A random walk model of fast-phase timing during optokinetic nystagmus

 Most vertebrate animals produce optokinetic nystagmus in response to rotation of their visual surround. Nystagmus consists of an alternation of slow-phase eye rotations, which follow the surround, and fast-phase eye rotations, which quickly reset eye position. The time intervals between fast phases vary stochastically, even during optokinetic nystagmus produced by constant velocity rotation of a uniform surround. The inter-fast-phase interval distribution has a long tail, and intervals that are long relative to the mode become even more likely as constant surround velocity is decreased. This paper provides insight into fast-phase timing by showing that the process of fast-phase generation during constant velocity optokinetic nystagmus is analogous to a random walk with drift toward a threshold. Neurophysiologically, the output of vestibular nucleus neurons, which drive the slow phase, would approximate a random walk with drift because they integrate the noisy, constant surround velocity signal they receive from the visual system. Burst neurons, which fire a burst to drive the fast phase and reset the slow phase, are brought to threshold by the vestibular nucleus neurons. Such a nystagmic process produces stochastically varying inter-fast-phase intervals, and long intervals emerge naturally because, as drift rate (related to surround velocity) decreases, it becomes more likely that any random walk can meander for a long time before it crosses the threshold. The theoretical probability density function of the first threshold crossing times of random walks with drift is known to be that of an inverse Gaussian distribution. This probability density function describes well the distributions of the intervals between fast phases that were either determined experimentally, or simulated using a neurophysiologically plausible neural network model of fast-phase generation, during constant velocity optokinetic nystagmus. Received: 1 June 1995/Accepted in revised form: 15 February 1996     

Automatic detection and removal of fast phases from nystagmographic recordings by optimal thresholding

Recording of ocular nystagmus during vestibular tests does not measure the true response of the vestibulo-ocular reflex (VOR), because the VOR response (so-called slow phase of nystagmus) is interrupted by resetting saccades (so-called fast phase of nystagmus). In order to extract the real VOR contribution, saccades must be removed. In most of the nystagmus processing algorithms, saccade removal requires a human operator to choose a suitable eye velocity threshold able to separate fast from slow nystagmus phases. In the present report a fully automatic removal system is presented which selects an optimal velocity threshold by computing the VOR frequency response and maximizing its coherence function.     

Static cervical-ocular reflex and optokinetic reflex interaction in rabbits

Summary The effect that tonic eye deviations, induced by angular deviation of the torso, have on the characteristics of optokinetic (OK) nystagmus was studied in rabbits. When the slow component of the OK nystagmus moved in the direction of the tonic eye deviation, the amplitude of the slow and fast components of the nystagmus was decreased and their frequency was increased, whereas when the slow component moved in the opposite direction, the amplitude and the frequency of the nystagmus were not different from those when the head and torso were aligned.Under the influence of neck reflexes, the total range of eye movements was double that when the torso was aligned with the head. The place in the orbit where the fast-component is initiated — the so-called fast-component threshold — was deviated in the direction of the neck-reflex-induced tonic eye deviation. The characteristics of the fast component, however, except for its amplitude, were not affected by the change of location of the fast-component threshold.These data indicate that the OK reflex function, as judged by measurement of the slow component velocity, is not affected by neck-vestibular reflexes. They also show that the fast-component threshold is dependent on parameters other than the actual orbital position and that there must be an internal representation of the range of possible eye movements within the brain to regulate the production of fast components.Abbreviations OK optokinetic - CW clockwise - CCW counterclockwise - CNS central nervous system This work was supported by grants NS07059, NS09823, and NS08335 from the National Institutes of Health     

Development of Eye Position Dependency of Slow Phase Velocity during Caloric Stimulation

The nystagmus in patients with vestibular disorders often has an eye position dependency, called Alexander’s law, where the slow phase velocity is higher with gaze in the fast phase direction compared with gaze in the slow phase direction. Alexander’s law has been hypothesized to arise either due to adaptive changes in the velocity-to-position neural integrator, or as a consequence of processing of the vestibular-ocular reflex. We tested whether Alexander’s law arises only as a consequence of non-physiologic vestibular stimulation. We measured the time course of the development of Alexander’s law in healthy humans with nystagmus caused by three types of caloric vestibular stimulation: cold (unilateral inhibition), warm (unilateral excitation), and simultaneous bilateral bithermal (one side cold, the other warm) stimulation, mimicking the normal push-pull pattern of vestibular stimulation. Alexander’s law, measured as a negative slope of the velocity versus position curve, was observed in all conditions. A reversed pattern of eye position dependency (positive slope) was found <10% of the time. The slope often changed with nystagmus velocity (cross-correlation of nystagmus speed and slope was significant in 50% of cases), and the average lag of the slope with the speed was not significantly different from zero. Our results do not support the hypothesis that Alexander’s law can only be observed with non-physiologic vestibular stimulation. Further, the rapid development of Alexander’s law, while possible for an adaptive mechanism, is nonetheless quite fast compared to most other ocular motor adaptations. These results suggest that Alexander’s law may not be a consequence of a true adaptive mechanism.     

Time constants of vestibular nuclei neurons in the goldfish: A model with ocular proprioception

A simple model of the vestibular-ocular reflex with a proprioceptive eye velocity feedback loop is used to simulate recent data on the vestibular responses of neurons in the vestibular nuclei of spinal goldfish. The data support the hypothesis that a proprioceptive feedback loop elongates the vestibular nucleus time constant to equal that of the slow phase eye movements of vestibular nystagmus.     

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.     

Convergence rotatory nystagmus under unusual conditions of semicircular canal and otolith stimulation

The characteristics of interaction between two vestibular subsystems (otiliths and semicircular canals) were studied by means of binocular (bilateral) videooculographic recording of eye movements in 43 men aged from 19 to 41 years that had been found healthy upon aviation physical examination. The time course of horizontal vestibular nystagmus was analyzed separately for each eye in subjects who bent forward and straightened up in the sagittal plane while being rotated about the vertical body axis in an electrically driven rotating chair. This combined rotation caused interocular asymmetric nystagmus in 91% of the subjects and convergence rotatory nystagmus in 42% of the subjects. A hypothesis on the mechanism of interocular asymmetric nystagmus caused by the combined rotation and convergence rotatory nystagmus as its special case has been advanced. The hypothesis allows for independent nystagmic mechanisms (subsystems) for the right and left eyes.     

Modeling dynamical interactions between fast and slow movements: fast saccadic eye movement behavior in the presence of the slower VOR

An ongoing controversy has to do with the interactions between “fast” (saccadic, quick phase) and “slow” (all other) eye movements. By attacking such issues with both experimental and especially simulation studies using our nonlinear sixth order reciprocally innervated model of the eye mechanical system, insights can be gained into the nature of these nontrivial phenomena. In our present study we relied both (1) on simulation of saccades under a wide range of experimental conditions [vestibular ocular reflex (VOR) velocities from -100 to 100 deg/sec, VOR induced position ranges from -30 to 30 degrees, time-optimal saccades ranging from 2 to 40 degrees], and (2) on using a wide variety of computer simulation of eye movement models, ranging from nonlinear ones with first and especially second order multipulse step controller signal structures, to different controller signal interaction schemes, to simulation using linearized models. We have isolated two important nonlinear phenomena: a level I nonlinear mechanical interaction, dependent not only on the initial velocity but also on the “position effect,” a new finding; and a level II nonlinear neurological interaction, close to “squelching” of the VOR controller signals by the dominating saccadic signal. Furthermore, we have used our simulation findings to reinterpret others' experimental data on eye movement interactions, including saccadic-smooth pursuit, saccadic-vergence, and vestibular nystagmus.     

On the predominance of anti-compensatory eye movements in vestibular nystagmus

The predominance of anti-compensatory eye movements in vestibular nystagmus recorded during sinusoidal and post-rotational tests is interpreted in terms of a mathematical model of the vestibulo-ocular system. Namely, a direct pathway between the vestibular nuclei and the saccadic mechanism is assumed. In the range of frequencies of natural head movements this pathway carries on a signal proportional to head angular velocity. Therefore, during active head movements the saccadic mechanism is forced to produce quick eye rotations in the direction of head movement and, thus, to cooperate in the task of picking up visual targets outside the visual field. During passive head movements giving rise to nystagmus the assumed pathway contributes to reduce the error in eye resetting due to the saccadic delay. Analytical considerations and simulation results seem to prove the adequacy of the proposed model.Work supported by the National Research Council (C.N.R.), Rome, Italy     

Activity of premotor vestibular neurons in the alert cat

The activity of medial vestibular nucleus neurons projecting to the contralateral abducens nucleus (premotor vestibular neurons) has been recorded during spontaneous and vestibular induced eye movements in the alert cat. Recorded neurons were identified by their antidromic activation from the abducens nucleus and by the post-synaptic field potential induced in this nucleus. The activity of identified medial vestibular neurons increased significantly with horizontal eye position and velocity toward the contralateral side, and decreased abruptly during ipsilateral saccades. The activity of these neurons was also related to head velocity toward the ipsilateral side. The functional role and origin of eye position and velocity signals present in these vestibular neurons are discussed.     

A burst-feedback model of fast-phase burst generation during nystagmus

 Vestibular and optokinetic nystagmus are characterized by alternating slow-phase eye rotations that stabilize the retinal image, and fast-phase eye rotations that reset eye position. Nystagmus is coordinated in the brainstem by burst neurons that fire an intense, temporally circumscribed burst that terminates the slow phase and drives the fast phase. This paper demonstrates that such a burst can be generated during nystagmus using a simple neural network model containing only known brainstem neurons and their interconnections. These include the feedback connections of the burst neuron (burst feedback). The burst neuron excites itself directly, and disinhibits itself by inhibiting the pause neuron (positive feedback). It also inhibits itself by inhibiting the vestibular neuron (negative feedback). The burst neuron begins to fire after its inhibitory bias is overcome by excitation from the vestibular neuron, and burst neuron positive feedback then produces an intense burst with an abrupt onset. The burst causes the vestibular and pause neurons to pause. The benefit of the pause neuron loop is that it contributes to burst neuron positive feedback when it is needed at burst onset, but that contribution is eliminated when the pause neuron pauses and opens the loop. The burst can then terminate, with an offset duration proportional to burst amplitude, under the control of burst neuron self-excitation and inhibitory bias. Model neuron behavior is comparable to that of real brainstem neurons. Synchronized bursts can be produced over the population of burst neurons in a distributed version of the network. Variability in connection weights in the distributed network results in variability in prelude activity among burst neurons that is similar to the spread in lead observed for real burst neurons during nystagmus. Received: 11 April 1996 / Accepted in revised form: 6 August 1996     

A model of Alexander's law of vestibular nystagmus

The observation that the amplitude of vestibular nystagmus grows as gaze is increased in the direction of the nystagmus fast phase and diminished with gaze in the opposite direction is known as Alexander's law. We have developed an analog computer model to simulate Alexander's law in nystagmus secondary to dysfunction of a semicircular canal. The model utilizes relevant brainstem anatomy and physiology and includes gaze modulation of vestibular signals and push-pull integration to create eye positition commands. When simulating normally functioning semicircular canals, the model produced no nystagmus. When simulating total impairment of the canal on one side with gaze directed maximally in the opposite direction, the model produced a large amplitude nystagmus with linear slow phases directed toward the affected side. As gaze was changed from far contralateral to ipsilateral, the nystagmus gradually diminished to zero. When simulating partial impairment of one canal, the nystagmus was smaller in amplitude and absent in ipsilateral gaze.     

A model of the nystagmus induced by off vertical axis rotation

A three-dimensional model is proposed that accounts for a number of phenomena attributed to the otoliths. It is constructed by extending and modifying a model of vestibular velocity storage. It is proposed that the otolith information about the orientation of the head to gravity changes the time constant of vestibular responses by modulating the gain of the velocity storage feedback loop. It is further proposed that the otolith signals, such as those that generate L-nystagmus (linear acceleration induced nystagmus), are partially coupled to the vestibular system via the velocity storage integrator. The combination of these two hypotheses suggests that a vestibular neural mechanism exists that performs correlation in the mathematical sense which is multiplication followed by integration. The multiplication is performed by the otolith modulation of the velocity storage feedback loop gain and the integration is performed by the velocity storage mechanism itself. Correlation allows calculation of the degree to which two signals are related and in this context provides a simple method of determining head angular velocity from the components of linear acceleration induced by off-vertical axis rotation. Correlation accounts for the otolith supplementation of the VOR and the sustained nystagmus generated by off-vertical axis rotation. The model also predicts the cross-coupling of horizontal and vertical optokinetic afternystagmus that occurs in head-lateral positions and the reported effects of tilt on vestibular responses.     

A new light on caloric test--what was disclosed by three dimensional analysis of caloric nystagmus?

For better understanding of caloric nystagmus, this phenomenon will be reviewed historically in three stages. 1) The first light on caloric nystagmus was thrown by Barany 1906. Through direct observation of eye movements, Barany established the caloric test as an important tool to determine the side of lesion for vertigo. 2) The second light is shed by electrooculogram (EOG) from the late 1950th. EOG enabled qualitative analysis of caloric nystagmus, and proved Barany's convection theory, but resulted in neglect of vertical and roll eye movements. 3) The third light is gained by 3D recording of eye movements started from the late 1980th. 3D recordings of eye movements enabled us to analyze the spatial orientation of caloric nystagmus, and disclose the close correlation of the nystagmus components in the head vertical and the space vertical planes, suggesting a contribution of the velocity storage integrator. The 3D property of caloric nystagmus will be explained in detail.     

The interstitial nucleus of Cajal of the cat. I. Neurons activity related to vertical eye movements

Interstitial nucleus of Cajal (INC) neurons activity was studied during vertical optokinetic nystagmus (OKN) and after-nystagmus (OKAN) in awake cats lying on their right side. The activity of one hundred neurons was recorded in the left INC and analysed in relation with the vertical component of OKN and OKAN. The activity of 27 neurons was correlated either to eye position or to both eye velocity and eye position; 18 of these neurons were recorded in their on-direction and their off-direction. The analysis of the 18 neurons showed that the activity of 8 of them was correlated to eye position in the on-direction and in the off-direction and the correlation to eye position was higher than to eye velocity; these neurons are considered as position neurons. Seven other neurons had a higher correlation to eye position that to eye velocity in the on-direction and this relation reversed in the off-direction, these neurons are considered as position-velocity neurons. Thirty two burst-neurons were activated only during quick phases of OKN and OKAN and they were silent during slow phases and periods of fixation. Nine burst neurons had an upward on-direction and 23 neurons a downward on-direction. The eye velocity-average burst frequency (ABF) and quick phase duration-burst duration relationships had low correlations and suggested that INC burst neurons were excitatory premotor neurons. Statistical analysis showed that downward on-direction burst neurons had a higher ABF that upward on-direction burst neurons. Moreover, during OKN and OKAN, the velocity sensitivity of INC burst neurons was the same. The activity of the remaining neurons (41 neurons) was not quantitatively correlated to vertical and horizontal eye movements; they were classified as irregular tonic neurons. This study shows that INC neurons carry an eye position signal which was never reported before. This supports the results of INC lesion studies which showed that INC is involved in the vertical velocity to position integration. Moreover, there is an up versus down asymmetry in the frequency of INC burst neurons.     

Eye movements induced by linear acceleration in humans.

The otolith-function study is remarkably behind the semicanal-function study. In the present paper, we introduced briefly our on-going studies on eye movements including nystagmic elicitation during lateral (Gy) linear acceleration with step and sinusoidal modes using a sled-type accelerator. The eye movements were recorded by EOGs (DC) from subjects who looked at an imaginary target of their straight ahead in darkness during G-loading up to 0.5 G. Corresponding to the +Gy and -Gy segments, nystagmus and/or deviation in eye position were frequently induced in some subjects, but none or slightly in the other. The nystagmus changed the beating direction dependently on the Gy direction, while the eye-deviation could be either direction of compensatory or anticompensatory. In half of subjects, nystagmus elicitation was absent or low at 0.3 G, while it tended to increase above 0.3 G. The nystagmic elicitation was similar to each other between the both modes of acceleration, and directional preponderance (DP) was observed in some subjects. There was no correlation between the DP and the nystagmic slow-phase velocity. Functional meanings of these findings were discussed.     

Quantitative analysis of benign paroxysmal positional vertigo fatigue under canalithiasis conditions

In our daily life, small flows in the semicircular canals (SCCs) of the inner ear displace a sensory structure called the cupula which mediates the transduction of head angular velocities to afferent signals. We consider a dysfunction of the SCCs known as canalithiasis. Under this condition, small debris particles disturb the flow in the SCCs and can cause benign paroxysmal positional vertigo (BPPV), arguably the most common form of vertigo in humans. The diagnosis of BPPV is mainly based on the analysis of typical eye movements (positional nystagmus) following provocative head maneuvers that are known to lead to vertigo in BPPV patients. These eye movements are triggered by the vestibulo-ocular reflex, and their velocity provides an indirect measurement of the cupula displacement. An attenuation of the vertigo and the nystagmus is often observed when the provocative maneuver is repeated. This attenuation is known as BPPV fatigue. It was not quantitatively described so far, and the mechanisms causing it remain unknown. We quantify fatigue by eye velocity measurements and propose a fluid dynamic interpretation of our results based on a computational model for the fluid–particle dynamics of a SCC with canalithiasis. Our model suggests that the particles may not go back to their initial position after a first head maneuver such that a second head maneuver leads to different particle trajectories causing smaller cupula displacements.     

Interaction of the angular and linear components of the horizontal vestibulo-ocular reflex in the pigeon

Pigeons were exposed to centric and eccentric horizontal rotations in darkness by velocity trapezoid. Different in sign the duration alterations of the opposite directed horizontal eye nystagmus occurred during otolith membrane shifts in sagittal as well as frontal planes. A direct dependence was found between the duration alterations of the primary nystagmus phase and the peak value alterations of its slow phase velocity under increased (but not decreased) centrifugal force. In the both cases, if duration of the primary nystagmus phase was enlarged, duration of its secondary phase was diminished and vice versa. It suggests the otolith component does not decay up to zero by constant velocity and at once after rotation; by deceleration it is biphasic. In affirms the own hypothesis that the linear component is asymmetric central neuronal activity that modifies the canal component even if this activity by itself is not enough for eye movement initiation.     

Eye movements in Daphnia pulex (De Geer).

1. The various types of eye movement exhibited by the cyclopean eye of Daphnia pulex were studied using high speed motion photography. 2. This rudimentary eye, which consists of only 22 ommatidia, can move through approximately 150 degrees in the sagittal plane and 60 degrees in the horizontal plane. 3. Four classes of eye movement were found: (1) a high speed tremor at 16 Hz with an amplitude of 3-4 degrees, which resembles physiological nystagmus, (2) a slow rhythmic scanning movement at 4 Hz, and 5-6 degrees amplitude, (3) large fast eye movements similar to saccadic eye movements and (4) optokinetic nystagmus produced by moving striped patterns. 4. Where the fast tremor occurred concurrently with the slow rhythmic scan, a Fourier analysis revealed that the former was the fourth harmonic of the latter.