicitly near the RPE cells. Also shown explicitly, but less obviously, is the Outer Limiting Membrane. This membrane is represented by the black rectangles between the photoreceptor cells. The rectangles are shown long enough to accommodate a variety of Mueller Cells (glia) in the space between the photoreceptor cells. These two barriers, the OLM and the Mueller cells squeezed between the PC’s, provide both chemical and electrical isolation between the IPM and the INM. Bruch’s membrane and the tightly packed RPE cells provide the same isolation between the IPM and the choro-vascular matrix. Both the microtubules and the poditic terminal of the photoreceptor cells are in electrical contact with the IPM. Simultaneously, the axon of the PC connects electrically with the INM, and other elements within the INM. This difference in electrical paths plays an important role in the electrical waveforms generated by the visual system. It is particularly relevant to the


Figure 7.2.1-1 The photoreceptor cell-IPM-RPE interface. See Text.

Tutorial on Biological Vision- 85 recording of an ERG. Cell 1 is shown in partial detail and stressing its generation of the raw disks. These disks are formed from the secreted protein, opsin, at the location represented by the black dot. The material is shaped into disks within the extrusion cup and calyx of the inner segment. The disks are pushed toward the RPE cells by the secretion of subsequent protein material. Upon reaching the RPE, the disks are phagocytized as shown. Cell 2 is drawn in more detail. It shows the cell creating the disk stack within the extrusion cup and calyx. However, it also shows the presence of the IPM in the space between the plane of the inner segments and the plane of the RPE cells. This matrix is saturated with chromophoric material being transported by the IRBP’s. In cell 2, it is assumed this material corresponds to the ultraviolet sensitive chromophore. It is shown as transparent. The material is shown as coating both sides of each disk formed as in Cell 1. Such a cell, coated with Rhodonine(11), is well represented in the human retina. Cell 3 repeats much of the detail of cell 2 while assuming the chromophore coating the disks corresponds to the long wavelength chromophore, Rhodonine(5). This material appears azure by reflected light but absorbs maximally at 625 nm. An additional feature is shown in this view. This is the presence of a concentration of material near the disk stack. This material contains both excess chromophore present in low concentration within the vicinity of the disk stack and the materials needed to provide electrostenolytic power to the dendrites to be discussed in conjunction with Cell 4. No cell membrane is shown surrounding any of the disk stacks in this figure. It should be noted that the functional (anisotropic) absorption spectrum of the chromophores when deposited on the disks can only be observed by light applied axially to the disk stacks. This phenomenon is due to the molecular alignment of the liquid crystalline chromophores on the individual disks and the resultant enhanced absorption due to the larger absorption cross section of the resulting configuration. If transverse illumination is applied to a disk stack, the peak absorption will always occur at the isotropic absorption peak of the Rhodonines no matter the chromophore present. Cell 4 shows the disks coated with the mid wavelength chromophore, Rhodonine(7) which appears magenta by reflection or transmitted light due to its strong absorption at 532 nm. It also shows the dendrites (microtubules) within the furrows of the disk stack. These dendrites emanate from the inner segment via the cilium transport and interface with the Activa within the inner segment (not shown) before connecting with the pedicle of the cell via the axon shown as an arrow. Cell 5 is shown for completeness. It is morphologically and cytologically identical to cells 3 & 4. The only difference between them is the presence of a different chromophore coating the disks of the outer segment. Here, it is Rhodonine(9) which appears yellow-orange by reflected or transmitted light and absorbs maximally at 437 nm. Cells 6 & 7 show the consequences of a retinal tear. While the Outer Segment in 6 remains aligned and will reconstitute itself over time, the Outer Segment of cell 7 has become misaligned. Although it will probably realign itself over time, there may be residual material left in the IPM space and/or the IPM may show a bulge in this area. A bulge will generally result in the inability of the image to be focused properly on this area of the retina. It should be noted that such a tear is particularly likely because of the lack of membranes surrounding the individual disk stacks. Any plane intersecting the disk stacks between the outer extremities of the inner segments and the outer extremities of the RPE cells represents a structurally weak area of the retina [18.8.4].

86 Guide to Processes in Biological Vision Cell 8 is shown for completeness. It represents a set of possible conditions. It is most representative of an immature cell. Until such a cell reaches the stage of creating disks of full diameter and nominal spacing, it may exhibit a cone-shaped disk stack. This is an abnormal condition over the long term. Once the calyx is fully formed and sufficient protein material is present in the extrusion cup, the formation of a fully formed stack of constant diameter disks can be expected. It is possible that this will not occur until the additional back pressure provided by the presence of the RPE cells blocking the growth of the disk stack becomes important. In any case, a conical shape for the outer segment of a photoreceptor cell cannot be sustained over a period longer than a week due to the growth of the stack. The figure does not address the geometrical grouping of the photoreceptors in the plane of the retina. While this grouping is frequently obvious in other phyla, discerning it in most chordate species is difficult. The instrumentation difficulties have been significant in the past. Failure to recognize the presence of ultraviolet spectral absorbers has been a problem until recently. Failure to recognize the distinct characteristics of the awareness and analytical modes of signal processing have also contributed to the problem. The high degree of consistency in the composite spectra of the eye no matter the position in the retina would suggest the concentration of the different spectral absorbers is nearly constant.

7.3 Where did the cones go–the dynamics of the PC/IPM/RPE interface The duplex concept of vision was developed in ancient times to describe the difference in color performance of vision at high and low light levels. It has had a tortured existence. In the early days of light microscope-based morphology (1900's) man’s proclivity to separate any aggregate of samples into two groups came to the fore. This resulted in the definition of rod-shaped and cone-shaped photoreceptor cells. The initial definition was based on the putative shapes of the outer segments of the cells, which could only be poorly resolved with the available visual microscopes. At that point, the search was begun to associate these two morphological classes with the physiological performance of vision. Little progress was made. Better microscopes failed to confirm the hypothesis based on the outer segments. In the 1950's, Wald proclaimed that the outer segments of all photoreceptors were cylindrical in shape. At that point, the conservatives decided it was the inner segments of the photoreceptors that were either cylindrical or conical. Modern electron microscope studies do not support this thesis. The dichotomy of rods and cones was extended to the physiological arena to explain the difference in day and night vision before quantum-mechanics was even a dream. Organic chemistry was also in a primitive state by the standard of today. With the explanation of the loss of long wavelength vision at night due entirely to quantum-mechanical considerations, the rod/cone concept is weakened significantly. With more precise measurements of the scotopic absorption spectrum, this spectrum is seen to be different from the isotropic spectrum of the chromophores. This weakens the rod/cone concept even further. These measurements show the scotopic absorption is not mono-modal but bimodal. It also shows the scotopic spectrum is not congruent with the isotropic absorption spectrum peaking near 500 nm. Finally, homoeostasis calls for the continual birth, growth and phagocytosis of the disks in a given disk stack. This growth cycle guarantees that no conical shaped disk stack can exist for more than a week as part of a functioning photoreceptor cell. Only immature or dysfunctional PC’s can exhibit a conical outer segment. When this fact is combined with the fact that the complete spectrum of biological vision can be explained without requiring an achromatic sensor, an important result emerges. A phrase recently in the news seems most appropriate. The concepts of cones and rods as physiological, or morphological, entities belongs in the “ashcan of history.”




8. More detailed architecture of higher chordate visual system

The organization of the cortex varies significantly between major phyla in order to accommodate the variation in topography of the animal. In Arthropoda, lower Mollusca, and lower Chordata, the eye is mounted firmly to the underlying body structure. In the more advanced members of Mollusca, there is one degree of freedom (although limited) between the eye and the head. There are two degrees of freedom between the eye and head of Chordata. The angular extent of these degrees of freedom vary considerably within the phylum. The Top level Schematic of the visual system in Chordata is presented in Figure 8.1.1-1 [15.2.3]. A number of features of this figure need highlighting before continuing. First, it is seen that the eye in vertebrates is structurally and dynamically separated from both the brain and head (and/or body). Most of the other sensory input information is provided to the brain in a form that is uniquely described as to its source location on the skin and/or its characteristics relative to the position of the semi-circular canals of the inner ear. There are two important aspects of this difference in topography. First, there are two degrees of freedom between the eye and the head and six degrees of freedom between the head and the inertial reference of the outside world. The ocular globe is actually constrained by three sets of muscles. However, the oblique set are only used to correct for a lack of complete orthogonality between the other two. The eye shows no ability to roll about the line of fixation. Skavenski, et. al. have further delineated the skeletal platform into separate elements for the head and body in order to present their data3. In general, the head shows three degrees of angular freedom relative to the body and the body itself can exhibit six degrees of freedom, although rolling about the line of sight is an unusual one.


Figure 8.1.1-1 Top level schematic of the visual system in Chordata. Note the two external feedback loops represented by the signals from the photoreceptors flowing to the LGN and PGN and back through the superior colliculus to the muscles controlling the head, eyes, eyelids and aperture. The path labeled G is the luminance portion of the awareness path. The path marked G’ is the portion associated with the analytical path. The performance of these loops is augmented by instruction signals received from Brodmann’s area 6 of the cortex. See discussion supporting figure 1.5.2-2 of the supporting document for additional nomenclature.

8.1 The role of delay in the signal processing of vision The configuration of the PGN/pulvinar, superior colliculus and the interconnections between them is only shown conceptually in the above figure. The functional roles assigned to these elements can be expanded as shown in Figure 8.1.1-2. This figure will be discussed further in the following sections. At this level, it shows the principle signaling paths found in the human visual system and their relationships. It also illustrates the major delays involved in the system related to the projection of signals over long distances by the Stage 3 circuits. Finally, it shows the key location of the Precision Optical System in the visual system.


Figure 8.1.1-2 Top level functional diagram of the cortical portion of the visual system. The emphasis is on those elements subsequent to the optic nerve. See text. The significant differences between the two major visuotopic signaling paths are shown. The awareness mode directs signals from the peripheral retina through the LGN/occipital couple. Simultaneously, the analytical mode directs signals from the foveola through the PGN/pulvinar couple. Abstract signals from both couples are forwarded to the saliency map (probably located within area 7 of the cerebral cortex) via area 7 of the parietal lobe. The higher cognitive centers (concentrated in the anterior lobe) can directly access the map from this location. The POS is optimally positioned to respond to alarm mode signals from the LGN. It is also as close to the eyes, from a delay perspective, as it is possible to get. The POS is actually located in the notch immediately behind the two ocular globes. They are as close as possible to the point where the optic nerves exit the ocular globes. Only the slack in these myelinated nerves associated with rotation prevent the signal delays from being even less. Similarly, the command signals transmitted back to the ocular muscles travel the shortest distance possible (over myelinated axons). The minimal delays within the POS not only contribute to rapid responses to alarm mode signals, they allow the high speed operation of the POS servomechanism. This critical feature is used in conjunction with tremor to support the rapid analysis of fine detail (and in man, the ability to read).

8.2 The role of computational anatomy in vision

92 Guide to Processes in Biological Vision Most of the delays shown in the above figure are independent of the position of the source information in the retina. The delays are primarily due to the physical distance between various feature extraction engines. In addition, the figure does not address the visuotopic aspects of the signals presented to different feature extraction engines. A powerful technique offers to significantly reduce the signal processing load of these engines [15.2.8]. It also removes the need for any transcendental (primarily trigonometric) mathematical calculations within the visual system. The technique is known as computational anatomy within the vision community. It is an application of a technique known more generally as conformal transformation within higher mathematics. The technique aims to reduce the signal processing load by rearranging the geometrical distribution of the individual neural channels as they travel between two locations. Two prominent applications of this technique have been documented. The features known as Meyer’s loops appear in both applications.

8.2.1 Temporal computational anatomy The pair of features designated Reyem’s loops and Meyer’s loops reduce the signal processing load of the LGN considerably. Reyem’s loops do this by dispersing the time of arrival of signals at the LGN based on the position of the source within the retina. By measuring the time delay between the signals, a signal proportional to the distance of the source from the fixation point is easily computed. This signal is the principle signal in the alarm mode of vision. However, this dispersion is not of value in the signal processing of the occipital lobe. Therefore, Meyer’s loops are arranged to negate the time dispersal introduced by Reyem’s loops. Reyem’s loops are morphologically less prominent than Meyer’s loops. They are formed by the variable length of the ganglion cell axons within the curved retina. These axons are unmyelinated until the reach the lamina cribosa. Therefore, the signals move at a much slower speed than the same signals within in Meyer’s loops. To achieve the same time delay, the axons of Reyem’s loops can be much shorter.

8.2.2 Geometric computational anatomy Much research has been performed attempting to map the signals representing the image in object space as they appear at different planes in the visual system. Because of the difference in index of refraction of the vitreous humor, the image projected onto the retina is not a faithful spatial representation of object space. It is not truly visuotopic. Such a lack of conformality can be corrected by rearranging the spacing and position of the individual neurons as they travel to the LGN. However, true conformality may not be desirable. Data is available describing the spatial mapping of the LGN. This mapping is frequently compared to the visuotopic input. The map of the LGN is frequently compared to the visuotopic situation using the term retinotopic under the paraxial optical assumption. The paraxial optical assumption makes the unjustified assumption that the retinal image is a faithful reproduction of object space. Recently data has become available describing the mapping of the striate portion of the occipital lobes. When interpreted carefully, this data shows two significant features. The occipital lobe does not contain a high resolution map of the area called the foveola. It actually contains a very poor map of the foveola. More significantly, the map is not visuotopic. It contains a very distinctive distortion produced by a logarithmic conformal transformation. This transformation has a number of unique features. A primary feature is that it converts circles in object space centered on the point of fixation into straight lines in occipital space. Thus, any pie shaped sector in object space is represented by three straight lines in occipital space. This geometrical change greatly simplifies the correlation

Tutorial on Biological Vision- 93 process that is key to feature extraction, perception and eventually cognition. Note that the correlation processes used in the occipital lobe become less and less visuotopic as individual features are extracted. Once extracted, these features are described in abstract vector form. This form cannot be related to elements or features in object space. The spatial maps of the occipital lobe reflect the receptive field of the individual neurons at that point rather than any visuotopic relationship.

8.3 The role of tremor in the signal processing of vision The lower left corner of the above figure shows a feature that has long confounded electrophysiologists. The muscles of the eye show a unique configuration. They have one portion that responds tonically to low frequency signals. These responses can involve large angles of rotation. They also have a distinct portion that responds very rapidly, but over low angular excursions, to higher frequency signals. When the data is coupled with the psychophysical experiments of Yarbus and Ditchburn, the purpose of this unique feature becomes clear. The high frequency response is used to introduce tremor into the visual system. Section 5.2.2 explained how the adaptation amplifier circuit included a method of removing the slowly changing components of the input signal from the faster changing component. This mechanism gives the visual system a very large dynamic range relative to the input intensity level. It also leaves the system blind to any constant intensity elements in the scene. This is quite adequate for many lower chordates who use their vision primarily for alarm purposes, (sedentary rabbits) or to track food that moves within their field of view (frogs). However, it is completely inadequate for predators. Predators must be able to discern food that is stationary with respect to their background. To overcome this problem, many members of Chordata (and through convergent evolution, some members of Mollusca) have introduced a fine angular vibration into their visual systems. This tremor causes all intensity changes (contours) in object space to appear to move with respect to the line of sight of the retina. This technique largely restores the imaging capability of the visual system while maintaining its large dynamic range with respect to average scene intensity. The tremor amplitude need not be large. However, it becomes less effective if it has an amplitude less than the diameter of one photoreceptor cell. The requirement for the product of tremor and contrast contours in a scene if it to be discerned by a human is easy to demonstrate. Using an optometrist’s perimeter with an unblemished white screen, look through the eyepiece and hold the line of fixation constant. Within three seconds, the subject will note the center of his field of view changing to a large blob best described as a neutral gray. The fact that the scene does not go to black makes another point. It shows that the visual system is not direct coupled (using the vernacular of the electrical engineer). The visual system cannot report an absolute intensity level. More complex test equipment can zero out the motion introduced by natural tremor. Then, even printed text will disappear from the field of view within three seconds and be replaced by a neutral gray blob. Tremor is the key to the ability of the human to read and analyze fine detail. Sections 8.4 and 9.2 discuss this capability. While the human cannot control the amplitude or existence of tremor, it appears that a variety of lower animals can. The big cats and the felines are examples. The alligator and crocodile are others. Some birds like the kites and hawks are also examples. These animals seem able to stop the tremor

94 Guide to Processes in Biological Vision when they want to detect motion within an otherwise stationary scene. They can then start the tremor to provide background scene information. Studies of the arc-second level tremor signals were difficult until recently. Instrumentation with both the necessary sensitivity and precision was difficult to construct. However, recent data has proved that tremor is not merely a random noise level. It is a highly structured signal. The vertical and horizontal components of this signal are largely independent. This fact provides the second clue about tremor. It is the source of the analytical capability of the higher members of Chordata (and apparently some higher members of Mollusca). Tremor is used to convert every lightness contour in object space into a temporal feature that can be transmitted from the retina to the brain for further processing. To do this in an unambiguous way, the information must be separated into vertical and horizontal components. This is achieved by time sharing the tremor motion between the vertical and horizontal directions [7.3.5]. Going back to the ancient concept, tremor and saccades can best be visualized by thinking of a narrow beam of light emanating from the eye and scanning a scene. Once the beam falls on an object of interest, the beam performs a very minute scan of the object in two dimensions to discover its shape. In the real case, the beam consists of multiple, tightly grouped, small beams. The receptive fields, rather than the projected fields of individual beams relate to the individual photoreceptors of the eye. Thus, the eye scans an object of interest using a two-dimensional array of photoreceptors. The above signals generated by the foveola are forwarded to the PGN/pulvinar couple for further processing. The peripheral signals are forwarded to the LGN/occipital couple.

8.4 The correlation process of the PGN/pulvinar couple The PGN/pulvinar couple, under the control of the TRN and working with the rest of the POS, is responsible with the initial feature extraction process associated with analytical vision. The PGN is organized as a multiple plane correlator where each plane is a two dimensional surface. The neurons forming this surface are arranged largely visuotopically because of the small area of the retina served, typically 1.2 degrees in diameter. For this size field, the paraxial (Gaussian) optical assumption applies. Under the control of the TRN, the POS scans the field of view forming the temporal electrical signals defined above. These signals are received at the PGN and inserted into different signal planes based on their time of arrival. Their time of arrival is correlated with the vertical and horizontal components of the tremor. This process generates two distinct, but closely related, images. One is focused on the horizontal edges in the scene. The other is focused on the vertical edges. By performing a simple linear correlation along each resolved line in each plane, the location of all significant line segments can be determined. This information is available as a vector describing both the length and location of each line segment. The PGN/pulvinar couple is tasked with further reducing the above library of line segments into interps. Interps define the basic unit of information about a scene element. The interp is an abstract message describing the particular arrangements of line elements found within the field of view of the foveola during any one glimpse of between 50 and 200 msec. [19.8.2] These interps can be compared with the library of interps previously encountered and stored in the pulvinar. For each match, the PGN/pulvinar couple issues a higher level, and more abstract, interp describing what the simple interp represents. The correlator of the PGN consists of about 23,000 nodes in each plane. These nodes represent the circular area of the foveola. The foveola has a diameter of about 175 photoreceptors. Depending on the language being read, the PGN can examine and interpret one short word or two syllables during

Tutorial on Biological Vision- 95 one 200 msec glimpse. The POS then commands the oculomotor system to perform a flick to the next word group or pictogram. This interpretation procedure is repeated until the end of a line of symbols is reached. At that point, a saccade is performed to return to the next line of text. The PGN/pulvinar couple also appears to contain a short term memory (a shift register) that allows it to assemble strings of these initial interps and compare them to previously stored interp strings. Where a match is found, the couple issues a higher level abstract signal known as a percept. The percept may represent a short phrase or a complete thought. If the PGN/pulvinar couple cannot match either a low level interp or a string of interps, it can enter a learning mode that will impress the new pattern into its permanent memory. If a percept cannot be identified, a similar learning procedure may be invoked. However, this procedure may involve the higher cognitive centers in the learning process. Invocation of one of these learning procedures slows the reading process substantially.


9. The Performance of the Nominal Human Visual System

The performance of the human visual system has been studied from many perspectives. Only a selected set of these perspectives can be addressed in this tutorial. The supporting work devotes several hundred pages to these analyses and experiments. In an attempt to summarize the following material, some terms may not be defined in detail. The Glossary, and the summary of the parameters associated with the Standard Eye, listed in Section 1 should be consulted where necessary. The previous studies of visual performance have generally fallen into two categories, electrophysiological (generally invasive) techniques and psychophysical (generally non-invasive) techniques. The former has generally provided more definitive data. However, both have contributed greatly to the development of the models presented above. The challenge has frequently been to decide which data sets included the fewest number of uncontrolled variables. Once this was determined, rationalizing the initially disparate data sets was frequently possible. This section will take another step forward. It will divide the performance of the visual system into those that occur in visuotopic space and those that occur in abstract vector space. Those performance parameters related to visuotopic space can be measured electrophysiologically. They have been measured at the stellate cells of the PGN and LGN. Some performance parameters have been measured at the occipital lobe. However, these measurements have reflected the receptive field of view of the individual occipital cells (referred to visuotopic space) more than the performance of the system. Section 9.1 will address the functional performance of vision from the electrophysiological perspective. Until recently, those signals related to abstract vector space could only be evaluated psychophysically. These abstract signals relate directly to the processes of perception. Two new techniques have recently appeared that show considerable potential for evaluation abstract visual signals. Magnetically augmented visual evoked potential (VEP) and magnetic resonance imaging (MRI) measurements have presented entirely new capabilities. However, the current capabilities of these techniques remain temporally and spatially limited. Substantial progress is being made in understanding the operation of the brain at the abstract signal level. Section 9.2 will look briefly at the subjects of stereopsis, analysis of a bucolic scene, and reading. These discussions will provide references to more extensive material in the underlying work. Section 9.2.4 will provide some introductory words concerning the distinction between perception and cognition. It is extremely important to recognize these differences when reading the current

Tutorial on Biological Vision- 97 research literature. There is a major difference between perceptual awareness and cognitive awareness. The difference is critical to explanations of such phenomenon as blindsight and to further definition of the capabilities of the “zombie.” The section will point to the more detailed models available in Chapter 15 of the underlying work.

9.1 Functional Performance related to Physiology Many individual mechanisms come together in a variety of ways to complicate the description of visual performance in animals. This section will separate these mechanisms as much as possible to illustrate several specific performance characteristics. Sometimes, documenting the presence of more than a single mechanism is necessary. Sometimes, the signatures of other mechanisms are only slightly visible in a given performance characteristic. A mechanism of primary significance to the physiological performance of the human eyes is the twoexciton mechanism of long wavelength vision. It is the source of the change in the spectral performance between photopic and scotopic. The transition is a continuous one with the spectral performance changing continuously within the mesopic range. Without this phenomenon, normal human vision would be limited to wavelengths shorter than 600 nm. Many performance phenomena of human vision derive from the adaptation mechanism of the adaptation amplifier. The transition from photopic to scotopic vision is a direct result of the adaptation mechanism. Because of the large dynamic range of this mechanism, earlier investigators have invariably defined some form of a duplex mechanism to account for it. This duplex mechanism has generally been associated with the putative (but poorly supported) morphological dichotomy separating photoreceptors into the rods and cones. The dark adaptation phenomenon (Section 9.1.4), the color constancy phenomenon (Section 9.1.5), and the spatial (and temporal) frequency characteristic (Section 9.1.6) are all based on the adaptation mechanism.

9.1.1 The transient performance of the photodetection process–the P/D Equation The overall photodetection process involves the conversion of incident photons into an electrical signal by the photoreceptors [7.2]. This process is frequently divided into two distinct conceptual processes in the literature. The first is the photodetection process where the incident photons are converted into excitons (or stereo-isomers in the older literature). The second becomes the transduction process where excitons are converted into a stream of free electrons in the electrolytic circuitry. Unfortunately, the process is controlled by a single differential equation. This fact makes the above division of the overall task inappropriate. Such a division actually obscures the boundary conditions applicable to the differential equation. The dynamics of photodetection in vision is based on the energy band structure and the physical dimensions shown in Figure 6.7.1-1. Under dynamic conditions, each photon absorbed within the liquid crystalline structure of the chromophores creates an exciton at that location. This exciton must travel to the edge of the disk where it can interact with a microtubule. If only a single exciton is created, the trajectory of the exciton is difficult to describe. However, if several excitons exist in the π* band simultaneously, their mutual repulsion defines both the path and the velocity along that path quite well. When an exciton reaches the microtubule interface, it can be de-excited by transferring its energy to an electron-hole pair in the base region of the Activa formed at the microtubule interface. In this process, the exciton returns to the n-band as an unexcited electron. The total number of unexcited electrons in the n-band determines the absorption coefficient of the

98 Guide to Processes in Biological Vision liquid crystalline chromophore. The time that an electron is absent from the n-band due to excitation is a function of the diameter of the disk and the parameters controlling the velocity of excitons within the π* band. This velocity is strongly dependent on the local temperature. While the temperature is invariant in endothermic animals, it varies significantly in exothermic animals. This variation is a valuable source of data in the laboratory. Much of the data confirming the equations presented below come from experiments performed at varying temperatures [7.2.6]. Good data requires the temperature to be recorded to a precision exceeding one degree Celsius. By writing a two-part differential equation describing the above mechanism, the dynamics of the overall photodetection/de-excitation (P/D) process can be described. The first part of the equation describes the excitation and de-excitation events described above. The second part, or secondary equation, describes the time delay between excitation by absorption and de-excitation at the interface. When written in this form, the equation is very similar to the well known (among nuclear physicists) equation describing the creation of nucleotides in a nuclear reactor. However, in the nucleotide case, the transmuted material does not return to its original state while still in the reactor. The solution to the overall differential equation, using the proper boundary conditions, describes the photodetection/de-excitation process in detail. To solve the above differential equation requires that the time delay be described in the secondary equation using complex mathematics. The imaginary operator, j, must be used if the complete solution is wanted. The resulting solution contains j in only one term. This term describes an absolute delay that has been ignored by earlier investigators. The short lifetime of the excitons within the visual process leads to two distinctly different solutions to the P/D Equation. If the stimulus is applied for a period shorter than the time constants of the intrinsic process, the stimulus can be considered a mathematical impulse of zero duration. The amplitude of the response is then proportional to the integrated flux of the stimulus. If the stimulus is of longer duration than the time constants of the mechanism, it must be considered a mathematical step function. In this case, the response achieves a steady state condition during stimulation. Usually, stimuli lasting between 0.1 and 50 milliseconds should not be used in experiments to confirm the P/D Equation, unless the investigators are prepared to handle the mathematics of a complex transient case. The following material will only describe the impulse solution of the P/D Equation. The supporting document provides data on the response to longer duration stimulation [Appen. A].

9.1.1.1 The solution of the P/D Equation for the transient case The overall differential equation for the P/D Equation is given in Section 7.2.4 of the supporting document. The solution to the P/D Equation, describing the current injected into the neural system by a single disk in response to an impulse stimulus, is given below. The equation uses four parameters and the imaginary operator, j. The first two parameters are the intensity of the stimulus, F, and the duration of the stimulus, t (or the product of these two terms). The other two parameters are the absorption cross section of the liquid crystal chromophore, σ, and the time constant of the de-excitation process, τ.


Eq. 7.2.4-1

under the condition that σ•F•τ does not equal 1.00. A different solution to the differential equation must be found for the condition σ•F•τ = 1.00. This solution will be discussed in Section 9.1.1.2. The general solution has been divided into three terms. Each term exhibits a unique feature. For σ •F•τ > 1.00, the first term approaches a value of –1.00 and can be ignored. However, for lower values of σ •F•τ, the term is positive and decreases in proportion to this product. Note carefully that the delay term (the first exponential term) contains the imaginary operator, j. This notation represents an absolute delay in the overall response. It forces each individual response to diverge from the baseline at a different time. This term has not appeared previously in the literature although it is apparent in the empirical record. The third, or amplitude, term is also exponential in character. It does not contain j but it does involve the difference between two exponentials. An interesting fact is that the sign of these two exponentials reverses as σ •F•τ passes through 1.00. Where the first term dominates the rising portion of the amplitude response for σ•F•τ > 1.00, it becomes the dominant factor in the falling portion of the response for σ•F•τ < 1.00. The opposite relationship applies to the second exponential term. Each exponential term includes a temperature sensitive component, KT. T represents the temperature of the chromophores in degrees Celsius and the number eight suggests the narrow biological range of this variable. For a human with a temperature of 37 Celsius, KT is equal to 1.00. CT is equal to 0.002 seconds and the term, kd, is a scaling factor to be evaluated empirically. The total response predicted by this equation is shown in Figure 9.1.1-1 with typical values for the variables. Noting that neither the leading edges nor the trailing edges correspond to a single time constant in the above equation is important. This makes it difficult to relate the response to the empirical record. However, a unique condition makes the problem much easier. When σ •F•τ = 1.00, a simpler form of the equation is obtained. It has been labeled the Hodgkin Solution.


Figure 9.1.1-1 Theoretical responses to an impulse as predicted by the photoexcitation/de-excitation equation. The latency is shown explicitly, by the departure from the baseline, as a function of the peak flux density, F, in photons/micron2-sec. For other temperatures, the time scale can be multiplied by the appropriate value of KT. The value of s is appropriate for perpendicular illumination, or a stack of individual disks. The Hodgkin Solution (s•F•t = 1.000) occurs at F = 12.

9.1.1.2 The Hodgkin Solution to the P/D Equation For σ •F•τ = 1.00, L’Hospital’s Rule must be applied to solve the overall differential equation of the P/D Process [7.2.4]. Interestingly, the solution is simpler and only involves one exponential in the amplitude term. The absolute delay term is also simpler and the scale factor disappears. The following equation represents the complete solution at the singularity.

Eq. 7.2.4-3

where τ is the same intrinsic time constant of the de-excitation process found in the complete equation. KT remains the thermal coefficient modifying that time constant as a function of temperature. The imaginary term remains well behaved and the amplitude term is recognizable as the equation of Poisson’s Distribution of the second kind. The only variable is the time, t. The peak

Tutorial on Biological Vision- 101 amplitude of the response always occurs at the same time following the appropriate delay. Hodgkin first proposed this mathematical form as the general solution to the P/D Process in 1964. However, he could not fit this equation to most of the data without adopting a piecewise approach. As shown above, the Poisson Distribution is a special case of the general solution. This special case, for σ•F•τ equal to 1.00, is labeled the Hodgkin solution in the supporting document [7.2.4]. A set of templates can be prepared for the Hodgkin Solution and different time constants. After overlaying the templates on the experimental data, the curve best fitting the Hodgkin Solution is easily identified. Finding the time constants and other factors in the general solution describing other responses is then easy. For the values shown in Figure 9.1.1-1, the singularity at σ•F•τ = 1.00 occurs for a photon flux of 12 photons/μ2. The value of the time constant, τ, is typically 12.5 milliseconds for humans.

9.1.1.3 Empirical confirmation of the P/D Equation Excellent empirical data has appeared since the 1970's for the P/D response of a variety of animals. Electrophysiological data has been obtained under both in-vivo conditions and quasi-in-vivo conditions (whole, and largely undisturbed, retinas). Psychophysiological data has also been obtained via the ERG. With the availability of the P/D Equation, this data can be analyzed more thoroughly. The data based on the ERG does measure the anisotropic absorption. However, the ERG response includes other information that must be factored out of the measurements [11.1.5]. A problem has arisen with respect to most of the electrophysiological data. The best data has been obtained using the suction pipette technique. However, most of this data has been collected using transverse illumination relative to the axis of the outer segment. The data is thereby limited to the isotropic absorption spectrum of the photoreceptor. This situation explains why all of the photoreceptors tested using this protocol displayed the same spectral response despite their visual appearance. Neither the spectral response nor the absorption cross section measured using transverse illumination is indicative of the anisotropic (operational) absorption of the photoreceptor cell. While not highlighted in the literature, the pipette has been converted into a Faraday Cage from the electrical perspective. When collecting data, each waveform exhibits a different absolute delay (latency), a different peak amplitude, and a different slope associated with its leading edge. The simultaneous changing of all three of these parameters are the primary cause of difficulty for previous investigators attempting to find an empirical solution to the P/D Equation. The P/D Equation is a first order equation that departs from the baseline abruptly following a delay (latency) given by the imaginary term in the equation. A less abrupt departure usually indicates test set limitations. Care should be taken not to normalize the P/D responses measured in the laboratory. While useful for pedagogical purposes, this manipulation distorts the rates of rise and fall of the waveforms.

9.1.2 Spectral performance of the human eye The spectral performance of the human eye involves many distinct mechanisms operating over their own individual performance ranges. This makes a complete understanding of this performance parameter difficult. It also highlights the need to control, or document, many variables if precise data is to be obtained in the laboratory. Traditionally, two distinct operating regions have been defined when studying spectral performance. The photopic region is related to daylight vision. The scotopic region is related to vision under lowlight conditions. An intermediate mesopic region is largely undefined and undocumented. Specific

102 Guide to Processes in Biological Vision definitions of the photopic and scotopic regions, based on the intensity of the illumination (irradiation), do not appear in the literature. Instead, they have come to be defined in terms of the diameter of the test stimulus used in threshold sensitivity measurements. This situation is unacceptable scientifically. These regions are assigned specific limits in the supporting documentation [17.2]. Initially, this section will address the spectral response of only the human retina. The welldocumented results will be surprising to most. Unfortunately, due to safety concerns, they only cover the scotopic performance region. Then the impact of the lens of the eye on overall performance will be reviewed. Unexpected results also appear in this area. With this foundation, it becomes straightforward to differentiate between the scotopic, mesopic and photopic regions of human vision. Finally, the occurrence of certain well-known anomalies will be reviewed. To reproduce the results in this section requires a source of adequate color temperature. An optimum source would have a color temperature of 7053 Kelvin. For sources with a color temperature below 3600 Kelvin, a simple algebraic correction (based on a black-body spectrum) cannot be applied. The normal psychophysical measurements are made at the threshold level. This level changes as a function of wavelength. In addition, its statistical character also changes with intensity. The proper correction requires a detailed model of the signal-to-noise environment of the visual system [11.7].

9.1.2.1 Scotopic performance based on underlying photoreceptors–the full tetrachromat In 1992, two researchers had a rare opportunity. They were able to examine a subject who had lost the lens from one eye in an accident as a child. The aphakic subject was one of them. The experiments were carried out down to a wavelength of 314.5 nm under what they described as scotopic conditions. However, the angular field of view of the targets was only 38 minutes of arc. This value is even smaller than the standard for photopic sensitivity measurements. Scotopic intensity levels were used to be sure no damage was caused to the subject. The results are shown in Figure 9.1.2-1 combined with the data of two other contemporary researchers studying aphakic individuals. Also shown are the individual spectral responses of human vision described in this tutorial. They are normalized to unity for convenience. The lower horizontal line shows the halfamplitude level. This allows one to estimate the width of each spectral response quickly. As expected under scotopic conditions, the spectral response of all subjects was limited in the long wavelength region. What was new was the fact that the subjects exhibited a spectral sensitivity in the ultraviolet that was approximately the same as in the short and medium wavelength regions. A monochromator was used to illuminate a series of 10 nm wide interference filters spaced across the spectrum of interest. An artificial pupil was used to eliminate any variation due to potential changes in pupil size. The notations “w/B & W” and “w/o B & W” refer to the data of Boettner & Wolter collected in 1962. They studied the absorption of the ocular media in front of the retina other than the lens.

Tutorial on Biological Vision- 103 When the spectral responses shown at the bottom of the figure are introduced into the logarithmic sum calculation used in the luminance channel of vision [16.2.2], an equivalent theoretical response is obtained. The computed spectrum can be made virtually identical to any of the measured spectra by adjusting the amplitude coefficients slightly. The calculated spectra show the same filling in of the gaps between the individual spectral responses expected by the logarithmic calculation. The accuracy of this match will be addressed below. It is noteworthy that the spectral absorption of the human retina at low light level does not correspond to the CIE defined scotopic absorption in any way. It is not equivalent to the spectral absorption of the mid-wavelength chromophore as defined by the CIE. It is not even monomodal. This is further evidence of the inadequacy of the CIE linear model.

Figure 9.1.2-1 The tetrachromatic spectral performance of the human retina. Data points and smoothed curves are from Griswold & Stark. The individual spectra are from this work. Note, the low level of irradiation used by Griswold & Stark prevented the subject sensing the L–channel. Only the scotopic response (but extending to 360 nm) was obtained.

When these same individual spectra are used in the logarithmic differencing calculation use in the chrominance channel of vision, the computed difference spectra are as shown in Figure 9.1.2-2. This figure shows the signal expected in the O–, P– and Q–channels and the transition points between them. The transition points occur near the peaks in the underlying individual spectra, at 437 and 532 nm. Spectral discrimination by the retina alone is lost at wavelengths below 342 nm and above 655 nm [17.3.2]. The fact that the chrominance discrimination of the human eye depends on the performance of the O–channel, and the performance of the O–channel depends on the sensitivity of the UV sensitive photoreceptors, will become important in Section 9.1.3. Without the O–channel capability, color discrimination would cease for wavelengths of less than 437 nm in humans. The spectral sensitivity of the UV channel plays a significant role in the chromatic performance of the human eye. Without this channel, royal purple would be just another shade of blue. Ignoring the contribution of the UV-channel to the perception of brightness may be acceptable for entry level pedagogical purposes. However, discounting completely the contribution of the UV–channel to the perception of color is not acceptable. This sensitivity introduces a real problem in color printing. The problem is discussed in Section 9.1.3.

Figure 9.1.2-2 Theoretical chrominance discrimination functions. With adequate illumination, the normal human eye senses the color of a narrowband light using the O–channel between 395-437 nm. It uses the P–channel between 437-532 nm and the Q–channel between 532-625 nm.

104 Guide to Processes in Biological Vision 9.1.2.2 Scotopic spectral performance based on the complete eye–the blocked tetrachromat Griswold & Stark also studied the spectral response of the normal eye using the same equipment. Their results are presented in Figure 9.1.2-3. This is believed to be the best scotopic luminous efficiency function available. The range bars show the quality of the data to be approximately +/– 25%. The continuous line through the data represents the calculated luminous efficiency function based on the proposed individual spectral responses of this work. The line remains within the range bars at all measured values. Note the measured increase in human retinal sensitivity in the 300-340 nm region. This is explained by the narrow absorption spectrum of the lens. Its maximum absorption is in the 355-360 nm region [17.2.2]. Because of the very great dynamic range of the visual system, the sensitivity in the region between 300 and 330 nm may not be negligible under special conditions. It is suggested that this distinct rise in human spectral sensitivity accounts for the perceived dazzling aspects of the ultraviolet lights used in many discotheques. This rise in sensitivity is not included in the CIE Scotopic Luminous Efficiency Function.

9.1.2.3 Photopic spectral performance based on the complete eye–the blocked tetrachromat

Figure 9.1.2-3 The complete scotopic luminous efficiency function for the human eye. There is a Bezold-Brucke peak in this waveform in the 485494 nm region. Data points from Griswold & Stark, 1992. The solid line is the function predicted by this model.

As discussed above, the luminosity function varies significantly with the state of adaptation of the eye, with irradiation level, with the color temperature of the source irradiation and to a lesser extent with age [17.2]. Little data is available relative to age (less than 40 subjects). However, the available data suggest the transmission of the lens group varies less with age than the dispersion in performance due to other variables4. Figure 9.1.2-4 provides an overview of the subject matter for the complete eye. The luminous efficiency function is a continuous variable as a function of illumination, although it does exhibit two regions of reasonably constant shape. These are the photopic and scotopic regions. The hyperopic region exhibits significant saturation in the M–channel region. The mesopic region exhibits a continuous change in spectral performance that will be addressed below. The spectral absorption characteristics of the four chromophores of long wavelength trichromats are shown normalized at the bottom of the figure. The overall spectral performance is a direct function of these underlying spectral absorption characteristics, although this is not obvious because of the logarithmic signal processing employed. This signal processing also results in the two auxiliary peaks at 487 and 580 nm known as the Bezold-Brucke and Purkinje peaks respectively. These artifacts will be discussed in Section 9.1.2.5. The auxiliary peak at 580 is frequently reported as the actual peak in

Tutorial on Biological Vision- 105 the absorption function of the long wavelength chromophore. It is not. The hatching on the left suggests the absorption introduced by the lens group of large terrestrial chordates. This absorption varies with the thickness of the lens group. The larger the animal, the longer wavelength for the cutoff wavelength of this mechanism. Referring to the above discussion, the photopic spectral performance of the human eye is shown by the solid line marked photopic on the right and showing the dip at 350-370 nm on the left. Performance within the hatched area with a border is limited by the lens. Performance within the hatched area without a border is limited if an inadequate light source is used in the laboratory. By truncating this curve in the region of 400 nm and smoothing it with a 30 nm wide filter characteristic, the nominal CIE (1924) Luminous Efficiency Function is obtained. However, the shoulder in the region of 487 nm is lost and the averaged response exhibits a peak in the region of 532 nm (based on an equal photon flux per unit wavelength presentation). A peak of 555 nm can be obtained by replotting the data on an equal energy per unit wavelength basis.

Figure 9.1.2-4 (Color) The tetrachromatic luminous efficiency function of human vision along with its components and variations. The figure highlights the importance of logarithmic signal processing in vision.

9.1.2.4 Spectral performance in the mesopic region The mesopic region of vision is awkward to describe because it involves two active variables operating simultaneously. To separate these, a sub region called the mesotopic region will be defined. This performance region can be explored by using a fixed diameter pupil of small size to eliminate the performance variation due to the operation of the iris. Figure 9.1.2-5 builds on the baseline developed above. It has been tailored to illustrate the spectral response of the eye under mesotopic conditions [17.2.3] and to omit any further discussion of the ultraviolet region. Here again, the nominal absorption spectra of each chromatic channel are shown. The nominal photopic spectral response is shown by the solid line enclosing all of the shaded area. Note that the photopic spectrum extends beyond 750 nm at levels one million times lower than at the peak.

106 Guide to Processes in Biological Vision At very low light levels, the L–spectral channel disappears from the observed spectrum due to the two-exciton effect discussed earlier. The continuous loss in sensitivity in the long wavelength region of the spectrum is obvious as the stimulus level is decreased. The curve labeled mesotopic #1 represents a loss in sensitivity of 10:1 relative to the sensitivity normally observed at the lower limit of the photopic region. Mesotopic #2 represents a loss of 100:1 compared with the lower limit of the photopic region. The scotopic spectral response is normally encountered at light levels 1000:1 below the lower limit of the photopic region.

9.1.2.5 Artifacts of the logarithmic summation process If the eye is chromatically adapted at the top of the mesotopic region by suppressing the Mchannel sensitivity, or if the spectrum of the stimulus is deficient in the M-channel region, the regions labeled the Bezold (Bezold-Brucke) Effect and the Purkinje Effect can be observed. See Section 17.2.3.4. The Purkinje Effect is ultimately lost as the sensitivity of the L–channel is lost.

Figure 9.1.2-5 (Color) Caricature of human luminance threshold response under mesotopic conditions (pupil size fixed). Mesotopic levels #1 & #2 are one and two orders lower in threshold than for the lower edge of the photopic condition (lower limit of color constancy).

To isolate the long wavelength spectrum in the psychophysical laboratory, suppressing the sensitivity of the mid-wavelength spectral channel by at least a factor of 1000 is necessary. This is seldom achieved because of the intensity of the adapting light required. If inadequate attempts are made in the psychophysical laboratory to isolate the long wavelength spectral channel, the observed spectrum is that of the Purkinje Peak, an artifact. It exhibits a peak wavelength between 575-580 nm under most conditions. This is the peak usually labeled the spectrum of the long wavelength spectral channel in the experimental literature. The short wavelength artifact at 480-490 nm is less often reported in the empirical literature.

9.1.2.6 The empirical database versus the current CIE spectral performance standards The available animal data on the individual spectral channel absorptions agree very well with the derivations presented here. The human data is poorer for several reasons. The general prohibition against invasive experiments has largely prevented acquisition of precise electrophysiological data. The resulting focus on psychophysical techniques has introduced its own group of problems. The psychophysical data has been collected using a variety of methods and protocols. Several of these protocols are clearly inadequate. They generally do not employ sufficient suppression of the mid wavelength spectral channel when trying to isolate the long wavelength channel. Thus, the preponderance of the putative long wavelength data shows the Purkinje Peak in the region of 580 nm. One investigator recorded a peak at 610 nm and then placed an unsubstantiated comment in the caption saying “The peak near 610 nm cannot be due to a cone pigment.” He did not offer any

Tutorial on Biological Vision- 107 alternate interpretation of the data [17.2.2]. Data recorded before 1975 usually shows significant smoothing of the spectral responses due to the use of spectral filters wider than 15 nm. The result is a smoothing and broadening of the recorded spectra because of the Central Limit Theorem. The Central Limit Theorem says that poor instrumentation and excessive mathematical manipulation leads to Gaussian spectra. This is evident in the CIE (1924) Luminous Efficiency Function. This function was assembled piecewise from the spectrally non-overlapping investigations of multiple workers. It was then smoothed. In later years, it was interpolated and extrapolated. Professor Wright, one of the last living investigators who provided the underlying data, made an important comment concerning the CIE photopic spectral absorption function of 1924 in 1969. “When I look at the revised table of the x-bar, y-bar, z-bar, functions, I am rather surprised to say the least. You see, I know how inaccurate the actual measurements really were. (Laughter) Guild did not take any observations below 400 nm and neither did I, and neither did Gibson and Tyndall on the V-sub lambda curve, and yet at a wavelength of 362 nm, for example we find a value y-bar of .000004929604! This, in spite of the fact that at 400 nm the value of y-bar may be in error by a factor of 10. (Laughter)” The CIE Standards were originally developed for use in the applied fields of illumination engineering and photography. They have little role in research and should never be used as an absolute standard representing the performance of the eye.

9.1.3 Chromatic performance of the complete human eye–a blocked tetrachromat The material developed above leads to a new physiologically-based Chromaticity Diagram. This diagram is of particular value in research. It is not intended to replace th current CIE standards. They have become too imbedded in commercial lighting practice. However, the new diagram does provide a theoretical foundation that highlight the problems with them.

9.1.3.1 Overview Early vision researchers made the assumption that vision was based on the linear summation of light as sensed by a small group of individual spectral channels. The general assumption was the group consisted of three spectral channels. An additional assumption was that the spectral response of the middle spectral channel dominated the overall spectral response, known then by various titles. A common title for this response was the luminous efficiency function. These assumptions were codified by the CIE during the 1920's and 1930's. Based on the above assumptions, a chromaticity diagram was also codified by the CIE. This occurred initially in 1951. Nearly every assumption involved in the above CIE Standards has proven inappropriate. The actual situation can be derived from the block diagram of vision as documented in Figure 3.1.1-3. The visual system is logarithmically based and is not based on linear algebra. The number of spectral channels in human vision is four. This is true although one channel is truncated. Further, the signals related to chromatic vision are not summed. They are differenced. No direct relationship exists between the achromatic luminance channel of vision and the chromatic chrominance channels. They are not serially related as assumed in many theoretical discussions. A similar situation has occurred concerning the Univariance Principle [17.1.5]. Rushton introduced this highly conceptual principle and initially documented it in 1972. The wording of the concept has been modified considerably as time has passed. It was derived using a floating model based entirely

108 Guide to Processes in Biological Vision on the assumption of an achromatic “rod” with a spectral absorption matching the scotopic spectrum. This is a problem since no single chromophore has ever been isolated with the spectral response equivalent to the scotopic spectrum. The concept centers on the notion that the wavelength of an absorbed photon cannot be determined by the eye. However, the differential logarithmic processing of the chrominance channels shows this to be unrealistic. See Section 3.1.1. For a stream of monochromatic photons with wavelengths between 437 and 625 nm, some will be absorbed by each of at least two spectral channels. The chrominance channels produce net responses that are linearly related to the wavelength of the incident photons. See Section 9.1.2. While not calibrated within the brain, the wavelength of the photons is clearly perceived by the brain. Similar results are obtained by a broadband spectrum. The brain perceives the color of the source as equal to the mean wavelength of the spectrum of that source.

9.1.3.2 Formulation of a new physiologically based color space Physiologically, the three chrominance channels of human vision are treated as totally independent in the CNS. Mathematically, this independence is best described in terms of orthogonality. Equally important, the algebraic differences between the logarithmic signals at the pedicles of the photoreceptor cells result in nearly linear chrominance signals as a function of wavelength. Exactly how these relationships are presented could be a matter of preference except for an additional set of desirable conditions. It would be useful if the relationships could be shown in a conformal form and that the scales could be related directly to wavelength. Conformality insures proper portrayal of mathematical relationships between the quantities [17.3.3]. The easiest way to achieve these goals is to employ a three-dimensional color space conformally transferred onto a Cartesian coordinate system. Since it has been shown that signals in the O–, P– & Q–channels are nearly linear with respect to wavelength, it is intriguing to attempt to use a spectral locus conformally transformed onto such a Cartesian system [16.1.3]. Figure 9.1.3-1(a) shows the spectral locus of a tetrachromat. The nominal points of transition between the O–, P– and Q– channels are noted at 437 and 532 nm. (b) illustrates the resulting totally conformal threedimensional color space. Note that the spectral locus is continuous. The space would form a true cube if it were truncated at the peak wavelength of each chromophore, i. e., 342, 437, 532 and 625 nm. However, this smaller color space would not accommodate the larger perceivable color space of tetrachromatic vision. The full space is technically a right parallelopiped. The orientation with 300 nm at the extreme upper corner was chosen arbitrarily. The long wavelength limit was matched to the perceived “color reversal” that occurs at 655 nm [17.3.2]. These choices give a New Chromaticity Diagram that is compatible with much of the recent psychophysical literature. Note that a null appears in each of the three chrominance equations. The location of this null in object space depends on the state of adaptation of the eye. When transferring the chrominance equations to this color space under dark adapted conditions, the null in the equation for Q occurs at 572 nm. The null in the equation for P occurs at 494 nm and that for O occurs near 395 nm. These values are shown by the long dashed lines. This cubic form shows unambiguously how the perception of "white" is achieved [17.3]. When O = P = Q = 0, there are no chrominance signals to transfer from the retina to the brain. However, the luminance channel uses different mathematics. A luminance signal is still present and it is transferred to the brain. The above equation defines the “white point,” W. Based on the above determinations, the “white point” for a tetrachromat occurs at the intersection of 395, 494 and 572 nm using the folded spectrum locus as a scale. Note that this point is not described by the sum of any

Tutorial on Biological Vision- 109 signals. It is described by the condition where the three difference equations are all equal to zero. This color space differs fundamentally from the conventional assumption of additive color. Additive color assumes that white is described by the sum of the intensities associated with a group of spectral terms. Since the O–, P– & Q– signals are nearly linearly related to wavelength and all are equal to zero at the intersection W, considering this point a displaced zero within the conformal space is convenient. As a result, any color can be uniquely described using its O–, P– & Q– coordinate values. The absorption of the lens restricts the spectral performance of the human eye at wavelengths shorter than 395– 400 nm as shown. 395 nm will be used at the nominal limit as a convenient equality with the above null in the O–channel. As a result, the human subject only uses the color spectrum within a narrower parallelopiped enclosed by 395, 437, 532 and 655 nm. Technically, a human can perceive individual colors at any point within this volume. However, good discrimination performance in the region between 395 and 437 nm requires daylight illumination (or an artificial source at an optimum color temperature of 7053 Kelvin). Since a three-dimensional color space is more difficult to manipulate, and addition of a luminance axis leads to a fourth dimension, seeking a two-dimensional presentation is useful. However a twodimensional representation of a three-dimensional space is by definition non-conformal. (c) shows a degenerate form of the color cube that provides a 2-dimensional color space compatible with the conventional interpretation of a trichromat. This space extends beyond the spectral peak at 437 nm to support the perceptual color space extending to 395 nm. This extension from 437 to 395 nm is not continuous with the lower part of the figure. While both sections are conformal, no conformality exists across the 437 nm line. Note the difference in coloration at wavelengths less than 437 nm. A constant color is shown horizontally for each wavelength. A theoretical “white” cannot be shown explicitly as a single point in this representation. A true white would be represented by a simultaneous null at both 395, 572 nm and 494,572 nm. (D) shows a pseudo-color cube that is easier to work with where a truer representation is needed. It folds the spectral locus at 437 nm but keeps it in-plane. It applies to the complete tetrachromat and shows its complete perceptual color space on a flat surface. As in (C), the left and right sections of the figure are conformal. Here again, no conformality exists across the vertical spectral line. Theoretical “white” cannot be shown explicitly as a single point in this representation either.


Figure 9.1.3-1 (Color) Formation of candidate conformal color spaces. A; the spectral locus from 300 to 655 nm used as a number line. B; the spectral locus bent at 532 nm to form a plane and bent again out of that plane at 437 nm to form a “color cube.” C; the spectral locus bent at 532 nm as above but not bent at 437 nm. This configuration contains a discontinuity at the 437 nm level. The spectrum is truncated at 395 nm for convenience. D; the spectral locus bent at 532 nm to form a plane and bent again at 437 nm but staying in-plane. Lower left frame; 2-dimensional representation showing O–, P– & Q– scales. Lower right frame; 2-dimensional representation showing unique color names defined in the text.


9.1.3.3 A new physiologically based chromaticity diagram for research A New Chromaticity Diagram for Research can be prepared using absolute scales in a rectilinear twodimensional graph space with minimum compromise [17.3.3]. However, several caveats must be attached to the figure. First, the color space only applies to blocked tetrachromats (primarily chordates with ocular globes > 20 mm in diameter). Second, the color space is primarily used for stimuli with half-amplitude full spectral widths greater than 50 nm. If multi-modal, each mode of the stimuli will meet the above criteria. Third, when narrower band stimuli are used in the short wavelength regions, the impact of the O-chrominance channel must be recognized. Fourth, if a color temperature of less than 3600 Kelvin is provided by the ultimate source, filters of any spectral width can be used with this diagram. These caveats are designed to surface the fact that the perceived colors in the spectral region of 400 to 437 nm will differ depending on the test circumstance. They depend on the color temperature of the light source and the selection rules used by the brain. The second and fourth caveats insure that the subject will not perceive saturated purples at test wavelengths below 437 nm. In the absence of these two caveats, the subject may perceive saturated purples correctly. With these caveats, the resulting complete graph of perceived color by humans is shown in Figure 9.1.3-2. The presentation is completely conformal except along the discontinuity at 437 nm. This method of presentation of the human color gamut does not require the introduction of a “purple line” and there are no “non-spectral colors.” Saturated magenta, for instance, is a bimodal color obtained by mixing 437 nm radiation and 655 nm radiation. Note the word perceived in the above paragraph. This is a Diagram of the response of the human eye in perceptual space, not the nominal stimulus applied to the eye in object space as used to define the CIE Chromaticity Diagram. As presented, it is applicable to the nominal eye under dark adapted conditions. This state of adaptation is presumed to be the same as that achieved when viewing an equal quanta per unit wavelength source, e. g., a “daylight” source with a color temperature of 7053 Kelvin for the normal human eye. Using this presentation format, the wavelength scales are linear and the field of the graph is conformal. All of MacAdam’s circles (ellipses in CIE color space) remain circles in this presentation [17.3.3]. A unique color can be defined precisely and unequivocally using only two wavelength numbers. Furthermore, the result of adding two lights of known spectral distribution can be determined using simple arithmetic and geometry. In practice, white is always perceived at one point, the point where the value of both P and Q are zero. A perception of pure white can be obtained by mixing only two monochromatic spectral wavelengths, 494 and 570 nm, in object space under dark (and presumably equal flux) adaptation. A perception of white can also be obtained by mixing any two lights having means applicable to their spectral distributions that equal 494 and 570 nm. The CIE Chromaticity Diagrams are misleading in this area because of their lack of conformality. Therefore, the conventional practice is to use three lights and vary their relative intensity levels until the condition P = Q = 0 is obtained empirically.


Figure 9.1.3-2 (Color) A new physiologically based Chromaticity Diagram for Research applicable to the Hypertopic and Photopic regions. The colors shown are only for discussion purposes. Monitors and “North American” process color printing cannot reproduce the correct colors for wavelengths below 447nm. At least some “European” process color printing can reproduce the purples between 400 & 430 nm but at the expense of the blues between 440- & 470 nm. The figure is conformal and shows the limits of chromatic discrimination in the O, P and Q chrominance channels. A nominal source color temperature of 7053 Kelvin is assumed. It is equivalent to nominal daylight and is very similar to a D65 source. In the region beyond 655 nm, the perceived color of an object is no longer monotonic. The perception of color in the region between 400 and 437 nm is restricted when using normal incandescent illumination. The purples will appear as blues under this illumination.


9.1.3.4 The definition of Unique Colors and color axes A long-standing problem exists in attempting to name the colors perceived based on narrowband (nominally monochromatic) and broadband sources. Similarly, an argument has persisted since the 1900's concerning the principal axes of the perceived human color space. These two problems will be addressed in sequence. Many authors have attempted to define unique colors in the past. Their starting point was invariably psychophysically-based or semantics-based. The physiologically-based color space defined above provides a set of color coordinates tied directly to the physics-based spectrum of vision. Colors defined in this way are truly unique. Look first at monochromatic sources. The lower right frame of Figure 9.1.3-2 provides an opportunity to define a defendable set of unique colors. These colors can be defined in terms of their monochromatic wavelength or the mean of their broader irradiation spectrum. Six “unique color” points appear on the new chromaticity diagram. They can be associated with the common names, white, green, aqua, yellow, red & either blue or violet [17.3.4]. The last option between blue and violet is important and will be addressed below. The definition of these six colors is based on the geometry of the new chromaticity diagram that, in turn, relates directly to the signal manipulation within the retina. Four of the six colors are related to nulls in one of the two chrominance channels and one of them is due to a null in both chrominance channels. The easiest to define mathematically are those occurring along the axes. The following precise wavelength values are subject to refinement in the laboratory. They can be considered accurate within +/- 2 nm. Also given are the approximate Munsell hue coordinates, at high saturation (but not constant numerical saturation), of these unique colors [17.3.5]. These hue values are also subject to refinement in the laboratory and will be discussed further below. These unique colors are defined here: + Unique green (at the intersection of the vertical and horizontal axes, 532 nm, Munsell value 3G), + Unique aqua (at 494 nm on the vertical axis and 532 nm on the horizontal axis, Munsell value 5BG), and + Unique yellow (at 532 nm on the vertical axis and 572 nm on the horizontal axis, Munsell value 10Y). The next obvious unique color is white. It is represented functionally by null signals in both of the chrominance channels. This occurs on the diagram at: + Unique white (ordinate value of 494 nm and abscissa value of 568 nm, Munsell value undefined). The final two values are more difficult to define. Several criteria can be used. The criteria are not the same for both cases. Temporarily overlook the discontinuity associated with the New Chromaticity Diagram for Research at 437 nm. The most saturated spectral blue perceived by most observers occurs near the peak in the S–channel at 437 nm. On the other hand, the perceived spectral color at 395 nm is unsaturated (based on very limited data) and will be labeled lilac. Between these two spectral wavelengths is a region of higher saturation best described as purple. Using these labels, two more colors can be defined.

114 Guide to Processes in Biological Vision + Unique Blue (ordinate value of 437 nm and abscissa value of 532 nm, Munsell value of 10B) + Unique violet (ordinate value 437 nm and abscissa value of 572 nm, Munsell value of 10PB) Discussing the precise colors perceived in the region between 395 and 437 nm is difficult based on the literature. This is partly because of the inadequate color temperature of the light used in most psychophysical experiments. Only museums seem to take pains to insure a color temperature source adequate to reproduce deep purples in the works of the old masters. A problem also occurs in defining unique colors with respect to the red region of the spectrum. A need exists to define both a spectral red and the red associated with the end of the 494 nm axis. In conformity with the above nomenclature, unique red can be defined with respect to the spectral peak in the absorption of the L–channel. This occurs at a nominal 625 nm. However, most people perceive this color as distinctly orangish. A better definition would be to define red based on its dominant wavelength. Beyond 655 nm, the color of the perceived radiation becomes less red and more orange. + Unique Red (ordinate value 532 nm and abscissa value of 655 nm, Munsell value of approximately 2YR) Based on the above definition, a red at 494,655 nm needs to be defined. For reasons that will be discussed below, this red will be labeled Hering red. + Hering Red (ordinate value 494 nm and abscissa value of 655 nm, Munsell value of approximately 5R) Following the above logic to its conclusion should define a unique magenta. However, another problem surfaces. Should the short wavelength ordinate be at 437 nm or at 395 nm? At this time, an arbitrary choice will be made based on common usage. Magenta will be defined as a mixture of blue and red. + Unique Magenta (ordinate value 437 nm and abscissa value of 655 nm, Munsell value of approximately 6RP) The color mauve will be defined at the intersection 395,655. + Unique Mauve (ordinate value 395 nm and abscissa value of 655 nm, Munsell value of approximately 2RP) As discussed below, the distinction between Magenta and Mauve becomes important in printing using “process color.” The above definitions apply to essentially monochromatic “colors.” These can be obtained using high intensity broadband sources and narrowband filters (of only a few nanometers width). When it is desired to work with less spectrally pure illumination, a more complete set of definitions are needed to explicitly define the colors perceived by humans. These specifications appear in Section 17.3.4 in the supporting document. A variety of auxiliary axes can also be used with the New Chromaticity Diagram for Research [17.3.3]. The above color space and unique colors can also be compared with a variety of other color spaces appearing in the literature [17.3.5] Munsell made a fortunate choice in the 1900's. He subdivided his color circle into ten equally spaced sectors and then assigned names to them. These sectors were independent of any theoretical axes

Tutorial on Biological Vision- 115 promoted by the vision research community. As noted in the above definitions, his major radial axes conform very well to the physiological color space of human vision. The above definitions provide a clear distinction between the so-called Young-Helmholtz and Hering axes of the human color space. Both sets of axes are defined relative to the white point at 494,572 nm. The Hering axes are uniquely defined based on the physiology of vision (although not in the way Hering proposed). The Hering axes correspond to the null conditions, P = 0.00 (ordinate of 494 nm) and Q = 0.00 (abscissa of 572 nm). They are named based on the above definitions; the “Hering Red”Aqua axis and the yellow-violet axis. A label such as yellow-blue does not describe the Hering axis correctly. The correlation of the physiological color space with the Young-Helmholtz axes is more difficult. The colors associated with these axes have never been defined precisely. The axes are conceptually defined based on their concept of a tricolor theory of vision (Note they lived at different times). The definition of the three primary colors has been a problem ever since Young changed his mind between 1800 & 1802. Based on the physiological color space, the three axes can be drawn from the white point at 494,572 nm through the three peak wavelengths of the chromophores. However, this leaves the red axes represented by a color perceived as orange by most observers. More awkwardly, any three radials drawn to represent the Young-Helmholtz axes, leave large areas of the color space outside a triangle connecting the three extreme points of the axes. This problem graphically illustrates the problems with the Young-Helmholtz theory based on additive color. The human color space is not trilateral. The three axes of the Young-Helmholtz theory of vision can be drawn from white through the spectral wavelengths of 437, 532 and 655 nm. Alternately, they can be drawn through the spectral wavelengths of 395, 532 and 655 nm. The choice is left to the reader. No unique axes exist in physiological color space associated with the Young-Helmholtz theory of vision.

9.1.3.5 Problems in displaying the complete human color gamut The complete reproduction of the color gamut of the blocked-tetrachromat human requires four lights not three. As a result, no monitor display based on a three-color presentation can completely represent the human color gamut. Similarly, the process color system commonly used in commercial printing cannot completely represent the human color gamut. The problem related to color printing has recently been highlighted by a color figure by Dowling printed in both Europe and the USA [17.3.3.6.2]. The problem relates to the discontinuity associated with the 437 nm ordinate in human color space. The subtractive color used in the process in the USA closely matched the magenta defined above. Its short wavelength component had a mean spectral value greater than 437 nm. As a result, the reproduced spectrum in the picture printed in the USA presents a saturated blue but is lacking in saturated purple. The subtractive color used in the process in Europe more closely matched the Mauve defined above. Its short wavelength component had a mean spectral value of less than 437 nm. As a result, the reproduced spectrum in the picture printed in Europe is lacking in saturated blue but presents a more saturated purple. Currently, Pantone™ is attempting to market a process for color printing they label Hexachrome™. It improves the rendition of greens and oranges by using six separate inks to reproduce a color gamut that more closely matches the human color spectrum. However, it does not address the problem in the purpleblue area.

9.1.3.6 The CIE Chromaticity Diagrams based on the physiological diagram The CIE (Commission Internationale de l’Eclairage) adopted a conceptual framework, believed at the time, to describe the performance of the human visual system with respect to object space. Based on an assumption of linearity, the framework encountered problems early. To minimize these

116 Guide to Processes in Biological Vision difficulties, it defined a Standard Observer that relied upon a set of entirely “imaginary primary stimuli X,Y,Z.” These imaginary stimuli were then fixed in amplitude with reference to an equal-energy stimulus. The CIE framework did not allow for the possibility that the retina and signal processing circuits of the human eye were sensitive to ultraviolet radiation. This caused a great deal of difficulty when Judd and others reported higher sensitivity near 400 nm than anticipated by the CIE. standards. With our current knowledge of the tetrachromatic and logarithmic nature of the human retina, the entire philosophical framework of the CIE is left exposed to question. Based on the physiologically based Chromaticity Diagram presented above, the CIE Chromaticity Diagrams can be interpreted more realistically and their shortcomings annotated [17.3.5.3]. Figure 9.1.3-3 shows the New Chromaticity Diagram projected onto the x-y coordinates of the CIE 1934 Chromaticity Diagram. While the New Chromaticity Diagram is conformal with the basic physiological processes involved, the CIE Diagram clearly is not. Straight lines of constant P– or Q–channel performance are curved significantly. The contribution of the O–channel is collapsed almost entirely into the lower left corner (negative values of y).

Figure 9.1.3-3 A reinterpreted CIE Chromaticity Diagram. The P-channel and Q-channel isoclines are shown overlaying this figure. The gray area shows a distorted quadrilateral (rectangle on the New Chromaticity Diagram) representing the color space achievable using three narrow band spectral sources with peak spectral wavelengths near 485, 540 & 580 nm (a tricolor monitor). Note the absence of a straight “purple line.” The dashed rectangular box shows the area usually explored in chromatic sensitivity experiments. Note also the curvature in the P-channel isoclines near 520-530 nm.

The non-conformality of the CIE 1931 Diagram has been known for a long time. The curvatures of the isoclines of this diagram are so severe that calculating so-called copunctal points (suggested by a linear analysis based on Grassman) is unproductive. Most such attempts have only made measurements within the dashed box between the white point and 575 nm. Note also the lack of a straight purple line. Of greater importance is the total absence of an alychne. The alychne was defined by Judd based on a linear model of vision. The alychne is defined as a straight line in the CIE 1931 Diagram on which are found the chromaticity points of all stimuli (all CIE stimuli are nonreal by definition) having zero luminance. Such points do not exist in a logarithmic model. Several new empirically based CIE diagrams have been proposed to replace the original X,Y,Z-based diagram (and they have been accepted as working standards by the CIE). The CIE UCS Chromaticity Diagram of 1960, and the subsequent CIE L*, a*, b* and CIE L*,u*, v* diagrams of 1976 are also empirically based. They approach the conformal color space presented in Section 9.1.3.3 (not figure 9.1.3-3). However, the New Chromaticity Diagram avoids the approximations inherent in an empirical diagram.

9.1.4 Adaptation is a crucial mechanism in biological vision

Tutorial on Biological Vision- 117 While recognized as a problem for a very long time, a detailed explanation of the mechanism of adaptation has not appeared in the literature. The conventional wisdom has focused on the “dark adaptation” aspect of vision. In that limited context, adaptation has been associated with the chemical restoration of the chromophores of vision. It is a fact that the chromophores of vision play a negligible role in adaptation. Adaptation is a bilateral process associated with the first stage of electrolytic amplification within the photoreceptor cells. It is a highly asymmetrical process due to its method of implementation. As usually discussed, adaptation is a large signal process. The reduction in sensitivity (light adaptation) in the presence of strong illumination occurs very fast. Light adaptation occurs so rapidly, it is seldom studied. However, good information is available on both light and dark adaptation. The longest time constant of the underlying mechanisms is less than two seconds. The restoration of sensitivity (dark adaptation) is a much slower process. The time intervals normally documented are 5-45 minutes long. Within this interval, a variety of individual mechanisms are active. Because the dark adaptation characteristic frequently exhibits two branches, many authors have attempted to relate it to the duplex theory of vision. This has generally led to consternation when attempting to interpret the data. During the 1930's Hecht, et. al. performed a comprehensive study of the light and dark adaptation performance of human vision [17.6.1]. Their work was reported in a series of extensive papers. The papers have been quoted, largely without change, for more than 60 years. The only change has been a tendency to truncate their data near 20 minutes. This practice avoids needing to address the awkward fact that the traces show a distinctive rise (relative to a smooth curve drawn through the points) before continuing to decrease. These rises are key to understanding the operation of the dark adaptation mechanisms. In their 1937 paper, they detail five special points regarding their test arrangements. One of the most important is that their measurements do not represent the absolute threshold of visibility. They suggest the test illumination intensity was about three times threshold. They did not discuss how they determined the factor of three. A precision error of 300% is a large factor in modern laboratory measurements. They also describe several piecewise adjustments to bring their data into better conformity. They used a “violet filter” and a “red filter.” They describe their adapting light as “whole (white) light” and say their light source was a flashlight bulb operating at 3.8 volts and 0.28 amperes. It would be expected that the color temperature of this bulb is near 2400 K. By today’s standards, their instrumentation, conception of the operation of the eye, and protocols were primitive. They expected the violet light to provide the greatest and the red light to provide the least definition between their putative cone and rod threshold sensitivity. However, their findings did not support that assertion. They said: “Nevertheless, even with red light, rod adaptation makes its appearance.” This characteristic has been confirmed often subsequently. Each individual spectral channel exhibits an adaptation characteristic of its own. Although later references to the work of these authors frequently refer to the two branches of the typical adaptation characteristic in humans as related to two separate photoreceptor types, the “rods” and “cones,” these authors also introduced another regime. Quoting from their 1937 paper; “There are two types of rod dark adaptation, a rapid and a delayed, which are probably the manifestations of two methods of formation of visual purple in the rods after its bleaching by the pre-adaptation lights.” Here, the generic term rods should be replaced by the term photoreceptor cells. The speculation concerning two methods of chromophore formation can be replaced with a description of the adaptation amplifier performance. The difference between their rapid and delayed response (which does not relate to the chromophores) can be explained in detail based on the adaptation amplifier of the PC and its electrostenolytic power supply.

118 Guide to Processes in Biological Vision The knowledge available at the time did not support a detailed explanation of the underlying mechanisms involved in sensitivity recovery (dark adaptation). Lacking such an explanation, the variation in the responses as a function of prior adaptation, of position in the retina and of color of the stimulus was quite baffling. This predicament was enhanced by the tendency in the community to normalize data with respect to time zero. In their early work, Hecht, et. al. frequently drew trend lines through their data that did not intersect. At other times, the trend lines were connected to form a sharp corner. When drawn in the latter form, their presentations suggest the presence of two separate exponential-like sections to the response. However, where amplitude scales are provided, it is seen that the curves are not simple exponentials. A close look at the underlying mathematics of the process shows the two branches are not due to separate mechanisms.

9.1.4.1 Overview By examining the overall block diagram of the visual process, and the individual mechanisms discussed above, the phenomenon of dark adaptation can be placed in perspective. Understanding the operation of the adaptation amplifiers of the photoreceptor cells are key to understanding this characteristic [17.6.1]. Figure 9.1.4-1 provides a physiological description of the photodetection process related to adaptation. It shows only a portion of Figure 5.2.4-1, with emphasis on the adaptation amplifier and its power supply. The power supply consists of an electrostenolytic process (described by circuit element R2). This process transfers charge to the axon capacitance, CA. Charge on this capacitor is drawn off only through the Activa. The diffusion through, and concentration within, the IPM of reactants in the electrostenolytic process are described by elements C2 through C4 and R3 & R4. After an extended period in the dark, the potential VC equals – 154 mV. The following points should be recalled from earlier sections in this work: 1. The iris operates over a narrow range of the overall visual range. It operates in the lower photopic and upper mesopic region. Many researchers (including Hecht, et. al.) have employed a small diameter artificial pupil to eliminate the effect of the iris in adaptation measurements.


Figure 9.1.4-1 Physiological map of the visual system related to adaptation. Only the adaptation amplifier of the photoreceptor cell is shown. The load in the collector circuit has been shown explicitly. VC is the collector potential, CA is the axon capacitance, and R1 corresponds to the impedance of the electrostenolytic process. R2 & C2, R3 & C3, etc. correspond to equivalent impedances related to the diffusion of chemicals to the electrostenolytic site. 2. the chromophores of the disk stack act as the photodetectors in vision. They convert photons into excitons. In endothermic animals, these excitons travel to the microtubule and are de-excited within milliseconds of their generation 3. In the three shorter wave length photodetection channels, individual excitons can interact with the base region of the Activa within the adaptation amplifier circuit to create an electron-hole pair. The electrons are the majority carriers in this “n” type material. They move more rapidly and farther than the holes. 4. In the long wavelength region, represented only by the L-channel, two excitons merge to form a biexciton before inducing an electron-hole pair in the Activa base region. This process introduces another functional relationship into the photodetection process. 5. The adaptation amplifier Activa is operated in the open base, common emitter configuration with a collector supply voltage resulting in a collector to base potential near breakdown potential. Under this condition, avalanche gain is achieved (note the barred line through the collector symbol). This condition provides an amplification factor that is highly sensitive (related exponentially) to the collector potential. Since the base is operated without any bias lead attached to it, the current in the collector and emitter leads must be the same. Whenever electron-hole pairs appear in the base region, current will flow in the collector circuit. In the absence of any electron-hole pairs in the base region, the collector current is zero. This last fact is important. It allows the transient performance of the photodetection stage to be evaluated, during dark adaptation, to an arbitrary degree of precision.

120 Guide to Processes in Biological Vision The performance of the adaptation circuit changes very rapidly during the initial time of illumination (light adaptation). The illumination causes a rapid rise in current through the collector of the Activa. This current lowers the collector potential rapidly as it discharges the axon capacitance. As this potential falls, the avalanche-gain of the collector also drops exponentially. As a result, the overall gain of the system falls with a time constant measured in fractions of a second. Operation of the adaptation circuit is different during sensitivity recovery (dark adaptation). The axon capacitance is recharged more slowly through resistance, R1. As long as the potential on C3 is equal to the potential on C4, the load impedance consists of only R1 and CA. The circuit shows an exponential recovery following the cessation of illumination. This time constant is measured in minutes (8-12 minutes). However, if the potential on C3 falls below that on C4, the overall circuit is represented by a third order differential equation. The solution to a third order equation is the product of an exponential and a sinusoid as will be developed below. The period of the sinusoid is also measured in minutes (12-24 minutes).

9.1.4.2 Mathematics of the dark adaptation process Understanding the operation of the adaptation process is complicated by the protocol of the psychophysiologist. Instead of measuring the output waveform of the process as a function of input intensity, they typically measure the input intensity required to achieve a perceived visual threshold. As a result, the input intensity profile exhibits a hyperbolic form. This form is described by the input intensity = perceived threshold divided by the amplification of the signal channel, where the amplification changes as a function of time. The similarity of the reported responses to exponential functions is misleading. The basic functions are hyperbolic. Extracting the time constants of the underlying mechanisms is difficult based on this hyperbolic form of presentation. The time constant corresponds to the time when the signal amplitude is equal to 158% of its terminal value. Four separate mechanisms are found to participate in sensitivity recovery. First, a finite delay exists in the P/D Equation following the cessation of illumination. This cessation is followed by an exponential decline in photo current in the base region of the adaptation amplifier. The time constant of this decay can become several seconds for illumination levels below the Hodgkin solution (in the scotopic and mesopic regions). On the other hand, it is measured in milliseconds at photopic levels. Without an artificial iris, the opening of the iris must also be considered when recovering from high retinal illumination levels. The time constant of this opening is typically six seconds and the amplitude change is nominally 16:1. The above factors influence the response within a few seconds of a light level change. The remaining adaptation factors typically exhibit time constants of minutes. The next factor in sensitivity recovery involves the charging time constant of the adaptation amplifier collector circuit. Following high levels of illumination, the collector potential is near –22 mV. If the eye is subjected to no illumination, no current will flow through the adaptation collector. The restoration of the nominal –154 mV of the adaptation collector in the dark can only be accomplished through the charging of the axon capacitance by the electrostenolytic power supply circuit. This circuit involves both a chemical reaction and the chemical diffusion required to support the reaction. The overall circuit, including the impedance of the electrostenolytic process and the collector capacitance, can be represented by a third order differential equation. The potential of the collector is described by the solution of this differential equation. The solution of third order differential equation has the form; z = (1-e–at) (1– b•e–at •sine ωt) b is a constant dependent on the pre-adaptation level This form is frequently described as a damped sinusoid when the time constant 1/a is much longer

Tutorial on Biological Vision- 121 than the period 1/ω. In vision, the time constant is frequently shorter than, or similar to, the period. Hence, the expression will be described as an exposine (a sinusoidally modulated exponential). During sensitivity recovery (dark adaptation), the psychophysiologist probes the visual system with a small diameter dim light lasting only a short time. As discussed earlier, the current through the adaptation amplifier, is given by the number of electron-hole pairs formed in the base region times the avalanche gain applied to these charges as they move through the collector region. The avalanche gain is exponentially related to the above exposine function. The result is a signal, zz, at the output of the adaptation amplifier due to a small pulse of input illumination. zz = K•(illum)•em•z

where m is approximated by a constant and z relates to the current through the Activa.

At the end of the pre-adapting illumination, the current through the Activa ceases, except for the small pulses of illumination used as a test probe. The collector potential is now below its quiescent value of -154 mV. The electrostenolytic power source begins to reestablish the quiescent potential by supplying current to the collector potential. As this potential rises, the avalanche gain rises exponentially and the intensity of the test probe required to reach threshold is greatly reduced. This change in gain with collector potential explains the large range in the sensitivity of the eye to illumination (after factoring out the smaller ranges due to the iris and the P/D Equation). The data points shown in Figure 9.1.4-2 are reproduced from one of the most widely published graphs of Hecht, et. al5. Solving the above expressions for the required threshold illumination, and plotting them on the same logarithmic scale, results in the two smooth curves shown. The solid curve represents only the exponential component of the solution to the third order differential equation. It clearly shows the unique shape of the reciprocal of an exponential function with a time constant of thirty minutes. The dashed curve shows the complete solution to the differential equation. It shows the product of the damped sinusoid and the exponential. By selecting the time constant and period of the waveforms, the data points can be matched very well. The precision of the model is sufficient to highlight the unexpected decrease in sensitivity (upward excursion of the data points) in the recorded data near 35 minutes. For the conditions Hecht defined, the time constant of the exponential function is 30minutes. The period of the sinusoidal function is 12 minutes. The modulation, b, is approximately 25%. This modulation suggests a significant involvement of the diffusion Figure 9.1.4-2 Dark adaptation curve of a human mechanism in supporting the electrostenolytic observer, following a 2 minute exposure to an process at 400,000 trolands. adapting light of 4 x 105 td. The solid and dashed lines are from this theory. The dotted line 9.1.4.2 Characteristics of dark indicates the value of the time constant of an adaptation exponential plotted as a reciprocal. The data points are from Hecht, et. al, 1937. The test spot With the above background, interpreting the was violet, had a diameter of 3 degrees, a duration other curves of Hecht, et. al. more completely is of 200 ms, and fell 30 degrees from the fovea.

122 Guide to Processes in Biological Vision straight forward. Traditionally, dark adaptation data has been presented normalized with respect to zero time. This has led to difficulty in interpretation. The impression is left that the ultimate sensitivity of the eye varies. However, normalization with respect to infinite time places the sensitivity of the eye in correct perspective. It also shows the underlying mechanisms better. Figure 9.1.4-3 displays the classic data of Hecht, et. al. normalized (by them) to infinite time. Their test configuration was quite complex and seldom described. “The eye was first adapted to “white” light for 2 min at the fixed retinal illuminance shown using a 30 degree diameter field. The “violet” test stimulus consisted of a five degree diameter field presented in 0.2 sec pulses. Both fields were presented in Maxwellian view. For the test stimulus to be treated as visible, the observer had to detect it in a broad black cross. Filled in symbols indicate that a violet color was apparent at that threshold. Empty symbols indicate a colorless sensation. The authors estimated the threshold was approximately three times the absolute threshold.” The comments of the authors on page 838 show the bafflement encountered. “What is startling, however, is that color is definitely associate with threshold intensities well below those which show no color following adaptation to the high intensities. We do not know what this means, and whether it is a special property of violet light;” The explanation is straight forward now. The color threshold is a characteristic of the CNS and the signal level reaching the CNS is controlled by the gain of the adaptation amplifier times the intensity of the illumination. The perception of color is not directly related to the intensity of the stimulus. The figure has been redrawn to show the very high intensity level associated with the 400,000 troland test versus the lower intensity tests. For this figure, the potential change in sensitivity due to the iris opening is presented in this trace. It operates with a six-second time constant during the first part of the response. Its amplitude contribution is suggested by the location of the horizontal line about one order of magnitude below the initial value. Interpreting the figure begins by noting the lower trace. It was the result of a very low intensity preadapting light. It is suggested that the iris played no role in this response and that the collector capacitor was recharged without significant impact on the diffusion parameters supporting the electrostenolytic power source. As a result, the response resembles a reciprocal of an exponential function. The time constant of this trace is between eight and ten minutes. As the intensity of the pre-adapting illumination is raised, the operation of the iris comes into play (unless replaced by a fixed pupil). More important, the diffusion mechanism comes into play in support of the electrostenolytic process. The activity of this mechanism causes the overall circuit to begin operating

Tutorial on Biological Vision- 123 as a third order system. The time constant related to the exponential begins to increase since the effective resistive impedance of the power supply becomes larger. The modulation coefficient relating to the sinusoidal modulation also begins to increase. As a result, the individual responses begin to approach the shape of the response at 400,000 trolands discussed above. The shoulder for each waveform in the figure (the α-break) corresponds to the first positive peak in the sine wave component of the response. Hecht, et. al. provided data on the variation of sensitivity recovery relative to two other variables. They described the sensitivity recovery as a function of color of the preadapting light. They also Figure 9.1.4-3 Recovery of threshold sensitivity for extra-foveal described this sensitivity as a vision (30 degrees temporal from the fixation point). Data function of the distance of the normalized to the terminal condition. Data from Hecht, et. al., pre-adapting light from the line 1937. of fixation. This data is easily interpreted in terms of the ability of the interphotoreceptor matrix to support diffusion of the necessary chemicals to the site of the electrostenolytic process. It suggests that the impedances R2 and R3 are shared between the photoreceptors next to each other. It also suggests that the value of these impedances varies in a systematic way with location in the retina and the species under study. It also suggests Oguchi’s Disease is related primarily to the low collector potential of the adaptation amplifiers. This condition suggests a mechanical, hydraulic or chemical problem acting as a neuro-inhibitor.

9.1.4.3 The primary role of the iris is to control image quality, not intensity Because of its prominence, the opening and closing of the iris have long been related to the control of the illumination intensity applied to the retina. The human visual system has a total dynamic range exceeding 50,000:1. Less than 0.1% of this range (about 16:1) is contributed by the iris changing the size of the pupil. The physiological optics, of each eye, forms a unique wide-angle optical system with a field of more than 114 degrees. To achieve this performance, the optics employs a “lens” with a variable index of refraction. The index varies both with distance along the optical axis and radially from that axis. Stiles & Crawford explored the impact of this variation in great detail. However, their empirical results were not related directly to easily understood performance parameters. Their general conclusions were two. The optical rays passing through the lens at different distances from the optical axis, and at different angles relative to the optical axis, did not pass through the same zone of

124 Guide to Processes in Biological Vision the retina as their compatriot rays. Instead of all rays from a given spot in object space forming a small circular image on the retina, the combined rays formed a coma. The result of this aberration is a loss in both spatial resolution and contrast in the image on the retina The iris is designed to rationalize two requirements [7.4.8]. It is designed to provide maximum light collecting capability when the subject must explore the scene at low light levels. It is also designed to reduce the aberrations due to the Stiles-Crawford Effects when examining fine detail at high illumination levels. In humans, minimizing aberration under high illumination conditions is the most important function. The optics of the eyes are essentially perfect (diffraction limited) when the pupil is at minimum size. When the irises of the eyes are fully open, the optical system is highly aberrated. The primary role of the iris is to minimize the diameter of the pupil when the incident light level is adequate. In normal humans, the pupil is minimized throughout the photopic range. In fact, pupil size is a criteria in defining the lower limit of the photopic range.

9.1.5 The phenomenon of Color Constancy The subject of color constancy has achieved new popularity lately as researchers in machine vision seek to emulate this biological vision capability. The capability is intimately related to two features of the visual system. It depends on the previously unpublished transfer function of the adaptation amplifier and the logarithmic signal conversion performed by the distribution amplifier. Both amplifier circuits are found in each photoreceptor cell. The goal of each adaptation amplifier is to insure a constant average output signal amplitude at the pedicle of each photoreceptor throughout the photopic region of operation. In fact, the photopic region is defined by this property. The adaptation amplifier achieves this performance by introducing a very large amount of negative internal feedback into the circuit. Most biological investigators are unfamiliar with internal feedback. It does not use an external signal path from the output to the input. Instead, the feedback is achieved internally due to a shared impedance between the input and output circuits of an amplifier. The negative feedback is introduced via the impedance in the emitter lead of the adaptation amplifier. Because of the high gain in the collector circuit due to the avalanche effect, this feedback introduces a zero in the transfer function of the amplifier at zero frequency. The effect of this process is to remove the average value of the signal related to the average value of the illumination. Three consequences arise from this effect. The signal at the output of the pedicle maintains the contrast present in the original image. However, the signal is largely independent of the absolute light level of the image. The chrominance signals are derived from the ratios between the signals from the individual spectral channels. Since these ratios are now independent of the original average signal levels, the phenomenon of color constancy is perceived. The mechanism causing color constancy is also the cause of the automatic adjustment of the “white point” under conditions of differential spectral illumination. The adaptation amplifiers associated with a specific spectral channel operate similarly when their average irradiation level is changed. If an excess of blue light is used to illuminate a scene, The adaptation amplifiers will compensate for this by lowering their amplification factor. As a result, the signal level at the pedicles of the S–channel photoreceptors will be held at a constant level. Since these levels have not changed, the chrominance channels will still exhibit nulls in their signals when the average signals in the different spectral channels are differenced. The brain will perceive a white value in spite of the new average scene illumination levels See Section 9.1.3. A tertiary consequence of the zero in the transfer function at zero frequency was discussed earlier.

Tutorial on Biological Vision- 125 The eyes of chordates are blind in the absence of tremor.

9.1.6 The contrast performance of the visual system The contrast performance of the visual system can be described using a variety of protocols. The temporal contrast can be evaluated at a specific point in the visual field. Alternately, the spatial contrast can be evaluated over a region centered on a specific point in the visual field. Both modes of evaluation can be defined using a stimulus of constant spectral quality or of variable spectral characteristics. The result is a large family of contrast performance characteristics. A hidden problem is found in many protocols found in the literature. All visual signals are translated into temporal signals for transmission through the visual channels. The temporal response of each spectral channel of the visual system includes a zero at zero frequency. Therefore, it is very important to document and control any temporal aspects of a test stimulus designed to evaluate the spatial performance of the system. For test signals presented to the eye for short periods (typically less than ten seconds) the temporal response of the adaptation process introduces a variable into the experiment. In tests presenting the spatial test stimulus to the eye for an interval of less than one second, the temporal response associated with the P/D process should also be considered. Many investigators have failed to perform their experiments at sufficiently low spatial and temporal frequencies to document the zero signal amplitude at zero frequency in the visual system. This is an intrinsic feature of the system. These experimenters frequently describe the visual system as a low pass system rather than a bandpass system. In other experiments, spectral signals have been used that are not well matched to the spectral absorption channels of vision. Failure to match the spectral channels reduces the contrast and the signal-to-noise ratio in the individual chrominance channels of the visual system. The interpretation of the results is more difficult under these conditions. The contrast performance, particularly the color contrast performance, differs between the foveola and the peripheral retina [17.3.1]. This difference involves intrinsic operating differences between the awareness and analytical modes of vision. Complexities also arise related to how the information processed by these two modes is merged in the brain. The results of experiments involving stimuli with a spatial extent of more than 1.2 degrees diameter centered on the point of fixation can be diluted due to these differences.

9.1.6.1 The (achromatic) contrast temporal frequency transfer function (CTF) The contrast performance of the visual system in the temporal domain has been studied for a very long time using a variety of methods. Many of these studies occurred without an adequate model of the system, were exploratory in character, and appeared at the time to conflict with each other. Most of these conflicts can be resolved when the complexity of the achromatic temporal contrast transfer function (CTF) is examined. The key areas of conflict revolve around inadequate documentation of the low frequency performance of the system and inadequate documentation of the light level employed. The overall temporal transfer function of the visual system is quite complex [17.6]. Ignoring the operation of the iris, it still contains a zero in its numerator and four poles in its denominator (one of the latter being variable with applied light level). The most important low frequency limitation on the visual system is due to the load characteristic of the adaptation amplifiers of the photoreceptor cells. The primary role of this load is to remove the sensitivity of the eye to slowly varying changes in illumination so that it can operate successfully over a dynamic range of about 107:1. To do this, the signal passband is restricted to frequencies above

126 Guide to Processes in Biological Vision about f1/2 = 0.1Hz (based on a three-second time constant and f1/2 ~ 1/πT). The high frequency performance of the visual system is affected significantly by the retinal illumination used in experiments. This is due primarily to the P/D Process discussed in Section 9.1.1. The upper frequency response of the system at a given level can vary more than two to one due to this parameter alone. Therefore, documentation of the illumination intensity used (and its color temperature) is important. Because of this variation, differences in performance based on pupil size are also to be expected. When the illumination level is sufficiently high, the bandwidth of the P/D Process and the adaptation circuits are sufficiently high that the limitations due to the Stage 3 propagation circuits become significant. Figure 9.1.6-1(a) shows the terms in the modulation transfer function of the visual process as they relate to the above stages. Note the use of the imaginary operator, j, in the equation. The stage 0 term is due to the operation of the iris and the servo loop controlling it. This equation has S, representing frequency, in the numerator. The form of the equation is that of a high-pass filter. It results from the presence of a lowpass filter in the feedback path controlling the iris. The stage 1 term is taken directly from the P/D equation of the visual process and represents the mechanism associated with the chromophores within the outer segment of each photoreceptor cell. It is the Laplace transform of the transient response developed in Section 9.1.1 [12 & Appen. A]. The denominator contains two terms and one of them is a direct function of the illumination level. A special mathematical case applies when the two time constants are equal. In this special case, the transient equation of the P/D Process reduces to Hodgkin Solution proposed in 1964. The stage 2 term also has S in the numerator. This is the term associated with the adaptation amplifier within the inner segment of each photoreceptor cell. The stage 3 term is that of a lowpass filter. It represents the integrators associated with the stellate cells in the PGN and LGN at the end of the projection circuits associated with the ganglion cells of the retina. Figure 9.1.6-1 (b) shows the product of the individual MTF terms forming the overall modulation transfer function of (at least) the portion of the visual system related to the foveola. It highlights the fact that the time constant SP2(I) is a variable and its low pass characteristic varies accordingly. The variation is shown for a ±16% range about the value of 30 candela/meter2. The black lines show the normal characteristics of the graph with the effect of the iris shown by dashed lines on the left. The operation of the iris introduces hysteresis. The response varies with the protocol used in the measurements. An artificial pupil can be used to eliminate this problem. It is useful to note the local slope (numbers next to segments of curves) of the overall modulation transfer function. This slope shows the number of individual filter stages that are actively affecting the operation of the overall signal path at a given frequency. At very low light levels, the value of SP2(I) may become lower than SP1. This condition requires a relabeling of the flags in the figure, which suggest areas of dominance by the different terms in the equations. At very low frequencies and illumination ranges where the iris is active, the slope of the overall MTF

Tutorial on Biological Vision- 127 becomes +2 and the visual response falls very rapidly with decreasing frequency. At the higher frequencies, the form of the overall MTF is seen to vary considerably with the illumination level due to SP2(I). The form is precisely that measured by Kelly and others for a small field of view centered on the line of fixation. A trained eye is frequently required to recognize the short segment labeled –1. The maximum slope at high frequencies measured in the laboratory is frequently minus three. However, some experimental data has suggested a slope of minus four or even minus five in this region.

Figure 9.1.6-1 Nominal characteristic of the contrast temporal frequency (CTF) function of human vision. The analysis and diagrams apply specifically to the foveola. The variation about the high frequency response represents a ±16% range about the value of 30 candela/meter2.

9.1.6.2 The (achromatic) contrast spatial frequency transfer function (CSF) The mechanism of tremor provides a method of converting the temporal contrast frequency transfer function (CTF) of the electrophysiological system into an equivalent spatial contrast frequency

128 Guide to Processes in Biological Vision transfer function. When combined with the spatial contrast frequency function of the physiological optics, a complete spatial contrast frequency transfer function (CSF) is obtained [17.6.3]. This response is frequently labeled the modulation transfer function (MTF) of the system. The equation and a graphic representation of this spatial contrast function are shown in Figure 9.1.6-2(a) and (b). The result shown in the lower part of the figure shows that the slope of the asymptotes can be used to evaluate the character of an equivalent measured function in the laboratory. As in the previous derivation, the MTF of the optical system is seen to play a minor role in the operation of the eyes for the on-optical-axis condition. A similar situation applies to the foveola at the point of fixation. The spatial performance of the visual system as a function of frequency is largely independent of the optics of the eye until large angles (more than 5-10 degrees) from the point of fixation are explored. Under these conditions, the performance of the optical system falls dramatically. As mentioned above, the method of presentation of the test stimuli can affect the observed performance significantly. Besides controlling the temporal aspects of the presentation, some investigators have sought to eliminate certain edge effects (Gibb’s Phenomenon) related to squarewave or sinusoidal bar-patterns of finite spatial duration. The techniques are usually based on Gabor Patterns, where the contrast of the overall pattern is made to vary according to a normal distribution curve. The modulation is then highest at the center and falls monotonically to zero near the edges (in either one or two dimensions). While the performances are theoretically different, the practical results have not changed greatly by using the Gabor Patterns [17.6.3]. Figure 9.1.6-2(b) includes two additional lines presenting the data curves obtained by a recent MODELFEST carried out over the internet. The diamonds represent data collected using fixed size Gabor patches. The squares represent data collected using Gabor patches with a fixed number of cycles in a pattern. The theory presented is in good agreement with the data collected by that group at a nominal illumination level of 30 cd/m2. At this low illumination, the value of SP2(I) is lower than SP1. Note the transition from a nominally horizontal slope at the peak in the threshold waveform to a slope of –1. This slope is only recognizable when the parameters SA and the higher of either SP1 or SP2(I) are separated well numerically. At frequencies higher than these frequencies, the slope of the composite function becomes –2. It is proposed that this theory is the first work ever to suggest the reason for this dip found so frequently in the literature. The dip has traditionally been ignored by the computational modelers.


Figure 9.1.6-2 Nominal characteristic of the contrast spatial frequency (CSF) function of human vision. The analysis and diagrams apply specifically to the foveola. Top; equation of the overall MTF. Bottom, the overall MTF (heavy solid line) with the time constants changed to represent a real situation. Data points and light lines from MODELFEST data (see text).

9.1.6.3 The chromatic contrast transfer function (CCF) Although several investigators have used the term chromatic contrast transfer function (CCF), it has seldom been defined explicitly. Sometimes it has been used to describe essentially monochromatic temporal or spatial measurements. More often, it has been used to describe temporal or spatial measurements based on a broadband color filter. Occasionally, it has been used to describe differential measurements involving two different colors presented sequentially. The mean wavelength of the filtered light used has seldom been identified. Without this information, interpreting the collected data precisely is difficult. An additional complication arises in CCF experiments due to the asymmetry of the stage 3 signal projection circuits. This asymmetry causes a variation in perceived color as a function of time. A test stimulus presented for 0.5 seconds is frequently judged to be different from the same stimulus

130 Guide to Processes in Biological Vision presented for two seconds. Experiments can be defined that evaluate the chromatic frequency response of the system under a variety of conditions. The preferred experiments would be those evaluating either the P– or Q–channel independently. This requires careful choice of the illumination employed. For the P–channel, the preferred light sources are located along the Q = 0.00 (572 nm) axis of the New Chromaticity Diagram for Research. Values along this line will not introduce any signal in the Q–channel. Similarly, to evaluate the Q–channel, two light sources well separated along the P = 0.00 (494 nm) axis should be chosen. The use of narrow band spectral lights introduce the awkward fact that at least one stimulus will excite both the P– and Q–channels. A residual signal is likely in the luminance, or R–, channel unless the amplitudes of the chosen signals are appropriately matched to the luminance function of the system. Demonstrating this condition is difficult because the human observer is not able to distinguish a luminance contrast from a chrominance contrast under threshold conditions. The model used here can describe the theoretical performance expected under any of the above conditions [17.6.3]. However, the equations become quite complex. As suggested above, the CSF of each color component must be evaluated separately and then a difference taken. While the equations are complex, the performance of the system remains limited at the highest frequencies by the stage 3 terms in the equations and at the lowest frequency by the zeroes associated with the adaptation terms. Section 17.6.3.5 of the supporting work provides the details of the processes involved. It also shows the excellent match obtainable between the calculated and measured results under specific test conditions.

9.2 Functional Performance related to Perception As noted earlier, only selected areas related to the functional aspects of perception will be addressed here. References will be provided to more extensive material in the underlying document. Since the mid 1990's, it has become abundantly clear that the operations of the visual system related to stereopsis, the study of fine detail, and reading do not involve the so-called primary visual cortex (also known as area 17 in Brodmann’s notation or V1)[15.1.1]. As shown in Section 8, the functions associated with feature extraction, leading to interpretation and perception, are controlled and implemented within the Precision Optical System (POS). The POS consists of the retina, oculomotor system and the thalamic portions of the diencephalon. The thalamus, with potential help from the cerebellum, perform most of the analytical steps related to interpretation and perception (as distinct from cognition). The vectorized output of these mechanisms are delivered directly to the parietal lobe of the cerebral cortex via the pulvinar pathway (not via area 17). Exactly how and where this information is stored in the saliency map of the subject is still unknown. A set of block diagrams, schematics, etc of the visual system (updated as of 2003) are available in Section 15.5 & 6 of the supporting document.

9.2.1 The horopter The term horopter is used to describe both a conceptual model of the visual function as it relates to object space and an instrument used to make measurements according to that model [7.4.1]. This section will only address the conceptual model. The conceptual model of the horopter has frequently been refined into what is represented as a theoretical model. Measurements designed to confirm

Tutorial on Biological Vision- 131 such theoretical horopters generally have not. Significant systematic deviations are usually found. These deviations are frequently labeled the Hering-Hillebrand deviations. These deviations, and an improved model will be reviewed in the next section.

9.2.1.1 Representations of the horopter Figure 9.2.1-1 shows the frequently reproduced conceptual figure of the empirical horopter dating from at least Ogle (1950). The deviation of the horopter from the Vieth-Muller circle is shown. The fields of view of the foveola have been added for clarity. Describing the Hering-Hillebrand deviations precisely using graphs at this scale is difficult. It is also a bit embarrassing to point out that the versions of the figure by Tyler & Scott in Record (pg 656), by Tyler in Schor & Ciuffreda (pg 222), and in Howard & Rogers (pg 27) are drafted improperly. They all have the Vieth-Muller circle passing through the point of rotation of the eyes and the point of fixation. Such a circle is more commonly known as the circle of equal convergence. The Vieth-Muller circle is defined with respect to the 1st principal point of each eye and the point of fixation. Although it is usually reproduced without attribution, the concept appears to go back to Alhazen in the 11th Century (Howard, pp 50-52). Interest in it was only revived by Hering in the 19th Century. As usually reproduced, it is drawn without scales and any definition of the criteria used to draw it. Tyler, writing in Schor & Ciuffreda, notes that the form of the empirical horopter is not as shown in the figure under many conditions. He demonstrated that it even changed in local areas depending on the nature of the stimulus used. Tyler discusses the empirical horopter in terms of Panum’s area. He then concluded with, “the traditional concept of Panum’s area as a fixed property of a given retinal region must be abandoned.” This is clearly the case. The situation will be discussed in greater detail below. The description of the empirical horopter depends greatly on the geometry of the stimulus used, the criteria used to define the limit, the light level and whether the stimuli are presented dichotically or dichoptically. Failure to account for these parameters leads to much of the conflict found in the literature concerning Panum’s area. Figure 9.2.1-2 provides an extended theoretical framework based on a correct Vieth-Muller circle, the equations of Ogle plus several other Figure 9.2.1-1 A typical empirical horopter additions. Ogle’s equations introduced a series frequently used in pedagogy, with the so-called of ellipses transitioning from the Vieth-Muller fronto-parallel plane (X,Y) defined. Frequently circle to the horizontal axis of the frontocalled a fusion horopter and drawn without scales. parallel plane through the point of fixation. The Vieth-Muller circle is drawn incorrectly. The With the parameter H = 0.0, the Vieth-Muller 1.2 degree fields of view of the foveola have been circle is obtained. If H = 2a/b, where a is the added. inter-pupillary distance and b is the distance to the point of fixation from the mid point of the inter-pupillary line, the horizontal axis is obtained. Intermediary values of H equate to intermediate ellipses as shown. One of these ellipses is particularly important because it corresponds to the surface of best focus for an equivalent “cyclopean eye,” or the actual eyes where a is much smaller than b. This ellipse will be important when looking at the data. The impact of the depth of focus of the visual system on horopter measurements suggests the data in the literature may be skewed

132 Guide to Processes in Biological Vision toward the ellipse of best focus unless precautions are taken. Little data is available on the precise shape of the focal surface of the human visual system in object space. The variable focal length with field angle of the design could introduce unexpected variations in the shape of that surface. Because the off-axis resolution of the system decreases so rapidly, the subject is largely academic. It will be assumed here that the eye is in optimum focus for all field angles when focused at infinity and that any accommodation changes the focal surface proportionally for all field angles. The figure also includes the approximate limits (the dashed lines intercepting the ellipses) of the empirical horopter based on the binocular field of view. Finally, a deviation from the true vertical axis is shown. This small deviation of zero to two degrees is due to the Volkmann-Helmholtz Effect. This Effect is due to the relative tilt of the vertical axis of the eyes when they converge6. This is due to the non-orthogonal motions introduced by the oculomotor muscles. When aligned for vision at infinity, the Effect is negligible. At near distances, the Effect can cause the empirical horopter to tilt away from the eyes for points above the horizontal by up to two degrees. Finally, the figure includes the small circular area imaged by the foveola. This small area is the only area involved in stereopsis. By expanding the image, this small area is clearly the only area of the horopter that lies in the fronto-parallel plane. It is also the area of maximum spatial performance of the physiological optics. The data in chapter 4 of Ogle show that the actual horopter of an individual does not correspond to the Vieth-Muller circle or the fronto-parallel plane. His figure 11 would suggest the “typical” empirical horopter at 40 cm corresponds almost exactly with the ellipse of best focus (H = 1/b) rather than the ViethMuller circle.

9.2.2 Depth perception and stereopsis

Figure 9.2.1-2 Theoretical framework for displaying empirical horopter data. The ViethMuller circle is drawn correctly and a series of ellipses from Ogle are also shown. The limits on the field of binocular vision are shown and the area imaged by the foveola is highlighted. The potential shift in the vertical axis of the horopter is also shown. See text.

Humans are not generally aware of how dependent they are on their memory when viewing familiar scenes. Rather than re-scan an entire scene at a high level of precision, they rely on the contents of their saliency map to remind them of the details relating to large portions of the scene. This allows the analytical mode of vision to concentrate on changes that have occurred in the scene. The perception of depth involves two completely separate mechanisms [7.4.4]. Qualitative depth perception is a phenomenon associated with the awareness mode of vision. It is used by the LGN/occipital couple to process imagery from the peripheral retina. Qualitative depth perception employs a variety of cues, such as shadowing and relative motion, to create a coarse estimate of the three dimensional aspects of object space. It is very difficult to define the precision of depth perception in this arena. It tends to be binary in character. An object is closer than a nearby object

Tutorial on Biological Vision- 133 or it is not. Stereopsis is a mechanism associated with the analytical mode of vision. The PGN/pulvinar couple uses the two dimensional associative correlator within the PGN to calculate the location (in three dimensions) of every edge in its field of view. The pulvinar and higher level feature extraction engines then use these maps of edges to interpret and perceive all of the features within this field of view. This field of view corresponds to that of the foveola of the retina. The diameter of this instantaneous field is only 1.2 degrees. However, because of the agility of the human eyes, the system is able to rotate the eyes to examine every important object within the binocular field of vision. Because of its massive parallel processing capability, the PGN/pulvinar couple can assess an individual instantaneous image in a nominal 200 milliseconds. The system then performs a flick, or larger saccade, to observe the next important small field of view [7.3.3]. The precision of the depth perception achieved through stereopsis is quite high under photopic conditions. Estimates center on about 200 individual range bins along the line of fixation. This corresponds to steps of 0.5% of the distance to the nominal focal plane of the eyes. The relative capability of the peripheral retina and the foveola is shown in Figure 9.2.1-3.

9.2.3 The analysis of a scene and reading Humans are generally not aware of how much they rely upon memory in the visual process [19]. Memory is found at multiple functional levels. Much of it is not accessible to the cognitive portions of the brain. We are unaware of those portions. The awareness mode of vision, including the LGN and the occipital lobe (primary visual cortex, V1, etc.) play a minor role in the analysis of a scene. The awareness mode is used primarily to provide a context of the Figure 9.2.1-3 Stereoacuity displayed on a overall scene. The analytical mode, consisting horopter. Qualitative depth perception is optimal of the PGN/pulvinar couple and the rest of the along the ellipse of cyclopean focus. The Precision Optical System servo loop, plays the performance in this area is binary. Precision dominant role in the analysis of fine detail and depth perception is suggested by the radial length reading. The task of these elements is to of the cylinder shown. While the diameter of the convert the initially visuotopic image presented cylinder is only 1.2 degrees, it is estimated to to the retina into an entirely abstract contain 200 individual range bins along the line of (vectorized) perception of that scene (text) that fixation. can be stored in the saliency map of the cerebral cortex. The thalamic reticular nucleus plays the central role in supervising and controlling the information processed by both the awareness and analytical modes. When one walks into a familiar room, the eyes do not search the entire room in a series of saccades. Instead, their awareness channel of vision compares its crude image with the appropriate portion of its stored saliency map and prepares a list that only highlights changes from that map. The TRN accepts the list of highlighted features and instructs the POS to investigate each of those features at high acuity using the foveola. This procedure typically takes a second or two.

134 Guide to Processes in Biological Vision If a human enters a strange room, the time to interpret the entire scene is usually many seconds or more. The awareness channel of vision typically prepares a list of the coarse features of the room based on object size and contrast. When one enters a large hotel ballroom, one typically notes the large TV screens or the stage curtain first. One then notes either the head table or possibly a chandelier, depending on perspective. One then notices smaller nearby objects or people, etc. This procedure can easily take tens of seconds to create a new saliency map that only contains high acuity information concerning less than 25-50 objects in a room containing hundreds of objects or more. Whether analyzing a bucolic scene or text, the underlying process is much the same. The awareness mode elements annotate the most likely key regions of the scene, based primarily on size and complexity. They present their prioritized list of regions of the scene to the TRN. The TRN passes this annotated list along to the POS. The POS proceeds to analyze the scene in detail, subject to control and override by the TRN. The analytical process takes place in a series of steps. Each step involves a series of highly programmed procedures. The number of these steps and procedures preclude their detailed discussion here. They are developed in detail in Chapter 19 of the underlying work. It is most important to realize that any analytical routine is limited to the image projected onto the foveola. This image is initially analyzed into a series of contrast edges. Contiguous edges are grouped into a figure known as an interp within the psychology community. Several interps may exist in a single image. If so, these interps are assembled into a percept. A percept has generally been encountered before. By comparing the percept with the contents of memory, assigning a totally abstract designator to this visuotopic percept is frequently possible. This designator becomes the abstract percept passed up the line to the saliency map. For complex scenes (and text) an additional stage of assimilation may be involved. This involves moving the image on the foveola with the effect that the foveola scans the overall image. The result is a series of percepts acquired in time sequence. This stage is used to assemble the individual abstract percepts into a larger percept. As an example, the assimilated percept may say that the overall image is of my bedroom rather than of a bedroom. In the absence of any totally new and unexpected interps and percepts, all of the above analytical functions are performed within the PGN/pulvinar couple of the POS and the analytical mode of vision. If learning is involved, it appears the cerebellum, a large memory unit, may also play a role. Reading is a uniquely human skill. It involves an even longer series of preprogramed (learned) steps and procedures. As discussed briefly above, the cerebellum and the superior colliculus of the PGN appear to be involved in learning the required programmatic procedures. These procedures are culturally controlled. Indo-Europeans read small simple characters in groups arranged in rows extending from left to right. The people of the Middle East have adopted a similar procedure but different characters. They prefer to read from right to left. In the Orient, a system more akin to the ancient Egyptians has survived. They prefer to read more complex pictographs arranged in columns and read from top to bottom. Reading relies on the same signal processing functions as defined above. However, greater emphasis is placed on the analysis of fine detail, presented stylistically to the foveola of vision, and processed entirely within the analytical mode of vision [19]. The ability to read is centered almost entirely on the POS and the thalamus of the diencephalon. The information associated with a message is almost totally extracted and perceived before the forebrain becomes involved. This allows the forebrain to concentrate on cognition, the determination of the meaning of the message in a larger context. Because reading involves so many stylized features to achieve maximum performance, the subject

Tutorial on Biological Vision- 135 rapidly gets into a level of detail beyond the scope of this tutorial. Chapter 19 of the supporting document addresses reading in detail.


Figure 9.2.1-4 shows how a simple word is imaged on the foveola. It has been scaled to represent the word as presented under standard conditions. Each character occupies nominally five by five minutes of arc in object space. The background shows the nominal equivalent size of individual photoreceptors. The simple five-letter word “PRESS” fills about 43% of the diameter of the foveola. This fact suggests that the foveola can only analyze a word of less than ten characters within one nominal period of 200 msec. In practice, it employs a different strategy. It analyzes character groups of about five characters as shown and uses the rest of the available image space as part of a “lookahead” routine. The POS attempts to determine if the “space” following the character group is occupied by a significant character group or the space between words. A decision on this fact can change the saccade sequence to skip over empty space, or even go to the next line of text. Just going to the next line of text involves a complex series of procedures and saccades. The lower frame of the figure shows potential individual interps based on the edge contrast detection mechanism performed by the PGN. Depending on the contrast of the image, the PGN may detect the two edges of each stroke of a single printed character as shown for “P.” Alternately, it may only detect a single edge representing each stroke as shown for “R.” Figure 9.2.1-4 The Stellen E placed on the retina at 20/20. Top frame shows the word PRESS overlayed on the retinal mosaic. The arrows on the upper left show the size of 10 adjacent photoreceptors. The arrows on the upper right show the nominal size of the tremor (microsaccades). The bottom line shows the extent of the tremor if its amplitude is 40 arc seconds peak to peak. The top line shows its extent if its amplitude is 40 arc seconds RMS. Bottom frame presents the question of how a single character is parsed for transmission to the cortex.

alarm mode)

A Chinese pictogram can be imaged onto the retina similarly. However, care must be taken to insure that each stroke in the pictogram has a width of more than one minute of arc. A spacing of at least one minute of arc is also required between strokes under standardized conditions. This is the dominant factor in the design of simplified pictograms for use in children’s books and in text to be transmitted as captions within television presentations.

9.2.4 The difference between perception and cognition (the

The visual system is now understood well enough to begin moving into the questions of cognition as it relates to the frontal lobe of the cerebral cortex, and consciousness in general [15.1]. Prior to moving in this direction, it is absolutely critical that all terms be defined clearly and precisely. Normally, this level of definition is not found within the neuroscience community when discussing these subjects. The word awareness is a particular problem. It is proposed that the saliency map forms a unique location (boundary) within the neurological system. It separates the operations of the sensory systems which provide information to the saliency map and the higher level operations of the brain which access this data. The sensory systems provide the interpretation and perception of the raw input and derive the abstract (vectorized) signals placed in the saliency map. The higher level cognitive centers use this map to cognate on the environmental situation described by the saliency map and to prepare instructions to be implemented by the efferent neural systems.

Tutorial on Biological Vision- 137 In the above context, a subject can achieve perceptual awareness without achieving cognitive awareness. The former relates to the operation of the system prior to the saliency map and includes the performance of the “zombie.” It also includes the performance of many subjects exhibiting “blindsight.” These subjects are able to perceive and respond to threats and other visual symbology without being cognitively aware of the threat or symbology. There is another point of clarification related to the efferent signal paths of vision. It may be useful to consider the output of the higher cognitive centers as being passed to an equivalent of the saliency map before implementation. This equivalent may be directly related to what is frequently called the premotor areas (as differentiated from the motor areas) of the brain. This delineation would aid in separating those subjects who have cognitive awareness of an event but cannot report that awareness using the conventional methods (primarily speech). Such cases are becoming better known as the techniques of psychophysical evaluation become more sophisticated. Even ordinary subjects are frequently tongue-tied during moments of anxiety (even though they may point at something fervently or take other protective action). Many authors have opined on how a tennis player or baseball batter does not have sufficient time to recognize the ball and calculate its trajectory before he is required to take action. Similarly, anecdotal evidence exists that a track sprinter begins to leave the chocks before he has had time to recognize the sound of the starter’s gun. These situations require the introduction of additional terminology and the delineation of an additional functional capability [15.2]. Note the etymology of the word recognize (re-cognize). It implies the organism has been in a similar position previously. The alarm mode of vision, shown in Figure 8.1.1-2, is the underlying mode associated with these situations. It is designed specifically to detect threatening, or otherwise important, changes in the visual field. It has an analog in the audio system. These signals are extracted within the LGN and passed directly to the appropriate elements of the thalamus. The signals are sent directly to the POS, and the equivalent elements of the skeletomotor system to save time. They are sent to the TRN to allow it, in its supervisory role, to countermand the alarm signal if appropriate. The POS performs the interp and percept extraction tasks as described above. It forwards the results of its analytical tasks to the saliency map. However, it has been also programmed (through learning) to take certain actions immediately without further instructions from the TRN or any higher cognitive centers. When received by the controllers of the oculomotor and skeletomotor systems, action can be taken immediately. The action to be taken is highly dependent on prior learning. The time delays shown in the referenced figure become very important in this sequence of operations [15.2.2]. Until the abstract percepts are placed in the saliency map, the cognitive centers of the brain are not able to recognize these percepts. Once placed in the map, time is required for the engines of the cognitive centers to evaluate these percepts in a larger context. However, in the cases cited above, this recognition process is largely irrelevant. It is performed mostly as a matter of keeping good records. The motor systems of the organism have already taken the required action under the supervision of the TRN (as previously negotiated and authorized during the learning process). If the batter misses the pitch, blame the TRN and the motor response systems (and the coaches), but not the cerebral cortex. Section 15.6 of the underlying work develops the latest information in the rapidly changing fields related to perception and cognition.


Table of Contents 1. The last 500 Million Years of Evolution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 2. The Variation among Eyes is Enormous . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 2.1 Each Phylum has a distinctive eye architecture . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 2.2 The chordate eye and the significance of the reverse retina . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 3. The Eyes are only part of a Visual System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1 The Building Block Architecture of the Chordate Visual System . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1.1 The signal processing within the retina of man . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2 The major role played by the Diencephalon . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2.1 The operation of the TRN as the gatekeeper of sensory inputs and muscular/skeletal responses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2.2 The operation of the PGN/pulvinar couple . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2.3 The Precision Optical System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3 Plan and profile views of the human visual system . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.4 Functional signal pathways within the visual system . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.4.1 Effect of a “total commissurotomy” of the corpus callosum . . . . . . . . . . . . . . . . . . . . . . . 3.4.2 Agnosia as a function of location or of feature extraction engine . . . . . . . . . . . . . . . . . . 3.5 The thalamic reticular nucleus (TRN) as the gate keeper of vision . . . . . . . . . . . . . . . . . . . . . . . . . 3.6 Summary of overall visual operation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

15 16 20 23 25 25 25 27 32 35 36 37 37

4. Neurons are the electrolytic equivalent of man-made electrical circuits . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41 4.1 The electrolytic versus ionic argument of neuron operation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41 4.2 Semiconductor physics applied to the neuron . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42 4.2.1 The plasma membrane as an electrolytic component . . . . . . . . . . . . . . . . . . . . . . . . . . . 42 4.2.2 The juxtaposition of two asymmetrical plasma membranes–the ACTIVA . . . . . . . . . . . 43 4.2.3 The Electrostenolytic Process defines/replaces the ion-pump . . . . . . . . . . . . . . . . . . . . . 46 4.3 The operation of the electrolytic neuron . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48 4.3.1 The application of the ACTIVA and electrostenolysis to the synapse . . . . . . . . . . . . . . . 48 4.3.2 The synapse in a morphological and functional context . . . . . . . . . . . . . . . . . . . . . . . . . 50 4.3.3 The application of the ACTIVA and electrostenolysis to the Node of Ranvier . . . . . . . . 51 4.3.3.1 The Nodes of Ranvier within a single neuron . . . . . . . . . . . . . . . . . . . . . . . . . 51 4.3.3.2 The morphology/cytology of a Node of Ranvier . . . . . . . . . . . . . . . . . . . . . . . . 53 4.3.3.3 The Node of Ranvier alone . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53 4.3.4 The application of the ACTIVA and electrostenolysis to a ganglion cell . . . . . . . . . . . . 55 4.3.5 The application of the Activa to a bipolar or lateral cell . . . . . . . . . . . . . . . . . . . . . . . . . 56 4.3.6 The stellate cell recovers the encoded signals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56 4.3.7 Signal propagation by a neuron . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56 4.3.7.1 A coaxial axon is not a Herman Cable . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58 4.3.7.2 Understanding the group velocity, and other signal velocities within a neuron . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59 4.3.7.3 The marriage of the Node of Ranvier, electrostenolysis and the coaxial axon . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59 4.4 Metabolic support to the neuron . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60 4.4.1 Introductory electrostatics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61 4.4.2 Metabolic processes related to the operation of the neuron . . . . . . . . . . . . . . . . . . . . . . 61 5. The unique neuro-secretory photoreceptor cell . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.1 Functional divisions of the photoreceptor cell . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.2 Electrical configuration of the photoreceptor cell . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.2.1 Unique dendritic structure of the neuron . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.2.2 The unique adaptation amplifier formed within the microtubules . . . . . . . . . . . . . . . . .

63 66 66 66 67

Tutorial on Biological Vision- 139 5.2.3 The quantum-mechanical interface between the disks and the microtubules . . . . . . . . 5.2.4 The overall electrolytic configuration of the photoreceptor cell . . . . . . . . . . . . . . . . . . . 5.3 Secretory functions of the photoreceptor cell . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.4 Growth within the individual photoreceptor space . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.4.1 The life cycle of a rhodopsin based disk . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.4.2 The life cycle of a molecule of a chromophore . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

67 68 68 69 69 70

6. The Tetrachromatic Capability of the Typical Photoreceptor Group . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.1 The eyes are quantum detectors, not energy detectors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.2 Liquid crystal quantum physics is key to understanding spectral absorption . . . . . . . . . . . . . . . . 6.3 The four chromophores of biological vision . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.4 Non-spectral variants between chromophores due to their Vitamin A base . . . . . . . . . . . . . . . . . . 6.5 Isotropic and anisotropic absorption of the liquid crystalline chromophores . . . . . . . . . . . . . . . . . 6.5.1 Empirical verification of the isotropic and anisotropic spectra . . . . . . . . . . . . . . . . . . . . 6.6 The spectral characteristics of the in-vivo chromophores of biological vision . . . . . . . . . . . . . . . . . 6.6.1 The unique character of the long wavelength spectral channel . . . . . . . . . . . . . . . . . . .

71 72 73 74 77 77 77 78 78

7. The Unique Photoreceptor/IPM/ RPE environment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.1 Morphogenesis of the human eye . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.2 The complete mature PC/IPM/RPE complex . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.3 Where did the cones go–the dynamics of the PC/IPM/RPE interface . . . . . . . . . . . . . . . . . . . . . . .

81 81 82 86

8. More detailed architecture of higher chordate visual system . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.1 The role of delay in the signal processing of vision . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.2 The role of computational anatomy in vision . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.2.1 Temporal computational anatomy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.2.2 Geometric computational anatomy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.3 The role of tremor in the signal processing of vision . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.4 The correlation process of the PGN/pulvinar couple . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

89 90 92 92 92 93 94

9. The Performance of the Nominal Human Visual System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96 9.1 Functional Performance related to Physiology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97 9.1.1 The transient performance of the photodetection process–the P/D Equation . . . . . . . . 97 9.1.1.1 The solution of the P/D Equation for the transient case . . . . . . . . . . . . . . . . 98 9.1.1.2 The Hodgkin Solution to the P/D Equation . . . . . . . . . . . . . . . . . . . . . . . . . . 100 9.1.1.3 Empirical confirmation of the P/D Equation . . . . . . . . . . . . . . . . . . . . . . . . . 101 9.1.2 Spectral performance of the human eye . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101 9.1.2.1 Scotopic performance based on underlying photoreceptors . . . . . . . . . . . . . 102 9.1.2.2 Scotopic spectral performance based on the complete eye . . . . . . . . . . . . . . 104 9.1.2.3 Photopic spectral performance based on the complete eye . . . . . . . . . . . . . . 104 9.1.2.4 Spectral performance in the mesopic region . . . . . . . . . . . . . . . . . . . . . . . . . 105 9.1.2.5 Artifacts of the logarithmic summation process . . . . . . . . . . . . . . . . . . . . . . 106 9.1.2.6 The empirical database versus the current CIE spectral performance standards . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106 9.1.3 Chromatic performance of the complete human eye–a blocked tetrachromat . . . . . . . 107 9.1.3.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107 9.1.3.2 Formulation of a new physiologically based color space . . . . . . . . . . . . . . . . 108 9.1.3.3 A new physiologically based chromaticity diagram for research . . . . . . . . . 111 9.1.3.4 The definition of Unique Colors and color axes . . . . . . . . . . . . . . . . . . . . . . 113 9.1.3.5 Problems in displaying the complete human color gamut . . . . . . . . . . . . . . 115 9.1.3.6 The CIE Chromaticity Diagrams based on the physiological diagram . . . . 115 9.1.4 Adaptation is a crucial mechanism in biological vision . . . . . . . . . . . . . . . . . . . . . . . . . 117 9.1.4.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118 9.1.4.2 Mathematics of the dark adaptation process . . . . . . . . . . . . . . . . . . . . . . . . 120 9.1.4.2 Characteristics of dark adaptation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122 9.1.4.3 The primary role of the iris is to control image quality, not intensity . . . . . 123 9.1.5 The phenomenon of Color Constancy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124 9.1.6 The contrast performance of the visual system . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125

140 Guide to Processes in Biological Vision 9.1.6.1 The (achromatic) contrast temporal frequency transfer function (CTF) . . . 9.1.6.2 The (achromatic) contrast spatial frequency transfer function (CSF) . . . . . 9.1.6.3 The chromatic contrast transfer function (CCF) . . . . . . . . . . . . . . . . . . . . . . 9.2 Functional Performance related to Perception . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9.2.1 The horopter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9.2.1.1 Representations of the horopter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9.2.2 Depth perception and stereopsis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9.2.3 The analysis of a scene and reading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9.2.4 The difference between perception and cognition (the alarm mode) . . . . . . . . . . . . . .

125 127 129 130 130 131 132 133 136

Tutorial on Biological Vision- 141 List of Figures Figure 1.1.1-1 Phylogenic relationships tracing the presence of Vitamin A in various families . . . . . . . . . . . . . 2 Figure 1.1.1-2 Mapping of phylogenic families by environment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 Figure 1.1.1-3 An abbreviated Phylogenic Tree focused on the visual aspects of taxonomy . . . . . . . . . . . . . . . 4 Figure 2.1.1-1 Eye of the primitive mollusc, Nautilus . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 Figure 2.1.1-2 Evolution of the simple photospot into fundamental eye types by phylum . . . . . . . . . . . . . . . . 10 Figure 2.2.1-1 The Generic Chordate Eye as represented by Homo Sapien . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 Figure 3.1.1-1 Morphogenesis of the brain in the higher chordates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 Figure 3.1.1-2 Top level block diagram of the neural system . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 Figure 3.1.1-3 (Color) The luminance, chrominance and appearance channels of the eye of tetrachromats . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 Figure 3.2.1-1 The Precision Optical System highlighting the vergence subsystem . . . . . . . . . . . . . . . . . . . . . 26 Figure 3.3.1-1 Plan view of the human visual system as seen from BELOW. . . . . . . . . . . . . . . . . . . . . . . . . . 27 Figure 3.3.1-2 Profile view of the human visual system. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30 Figure 3.3.1-3 Fundamental signaling architecture of the human visual system. . . . . . . . . . . . . . . . . . . . . . . 32 Figure 3.4.1-1 A revised Functional Diagram of human vision, ca 2002 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35 Figure 3.6.1-1 A simplified Functional Diagram of human vision, ca 2003, showing the TRN . . . . . . . . . . . . 39 Figure 4.2.1-1 The juxtaposition of two asymmetrical triphosphoglycerides monolayer membranes . . . . . . . 43 Figure 4.2.2-1 The molecular structure of the Activa within the hillock of a neuron . . . . . . . . . . . . . . . . . . . . 45 Figure 4.2.2-2 The fundamental electrostenolytic process powering the neural system . . . . . . . . . . . . . . . . . . 47 Figure 4.3.1-1 A simple caricature of the morphology of a synapse . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49 Figure 4.3.2-1 The topology, circuit and four terminal network of the synapse . . . . . . . . . . . . . . . . . . . . . . . . 50 Figure 4.3.3-1 The first-order hydraulic plan of the brain . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52 Figure 4.3.3-2 Functional operation of a Node of Ranvier . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53 Figure 4.3.7-1 Summary of the signal propagation velocities in neural systems. . . . . . . . . . . . . . . . . . . . . . . . 57 Figure 4.3.7-2 The overall signal transmission environment for the propagation of action potentials . . . . . . 60 Figure 4.4.1-1 Details of the metabolism and hydraulic flow related to the neuron . . . . . . . . . . . . . . . . . . . . . 62 Figure 5.1.1-1 Caricature of a photoreceptor cell with RPE interface and Outer Limiting Membrane . . . . . . 65 Figure 5.2.4-1 The principal signal waveforms of the photoreceptor cell . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68 Figure 6.2.1-1 Energy Band structure for organic molecules. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74 Figure 6.3.1-1 The proposed chromophores of animal vision, the Rhodonines, based on Vitamin A1 . . . . . . . 76 Figure 6.6.1-1 The quantum-mechanical interface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79 Figure 7.1.1-1 Morphogenesis of the chordate eye . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81 Figure 7.2.1-1 The photoreceptor cell-IPM-RPE interface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84 Figure 8.1.1-1 Top level schematic of the visual system in Chordata . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90 Figure 8.1.1-2 Top level functional diagram of the cortical portion of the visual system . . . . . . . . . . . . . . . . . 91 Figure 9.1.1-1 Theoretical responses to an impulse as predicted by the photoexcitation/de-excitation equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100 Figure 9.1.2-1 The tetrachromatic spectral performance of the human retina . . . . . . . . . . . . . . . . . . . . . . . . 102 Figure 9.1.2-2 Theoretical chrominance discrimination functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103 Figure 9.1.2-3 The complete scotopic luminous efficiency function for the human eye . . . . . . . . . . . . . . . . . . 104 Figure 9.1.2-4 (Color) The tetrachromatic luminous efficiency function of human vision . . . . . . . . . . . . . . 105 Figure 9.1.2-5 (Color) Caricature of human luminance threshold response under mesotopic conditions . . . 105 Figure 9.1.3-1 (Color) Formation of candidate conformal color spaces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110 Figure 9.1.3-2 (Color) A new physiologically based Chromaticity Diagram for Research . . . . . . . . . . . . . . . 112 Figure 9.1.3-3 A reinterpreted CIE Chromaticity Diagram . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116 Figure 9.1.4-1 Physiological map of the visual system related to adaptation . . . . . . . . . . . . . . . . . . . . . . . . . 119 Figure 9.1.4-2 Dark adaptation curve of a human observer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121 Figure 9.1.4-3 Recovery of threshold sensitivity for extra-foveal vision . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123 Figure 9.1.6-1 Nominal characteristic of the contrast temporal frequency (CTF) function of human vision . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127 Figure 9.1.6-2 Nominal characteristic of the contrast spatial frequency (CSF) function of human vision. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129 Figure 9.2.1-1 A typical empirical horopter frequently used in pedagogy . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131 Figure 9.2.1-2 Theoretical framework for displaying empirical horopter data . . . . . . . . . . . . . . . . . . . . . . . . 132 Figure 9.2.1-3 Stereoacuity displayed on a horopter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133 Figure 9.2.1-4 The Stellen E placed on the retina at 20/20 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 136


SUBJECT INDEX action potential 41, 42, 53-56, 59, 60 activa 43-46, 48-57, 59, 62, 65-68, 79, 85, 97, 118-121 acuity 11, 134 adaptation amplifier 22, 67, 93, 97, 118-122, 124, 126 additive color 109, 115 agnosia 36, 37 alarm mode 16, 18, 25, 33, 38, 91, 92, 136, 137 amino acid 69 analytical mode 15, 16, 25, 36, 37, 91, 132-134 anisotropic absorption 74, 77, 78, 101 annelida 1, 2 area 17 20, 27, 30, 31, 33, 37, 130 area 18 30, 33 area 6 38, 90 area 7 27, 29-31, 36, 38, 91 area 7a 30, 31 avalanche gain 67, 68, 119, 121 awareness mode 37, 91, 132-134 axon segment 54 A-gap 45 a-wave 68 Bezold-Brucke Peak 104 bilayer membrane 43, 44, 46 blindsight 97, 137 broadband 72, 108, 113, 114, 129 Brodmann 20 b-wave 68 calyx 64-66, 68, 69, 82, 83, 85, 86 cerebellum 17, 19, 20, 24, 35-38, 130, 134 Coaxial cable 58, 59 colax 63-66, 83 color constancy 22, 97, 105, 124 computational anatomy 33, 38, 92 conexus 44, 52 contrast transfer function 125, 129 copunctal points 116 cortex 20, 23-25, 27, 29-39, 89-91, 130, 133, 136, 137 cyclopean eye 131 dark adaptation 97, 117-122 dendrolemma 48, 50, 66 dicarboxylic 47, 70 differencing 20, 22, 103 diode 43-46, 51, 56, 68 dogma 41, 42 electromagnetic propagation 57-60

electrostenolytic process 23, 46, 47, 49, 54, 61, 63, 118-123 ERG 59, 68, 85, 101 external feedback 90 Faraday cage 101 fMRI 16 GABA 23, 47, 48, 61-63 Gaussian 12, 13, 94, 107 glutamate 23, 46-48, 61-63 glutamate shunt 61 Grassman 22, 116 group velocity 25, 33, 57-59 half-amplitude 22, 77-79, 102, 111 Herman cable 58 Hodgkin solution 99-101, 120, 126 horopter 130-133 hydronium 45, 48, 53, 66 hysteresis 126 INM 53, 62, 68, 81, 83 interaxon 59, 60 internal capsule 34, 36 internal feedback 124 interp 94, 95, 134, 137 ion-pump 41, 42, 46, 48 IPM 63, 68-70, 81-86, 118 isotropic absorption 70, 77, 78, 85, 86, 101 Krebs 47, 61 lamina cribosa 92 latency 100, 101 light adaptation 117, 120, 121 liquid crystal 66, 71-75, 98 magnetic resonance 16, 23, 96 magnocellular 30, 55 mesopic 97, 101, 102, 104, 105, 118, 120 mesotopic 105, 106 Meyer’s loop 27, 33 microtubules 63, 64, 66, 67, 69, 79, 82, 83, 85 midbrain 17, 23, 25, 29, 30 modulation 121, 123, 126, 128 molecular absorption 73, 74, 77, 78 monopulse 53, 55 morphogenesis 18, 63, 81 MRI 96 narrow band 116, 130 neurite 51, 52, 59 Neuron Doctrine 41 neurotransmitter 41, 42, 47 neurotransmitter dogma 41, 42 neurotransmitters 48

Tutorial on Biological Vision- 143 neuro-facilitator 47, 48 neuro-inhibitor 47, 48, 123 nictating eyelid 14 Node of Ranvier 44, 51-55, 59, 60, 62 ocular globe 14, 89 P/D equation 79, 97, 98, 100, 101, 120, 121, 126 Panum’s Area 131 parvocellular 30, 55 Pauli exclusion principle 73, 78 percept 95, 134, 137 perceptual space 111 perigeniculate nucleus 25, 27, 29, 37 PGN/pulvinar couple 19, 20, 25, 27, 28, 33, 35-38, 91, 94, 95, 133, 134 phagocytosis 66, 69, 70, 82, 86 phase velocity 59 photodetection 74, 97, 98, 118, 119 photoexcitation/de-excitation 55, 70, 79, 100 photopic 79, 97, 101, 102, 104-107, 112, 118, 120, 124, 133 photoreceptor cell 8, 21, 22, 63-69, 78, 79, 82-84, 86, 93, 101, 119, 124, 126 pnp 41 poda 51 POS 25, 26, 30, 33, 37, 38, 59, 91, 94, 95, 130, 133, 134, 136, 137 Pretectum 17 process color 112, 114, 115 Pulvinar pathway 27, 29, 30, 32, 33, 130 Purkinje Effect 106 Purkinje peak 106 quantum-mechanical 43, 44, 51, 66, 67, 71-73, 79, 82, 86 resonance 16, 23, 73, 74, 96 resonance absorption 74 retinotopic 20, 92 Reyem’s loop 33 Rhodonine 69, 70, 75, 77, 83, 85 saccades 38, 94, 133, 136 saliency map 20, 29, 37, 38, 91, 130, 132-134, 136, 137 scotopic 79, 86, 97, 101-104, 106, 108, 120 servo loop 126, 133 servomechanism 25, 30, 33, 37, 38, 91

signal-to-noise ratio 72, 73, 125 simple eye 9, 10 SRBP 75 stellate cell 56 stereopsis 11, 12, 38, 96, 130, 132, 133 subtractive color 115 suction pipette 78, 101 superior colliculus 17, 19, 20, 26, 27, 29-31, 36, 38, 90, 134 synapse 23, 24, 41, 44, 48-53, 60 test set 41, 101 tetrachromats 3, 21, 111 thalamic reticular nucleus 17, 19, 20, 24, 25, 32, 33, 37, 133 thalamus 17, 18, 20, 23-25, 27, 29-32, 34, 36, 37, 130, 134, 137 time delay 25, 33, 37, 38, 59, 92, 98 topography 89 topology 45, 46, 50 traffic analysis 23, 31 transistor action 45 transport velocity 57, 58 tremor 16, 22, 25, 27, 38, 91, 93, 94, 125, 127, 136 trichromats 3, 104 Univariance 107 V1 33, 130, 133 V2 33 V3 33 V4 33 vascular matrix 83 VEP 16, 20, 96 vesicles 49, 70, 75 visual evoked potential 16, 96 Vitamin A1 2, 3, 75-77 Vitamin A2 2, 3, 77 Vitamin A3 3 volition mode 15, 25, 26 Y-channel 37, 38


Selected Endnotes 1. Trevarthen, C. & Sperry, R. (1973) Perceptual unity of the ambient visual field in human commissurotomy patients. Brain, vol. 96, pp 547-570 2. Kandel, E. Schwartz, J. & Jessell, T. (2000) Principles of neural science, 4th ed. NY: McGraw-Hill. pg. 498-500 3. Skavenski, A. Hansen, R. Steinman, R. & Winterson, B. (1979) Quality of retinal image stabilization during small natural and artificial body rotations in man Vision Res. vol. 19, pp. 675-683 4. North, A. & Fairchild, M. (1993) Measuring color-matching functions. Part II. Color Res. Appl. vol. 18, no. 3, pp. 163-170 5. Hecht, S. Haig, C. & Chase, A. (1937) The influence of light adaptation on subsequent dark adaptation of the eye. J. Gen. Physiol. Vol. 20, pp. 831-850 6. Tyler, C. & Scott, A. (1979) Binocular vision, Chapter 22 in Records, R. Op. Cit. pp 650-656

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