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M. L. Rosenberg, V. Punia, R. Bitra, M. Kroll; The Spontaneous Vertical Movements Seen During Fixation Are Chaotic. Invest. Ophthalmol. Vis. Sci. 2010;51(13):2538.
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© ARVO (1962-2015); The Authors (2016-present)
To better understand the physiology underlying the spontaneous vertical eye movements seen during fixation.
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.
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.
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.
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