Spectral analysis of dual jerk waveforms in congenital nystagmus

Congenital nystagmus (CN) is a disorder of the ocular motility characterized by oscillatory eye movements preventing the correct fixation of a target. Many typical waveforms of eye position recordings have been recognized and classified in the literature: in jerk CN a slow phase eye movement is followed by a fast phase, giving rise to a typical saw-tooth waveform, while in pendular CN the eyes exhibit a periodic motion, giving rise to an approximately sinusoidal waveform. Dual jerk waveforms seemed to show small, rapid oscillations superimposed on a jerk-like waveform, thus being originary classified as a mixture of jerk and pendular CN. On the contrary, a theoretical model of CN has appeared recently, which suggests a possible interpretation of the small amplitude oscillations in dual jerk waveforms as consecutive pieces of growing and decaying exponentials.By spectral analysis of dual jerk waveforms in a number of patients with CN, we show that the oscillations are truly sinusoidal in nature, thus suggesting the possibility of a different explanation of dual jerk waveforms in CN.Preliminary results of this work were presented at XIV ICMP —International Congress of Medical Physics, Espoo, Finland, 11–16 August 1985     

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

The study of eye movements and oculomotor disorders has, for four decades, greatly benefitted from the application of control theoretic concepts. 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. The 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.     

A hypothetical explanation of congenital nystagmus

Congenital nystagmus (CN) is a conjugate, rhythmic, eye movement disorder characterized by a wide variety of waveforms ranging from jerk to pendular types. No detailed mechanisms have been proposed to explain the generation of the CN wave-form This paper proposes a hypothetical mechanism for CN, and shows with computer simulations that a model based on this hypothesis can account for a variety of disparate waveforms. The basis of this model is a gaze-holding network, or neural integrator, that has both position and velocity feedback loops. The signals carried in these loops could arise from either afference or efference. In normal subjects, the position feedback would be positive and the velocity feedback would be negative. Both would help to increase the time constant of an imperfect neural integrator in the brain stem. We propose that in patients with CN the sign of the velocity pathway is reversed, making the neural integrator unstable. This instability could manifest as many different CN waveforms, depending on the direction and velocity of post-saccadic ocular drift and actions of nonlinearities within the position and velocity feedback loops. Thus a single underlying abnormality may be responsible for a variety of CN 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. Action Editor: Peter Latham     

Bifurcation theory explains waveform variability in a congenital eye movement disorder

In dynamical systems, configurations that permit flexible control are also prone to undesirable behavior. We study a bilateral model of the oculomotor pre-motor network that conforms with the neuroanatomical constraint that brainstem neurons project to cerebellar Purkinje cells on both sides, but Purkinje cells project back to brainstem neurons on the same side only. Bifurcation analysis reveals that this network asymmetry enables flexible control by the cerebellum of brainstem network dynamics, but small changes in connection pattern or strength lead to behavior that is unstable, oscillatory, or both. The model produces the full range of waveform types associated with the hereditary eye movement disorder know as congenital nystagmus, and is consistent with findings linking the disorder with abnormal connectivity or limited plasticity in the cerebellum.     

Foveation period and waveforms of congenital ocular nystagmus

Normal visual acuity requires a stationary retinal image on the fovea. If fixation instabilities cause movement of the retinal image across the fovea for a few degrees, visual acuity is diminished. Nystagmus as the fixation instability, consequently, may impair vision. Period of foveation is the area in the wave form, i.e. a brief period of time when the eye is still and is pointed at the object of regard. At this period eye velocity is at a minimum and visual acuity is the best. In the children with congenital ocular nystagmus, using usual clinical equipment (TC 1.0 and TC 0.3 s), was performed electronystagmography (ENG) and analysis of the obtained nystagmus waveforms. In the some patients visual acuity was also examined. The ENG records were classified according to Dell'Osso criteria for waveforms. The findings of jerk nystagmus with extended foveation (J(EF)) and of bidirectional jerk nystagmus (BDJ) were singled out. Foveation time, measured in these weveforms was compared with the visual acuity. Visual acuity was better in the jerk nystafmus weveforms with extended foveation period (J(EF)) than in bidirectional jerk nystagmus with shorter foveation time.     

The effect of a long stay under microgravity on the vestibular function and tracking eye movements

Pre-and postflight examinations of cosmonauts participating in missions ISS-3 to ISS-9 on the International Space Station were performed using a computer-aided method of integrated assessment of the oculomotor system. The role and significance of the vestibular system in the eye tracking were determined; the individual and general characteristics of spontaneous oculomotor reactions and oculomotor reactions induced by visual and vestibular stimuli after a long-term stay at zero gravity (126–195 days) were determined; and the changes in the indices of oculomotor reactions were monitored. Studies of the vestibular function, intersensory interactions, and the tracking function of the eyes in the crew members were performed on the second, fifth (sixth), and ninth (tenth) days of the readaptation period. The results of the postflight examinations showed a significant change in the accuracy, velocity, and temporal characteristics of eye tracking and an increase in the vestibular reactivity. It was shown that the structure of visual tracking (the accuracy of fixational eye rotations and smooth tracking) was disturbed (the appearance of correcting saccades, the transition of smooth tracking to saccadic tracking) only in those cosmonauts who, in parallel to an increased reactivity of the vestibular input, also had central changes in the oculomotor system (spontaneous nystagmus, gaze nystagmus). With one exception, recovery of the indices of the accuracy of tracking eye movements in cosmonauts to the background level in the selected period of examination was not observed, although a positive trend was recorded.     

A gene for X-linked idiopathic congenital nystagmus (NYS1) maps to chromosome Xp11.4-p11.3

Congenital nystagmus (CN) is a common oculomotor disorder (frequency of 1/1,500 live births) characterized by bilateral uncontrollable ocular oscillations, with onset typically at birth or within the first few months of life. This condition is regarded as idiopathic, after exclusion of nervous and ocular diseases. X-linked, autosomal dominant, and autosomal recessive modes of inheritance have been reported, but X-linked inheritance is probably the most common. In this article, we report the mapping of a gene for X-linked dominant CN (NYS1) to the short arm of chromosome X, by showing close linkage of NYS1 to polymorphic markers on chromosome Xp11.4-p11.3 (maximum LOD score of 3.20, over locus DXS993). Because no candidate gene, by virtue of its function, has been found in this region of chromosome Xp, further studies are required, to reduce the genetic interval encompassing the NYS1 gene. It is hoped that the complete gene characterization will address the complex pathophysiology of CN.     

Internuclear ophthalmoplegia

Internuclear ophthalmoplegia (INO) is a manifestation of intrinsic brainstem disease. It is caused by a lesion involving the medial longitudinal fasciculus between the abducens and oculomotor nuclei. Typically INO results from conditions which produce ischemia or demyelination in the brainstem. The chief clinical features are an adduction deficit in the eye on the side of the lesion and nystagmus in the contralateral eye on attempted lateral gaze.     

不同运动图象同时刺激左右眼时的交替视动震颤(OKN)现象

采用了同时对左右眼分别以不同的运动图象刺激的实验方法,来测量及分析其OKN眼动反应,探索在OKN反映中两眼之间的输入关系以及眼动控制机制。实验结果发现在两眼的刺激图象不一致时,眼动反应为交替的OKN反应,即中枢神经系统根据各眼的刺激速度,交替地控制产生OKN眼动反应。本文还从闭环控制上讨论了视网膜上速度误差信号的作用。     

不同运动图象同时刺激左右眼时的交替视动震颤(OKN)现象

采用了同时对左右眼分别以不同的运动图象刺激的实验方法,来测量及分析其OKN眼动反应,探索在OKN反映中两眼之间的输入关系以及眼动控制机制。实验结果发现在两眼的刺激图象不一致时,眼动反应为交替的OKN反应,即中枢神经系统根据各眼的刺激速度,交替地控制产生OKN眼动反应。本文还从闭环控制上讨论了视网膜上速度误差信号的作用。     

An investigation of the mechanisms of eye movement control

Summary Feedback mechanisms exist in all the periferal sense organs including the eye, which acts as a highly efficient position control servo system. Histological studies so far have not revealed the precise circuitry of the eye movement control system but some information about it can be obtained by a study of the sources of feedback. Existing theories have considered three types of feedback originating in the oculomotor tract, in the proprioceptive fibres of the extrinsic eye muscles and from retinal image displacement. In the present experiments an optical arrangement has been used to vary or eliminate the amount of information available from retinal image motion, and the response of the eye to simple harmonic displacement of a target has been recorded. The response curves of gain (eyeball movement divided by target motion) against frequency indicate that the system is lion linear when the image falls in the retinal region which is insensitive to position. Outside this area, retinal image position is used as negative feedback but the information from the oculomotor tract must be regenerative. There is also evidence for feedback proportional to the first derivative of eyeball position and this function is ascribed to the proprioceptive signals; this form of feedback appears to saturate for large amplitude movements, thus avoiding heavy damping of the flick movements.A schematic eye movement control system having the same characteristics as the eye is proposed. The transfer function of this system indicates that it should be unstable if the sign of the retinal image feedback loop is reversed. Experiments with this form of feedback show that steady fixation is impossible and the eye performs a pendular nystagmus.     

Characterisation of baseline oscillation in congenital nystagmus eye movement recordings

Congenital nystagmus is an ocular–motor disorder that develops in the first few months of life; its pathogenesis is still unknown. Patients affected by congenital nystagmus show continuous, involuntary, rhythmical oscillations of the eyes. Monitoring eye movements, nystagmus main features such as shape, amplitude and frequency, can be extracted and analysed. Previous studies highlighted, in some cases, a much slower and smaller oscillation, which appears added up to the ordinary nystagmus waveform. This sort of baseline oscillation, or slow nystagmus, hinder precise cycle-to-cycle image placement onto the fovea. Such variability of the position may reduce patient visual acuity. This study aims to analyse more extensively eye movements recording including the baseline oscillation and investigate possible relationships between these slow oscillations and nystagmus. Almost 100 eye movement recordings (either infrared-oculographic or electrooculographic), relative to different gaze positions, belonging to 32 congenital nystagmus patients were analysed. The baseline oscillation was assumed sinusoidal; its amplitude and frequency were computed and compared with those of the nystagmus by means of a linear regression analysis. The results showed that baseline oscillations were characterised by an average frequency of 0.36 Hz (SD 0.11 Hz) and an average amplitude of 2.1° (SD 1.6°). It also resulted in a considerable correlation (R² scored 0.78) between nystagmus amplitude and baseline oscillation amplitude; the latter, on average, resulted to be about one-half of the correspondent nystagmus amplitude.     

Self-consistent estimation of mislocated fixations during reading

During reading, we generate saccadic eye movements to move words into the center of the visual field for word processing. However, due to systematic and random errors in the oculomotor system, distributions of within-word landing positions are rather broad and show overlapping tails, which suggests that a fraction of fixations is mislocated and falls on words to the left or right of the selected target word. Here we propose a new procedure for the self-consistent estimation of the likelihood of mislocated fixations in normal reading. Our approach is based on iterative computation of the proportions of several types of oculomotor errors, the underlying probabilities for word-targeting, and corrected distributions of landing positions. We found that the average fraction of mislocated fixations ranges from about 10% to more than 30% depending on word length. These results show that fixation probabilities are strongly affected by oculomotor errors.     

Computer simulation of the neural discharge carried by the abducens nerve during eye fixation in the cat

The neural signal carried by the abducens nerve during eye fixations was simulated. The neural discharge was defined by the number of spikes carried by the abducens nerve within each ms. Calculations were based on real neurophysiological data. The computed neural signal showed frequency histograms and variance/mean ratios typical of Poisson distribution. A peak was obtained in the power spectral density function of the simulated neural signal. This peak appeared in the frequency range corresponding to the firing rate of single motoneurons for each eye position. It remained as a broad spectral peak after filtering by a second-order differential equation simulating the ocular mechanics. The obtained spectra are similar to the described power spectral density function of eye position recordings. Present results add evidence of a possible neural basis for ocular tremor.     

Modelling of congenital nystagmus waveforms produced by saccadic system abnormalities

 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. Received: 12 May 1999 / Accepted in revised form: 19 November 1999     

Video-oculography in Mice

Eye movements are very important in order to track an object or to stabilize an image on the retina during movement. Animals without a fovea, such as the mouse, have a limited capacity to lock their eyes onto a target. In contrast to these target directed eye movements, compensatory ocular eye movements are easily elicited in afoveate animals^1,2,3,4. Compensatory ocular movements are generated by processing vestibular and optokinetic information into a command signal that will drive the eye muscles. The processing of the vestibular and optokinetic information can be investigated separately and together, allowing the specification of a deficit in the oculomotor system. The oculomotor system can be tested by evoking an optokinetic reflex (OKR), vestibulo-ocular reflex (VOR) or a visually-enhanced vestibulo-ocular reflex (VVOR). The OKR is a reflex movement that compensates for "full-field" image movements on the retina, whereas the VOR is a reflex eye movement that compensates head movements. The VVOR is a reflex eye movement that uses both vestibular as well as optokinetic information to make the appropriate compensation. The cerebellum monitors and is able to adjust these compensatory eye movements. Therefore, oculography is a very powerful tool to investigate brain-behavior relationship under normal as well as under pathological conditions (f.e. of vestibular, ocular and/or cerebellar origin).Testing the oculomotor system, as a behavioral paradigm, is interesting for several reasons. First, the oculomotor system is a well understood neural system⁵. Second, the oculomotor system is relative simple⁶; the amount of possible eye movement is limited by its ball-in-socket architecture ("single joint") and the three pairs of extra-ocular muscles⁷. Third, the behavioral output and sensory input can easily be measured, which makes this a highly accessible system for quantitative analysis⁸. Many behavioral tests lack this high level of quantitative power. And finally, both performance as well as plasticity of the oculomotor system can be tested, allowing research on learning and memory processes⁹.Genetically modified mice are nowadays widely available and they form an important source for the exploration of brain functions at various levels¹⁰. In addition, they can be used as models to mimic human diseases. Applying oculography on normal, pharmacologically-treated or genetically modified mice is a powerful research tool to explore the underlying physiology of motor behaviors under normal and pathological conditions. Here, we describe how to measure video-oculography in mice⁸.     

Sugar radicals in DNA: isolation of neutral radicals in gamma-irradiated DNA by hole and electron scavenging

In this investigation of the radical formation and the reaction of radicals in gamma-irradiated DNA, we report the isolation of putative neutral radicals by the scavenging of holes by Fe(CN)6(4-) and of electrons by Fe(CN)6(3-). Experiments are performed under conditions that emphasize direct and quasi-direct effects (collectively called direct-type effects.) Samples containing Fe(CN)6(4-) show effective scavenging of holes and the ESR spectra obtained arise principally from DNA anion radicals and neutral radicals. On the other hand, for samples containing Fe(CN)6(3-), electron scavenging is highly efficient, and the resulting spectra arise principally from guanine cation radicals and neutral radicals. When both Fe(CN)6(4-) and Fe(CN)6(3-) are present, a near complete scavenging of cation radicals and anion radicals is observed at 77 K, and the ESR spectra that result originate predominantly with neutral radicals which are assigned predominantly to radicals on the sugar phosphate backbone. A notable finding is the presence of spectral components that indicate the formation, through the rupture of the C3'-O bond, of a neutral deoxyribose radical; a concurrent strand break must accompany formation of this radical. This radical was previously reported in argon-ion-irradiated DNA and now, for the first time, is reported in DNA irradiated with low-LET radiation.