Abstract
Purpose: :
To better understand the physiology underlying the spontaneous vertical eye movements seen during fixation.
Methods: :
We studied binocularly recorded eye movements and pupil size in six normal volunteers at 240 Hz using ISCAN ETL-500 Infrared Video graphic Binocular Recording system (Iscan, Inc., Burlington, Massachusetts). Subjects were instructed to fixate a point presented in the primary position for 40 seconds. A fake eye was recorded under 4 different conditions: once while being held up with one hand, once held with two hands, once on a table and once on the floor to simulate different degrees of movement. Blinks were removed. A 7 column time shifted matrix (A) was generated for each data set using a time delay of 25 seconds between each column and a singular value decomposition was performed. The singular values (S) from the fake eye were compared to those of the subjects’datasets. A state portrait using the first two vectors of the transformed matrix was plotted for each subject and for each tracing done on the fake eye.
Results: :
Plots of eye movements vs. time for subjects demonstrate non-periodic waves (oscillations) while plots of the fake eye had the appearance of noise. The normalized mean singular values from the S matrix for the fake eye averaged [1.0000, 0.0012, 0.0011, 0.0006, 0.0005, 0.0005, 0.0004]. Only the first singular value differs from the others (p<0.05). The normalized mean singular values for the subjects averaged [1.0000, 0.3312, 0.2188, 0.1588, 0.1292, 0.1157, 0.1108]. The first three singular values differ significantly from each other and the rest of the values by Student’s t-test (p<0.05). A phase portrait of the first vs. second vector from the transformed matrix of all subjects showed an attractor with a complex pretzel shape. A similar plot from the fake eye trials formed a tight ball with no consistent pattern.
Conclusions: :
The uniqueness of the first three vectors of the subject group supports the hypothesis that the waves of eye movements vs. time originate from a nonlinear deterministic dynamic system. The non-repeating pattern of the attractor suggests that this dynamic system may be chaotic. These results indicate that proper modeling of the system requires a multivariable nonlinear system of differential equations.
Keywords: pupil • eye movements • ocular motor control