Nonlinear dynamic systems evaluation of `rhythmic' eye movements (Optokinetic Nystagmus)

The last decade has seen a surge in the study of nonlinear dynamical behavior in physiologic systems. In this paper, some of the computational techniques most commonly used to investigate the nonlinear dynamics of these systems are described. Applications to eye movement analysis are included, including the validation of a mathematical model of optokinetic nystagmus (OKN) eye movements. OKN appears to have some nonlinear and deterministic component, along with significant randomness. Fast phase starting and ending points are somewhat predictable (deterministic), while so-called 'exceptional events' analysis shows that they also have a large random component. Surrogate data methods suggest that the population of slow and fast phases in OKN is more important than any specific relationship between adjacent slow and fast phases. Analysis of a statistical model for fast phase intervals indicates that the model data are slightly more random than the actual OKN.

[1]  Theiler,et al.  Spurious dimension from correlation algorithms applied to limited time-series data. , 1986, Physical review. A, General physics.

[2]  D. Ruelle,et al.  Ergodic theory of chaos and strange attractors , 1985 .

[3]  D. Ruelle,et al.  Fundamental limitations for estimating dimensions and Lyapunov exponents in dynamical systems , 1992 .

[4]  Gerd Pfister,et al.  Comparison of algorithms calculating optimal embedding parameters for delay time coordinates , 1992 .

[5]  A. Goldberger,et al.  Loss of 'complexity' and aging. Potential applications of fractals and chaos theory to senescence. , 1992, JAMA.

[6]  G. McGuire,et al.  Recurrence matrices and the preservation of dynamical properties , 1997 .

[7]  M. Shelhamer.  APPROACHES TO THE NONLINEAR DYNAMICS OF REFLEXIVE EYE MOVEMENTS , 1996 .

[8]  H. Schuster,et al.  Proper choice of the time delay for the analysis of chaotic time series , 1989 .

[9]  Albano,et al.  Filtered noise can mimic low-dimensional chaotic attractors. , 1993, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[10]  Benoit B. Mandelbrot,et al.  Fractal Geometry of Nature , 1984 .

[11]  D. T. Kaplan,et al.  Exceptional events as evidence for determinism , 1994 .

[12]  Farmer,et al.  Predicting chaotic time series. , 1987, Physical review letters.

[13]  P. Grassberger,et al.  NONLINEAR TIME SEQUENCE ANALYSIS , 1991 .

[14]  P. Grassberger,et al.  Measuring the Strangeness of Strange Attractors , 1983 .

[15]  George Sugihara,et al.  Nonlinear forecasting as a way of distinguishing chaos from measurement error in time series , 1990, Nature.

[16]  D. T. Kaplan,et al.  Aging and the complexity of cardiovascular dynamics. , 1991, Biophysical journal.

[17]  Mark J Shelhamer,et al.  Using measures of nonlinear dynamics to test a mathematical model of the oculomotor system , 1997 .

[18]  D. Ruelle,et al.  The Claude Bernard Lecture, 1989 - Deterministic chaos: the science and the fiction , 1990, Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences.

[19]  H.L. Galiana.  A nystagmus strategy to linearize the vestibulo-ocular reflex , 1991, IEEE Transactions on Biomedical Engineering.

[20]  F. Takens.  Detecting strange attractors in turbulence , 1981 .

[21]  C L Webber,et al.  Dynamical assessment of physiological systems and states using recurrence plot strategies. , 1994, Journal of applied physiology.

[22]  David Ruelle,et al.  Deterministic chaos: the science and the fiction , 1995 .

[23]  A. Passamante,et al.  Using higher-order correlations to define an embedding window , 1991 .

[24]  D. Ruelle,et al.  Recurrence Plots of Dynamical Systems , 1987 .

[25]  A. Provenzale,et al.  Finite correlation dimension for stochastic systems with power-law spectra , 1989 .

[26]  James Theiler,et al.  Estimating fractal dimension , 1990 .

[27]  Schwartz,et al.  Singular-value decomposition and the Grassberger-Procaccia algorithm. , 1988, Physical review. A, General physics.

[28]  J E Skinner,et al.  A reduction in the correlation dimension of heartbeat intervals precedes imminent ventricular fibrillation in human subjects. , 1993, American heart journal.

[29]  Andreas S. Weigend,et al.  Time Series Prediction: Forecasting the Future and Understanding the Past , 1994 .

[30]  William Sulis,et al.  Nonlinear Dynamics in Human Behavior , 1996 .

[31]  Mark Shelhamer,et al.  On the correlation dimension of optokinetic nystagmus eye movements: computational parameters, filtering, nonstationarity, and surrogate data , 1997, Biological Cybernetics.

[32]  James Theiler,et al.  Testing for nonlinearity in time series: the method of surrogate data , 1992 .

[33]  Robert M. May,et al.  Simple mathematical models with very complicated dynamics , 1976, Nature.

[34]  M. Shelhamer,et al.  Prediction of the sequence of optokinetic nystagmus eye movements reveals deterministic structure in reflexive oculomotor behavior , 1998, IEEE Transactions on Biomedical Engineering.

[35]  J. Elsner,et al.  Nonlinear prediction as a way of distinguishing chaos from random fractal sequences , 1992, Nature.

[36]  James M. Bower,et al.  Computational Neuroscience: Trends in Research 1995 , 1996 .

[37]  Martin Casdagli,et al.  Nonlinear prediction of chaotic time series , 1989 .

[38]  James P. Crutchfield,et al.  Geometry from a Time Series , 1980 .

[39]  M. Shelhamer,et al.  Correlation dimension of optokinetic nystagmus as evidence of chaos in the oculomotor system , 1992, IEEE Transactions on Biomedical Engineering.