causing diplopia (double vision). The eyes rotate inward or outward to place the image on the fovea, which fuses the two images into one. This retinal disparity is ...
Interaction of Disparity and Accommodative Vergence Michele L. Kung1, Tara L. Alvarez1, John L. Semmlow2,3 1
Department of Biomedical Engineering, New Jersey Institute of Technology, Newark, NJ Department of Biomedical Engineering, Rutgers University, 3Department of Surgery, Bioengineering, Robert Wood Johnson Medical School – UMDNJ, New Brunswick, NJ
2
Abstract – To fixate on a target that moves from far to near, two systems become activated; accommodation and disparity vergence. The goal of this study is to investigate how these systems interact through a new signal-processing algorithm known as independent component analysis. Preliminary data suggest that three underlying neural subcomponents are present where the two components of disparity vergence initiate the movement and the accommodative portion is activated to facilitate the steady state portion of the response. I. INTRODUCTION A vergence eye movement is defined as the inward or outward turning of the eyes. Disparity vergence occurs when images fall on opposite sides of the fovea (part of retina), causing diplopia (double vision). The eyes rotate inward or outward to place the image on the fovea, which fuses the two images into one. This retinal disparity is one of the key inputs into the disparity vergence control system. Accommodative vergence is driven by blur to change the shape of the lens in the eye. We are studying the interaction between the disparity and accommodative vergence systems. This will lead to further insight of how the two systems interact. This information can be used to help people with accommodative and disparity dysfunction. Disparity vergence uses dual control to obtain both speed and accuracy. The disparity vergence system has been modeled using the Dual Mode Theory as a two-component system, an initiating and a sustaining component. The initiating component is a feed forward, open loop control system, which depicts the system’s speed. The sustaining component is a feedback, closed-loop control system, which depicts the system’s accuracy. This model has been validated by neurophysiological data, which shows burst and tonic cells exist in the vergence neural circuit [1-2]. The burst cells correlate to the feed forward or pulse portion of the vergence model and the tonic cells correlate to the feedback or step portion of the vergence model. It is hypothesized that there is a third feedback driven component from the accommodative vergence system. Our study builds upon the work of Hung and colleagues where they studied the difference between disparity vergence with constant accommodation and disparity vergence with a change in accommodation [3]. This group studied variance and showed that a significant amount of variance existed during the transient phase after response latency, which corresponds to the two components, found in disparity vergence. However, their key finding was in comparing disparity vergence with constant accommodation vs. disparity vergence with a change in accommodation. More variance
was found in the later part of the disparity vergence with a change in accommodation compared to disparity vergence with constant accommodation suggesting that accommodation is present during the later steady state portion of the response. II. METHODOLOGY The convergence movements made by the eyes were measured using the Skalar Iris model 6500, an infrared limbus-tracking device that was placed on the subject’s head. These movements were recorded at a rate of 200 Hz. The resolution of the eye movement monitor was 2 minute arc with a linearity of ± 25 degrees. Throughout the experiment, the data was collected from each eye independently. A five point calibration was performed by illuminating the targets (either light emitting diodes (LEDs), or the reflected oscilloscope lines) in a sequence and recording the voltage value at each position, then doing a regression analysis to determine a linear equation for the conversion. After calibration, subjects would push a trigger button to initiate an experiment and a random time delay occurred (either LEDs or oscilloscopes) to remove anticipation by the subject. Furthermore, the four and six degree steps were randomly selected by the computer to avoid subject prediction. These responses were recorded for three seconds and experiments occur in complete darkness where the subject only observed the presence of the targets. The apparatus for the oscilloscope set up (haploscope) is shown in Figure 1a. It consists of two partially reflective mirrors positioned 45 degrees to the subject’s line of sight, two oscilloscopes that provide the step stimulus, and a limbic tracking system, which collects the eye movements. Each oscilloscope emits a line stimulus towards the mirrors, which in effect produce two lines that the subject would fuse into single line. After the subject pushed the trigger, the two lines would move in a step manner. The subject would follow the stimulus and would once again fuse the lines. The oscilloscopes project targets at a constant focal length from the subject to stimulate disparity vergence while keeping accommodation constant. 2 Mirrors Oscilloscope 2
Oscilloscope 1
Left Eye
Right Eye
Figure 1a – Haploscope Set up
Initial Target A A
4 Degree Final Target
B
6 Degree Final Target
Left Eye
S.C
S.C
Right Eye
Figure 1b – 3D Target Set up For the 3D Target Set-Up shown in Figure 1b, the stimulus always began at the same initial position using an illuminated LED. The computer initiated the shutting off of the initial LED and the lighting of the next LED where subjects were asked to track the new target positioned along the midline of the subject as shown in Figure 1b. The LED’s provided real targets in 3-D space, which stimulates disparity vergence with a change in accommodation. PCA analysis has shown that two components account for more than 90% of the variability in convergence eye movements. Therefore, Independent Component Analysis (ICA) was run with two components. ICA is a more advanced signal processing technique compared to the one used by Hung et al. It is a linear transformation method in which the statistical dependence of the components is minimized. ICA was used as a blind source separation method, to separate the components of the response [4].
I.C. I.C.
C
D
S.C
I.C.
S.C
I.C.
X = As Where X is the response, A is the unmixing matrix, and S is the two components found in disparity vergence. This analysis used the “Fast ICA” program developed by the ICA group at the Helsinki University [5]. III. RESULTS Vergence data is the plotted as difference between the left eye and the right eye movements.
Figure 4 ICA on haploscope (A,B) and led (C,D) vergence data shown for 4(A,C) and 6 (B,D) degree. S.C. (sustaining component), and I.C. (initiating component) labeled.
Figure 4 shows the ICA of haploscope (top) and led (bottom) vergence data shown for 4 degree (left) and 6 degree (right). The labels S.C. (sustaining component), and I.C. (initiating component) represent the two components found in the disparity system. IV. DISCUSSION Preliminary data suggest the steady state response to be from one second to two seconds. We see in the figure 4 A, B (haploscope), the sustaining component for the disparity vergence response with constant accommodation maintains a flat step response during the steady state portion of the response. The step component for the disparity vergence response with non-constant accommodation does not maintain a flat step response during the steady state portion of Figure 2. haploscope vergence data. 4 degree and 6 degree shown. the response but instead decays as indicated by arrows Figure 2 is haploscope vergence data, which is disparity (shown in figure 4 C, D). Based on this preliminary data we speculate this deviation may be a result of the vergence with constant accommodation accommodative vergence response. REFERENCES
Figure 3. LED vergence data. 4 degree and 6 degree shown.
Figure 3 is LED vergence data, which is disparity vergence with a change in accommodation.
[1] Gamlin, P.D.R. and Mays, L.E., Dynamic Properties of Medial Rectus Motoneurons During Vergence Eye Movements J. Neurophy, 1992; 67(1): 64-74. [2] Mays, L.E., Porter, J.D., Gamlin, P.D.R., and Tello C.A., Neural Controlof Vergence Eye Movements: Neurons Encoding Vergence Velocity J Neurophy., 1986; 56(4): 1007-1021. [3] Hung, G.K., Semmlow J.L., Ciuffreda, K.J., Identification of Accommodative Vergence Contribution to the Near Response Using Response Variance Invest Ophthalmol Vis Sci, 1983; 24(6):772-777 [4] Hyvarinen, A, Karhunen J., and Oja E., Independent Component Analysis New York, John Wiley & Sons, Inc. 2001. [5] http://www.cis.hut.fi/projects/ica/fastica/fp.html
