Characterisation of congenital nystagmus waveforms in terms of periodic orbits

Because the oscillatory eye movements of congenital nystagmus vary from cycle to cycle, there is no clear relationship between the waveform produced and the underlying abnormality of the ocular motor system. We consider the durations of successive cycles of nystagmus which could be (1) completely determined by the lengths of the previous cycles, (2) completely independent of the lengths of the previous cycles or (3) a mixture of the two. The behaviour of a deterministic system can be characterised in terms of a collection of (unstable) oscillations, referred to as periodic orbits, which make up the system. By using a recently developed technique for identifying periodic orbits in noisy data, we find evidence for periodic orbits in nystagmus waveforms, eliminating the possibility that each cycle is independent of the previous cycles. The technique also enables us to identify the waveforms which correspond to the deterministic behaviour of the ocular motor system. These waveforms pose a challenge to our understanding of the ocular motor system because none of the current extensions to models of the normal behaviour of the ocular motor system can explain the range of identified waveforms.

[1]  R. A. Clement,et al.  Dynamical systems analysis: a new method of analysing congenital nystagmus waveforms , 1997, Experimental Brain Research.

[2]  Louis F. Dell'Osso,et al.  A normal ocular motor system model that simulates the dual-mode fast phases of latent/manifest latent nystagmus , 2001, Biological Cybernetics.

[3]  B. Nevitt,et al.  Coping With Chaos , 1991, Proceedings of the 1991 International Symposium on Technology and Society - ISTAS `91.

[4]  F. A. Seiler,et al.  Numerical Recipes in C: The Art of Scientific Computing , 1989 .

[5]  David S. Broomhead,et al.  Modelling of congenital nystagmus waveforms produced by saccadic system abnormalities , 2000, Biological Cybernetics.

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

[7]  C. Harris Problems in modelling congenital nystagmus: Towards a new model , 1995 .

[8]  Frank Moss,et al.  Low-Dimensional Dynamics in Sensory Biology 1: Thermally Sensitive Electroreceptors of the Catfish , 1997, Journal of Computational Neuroscience.

[9]  Grebogi,et al.  Detecting unstable periodic orbits in chaotic experimental data. , 1996, Physical review letters.

[10]  Celso Grebogi,et al.  Extracting unstable periodic orbits from chaotic time series data , 1997 .

[11]  R. B. Daroff,et al.  Congenital nystagmus waveforms and foveation strategy , 1975, Documenta Ophthalmologica.

[12]  P Dassonville,et al.  Oculomotor localization relies on a damped representation of saccadic eye displacement in human and nonhuman primates , 1992, Visual Neuroscience.

[13]  Robert W. Kentridge,et al.  Eye movement research : mechanisms, processes and applications , 1995 .

[14]  W. Press,et al.  Numerical Recipes in C++: The Art of Scientific Computing (2nd edn)1 Numerical Recipes Example Book (C++) (2nd edn)2 Numerical Recipes Multi-Language Code CD ROM with LINUX or UNIX Single-Screen License Revised Version3 , 2003 .

[15]  R Reccia,et al.  Computer analysis of ENG spectral features from patients with congenital nystagmus. , 1990, Journal of biomedical engineering.

[16]  Nicholas B. Tufillaro,et al.  Experimental approach to nonlinear dynamics and chaos , 1992, Studies in nonlinearity.

[17]  Frank Moss,et al.  Characterization of low-dimensional dynamics in the crayfish caudal photoreceptor , 1996, Nature.

[18]  L. Optican,et al.  A hypothetical explanation of congenital nystagmus , 1984, Biological Cybernetics.

[19]  Daniel M. Wolpert,et al.  Signal-dependent noise determines motor planning , 1998, Nature.

[20]  William H. Press,et al.  The Art of Scientific Computing Second Edition , 1998 .

[21]  E. Ott Chaos in Dynamical Systems: Contents , 1993 .

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

[23]  Richard V Abadi,et al.  Waveform characteristics in congenital nystagmus , 1987, Documenta Ophthalmologica.

[24]  Eric L. Schwartz,et al.  Computational Neuroscience , 1993, Neuromethods.

[25]  John Porrill,et al.  Pseudo-inverse control in biological systems: a learning mechanism for fixation stability , 1998, Neural Networks.

[26]  R D Yee,et al.  A study of congenital nystagmus , 1976, Neurology.

[27]  Auerbach,et al.  Exploring chaotic motion through periodic orbits. , 1987, Physical review letters.

[28]  R. V. Abadi,et al.  Harmonic analysis of congenital nystagmus waveforms , 1991 .

[29]  Frank Moss,et al.  Low-Dimensional Dynamics in Sensory Biology 2: Facial Cold Receptors of the Rat , 1999, Journal of Computational Neuroscience.

[30]  William H. Press,et al.  Numerical recipes in C (2nd ed.): the art of scientific computing , 1992 .

[31]  M L Spano,et al.  Surrogates for finding unstable periodic orbits in noisy data sets. , 1999, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[32]  L. Osso CONGENITAL NYSTAGMUS WAVEFORMS AND FOVEATION STRATEGY , 1975 .

[33]  F A Miles,et al.  The neural processing of 3‐D visual information: evidence from eye movements , 1998, The European journal of neuroscience.