Richard A. Clement

Modelling of congenital nystagmus waveforms produced by saccadic system abnormalities.

Abstract. Models of the mechanisms of normal eye movements are typically described in terms of the block diagrams which are used in control theory. An alternative approach to understanding the mechanisms of normal eye movements involves describing the eye movement behaviour in terms of smooth changes in state variables. The latter approach captures the burst cell firing against motor error (difference between target gaze angle and current gaze angle) phase plane behaviour which is found experimentally and facilitates the modelling of variations in burst cell behaviour. A novel explanation of several types of congenital nystagmus waveforms is given in terms of a saccadic termination abnormality.

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.

Nonlinear time series analysis of jerk congenital nystagmus

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 recorded jerk CN waveforms, and also to simulated jerk waveforms produced by an established model in which the oscillations are a consequence of an unstable neural integrator. The results of the 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.

Fixed point analysis of nystagmus

Motor disorders frequently contain a rhythmic component, but the associated oscillations are not usually precisely periodic. This lack of strict periodicity can make it difficult to identify the effects of experimental manipulations on the oscillation. In this report, we describe the application of a numerical technique for identifying fixed points of a nonlinear map to the recovery of underlying periodicities of the eye movement disorder of nystagmus. The technique is illustrated by application to two different types of nystagmus. In addition we use a local analysis of the behaviour at the fixed points to distinguish between different bifurcations in the two examples with changes in gaze angle. We conclude that the technique reveals consistent effects of experimental manipulations, which may be useful for quantitative characterisation of experimental and therapeutic manipulations of motor disorders.

Simulation of oculomotility in Craniosynostosis patients.

Craniosynostosis syndromes can be associated with missing extraocular muscles, or muscles with abnormal insertions, and so provide useful test cases for assessing our understanding of the mechanics of the extraocular muscles. Patient with craniosynostosis syndromes often show eye movements in which a horizontal movement by one eye is accompanied by upshoot or downshoot in the other eye.An hypothesis which has been put forward to explain these movements is that the muscles in the patients are excyclorotated and that the upshoots and downshoots follow directly from the application of Hering’s law of equal innervation. We modelled the mechanics of the excyclorotated muscles and verified this hypothesis. However, excyclorotation of the orbit often occurs in combination with anomalous muscle anatomy in craniosynostosis syndromes. In keeping with this finding, we have found that surgical transposition of the rectus muscles is insufficient by itself to correct the anomalous eye movements, but that transposition in combination with weakening of the obliques is effective.

Levels of fixation

Objects are best seen when their images fall on the fovea and are held relatively steady. If retinal image slip velocities exceed 4 deg/sec, blur and oscillopsia occur. On the other hand, if the image velocities are dramatically reduced or even stabilized, then there is fragmentation and the eventual perceptual loss of the object of regard. Consequently, the phrase “relatively steady” is usefully defined by a range of retinal slip velocities. The search for how fixation is kept in check has led to the finding that there are a number of important control systems in operation. Their number and operation depend greatly on the nature of gaze (primary, secondary, or tertiary) and also whether the individual is seated in a laboratory with teeth embedded in a slab of wax viewing a single target or is moving freely in a multi-textured natural environment. For example, retinal image slip velocities when the head is stabilized using a bite-bar are usually less than 0.25 deg/sec, but these can rise to several degrees per second when the head is free to move (Figure 11.1). Sometimes these control systems do not function efficiently and on occasion can even fail catastrophically. In this case, steady fixation breaks down and a variety of ocular intrusions or oscillations occur. The purpose of this chapter is to first review the underlying mechanisms that are responsible for steady gaze and second to describe the levels of fixation instabilities that can occur when things go wrong.

Stability of the saccadic oculomotor system

A variety of different types of instability has been found in the saccadic system of humans. Some of the instabilities correspond to clinical conditions, whereas others are inherent in the normal saccadic system. How can these instabilities arise within the mechanism of normal saccadic eye movements? A physiologically-based model of the saccadic system predicts that horizontal saccadic oscillations will occur with excessive mutual inhibition between the left and right burst cells and with underaction of the pause cells. The amplitudes and frequencies of the oscillations had ranges of 0–6° and 6–20 cycles per second, respectively. Application of stability analysis techniques to the model reveals that development of the oscillations can be explained by the Hopf bifurcation mechanism. Future development of this approach will involve classifying pathological instabilities of the saccadic system according to the bifurcation involved in their generation.

Periodic orbit analysis reveals subtle effects of atropine on epileptiform activity in the guinea-pig hippocampal slice

Epileptiform activity is a state often induced in vitro in order to study seizures and antiepileptic/anticonvulsant drugs. Traditional methods of evaluating drug effects have commonly relied upon measuring changes in the frequency and duration of such events. We have used a recently developed mathematical technique based on periodic orbit analysis to investigate the effect of atropine (a muscarinic antagonist) on epileptiform activity induced by soman (an irreversible acetylcholinesterase inhibitor), 4-aminopyridine (a K+ channel blocker) and 8-cyclopentyl-1,3-dipropylxanthine (an adenosine A1 receptor antagonist) in the guinea-pig hippocampal slice. This technique showed that significant changes in periodic orbits can occur without an accompanying change in burst rate. These results suggest that periodic orbit analysis may be useful in detecting and predicting novel actions of anticonvulsant drugs.

A new framework for investigating both normal and abnormal eye movements

Any comprehensive framework for understanding eye movements has to include both normal and abnormal eye movement behaviour. One approach which is applicable to the entire range of oculomotor behaviour is provided by the techniques of nonlinear dynamics. The stability of models of the oculomotor system can be analysed in terms of the characteristics of their fixed points and periodic orbits, and the method of delays can be used to recover such parameters from measurements of eye position. Within this framework, quantitative comparisons can be made between the predictions of different models, and both normal and clinical eye movement recordings.

Classification of infantile nystagmus waveforms

Classification of infantile nystagmus waveforms is an important problem because the characteristic waveforms can be used to distinguish between infantile and acquired nystagmus. A clear description of the nystagmus is also a necessary first stage in understanding its origin. Currently infantile nystagmus waveforms are classified into at least 12 different types. In this study we analyse a database of nystagmus recordings in order to investigate if this classification can be simplified. Application of principal components analysis revealed that 96.9% of the variance of the waveforms is described by a linear sum of two component waveforms. The components consist of sawtooth and pseudocycloid waveforms that account for 78.7% and 18.2% of the variance respectively for the most common single cycle waveforms. This simplified description of infantile nystagmus highlights the importance of identifying the origin of the jerk component and its synchronisation with the pseudocycloid component for the characterisation and treatment of the nystagmus.