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     

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     

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.     

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.     

Bifurcations in a white-blood-cell production model

We study the dynamics of a model of white-blood-cell (WBC) production. The model consists of two compartmental differential equations with two discrete delays. We show that from normal to pathological parameter values, the system undergoes supercritical Hopf bifurcations and saddle-node bifurcations of limit cycles. We characterize the steady states of the system and perform a bifurcation analysis. Our results indicate that an increase in apoptosis rate of either hematopoietic stem cells or WBC precursors induces a Hopf bifurcation and an oscillatory regime takes place. These oscillations are seen in some hematological diseases.     

A normal ocular motor system model that simulates the dual-mode fast phases of latent/manifest latent nystagmus

 The fast phases of latent/manifest latent nystagmus (LMLN) may either cause the target image to fall within (foveating) or outside (defoveating) the foveal area. We previously verified that both types are generated by the same mechanism as voluntary saccades and propose a hypothetical, dual-mode mechanism (computer model) for LMLN that utilizes normal ocular-motor control functions. Fixation data recorded during the past 30 years from 97 subjects with LMLN using both infrared and magnetic search coil oculography were used as a basis for our simulations. The MATLAB/Simulink software was used to construct a robust, modular, ocular motor system model, capable of simulating LMLN. Fast-phase amplitude versus both peak velocity and duration of simulated saccades were equivalent to those of saccades in normal subjects. Based on our LMLN studies, we constructed a hypothetical model in which the slow-phase velocity acted to trigger the change between foveating and defoveating LMLN fast phases. Foveating fast phases were generated during lower slow-phase velocities whereas defoveating fast phases occurred during higher slow-phase velocities. The bidirectional model simulated Alexander's law behavior under all viewing and fixation conditions. Our ocular-motor model accurately simulates LMLN patient ocular motility data and provides a hypothetical explanation for the conditions that result in both foveating and defoveating fast phases. As is the case for normal physiological saccades, the position error determined the saccadic amplitudes for foveating fast phases. However, the final slow-phase velocity determined the amplitudes of defoveating fast phases. In addition, we suggest that individuals with LMLN use their fixation subsystem to further decrease the slow-phase velocity as the target image approaches the foveal center. Received: 16 June 2000 / Accepted in revised form: 20 May 2001     

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.     

Tests of Models for Saccade–Vergence Interaction using Novel Stimulus Conditions

During natural activities, two types of eye movements - saccades and vergence - are used in concert to point the fovea of each eye at features of interest. Some electrophysiological studies support the concept of independent neurobiological substrates for saccades and vergence, namely saccadic and vergence burst neurons. Discerning the interaction of these two components is complicated by the near-synchronous occurrence of saccadic and vergence components. However, by positioning the far target below the near target, it is possible to induce responses in which the peak velocity of the vertical saccadic component precedes the peak velocity of the horizontal vergence component by approximately 75 ms. When saccade-vergence responses are temporally dissociated in this way, the vergence velocity waveform changes, becoming less skewed. We excluded the possibility that such change in skewing was due to visual feedback by showing that similar behavior occurred in darkness. We then tested a saccade-related vergence burst neuron (SVBN) model proposed by Zee et al. in J Neurophysiol 68:1624-1641 (1992), in which omnipause neurons remove inhibition from both saccadic and vergence burst neurons. The technique of parameter estimation was used to calculate optimal values for responses from human subjects in which saccadic and convergence components of response were either nearly synchronized or temporally dissociated. Although the SVBN model could account for convergence waveforms when saccadic and vergence components were nearly synchronized, it could not when the components were temporally dissociated. We modified the model so that the saccadic pulse changed the parameter values of the convergence burst units if both components were synchronized. The modified model accounted for velocity waveforms of both synchronous and dissociated convergence movements. We conclude that both the saccadic pulse and omnipause neuron inhibition influence the generation of vergence movements when they are made synchronously with saccades.     

The oculomotor system--simulation of physiologic and pathologic horizontal saccadic eye movements

Horizontal saccadic eye movements were analyzed by way of the input- and output-functions of the oculomotor system. On the basis of the parameters of the model, it was possible to simulate both physiological and pathological saccades. In this paper we present the results of simulation experiments that were performed to study the influence of various ocular motor disorders. The parameters of the model proved a useful diagnostic aid.     

A competitive integration model of exogenous and endogenous eye movements

We present a model of the eye movement system in which the programming of an eye movement is the result of the competitive integration of information in the superior colliculi (SC). This brain area receives input from occipital cortex, the frontal eye fields, and the dorsolateral prefrontal cortex, on the basis of which it computes the location of the next saccadic target. Two critical assumptions in the model are that cortical inputs are not only excitatory, but can also inhibit saccades to specific locations, and that the SC continue to influence the trajectory of a saccade while it is being executed. With these assumptions, we account for many neurophysiological and behavioral findings from eye movement research. Interactions within the saccade map are shown to account for effects of distractors on saccadic reaction time (SRT) and saccade trajectory, including the global effect and oculomotor capture. In addition, the model accounts for express saccades, the gap effect, saccadic reaction times for antisaccades, and recorded responses from neurons in the SC and frontal eye fields in these tasks.     

A model that integrates eye velocity commands to keep track of smooth eye displacements

Past results have reported conflicting findings on the oculomotor system’s ability to keep track of smooth eye movements in darkness. Whereas some results indicate that saccades cannot compensate for smooth eye displacements, others report that memory-guided saccades during smooth pursuit are spatially correct. Recently, it was shown that the amount of time before the saccade made a difference: short-latency saccades were retinotopically coded, whereas long-latency saccades were spatially coded. Here, we propose a model of the saccadic system that can explain the available experimental data. The novel part of this model consists of a delayed integration of efferent smooth eye velocity commands. Two alternative physiologically realistic neural mechanisms for this integration stage are proposed. Model simulations accurately reproduced prior findings. Thus, this model reconciles the earlier contradictory reports from the literature about compensation for smooth eye movements before saccades because it involves a slow integration process. Action Editor: Jonathan D. Victor     

Which diameter and angle rule provides optimal flow patterns in a coronary bifurcation?

The branching angle and diameter ratio in epicardial coronary artery bifurcations are two important determinants of atherogenesis. Murray's cubed diameter law and bifurcation angle have been assumed to yield optimal flows through a bifurcation. In contrast, we have recently shown a 7/3 diameter law (HK diameter model), based on minimum energy hypothesis in an entire tree structure. Here, we derive a bifurcation angle rule corresponding to the HK diameter model and critically evaluate the streamline flow through HK and Murray-type bifurcations. The bifurcations from coronary casts were found to obey the HK diameter model and angle rule much more than Murray's model. A finite element model was used to investigate flow patterns for coronary artery bifurcations of various types. The inlet velocity and pressure boundary conditions were measured by ComboWire. Y-bifurcation of Murray type decreased wall shear stress-WSS (10%-40%) and created an increased oscillatory shear index-OSI in atherosclerosis-prone regions as compared with HK-type bifurcations. The HK-type bifurcations were found to have more optimal flow patterns (i.e., higher WSS and lower OSI) than Murray-type bifurcations which have been traditionally believed to be optimized. This study has implications for changes in bifurcation angles and diameters in percutaneous coronary intervention.     

Saccades during Attempted Fixation in Parkinsonian Disorders and Recessive Ataxia: From Microsaccades to Square-Wave Jerks

During attempted visual fixation, saccades of a range of sizes occur. These “fixational saccades” include microsaccades, which are not apparent in regular clinical tests, and “saccadic intrusions”, predominantly horizontal saccades that interrupt accurate fixation. Square-wave jerks (SWJs), the most common type of saccadic intrusion, consist of an initial saccade away from the target followed, after a short delay, by a “return saccade” that brings the eye back onto target. SWJs are present in most human subjects, but are prominent by their increased frequency and size in certain parkinsonian disorders and in recessive, hereditary spinocerebellar ataxias. Here we asked whether fixational saccades showed distinctive features in various parkinsonian disorders and in recessive ataxia. Although some saccadic properties differed between patient groups, in all conditions larger saccades were more likely to form SWJs, and the intervals between the first and second saccade of SWJs were similar. These findings support the proposal of a common oculomotor mechanism that generates all fixational saccades, including microsaccades and SWJs. The same mechanism also explains how the return saccade in SWJs is triggered by the position error that occurs when the first saccadic component is large, both in the healthy brain and in neurological disease.     

Immune network behavior—I. From stationary states to limit cycle oscilations

We develop a model for the idiotypic interaction between two B cell clones. This model takes into account B cell proliferation, B cell maturation, antibody production, the formation and subsequent elimination of antibody-antibody complexes and recirculation of antibodies between the spleen and the blood. Here we investigate, by means of stability and bifurcation analysis, how each of the processes influences the model's behavior. After appropriate nondimensinalization, the model consists of eight ordinary differential equations and a number of parameters. We estimate the parameters from experimental sources. Using a coordinate system that exploits the pairwise symmetry of the interactions between two clones, we analyse two simplified forms of the model and obtain bifurcation diagrams showing how their five equilibrium states are related. We show that the so-called immune states lose stability if B cell and antibody concentrations change on different time scales. Additionally, we derive the structure of stable and unstable manifolds of saddle-tye equilibria, pinpoint their (global) bifurcations and show that these bifurcations play a crucial role in determining the parameter regimes in which the model exhibits oscillatory behavior.     

Motor neuronopathy with dropped hands and downbeat nystagmus: A distinctive disorder? A case report

Background  

Eye movements are clinically normal in most patients with motor neuron disorders until late in the disease course. Rare patients are reported to show slow vertical saccades, impaired smooth pursuit, and gaze-evoked nystagmus. We report clinical and oculomotor findings in three patients with motor neuronopathy and downbeat nystagmus, a classic sign of vestibulocerebellar disease.     

Computer simulation of overshoot in saccadic eye movements.

The human horizontal eye movement system produces quick, precise, conjugate eye movements called saccades. These are important in normal vision. For example, reading tasks exclusively utilize saccadic eye movements. The majority of saccades have dynamic overshoot. The amplitude of this overshoot is independent of saccadic amplitude, and is such that it places the image of the stimulus within the retinal region of maximum acuity within a minimum of time. A computer based model of the saccadic mechanisms was used to study the origin of this overshoot. It was discussed that dynamic overshoot cannot be attributed to biomechanism properites of the eye movement mechanism, but must instead be explained by variations in the controlling nervous activity. The form of this neural controller signal is very similar to that required for a time optimal response of an inertial system.     

Human fast negative EEG potentials before express saccades

Fast negative EEG potentials preceding fast regular saccades and express saccades were studied by the method of backward averaging under conditions of monocular stimulation of the right and left eye. "Step" and "gap" experimental paradigms were used for visual stimulation. Analysis of parameters of potentials and their spatiotemporal dynamics suggests that, under conditions of the increased attention and optimal readiness of the neural structures, express saccades appear when the previously chosen program of the future eye movement coincides with the actual target coordinates. We assumed that the saccade latency decreases at the expense of the involvement of the main oculomotor areas of motor and saccadic planning in its initiation; an express saccade can be initiated also by means of direct transmission of the signal from the cortex to the brainstem saccadic generator passing by the superior colliculus. Moreover, anticipating release from the central fixation and attention distraction are necessary for the successful initiation of an express saccade.     

Probability of Seeing Increases Saccadic Readiness

Associating movement directions or endpoints with monetary rewards or costs influences movement parameters in humans, and associating movement directions or endpoints with food reward influences movement parameters in non-human primates. Rewarded movements are facilitated relative to non-rewarded movements. The present study examined to what extent successful foveation facilitated saccadic eye movement behavior, with the hypothesis that foveation may constitute an informational reward. Human adults performed saccades to peripheral targets that either remained visible after saccade completion or were extinguished, preventing visual feedback. Saccades to targets that were systematically extinguished were slower and easier to inhibit than saccades to targets that afforded successful foveation, and this effect was modulated by the probability of successful foveation. These results suggest that successful foveation facilitates behavior, and that obtaining the expected sensory consequences of a saccadic eye movement may serve as a reward for the oculomotor system.     

Latency of visually evoked saccadic eye movements

The validness of a model describing the relation between mean saccadic latency and stimulus asynchrony based on facilitation instead of suppression was tested experimentally. As a result, suppression of signals generated by the onset of a peripheral stimulus due to fixation of another target, giving rise to an increase of mean saccadic latency, does not seem very likely. The influence of the intensity of the fixation target on the latency of visually evoked saccades was studied. According to the facilitation model, the offset of the fixation target induces after an afferent delay, a transition of the state of the facilitation mechanism from the unfacilitated condition into a mode of maximal facilitation. The time-period during which this change is accomplished is called Facilitation-Rise-Time (FRT). An interpretation within the context of the facilitation model of gap-overlap latency data for different values of the intensity of the fixation stimulus suggests, in combination with computer-computations of the model, that lowering of this intensity causes an increase in FRT. The results in normal subjects of step stimulus experiments with a dim fixation point substantiate the hypothesis of a facilitation mechanism, which is triggerable not only by an external signal such as the offset of the fixation point, but also by some internal stimulus independent signal. Moreover, data for tracking by an amblyopic eye seem to support this conclusion. The findings of increased saccadic latencies in amblyopic and Optic Neuritis (ON) eyes suggest a slowing of processing of visual information in the sensory pathways from the central retina, subsequently utilized by the oculomotor system in the generation of saccades.(ABSTRACT TRUNCATED AT 250 WORDS)     

Blink Perturbation Effects on Saccades Evoked by Microstimulation of the Superior Colliculus

Current knowledge of saccade-blink interactions suggests that blinks have paradoxical effects on saccade generation. Blinks suppress saccade generation by attenuating the oculomotor drive command in structures like the superior colliculus (SC), but they also disinhibit the saccadic system by removing the potent inhibition of pontine omnipause neurons (OPNs). To better characterize these effects, we evoked the trigeminal blink reflex by delivering an air puff to one eye as saccades were evoked by sub-optimal stimulation of the SC. For every stimulation site, the peak and average velocities of stimulation with blink movements (SwBMs) were lower than stimulation-only saccades (SoMs), supporting the notion that the oculomotor drive is weakened in the presence of a blink. In contrast, the duration of the SwBMs was longer, consistent with the hypothesis that the blink-induced inhibition of the OPNs could prolong the window of time available for oculomotor commands to drive an eye movement. The amplitude of the SwBM could also be larger than the SoM amplitude obtained from the same site, particularly for cases in which blink-associated eye movements exhibited the slowest kinematics. The results are interpreted in terms of neural signatures of saccade-blink interactions.