Evaluation of Fiber Orientation Using Polarized Light and Fuzzy Inference Hubertus Axer, Andreas Prescher, Diedrich Graf v. Keyserlingk Lehrstuhl für Anatomie I, RWTH Aachen Pauwelsstr. 30, 52057 Aachen, Germany Telephone: ++49 241 8089100 Fax: ++49 241 8888 431 E-mail:
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ABSTRACT: Polarization microscopy was used to investigate different kinds of fibers. One example is the localisation of central nervous fiber tracts in the human brain stem, the other is the inclination of the collagen fibers in the linea alba of the abdominal wall. Nine polarization pictures under different azimuths (0° - 80°) were used to draw conclusions about the inclination of the fibers. Each point in the sample was represented by a pixel, and each pixel was characterised by a set of nine intensity values representing the different azimuths. The peak intensity was classified by the linguistic variable intensity and the number of intensities, which were higher than a treshold value, was classified with the linguistic variable peak-width. The combination of both linguistic variables lead to the classification of each pixel according to the inclination of the fibers at this point. Four classes of inclination of the fibers (flat to steep) could be visualised by different greyscales. The resulting map of fiber inclination corresponded well to anatomical knowledge independent from the kind of investigated fibers (nerves or collagen).
KEYWORDS: fuzzy logic, imaging, polarization microscopy, central nervous fibers, brain stem, collagen fibers, linea alba
INTRODUCTION Fibers are of great interest in human anatomy. Central nervous fibers are collected in bundles or fiber tracts, which interconnect brain regions and form neuronal networks. Interruption of such fiber tracts in the brain may produce severe deficits like aphasia or hemiplegia. A primary interest in neuroanatomy is to distinguish different fiber tracts and to describe them, because they represent different functional tasks. For clinical purposes it is most important to visualise central nervous fiber tracts in imaging procedures like magnetic resonance tomography (Peled et al. 1998). But also other kinds of fibers are of interest. The organisation and structure of collagen in the tissue correspond to the physical stress which has to be resisted by the tissue. On the other hand the knowledge about the arrangement of collagen in the abdominal wall influences the operative technique used to open the peritoneal cave (Rizk 1980). Nevertheless in a histological preparation an automatic analysis of inclination of every kind of fiber is difficult to assess. The information of the orientation of the fibers is a threedimensional information contained in the depth of a sample, which has to be transferred to twodimensional pictures. Our intention was to analyse histological samples regarding to the inclination of the fibers. Therefore polarization microscopy was used. Normal light can be polarized when it passes through a polarization filter (polarizer). Then the optically polarized light passes through the sample and into a second polarizer (analyzer), that polarizes light in a perpendicular plane with respect to the first polarizer. Birefringence is able to twist some of the light so that it can pass through the analyzer and can be imaged. The orientation of the fibers influences the transmission of plane-polarized light at different velocities at different azimuths. Birefringence is a phenomenon, which is due to highly ordered molecules as proteins in collagen or radially oriented lipids in myelin sheaths of nervous fibers. Because the presence of birefringence indicates polarity and order, it can be used to detect areas of different orientations of the fibers. It has been known for over 100 years that the myelin sheath of nervous fibers is birefringent (Klebs 1865, Schmidt 1923, 1924, Schmitt 1936, Kretschmann 1967, Wolman 1975). Polarization microscopy can be used to visualise long fiber tracts in the brain (Fraher et al. 1970, Miklossy et al. 1991). Collagen fibers on the other hand also show birefringent features. Specificity for collagen may be obtained by staining the samples with picrosirius red (Junqueira et al. 1979).
Especially parallel, horizontally cut fibers give a bright signal at a special azimuth whereas the signal decreases after rotation of 45°. That means that there is a peak of brightness under rotation of the polars. The steeper these fiber tracts are, the less bright this peak is. If the fibers are cut transversely then there is no peak, and the brightness does not change under rotation. Thus different fibers of different orientation and order produce areas of different brightness. The information about fiber inclination is contained in the sequence of all pictures produced under rotation of the polars or under rotation of the sample. Our intention was to find a method to interpret this sequence automatically and draw a map of the fiber inclination in the sample. Because the different intensities can be linguistically characterised as dark to bright, a procedure using fuzzy logic was obvious (Zimmermann 1996, Tizhoosh 1998).
METHODS
Figure 1: A The linguistic variable intensity. B The linguistic variable peak-width. C Important parameters: brightest value and peak width.
Four human cadaver brains were fixed in 4% formalin solution. The brain stems of these brains were cut horizontally at the level of the pons. The samples were sectioned on a freezing microtome at 60 µm. The sections were serially collected and coverslipped without staining procedure. For analysis of the collagen fibers the abdominal wall of a human cadaver was fixed in 4% formalin solution. The abdominal wall was cut horizontally at the middle line (perpendicular to the linea alba). The samples were sectioned on a freezing microtome at 40 µm. Afterwards the slices were stained with picrosirius red (sirius red F3B, direct red 80, CI number 35780; Aldrich Chemie, Steinheim, Germany). The staining protocol was as follows: 2 hours in 70% ethanol, 10 min. H2O-rinse, 90 min. picrosirius red (0.1 g sirius red F3B per 100 ml saturated aqueous picric acid), ascending ethanol solutions 70% - 100%, and 15 min. xylol. Afterwards the samples were coverslipped. The slices were placed between two rotatable crossed polarizing filters and illuminated with light. Digitalisation of the slices were performed with the monochrome camera Sony XC 75-CE which was connected to a personal computer equipped with a frame grabber card. The software used was OPTIMAS 4.10. This way greyscale pictures could be achieved. The crossed polars can be rotated without changing the orientation of the sample. So homologous pixels in the pictures under different rotation angles of the polars belong to the same point in the sample. Each sample produced nine different pictures under nine rotation angles (azimuths) from 0° to 80°. Thus a set of nine values of intensity under the different azimuths was assigned to each point in the sample. The greyscale intensities range from 0 to 255 and at first these intensities were normalised by division through 255.
Ax,y = { intensityx,y(0°), intensityx,y(10°), .. , intensityx,y(80°) } The nine values of intensity contain information about the orientation of the fibers at this point. The aim of this study was to classify the inclination of fibers in polarized light microscopic images. The most important information in the nine intensity values is contained in two parameters: One parameter should be the brightest intensity. The peak intensity will be higher the more flat and will be less the more steep the fibers run. The linguistic variable intensity was defined to characterise the peak intensity (Fig. 1A). Four different classifications of intensity were named as dark, less dark, less bright and bright. On the other hand the flatter the fibers are the more accentuated the peak will be. So another interesting parameter should be the width of the peak of the intensities measured above a treshold value (Fig. 1C). This second parameter is defined as the number of intensity values which are higher than the treshold value (in this case 0.6). The number can only reach between 0 and 9 and the linguistic variable peak-width was defined to classify the peak width (Fig. 1B) as none, few and many. A truth table was defined to classify the inclination of the fibers according to these two linguistic variables (table I). The table contains such rules like: if the highest intensity is bright and the peak width is few then the inclination of the fibers must be flat. This rule can be processed as µ flat = min ( µ bright, µ few ). Defuzzification will be done by searching the rule with the highest membership function and the pixel will be classified as flat, less flat, less steep or steep, which can be visualised as different colours (or greyscales). peak width\intensity none few many
dark no fibers no fibers artefact
less dark steep less steep less steep
less bright less steep less flat less flat
bright artefact flat flat
Table I: Truth table
RESULTS
Figure 2: Inclination map of the collagen fibers in the linea alba (arrow). Fig. 2 shows a result of mapping of the orientation of collagen fibers. The picture shows a section transverse to the linea alba (Fig. 2 arrow). The linea alba is a tendineous raphe or cord seen along the middle line of the abdominal wall. It consists of collagen fibers which close the ventral part of the abdominal wall. The inclination map demonstrates that in the middle part of the linea alba most fibers are cut horizontally (flat), whereas at the ventral and dorsal border of the linea alba many fibers are characterised as less steep. On the other hand, Fig. 3 shows some representative results of fiber mapping in the central nervous system. In the pons several clinically important fiber tracts were identified. In the base of the pons two main fiber systems traverse. One is the pyramidal tract which runs to the spinal cord. The pyramidal tract fibers are cut transversely (Fig. 3F) and they intermingle with horizontally cut pontocerebellar fibers (Fig. 3E). Fibers of the pyramidal tract system are classified as steep and the pontocerebellar fibers as flat. These two different fiber tracts could not be distinguished at only one of the original polarization images (Fig. 3 left picture). At the sides of the basis pontis the pontocerebellar fibers are collected in the pedunculus cerebellaris medius (Fig. 3G). The black isles between the pontocerebellar fibers are isles of grey substance, the nuclei ponti. Additionally the pedunculus cerebellaris superior is a dominant fiber tract (Fig. 3B).
Moreover, several clinically important fiber bundles could be visualised clearly: The fasciculus longitudinalis medialis (Fig. 3A) is involved in conjugated eye movements. The lemniscus lateralis (Fig. 3C) is a fiber bundle involved in hearing, and the lemniscus medialis and the fasciculus anterolateralis (Fig. 3D) are important for sensibility of the trunk and the extremities.
Figure 3: Inclination map of the nervous fibers in the pons.
DISCUSSION The combination of nine polarization pictures of one sample under different azimuths allows to draw conclusions about the inclination of the fiber tracts. The results achieved by the demonstrated fuzzy method correspond well to the known anatomical structure of these regions: The section through the pons gives an overview over the important fiber tracts, and these correspond to anatomical textbooks (v. Keyserlingk 1993, Niewenhuis et al. 1988). But the information contained in these maps of central nervous fiber tracts are not only useful for segmentation of different tracts, they provide additional information about the inclination of these. The information about the orientation of the fibers is contained in the depth of the sample and the polarization microscope produces pictures which are summation of birefringent features of the sample over the whole depth. The correctness of the results could be evaluated with confocal laser scanning microscopy. The fluorescence marker DiI (1,1’-dilinoleyl-3,3,3’,3’-tetramethylindocarbo-cyanine perchlorate) is able to stain nervous fibers. This way the fiber architecture of these regions can be visualised in detail (Axer et al. 1998). Nevertheless this confocal procedure is very time consuming. To achieve a map to overview the central nervous fiber tracts a method is needed, which is fast and easily applicable. The presented fuzzy procedure could be one possibility to do this. Moreover the method is able to investigate other kinds of fibers. The collagen fibers in the linea alba were histologically prepared in a totally different way, but the fuzzy procedure for analysis of the fiber inclination is the same as for central nervous fibers. The results demonstrate that in the linea alba the collagen fibers have different characteristic orientations. In the middle part the collagen fibers run transversely whereas the fibers at the ventral and at the dorsal part of the linea alba run more obliquely. The directions of the collagen fibers represent the directions of the abdominal muscles (m. obliquus ext., m. obliquus int., m. transversus abdominis) (Rizk 1980). The resulting maps of fiber inclinations may be used in different ways. One interesting possibility is to use the classification of pixels according to fiber inclination for morphometrical purposes. It is a procedure to distinguish different fiber tract systems and may be used to calculate values of areas, which are occupied by the different fiber tracts.
Another possibility may be to map serial slices of the brain in order to perform threedimensional reconstructions of these fiber tracts. This approach would lead to 3D-anatomic atlasses. Polarized light microscopy is able to detect much more other birefringent tissue components such as muscles (Jouk et al. 1995), elastin, bone and dentin, amyloid, extraneous artificially introduced materials or pathologic depositions of lipids (Wolman 1974). This demonstrates a wide field of possible applications for the presented method.
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