Eye-position dependence of torsional velocity during interaural translation, horizontal pursuit, and yaw-axis rotation in humans.

The translational vestibulo-ocular reflex (tVOR) stabilizes an image on the fovea during linear movements of the head. It has been suggested that the tVOR may share pathways with the pursuit system. We asked whether the tVOR and pursuit would be similar in their behavior relative to Listing's Law. We compared torsional eye velocity as a function of vertical orbital position during interaural translation, pursuit, and yaw-axis rotation. We found that the eye-position-dependence of torsion was similar during translation and pursuit, which differed from that during yaw-axis rotation. These findings further support a close relationship between the mechanisms that generate pursuit and the tVOR.

Automatic detection of camera translation in eye video recordings using multiple methods.

In video eye tracking, shifting of the camera relative to the head can introduce artifacts. This work proposes a new combination of image processing techniques to automatically detect and measure the relative translation of cameras separately imaging the left and right eyes. It uses a priori physiological knowledge to improve the accuracy of algorithms. The first method compares an eye image with a reference frame using cross-correlation methods. The second isolates the upper eyelid and compares it with a reference frame to improve approximation of camera translation. The third creates an eyelid template from multiple frames and cross-correlates it with each image frame. The later has the highest accuracy, with a mean error of 1.3 pixels. It is more robust since it eliminates features of the image that may introduce errors. This excellent accuracy makes the method a viable solution for the problem of camera movement relative to the head.

Cross-axis adaptation of torsional components in the yaw-axis vestibulo-ocular reflex.

The three pairs of semicircular canals within the labyrinth are not perfectly aligned with the pulling directions of the six extraocular muscles. Therefore, for a given head movement, the vestibulo-ocular reflex (VOR) depends upon central neural mechanisms that couple the canals to the muscles with the appropriate functional gains in order to generate a response that rotates the eye the correct amount and around the correct axis. A consequence of these neural connections is a cross-axis adaptive capability, which can be stimulated experimentally when head rotation is around one axis and visual motion about another. From this visual-vestibular conflict the brain infers that the slow-phase eye movement is rotating around the wrong axis. We explored the capability of human cross-axis adaptation, using a short-term training paradigm, to determine if torsional eye movements could be elicited by yaw (horizontal) head rotation (where torsion is normally inappropriate). We applied yaw sinusoidal head rotation (+/-10 degrees, 0.33 Hz) and measured eye movement responses in the dark, and before and after adaptation. The adaptation paradigm lasted 45-60 min, and consisted of the identical head motion, coupled with a moving visual scene that required one of several types of eye movements: (1) torsion alone (-Roll); (2) horizontal/torsional, head right/CW torsion (Yaw-Roll); (3) horizontal/torsional, head right/CCW torsion (Yaw+Roll); (4) horizontal, vertical, torsional combined (Yaw+Pitch-Roll); and (5) horizontal and vertical together (Yaw+Pitch). The largest and most significant changes in torsional amplitude occurred in the Yaw-Roll and Yaw+Roll conditions. We conclude that short-term, cross-axis adaptation of torsion is possible but constrained by the complexity of the adaptation task: smaller torsional components are produced if more than one cross-coupling component is required. In contrast, vertical cross-axis components can be easily trained to occur with yaw head movements.

On the distribution of fast-phase intervals in optokinetic and vestibular nystagmus.

Histograms of fast-phase intervals in human optokinetic and vestibular nystagmus were generated, and fitted to statistical distributions used in previous studies. The distributions did not depend on stimulation type (optokinetic or vestibular). An inverse Gaussian or a gamma distribution fitted the data better than did a reciprocal Gaussian distribution, but none fitted the data especially well. In some cases, however, the interpretation of these distributions is more physiologically satisfactory than in others. Recommendations are made on which class of models is preferred, and the experiments needed to support the particular models. Our results call into question the validity of previous studies that fit statistical distributions to data sets of a size comparable to ours.

Random walks, random sequences, and nonlinear dynamics in human optokinetic nystagmus.

Optokinetic nystagmus (OKN) is a reflexive eye movement with target-following slow phases (SP) alternating with oppositely directed fast phases (FP). We measured the following from OKN in three humans: FP beginning and ending positions, amplitudes, and intervals and SP amplitudes and velocities. We sought to predict future values of each parameter on the basis of past values, using state-space representation of the sequence (time-delay embedding) and local second-order approximation of trajectories. Predictability is an indication of determinism: this approach allows us to investigate the relative contributions of random and deterministic dynamics in OKN. FP beginning and ending positions showed good predictability, but SP velocity was less predictable. FP and SP amplitudes and FP intervals had little or no predictability. FP beginnings and endings were as predictable as randomized versions that retain linear autocorrelation; this is typical of random walks. Predictability of FP intervals did not change under random rearrangement, which is characteristic of a random process. Only linear determinism was demonstrated; nonlinear interactions may exist that would not be detected by our present approach.

Use of a genetic algorithm for the analysis of eye movements from the linear vestibulo-ocular reflex.

It is common in vestibular and oculomotor testing to use a single-frequency (sine) or combination of frequencies [sum-of-sines (SOS)] stimulus for head or target motion. The resulting eye movements typically contain a smooth tracking component, which follows the stimulus, in which are interspersed rapid eye movements (saccades or fast phases). The parameters of the smooth tracking--the amplitude and phase of each component frequency--are of interest; many methods have been devised that attempt to identify and remove the fast eye movements from the smooth. We describe a new approach to this problem, tailored to both single-frequency and sum-of-sines stimulation of the human linear vestibulo-ocular reflex. An approximate derivative is used to identify fast movements, which are then omitted from further analysis. The remaining points form a series of smooth tracking segments. A genetic algorithm is used to fit these segments together to form a smooth (but disconnected) wave form, by iteratively removing biases due to the missing fast phases. A genetic algorithm is an iterative optimization procedure; it provides a basis for extending this approach to more complex stimulus-response situations. In the SOS case, the genetic algorithm estimates the amplitude and phase values of the component frequencies as well as removing biases.

Adaptation of the phase of the human linear vestibulo-ocular reflex (LVOR) and effects on the oculomotor neural integrator.

The phase of the translational linear VOR (LVOR) can be adaptively modified by exposure to a visual-vestibular mismatch. We extend here our earlier work on LVOR phase adaptation, and discuss the role of the oculomotor neural integrator. Ten subjects were oscillated laterally at 0.5 Hz, 0.3 g peak acceleration, while sitting upright on a linear sled. LVOR was assessed before and after adaptation with subjects tracking the remembered location of a target at 1 m in the dark. Phase and gain were measured by fitting sine waves to the desaccaded eye movements, and comparing sled and eye position. To adapt LVOR phase, the subject viewed a computer-generated stereoscopic visual display, at a virtual distance of 1 m, that moved so as to require either a phase lead or a phase lag of 53 deg. Adaptation lasted 20 min, during which subjects were oscillated at 0.5 Hz/0.3 g. Four of five subjects produced an adaptive change in the lag condition (range 4-45 deg), and each of five produced a change in the lead condition (range 19-56 deg), as requested. Changes in drift on eccentric gaze suggest that the oculomotor velocity-to-position integrator may be involved in the phase changes.

Dynamics of the human linear vestibulo-ocular reflex at medium frequency and modification by short-term training.

We study here the effect of a short-term training paradigm on the gain and phase of the human translational VOR (the linear VOR: LVOR). Subjects were exposed to lateral sinusoidal translations on a sled, at 0.5 Hz, 0.3 g peak acceleration. With subjects tracking a remembered target at 1.2 m, the LVOR (slow-phase) under these conditions typically has a phase lead or lag, and a gain that falls short of compensatory. To induce short-term adaptation (training), we presented an earth-fixed visual scene at 1.2 m during sinusoidal translation (x 1 viewing) for 20 minutes, so as to drive the LVOR toward compensatory phase and gain. We examined both the slow-phase and the saccadic responses to these stimuli. Testing after training showed changes in slow-component gain and phase which were mostly but not always in the compensatory direction. These changes were more consistent in naive subjects than in subjects who had previous LVOR experience. Changes in gain were seen with step as well as sinusoidal test stimuli; gain changes were not correlated with vergence changes. There was a strong correlation between gain changes and phase changes across subjects. Fast phases (catch-up saccades) formed a large component of the LVOR under our testing conditions (approximately 30% of the changes in gain but not in phase due to training.

Nonlinear dynamic systems evaluation of rhythmic' eye movements (optokinetic nystagmus).

The last decade has seen a surge in the study of nonlinear dynamical behavior in physiologic systems. In this paper, some of the computational techniques most commonly used to investigate the nonlinear dynamics of these systems are described. Applications to eye movement analysis are included, including the validation of a mathematical model of optokinetic nystagmus (OKN) eye movements. OKN appears to have some nonlinear and deterministic component, along with significant randomness. Fast phase starting and ending points are somewhat predictable (deterministic), while so-called 'exceptional events' analysis shows that they also have a large random component. Surrogate data methods suggest that the population of slow and fast phases in OKN is more important than any specific relationship between adjacent slow and fast phases. Analysis of a statistical model for fast phase intervals indicates that the model data are slightly more random than the actual OKN.

A versatile stereoscopic visual display system for vestibular and oculomotor research.

Testing of the vestibular system requires a vestibular stimulus (motion) and/or a visual stimulus. We have developed a versatile, low cost, stereoscopic visual display system, using "virtual reality" (VR) technology. The display system can produce images for each eye that correspond to targets at any virtual distance relative to the subject, and so require the appropriate ocular vergence. We elicited smooth pursuit, "stare" optokinetic nystagmus (OKN) and after-nystagmus (OKAN), vergence for targets at various distances, and short-term adaptation of the vestibulo-ocular reflex (VOR), using both conventional methods and the stereoscopic display. Pursuit, OKN, and OKAN were comparable with both methods. When used with a vestibular stimulus, VR induced appropriate adaptive changes of the phase and gain of the angular VOR. In addition, using the VR display system and a human linear acceleration sled, we adapted the phase of the linear VOR. The VR-based stimulus system not only offers an alternative to more cumbersome means of stimulating the visual system in vestibular experiments, it also can produce visual stimuli that would otherwise be impractical or impossible. Our techniques provide images without the latencies encountered in most VR systems. Its inherent versatility allows it to be useful in several different types of experiments, and because it is software driven it can be quickly adapted to provide a new stimulus. These two factors allow VR to provide considerable savings in time and money, as well as flexibility in developing experimental paradigms.

Short-term vestibulo-ocular adaptation: influence of context.

A number of mechanisms and strategies are used to help an individual compensate for loss of labyrinthine function. One important example is the ability to produce a preplanned motor response that anticipates the motion of the head and so compensates for it. Closely tied to this phenomenon is the gating, in or out, of a learned response on the basis of the context in which it must occur. This issue is particularly relevant to designing programs of physical therapy that optimize performance for natural behavior. Here we discuss a model of short-term vestibulo-ocular adaptation-adjustment of vestibulo-ocular phase (timing)-and how it can be used to study context-dependent vestibulo-ocular learning. We will show how vestibulo-ocular phase can be adjusted by selectively altering the common velocity-to-position ocular motor neural integrator for one type of eye movement (vestibular) and not for another (saccades), or for one type of head movement (sinusoidal) and not for another (step). These results are another example of the remarkable flexibility of the vestibulo-ocular adaptive mechanism and further show that the fundamental process of integration for eye movements can be modified according to the pattern of afferent information.

Context-specific short-term adaptation of the phase of the vestibulo-ocular reflex.

The phase of the angular vestibulo-ocular reflex (VOR) is subject to adaptive control. We had previously found that adapting the phase of the VOR also produced changes in drift on eccentric gaze-holding, implying a change in the time constant of the velocity-to-position neural integrator. Here we attempted to dissociate changes in gaze-holding drift from changes in the phase of the VOR. In normal human subjects, for 2 h, we alternated 5 min of VOR phase adaptation (sinusoids, 0.2 Hz) with 5 min of making saccades in the light with the head stationary. Afterwards, changes in VOR phase were the same (32% of requested) as those obtained with 1 h of phase adaptation alone, but changes in drift following saccades were much smaller than those found after phase adaptation alone (0.8 degrees/s compared with 5 degrees/s). When measuring drift after VOR steps, however, the changes were closer to those found after phase adaptation alone (3.8 degrees/s). To test the relationship between gaze-holding drift after VOR steps and adaptive changes in VOR phase, we alternated sinusoidal VOR phase adaptation with normal VOR steps in the light. In this paradigm, the adaptive change in VOR phase was about the same as with phase-adaptation alone (35%), but there was now little drift after saccades (1.9 degrees/s) or after VOR steps (0.7 degrees/s). We conclude that the state of the velocity-to-position neural integrator can be altered selectively and rapidly depending upon the task required. Such context-specific adaptation is advantageous, because it allows adjustment of the phase of the VOR without degrading the ability to hold eccentric fixation.

Prediction of the sequence of optokinetic nystagmus eye movements reveals deterministic structure in reflexive oculomotor behavior.

Optokinetic nystagmus (OKN) is a reflexive eye movement with a characteristic pattern of alternating fast and slow phases (resembling a noisy sawtooth), but with significant variation in the timing and amplitude of its components. We attempt to predict the sequence of OKN fast and slow phases by embedding them in state space and forming local approximations to the resulting trajectories. There is significant predictability only in the sequence of fast phase starting and ending positions. This is presumably related to the desire of the oculomotor system to aim the eyes at a location in space where something important might be expected to appear, leading to a partially deterministic rule for generating the end points of the fast phases.

On the correlation dimension of optokinetic nystagmus eye movements: computational parameters, filtering, nonstationarity, and surrogate data.

We discuss the estimation of the correlation dimension of optokinetic nystagmus (OKN), a type of reflexive eye movement. Parameters of the time-delay reconstruction of the attractor are investigated, including the number of data points, the time delay, the window duration, and the duration of the signal being analyzed. Adequate values are recommended. Digital low-pass filtering causes the dimension to increase as the filter cutoff frequency decreases, in accord with a previously published prediction. The stationarity of the correlation dimension is examined; the dimension appears to decrease over the course of 120 s of continuous stimulation. Implications for the reliable estimation of the dimension are considered. Several surrogate data sets are constructed, based on both early (0-30 s) and late (100-130 s) OKN segments. Most of the surrogate data sets randomize some aspect of the original OKN, while maintaining other aspects. Dimensions are found for all surrogates and for the original OKN. Evidence is found that is consistent with some amount of deterministic and nonlinear dynamics in OKN. When this structure is randomized in the surrogate, the dimension changes or the dimension algorithm ceases to converge to a finite value. Implications for further analysis and modeling of OKN are discussed.

Short-term adaptation of the phase of the vestibulo-ocular reflex (VOR) in normal human subjects.

We investigated the effects of short-term vestibulo-ocular reflex (VOR) adaptation on the gain and phase of the VOR, and on eccentric gaze-holding in darkness, in five normal human subjects. For 1 h, subjects sat in a chair that rotated sinusoidally at 0.2 Hz while surrounded by a visual stimulus (optokinetic drum). The drum was rotated relative to the chair, to require a VOR with either a phase lead or lag of 45 deg (with respect to a compensatory phase of zero) with no change in gain, or a gain of 1.7 or 0.5 with no change in phase. Immediately before and after each training session, VOR gain and phase were measured in the dark with 0.2 Hz sinusoidal rotation. Gaze-holding was evaluated following 20 deg eccentric saccades in darkness. Adaptation paradigms that called only for a phase lead produced an adapted VOR with 33% of the required amount of phase change, a 20% decrease in VOR gain, and an increased centripetal drift after eccentric saccades made in darkness. Adaptation paradigms that called for a phase lag produced an adapted VOR with 29% of the required amount of phase change, no significant change in VOR gain, and a centrifugal drift after eccentric saccades. Adaptation paradigms requiring a gain of 1.7 produced a 15% increase in VOR gain with small increases in phase and in centripetal drift. Adaptation paradigms requiring a gain of 0.5 produced a 31% decrease in VOR gain with a 6 deg phase lag and a centrifugal drift. The changes in drift and phase were well correlated across all adaptation paradigms; the changes in phase and gain were not. We attribute the effects on phase and gaze-holding to changes in the time constant of the velocity-to-position ocular motor neural integrator. Phase leads and the corresponding centripetal drift are due to a leaky integrator, and phase lags and the corresponding centrifugal drift are due to an unstable integrator. These results imply that in the short-term adaptation paradigm used here, the control of drift and VOR phase are tightly coupled through the neural integrator, whereas VOR gain is controlled by another mechanism.

Effect of vergence on the gain of the linear vestibulo-ocular reflex.

We measured the linear vestibulo-ocular reflex (LVOR) and vergence, using binocular search coils, in 3 humans. The subjects were accelerated sinusoidally at 0.5 Hz and 0.2 g peak acceleration, in complete darkness, while performing three different tasks: i) mental arithmetic; ii) tracking a remembered target at either 0.34 m or 0.14 m distance; and iii) maintaining vergence at either of these distances by means of audio biofeedback based on vergence. Subjects could control vergence using the audio feedback; there was greater convergence with the near audio target. However, there was no significant difference in vergence between the near and far remembered target conditions. With audio feedback, the amplitude of smooth tracking was not consistently different for the near and the far conditions. However, the amplitude of tracking (saccades and smooth component) in the remembered target conditions was greater for near than for far targets. These results suggest that linear VOR amplitude is not determined by vergence alone.

Short-term vestibulo-ocular reflex adaptation in humans. I. Effect on the ocular motor velocity-to-position neural integrator.

We investigated the effect of short-term vestibulo-ocular reflex (VOR) adaptation in normal human subjects on the dynamic properties of the velocity-to-position ocular motor integrator that holds positions of gaze. Subjects sat in a sinusoidally rotating chair surrounded by an optokinetic nystagmus drum. The movement of the visual surround (drum) was manipulated relative to the chair to produce an increase (x 1.7 viewing), decrease (x 0.5, x 0 viewing), or reversal (x (-2.5) viewing) of VOR gain. Before and after 1 h of training, VOR gain and gaze-holding after eccentric saccades in darkness were measured. Depending on the training paradigm, eccentric saccades could be followed by centrifugal drift (after x 0.5 viewing), implying an unstable integrator, or by centripetal drift [after x 1.7 or x (-2.5) viewing], implying a leaky integrator. The changes in the neural integrator appear to be context specific, so that when the VOR was tested in non-training head orientations, both the adaptive change in VOR gain and the changes in the neural integrator were much smaller. The changes in VOR gain were on the order of 10% and the induced drift velocities were several degrees per second at 20 deg eccentric positions in the orbit. We propose that (1) the changes in the dynamic properties of the neural integrator reflect an attempt to modify the phase (timing) relationships of the VOR and (2) the relative directions of retinal slip and eye velocity during head rotation determine whether the integrator becomes unstable (and introduces more phase lag) or leaky (and introduces less phase lag).

Short-term vestibulo-ocular reflex adaptation in humans. II. Error signals.

We oscillated humans sinusoidally at 0.2 Hz for 1 h, using various combinations of rotations of the head and visual surround to elicit short-term adaptation of the gain of the vestibulo-ocular reflex (VOR). Before and after each period of training, the gain of the VOR was measured in darkness, in response to a position step of head rotation. A small foveal target served as well as a full-field stimulus at driving VOR adaptation. Oscillation of the visual surround alone produced a substantial increase in the VOR gain. When the visual scene was rotated in phase with the head but with a larger amplitude to produce a reversal of the VOR, the VOR gain increased if the movement of the visual scene was much greater than that of the head, otherwise the gain decreased. We interpreted these results with a model of VOR adaptation that uses as its "error signal" the combination of motion of images on the retina (retinal slip) and any additional slow-phase eye velocity, beyond that generated by the VOR through the vestibular nuclei, necessary to prevent such retinal slip during head rotation. The slow phase velocity generated by the VOR is derived from "inferred head rotation", a signal based on the discharge of neurons in the vestibular nuclei that receive both labyrinthine and visual (optokinetic) inputs. The amplitude and sign of the ratio of the "error signal" to "inferred head velocity" determined the amplitude and the direction (increase or decrease) of VOR gain adaptation.

Vergence can be controlled by audio feedback, and induces downward ocular deviation.

We measured horizontal and vertical eye positions, using binocular search coils, in three humans. Subjects could maintain vergence by means of audio biofeedback. Feedback consisted of a pair of audio tones, one variable and one fixed at a reference frequency. The variable tone was controlled by instantaneous vergence and provided immediate feedback on the vergence state. The reference frequency, which they attempted to match, was set to correspond to a target distance of either 0.34 m or 0.14 m. Subjects could maintain vergence consistently, even while undergoing lateral motions at 0.5 Hz and 0.2 g peak acceleration in darkness. There was also a consistent tendency for the eyes to deviate downward during near vergence. The results may be useful in experiments in which one wishes to control vergence without providing a visual reference which might inhibit conjugate eye movements.