Characterisation of congenital nystagmus waveforms in terms of periodic orbits

Clement, Richard A.; Whittle, J. P.; Muldoon, Mark; Abadi, Richard V.; Broomhead, D. S.; Akman, Ozgur E.

doi:10.1016/s0042-6989(02)00124-4

Cited by 20 publications

(15 citation statements)

References 20 publications

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“…The increase in d L comprises strong evidence against a limit cycle, and suggests a genuinely aperiodic system. This finding is consistent with a previous study which found evidence that the jerk CN attractor may contain several unstable periodic orbits (Clement et al, 2002c). Moreover, it implies that for a model to fully account for the data, it must result in a fast phase with greater complexity than a reinjection of the flow into the neighbourhood ofz, induced by a near-homoclinic orbit.…”

Section: Calculation Of Local Dimension Around the Jerk Cn Cyclesupporting

confidence: 92%

Nonlinear time series analysis of jerk congenital nystagmus

Akman

Broomhead

Clement³

et al. 2006

J Comput Neurosci

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Nonlinear dynamics provides a complementary framework to control theory for the quantitative analysis of the oculomotor control system. This paper presents a number of findings relating to the aetiology and mechanics of the pathological ocular oscillation jerk congenital nystagmus (jerk CN). A range of time series analysis techniques were applied to both recorded jerk CN waveforms and simulated waveforms produced by an established model in which the oscillations are a consequence of an unstable neural integrator. The results of the time series analysis were then interpreted within the framework of a generalised model of the unforced oculomotor system. This work suggests that for jerk oscillations, the origin of the instability lies in one of the five oculomotor subsystems, rather than in the final common pathway (the neural integrator and muscle plant). Additionally, experimental estimates of the linearised foveation dynamics imply that a refixating fast phase induced by a near-homoclinic trajectory will result in periodic oscillations. Local dimension calculations show that the dimension of the experimental jerk CN data increases during the fast phase, indicating that the oscillations are not periodic, and hence that the refixation mechanism is of greater complexity than a homoclinic reinjection. The dimension increase is hypothesised to result either from a signal-dependent noise process in the saccadic system, or the activation of additional oculomotor components at the beginning of the fast phase. The modification of a recent saccadic system model to incorporate biologically realistic signal-dependent noise is suggested, in order to test the first of these hypotheses.

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Section: Calculation Of Local Dimension Around the Jerk Cn Cyclesupporting

confidence: 92%

Nonlinear time series analysis of jerk congenital nystagmus

Akman

Broomhead

Clement³

et al. 2006

J Comput Neurosci

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“…In the last few years, however, there has been increasing interest in the use of nonlinear dynamics techniques to model oculomotor control, and to analyse eye movement time series [3], [37], [25], [18], [7], [20].…”

Section: Introductionmentioning

confidence: 99%

Eye movement instabilities and nystagmus can be predicted by a nonlinear dynamics model of the saccadic system

et al. 2005

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The study of eye movement control and oculomotor disorders has, for four decades, relied on control theoretic concepts for its theoretical foundation. This paper is an example of a complementary approach based on the theory of nonlinear dynamical systems. Recently, a nonlinear dynamics model of the saccadic system was developed, comprising a symmetric piecewise-smooth system of six first-order autonomous ordinary differential equations. A preliminary numerical investigation of the model revealed that in addition to generating normal saccades, it could also simulate inaccurate saccades, and the oscillatory instability known as congenital nystagmus (CN). By varying the parameters of the model, several types of CN oscillations were produced, including jerk, bidirectional jerk and pendular nystagmus.The aim of this study was to investigate the bifurcations and attractors of the model, in order to obtain a classification of the simulated oculomotor behaviours. The application of standard stability analysis techniques, together with numerical work, revealed that the equations have a rich bifurcation structure. In addition to Hopf, homoclinic and saddlenode bifurcations organised by a Takens-Bogdanov point, the equations can undergo nonsmooth pitchfork bifurcations and nonsmooth gluing bifurcations. Evidence was also found for the existence of Hopf-initiated canards. * Now at: Mathematics Institute, University of Warwick, Coventry CV4 7AL, UK 1The simulated jerk CN waveforms were found to correspond to a pair of post-canard symmetry-related limit cycles, which exist in regions of parameter space where the equations are a slow-fast system. The slow and fast phases of the simulated oscillations were attributed to the geometry of the corresponding slow manifold. The simulated bidirectional jerk and pendular waveforms were attributed to a symmetry invariant limit cycle produced by the gluing of the asymmetric cycles.In contrast to control models of the oculomotor system, the bifurcation analysis places clear restrictions on which kinds of behaviour are likely to be associated with each other in parameter space, enabling predictions to be made regarding the possible changes in the oscillation type that may be observed upon changing the model parameters. The analysis suggests that CN is one of a range of oculomotor disorders associated with a pathological saccadic braking signal, and that jerk and pendular nystagmus are the most probable oscillatory instabilities. Additionally, the transition from jerk CN to bidirectional jerk and pendular nystagmus observed experimentally when the gaze angle or attention level is changed is attributed to a gluing bifurcation. This suggests the possibility of manipulating the waveforms of subjects with jerk CN experimentally to produce waveforms with an extended foveation period, thereby improving visual resolution.

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“…CGN appears usually in early infancy and results in degrade vision and illusory motion of the visual field. CGN is a symptom of neurological disorder but its pathogenesis is still unknown [3,8]. The optokinetic nystagmus is characterized as involuntary eye movement response when moving stimulus in a large visual field is presented [11].…”

Section: Introductionmentioning

confidence: 99%

Fuzzy Approach to Saccades Detection in Optokinetic Nystagmus

Czabański

Pander

Przybyła

2014

Advances in Intelligent Systems and Computing

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Abstract. The electronystagmography (ENG) based analysis of the nystagmus provides valuable information about condition of the human vision system. The typical ENG signal corresponding to nystagmus has a form of a saw tooth waveform with slow and fast (saccade) components. The slow component is related to the stimulus while the saccade refers to a rapid reset of eye position. The accurate detection of saccadic eye movements is inevitable when determining the nystagmus characteristic. The paper presents saccades detection method that is based on fuzzy clustering. The proposed procedure is computationally efficient and allows for precise determination of the saccade position in the time domain.

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Characterisation of congenital nystagmus waveforms in terms of periodic orbits

Cited by 20 publications

References 20 publications

Nonlinear time series analysis of jerk congenital nystagmus

Nonlinear time series analysis of jerk congenital nystagmus

Eye movement instabilities and nystagmus can be predicted by a nonlinear dynamics model of the saccadic system

Fuzzy Approach to Saccades Detection in Optokinetic Nystagmus

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