Dynamical systems analysis: a new method of analysing congenital nystagmus waveforms

Abstract

Congenital nystagmus is an oculomotor disorder in which fixation is disrupted by rhythmical, bilateral involuntary oscillations. Clinically these eye movements have been described with some degree of success in terms of their peak-to-peak amplitude, frequency, mean velocity and waveform shape. However, it has not proved possible to diagnose any underlying pathology from the nystagmus characteristics. Here, we propose a new approach to understanding the nystagmus using dynamical systems theory. Our approach is based on the use of delay embedding techniques, which allow one to relate a time series of scalar observations to the state space dynamics of the underlying dynamical system. Using this approach we quantify the dynamics of the nystagmus in the region of foveation and present evidence to suggest that it is low-dimensional and deterministic. Our results put new constraints on acceptable models of nystagmus and suggest a way to make a closer link between data analysis and model development. This approach raises the hope that techniques originally developed to stabilise chaotic systems, by using small perturbations, may prove useful in the control of nystagmus.