Accuracy-precision trade-off in visual orientation constancy.

Using the subjective visual vertical task (SVV), previous investigations on the maintenance of visual orientation constancy during lateral tilt have found two opposite bias effects in different tilt ranges. The SVV typically shows accurate performance near upright but severe undercompensation at tilts beyond 60 deg (A-effect), frequently with slight overcompensation responses (E-effect) in between. Here we investigate whether a Bayesian spatial-perception model can account for this error pattern. The model interprets A- and E-effects as the drawback of a computational strategy, geared at maintaining visual stability with optimal precision at small tilt angles. In this study, we test whether these systematic errors can be seen as the consequence of a precision-accuracy trade-off when combining a veridical but noisy signal about eye orientation in space with the visual signal. To do so, we used a psychometric approach to assess both precision and accuracy of the SVV in eight subjects laterally tilted at 9 different tilt angles (-120 degrees to 120 degrees). Results show that SVV accuracy and precision worsened with tilt angle, according to a pattern that could be fitted quite adequately by the Bayesian model. We conclude that spatial vision essentially follows the rules of Bayes' optimal observer theory.

Fusion of visual and vestibular tilt cues in the perception of visual vertical.

We investigated the effect of visual and vestibular body-tilt cues on the subjective visual vertical (SVV) in six human observers at roll tilts of 0, 60, and 120 degrees . Subjects adjusted a small luminous test line parallel to the perceived direction of gravity, in the presence of a large peripheral visual frame line. These settings, referred to as the frame SVV, were compared with the SVV in complete darkness (dark SVV). The frame SVV was virtually identical to the dark SVV for frame lines parallel or orthogonal to the dark SVV. Away from these neutral positions, the frame induced a periodic SVV modulation, which was small in upright observers, but became quite pronounced when subjects were tilted. For upright, where the dark SVV was very accurate, the frame SVV showed errors in both directions, following a roughly symmetrical pattern. At 120 degrees tilt, where the dark SVV invariably showed tilt undercompensation (A-effect), the frame effect became asymmetrical, with a stronger tendency to improve than to worsen accuracy. We tested whether our findings could be explained by two spatial orientation models: Mittelstaedt's idiotropic model and a Bayesian scheme with a stage for the processing of visual cues. Both models show a periodic frame effect that becomes stronger with increasing body tilt and can explain why frame lines parallel or perpendicular to the dark SVV are ineffective. Based on their performance, we conclude that perception of the visual vertical is based on a centrally weighted fusion of visual, vestibular, and egocentric references.

Body-tilt and visual verticality perception during multiple cycles of roll rotation.

To assess the effects of degrading canal cues for dynamic spatial orientation in human observers, we tested how judgments about visual-line orientation in space (subjective visual vertical task, SVV) and estimates of instantaneous body tilt (subjective body-tilt task, SBT) develop in the course of three cycles of constant-velocity roll rotation. These abilities were tested across the entire tilt range in separate experiments. For comparison, we also obtained SVV data during static roll tilt. We found that as tilt increased, dynamic SVV responses became strongly biased toward the head pole of the body axis (A-effect), as if body tilt was underestimated. However, on entering the range of near-inverse tilts, SVV responses adopted a bimodal pattern, alternating between A-effects (biased toward head-pole) and E-effects (biased toward feet-pole). Apart from an onset effect, this tilt-dependent pattern of systematic SVV errors repeated itself in subsequent rotation cycles with little sign of worsening performance. Static SVV responses were qualitatively similar and consistent with previous reports but showed smaller A-effects. By contrast, dynamic SBT errors were small and unimodal, indicating that errors in visual-verticality estimates were not caused by errors in body-tilt estimation. We discuss these results in terms of predictions from a canal-otolith interaction model extended with a leaky integrator and an egocentric bias mechanism. We conclude that the egocentric-bias mechanism becomes more manifest during constant velocity roll-rotation and that perceptual errors due to incorrect disambiguation of the otolith signal are small despite the decay of canal signals.

Shared computational mechanism for tilt compensation accounts for biased verticality percepts in motion and pattern vision.

To determine the direction of object motion in external space, the brain must combine retinal motion signals and information about the orientation of the eyes in space. We assessed the accuracy of this process in eight laterally tilted subjects who aligned the motion direction of a random-dot pattern (30% coherence, moving at 6 degrees /s) with their perceived direction of gravity (motion vertical) in otherwise complete darkness. For comparison, we also tested the ability to align an adjustable visual line (12 degrees diameter) to the direction of gravity (line vertical). For small head tilts (<40 degrees ), systematic errors in either task were almost negligible. In contrast, tilts >60 degrees revealed a pattern of large systematic errors (often >30 degrees ) that was virtually identical in both tasks. Regression analysis confirmed that mean errors in the two tasks were closely related, with slopes close to 1.0 and correlations >0.89. Control experiments ruled out that motion settings were based on processing of individual single-dot paths. We conclude that the conversion of both motion direction and line orientation on the retina into a spatial frame of reference involves a shared computational strategy. Simulations with two spatial-orientation models suggest that the pattern of systematic errors may be the downside of an optimal strategy for dealing with imperfections in the tilt signal that is implemented before the reference-frame transformation.

Verticality perception during off-vertical axis rotation.

During prolonged rotation about a tilted yaw axis, often referred to as off-vertical axis rotation (OVAR), a percept of being translated along a conical path slowly emerges as the sense of rotation subsides. Recently, we found that these perceptual changes are consistent with a canal-otolith interaction model that attributes the illusory translation percept to improper interpretation of the ambiguous otolith signals. The model further predicts that the illusory translation percept must be accompanied by slowly worsening tilt underestimates. Here, we tested this prediction in six subjects by measuring the time course of the subjective visual vertical (SVV) during OVAR stimulation at three different tilt-rotation speed combinations, in complete darkness. Throughout the 2-min run, at each left-ear-down and right-ear-down position, the subject indicated whether a briefly flashed line deviated clockwise or counterclockwise from vertical to determine the SVV with an adaptive staircase procedure. Typically, SVV errors indicating tilt underestimation were already present at rotation onset and then increased exponentially to an asymptotic value, reached at about 60 s after rotation onset. The initial error in the SVV was highly correlated to the response error in a static tilt control experiment. The subsequent increase in error depended on both rotation speed and OVAR tilt angle, in a manner predicted by the canal-otolith interaction model. We conclude that verticality misjudgments during OVAR reflect a dynamic component linked to canal-otolith interaction, superimposed on a tilt-related component that is also expressed under stationary conditions.

Time course and magnitude of illusory translation perception during off-vertical axis rotation.

Human spatial orientation relies on vision, somatosensory cues, and signals from the semicircular canals and the otoliths. The canals measure rotation, whereas the otoliths are linear accelerometers, sensitive to tilt and translation. To disambiguate the otolith signal, two main hypotheses have been proposed: frequency segregation and canal-otolith interaction. So far these models were based mainly on oculomotor behavior. In this study we investigated their applicability to human self-motion perception. Six subjects were rotated in yaw about an off-vertical axis (OVAR) at various speeds and tilt angles, in darkness. During the rotation, subjects indicated at regular intervals whether a briefly presented dot moved faster or slower than their perceived self-motion. Based on such responses, we determined the time course of the self-motion percept and characterized its steady state by a psychometric function. The psychophysical results were consistent with anecdotal reports. All subjects initially sensed rotation, but then gradually developed a percept of being translated along a cone. The rotation percept could be described by a decaying exponential with a time constant of about 20 s. Translation percept magnitude typically followed a delayed increasing exponential with delays up to 50 s and a time constant of about 15 s. The asymptotic magnitude of perceived translation increased with rotation speed and tilt angle, but never exceeded 14 cm/s. These results were most consistent with predictions of the canal-otolith-interaction model, but required parameter values that differed from the original proposal. We conclude that canal-otolith interaction is an important governing principle for self-motion perception that can be deployed flexibly, dependent on stimulus conditions.

Visuospatial memory computations during whole-body rotations in roll.

We used a memory-saccade task to test whether the location of a target, briefly presented before a whole-body rotation in roll, is stored in egocentric or in allocentric coordinates. To make this distinction, we exploited the fact that subjects, when tilted sideways in darkness, make systematic errors when indicating the direction of gravity (an allocentric task) even though they have a veridical percept of their self-orientation in space. We hypothesized that if spatial memory is coded allocentrically, these distortions affect the coding of remembered targets and their readout after a body rotation. Alternatively, if coding is egocentric, updating for body rotation becomes essential and errors in performance should be related to the amount of intervening rotation. Subjects (n = 6) were tested making saccades to remembered world-fixed targets after passive body tilts. Initial and final tilt angle ranged between -120 degrees CCW and 120 degrees CW. The results showed that subjects made large systematic directional errors in their saccades (up to 90 degrees ). These errors did not occur in the absence of intervening body rotation, ruling out a memory degradation effect. Regression analysis showed that the errors were closely related to the amount of subjective allocentric distortion at both the initial and final tilt angle, rather than to the amount of intervening rotation. We conclude that the brain uses an allocentric reference frame, possibly gravity-based, to code visuospatial memories during whole-body tilts. This supports the notion that the brain can define information in multiple frames of reference, depending on sensory inputs and task demands.

Interaction between visual and vestibular signals for the control of rapid eye movements.

To investigate interactions between voluntary and reflexive eye movements, five subjects were asked to make pro- or anti-saccades to various oblique locations cued by a head-fixed flash while being rotated sinusoidally in yaw (0.17 Hz; 73 degrees /s peak velocity) in complete darkness. Eye movements were recorded with the coil technique. In the pro-saccade task, targeting responses showed clear compensation for the intervening nystagmus, but there was a marked increase in horizontal scatter. Most quick phases directed into the hemifield opposite to the flash (away trials) were suppressed from ~100 ms onward. By contrast, quick phases directed into the hemifield of the flash (toward trials) continued virtually unabated until visually triggered saccades began to appear. From 80 ms onward, these vestibularly triggered movements showed signs of metrical modification by the visual signal. In the anti-saccade experiments, suppression of quick phases away from the flash was just as strong as in the pro-saccade experiments, and error rates in these trials were almost as low as in stationary control conditions. Suppression of quick phases directed toward the flash was a new phenomenon that emerged only in anti-saccade experiments. Since this inhibition had a late onset and was only partial, error rates in anti-saccade toward trials were very high. At short latencies, both components of most rapid eye movements were wrongly directed toward the flash. This was followed by a stage with frequent incongruent responses in which unsuppressed quick phases provoked an incorrect horizontal movement, whereas the vertical component showed a correct anti-saccade response. At still longer latencies, most responses were correct in both components. The visual modification of short-latency responses in both tasks showed that rapid eye movements could not simply be classified as either voluntary or reflexive, but suggested that signals underlying each class could merge into a compromise response. That vestibular rotation during the anti-saccade task may cause a wrongly directed horizontal component resembling a quick phase, combined with a vertical component expressing a correct anti-saccade signal, reveals a remarkable independence at the component level. These observations suggest that voluntary and involuntary movements can be programmed in parallel. This behavior is explained most parsimoniously by assuming that the two signals converge at a component-coding stage of the system, rather than at a vectorial coding stage.

Collicular microstimulation during passive rotation does not generate fixed gaze shifts.

We investigated whether saccades evoked by electrical stimulation (E-saccades) in the superior colliculus can compensate for passive sinusoidal head rotation in yaw so as to keep the rapid gaze shift constant. After accounting for variations in E-saccade onset position, we found significant horizontal metric changes, proportional to head velocity, in 31 of 37 experiments in 2 monkeys. Vertical effects were small. In a substantial fraction of the experiments (14/37), these metric changes represented significant but often insufficient compensatory adjustments in the horizontal component, opposite to the direction of head movement. However, very robust violations of gaze-shift constancy were remarkably common: significant anticompensatory changes in the horizontal component occurred in 17/37 experiments. In these cases, typically involving larger E-saccades, the horizontal component increased in size with rotation into the half field containing the E-saccade and became smaller during opposite rotation. Further analysis showed that, instead of showing a dichotomy, the metric effect actually varied along a continuum from compensatory to strongly anticompensatory. In addition to these metric changes, we found a robust kinematic effect of head rotation in metrically matched E-saccades. In all experiments where the effect was significant (34/37), horizontal peak velocity increased for rotation into the half field where the E-saccade was directed and decreased for opposite rotation. This kinematic effect was again proportional to head velocity and predominant in the horizontal component. Comparison of yaw and pitch rotation at the same stimulation site showed that both expressions of vestibular-saccade interaction (metric and kinematic) tended to align with the direction of rotation. The component-specific nature of the modulation suggests that the effects may have been caused by convergence of saccadic and vestibular signals at a component-coding stage downstream of the colliculus. We suggest that the quick-phase system got access to the common pulse generator as soon as the collicular stimulation had opened the pause-cell gate. Adding such an anticompensatory signal would act to increase the E-saccade horizontal component when the monkey was rotated in the same direction and bring about a decrease in size and peak velocity when it was opposite. In the large majority of experiments the metric changes failed to maintain gaze-shift constancy, either because they were in the wrong direction or because they were too small. Possible reasons for this major departure from the properties of natural gaze shifts are discussed.

Human gaze stabilization during active head translations.

This study investigated how binocular gaze is controlled to compensate for self-generated translational movements of the head where geometric requirements dictate that the ideal gaze signal needs to be modulated by the inverse of target distance. Binocular gaze (eye plus head) was measured for visual and remembered targets at various distances in six human subjects during active head translations at frequencies of 0.25, 0.5, 1.0, and 1.5 Hz. We found that, during head translations, gaze changes were achieved by a combination of eye and head rotations. Accordingly, stabilization performance was characterized by the gaze response parameters sensitivity and phase, where sensitivity is defined as the ratio of gaze velocity and translational eye velocity and where phase refers to the phase delay of gaze velocity relative to translational eye velocity. In the analysis, we used a binocular coordinate system yielding a version and a vergence component. We examined how frequency and target distance, estimated from the vergence angle, affected sensitivity and phase of the version component of the gaze signal and compared the results to the requirements for ideal performance. The relation between gaze sensitivity and the inverse of distance was characterized by a linear regression analysis. The ratio of the slope of the linear regression and the slope required for ideal stabilization provided a measure for the degree of "distance compensation." The results show that distance compensation was better for a visual target than for remembered targets in darkness, and behaved according to low-pass characteristics in both target conditions. It declined from 1.00 to 0.84 for visual targets and from 0.87 to 0.57 for remembered targets in the frequency range 0.25-1.5 Hz. The intercept obtained from the regression yielded the gaze response at zero vergence and specified a "default sensitivity" of gaze compensation. Default sensitivity increased with frequency from 0.02 at 0.25 Hz to 0.10 degrees/cm at 1.5 Hz for visual targets and from 0.04 to 0.16 degrees/cm in darkness. The phase delays of the gaze response increased on average from 2 to 7 degrees in the frequency range 0.25-1.5 Hz. In comparison with earlier passive studies, active translation compensation in the dark is superior at all frequencies where comparison was possible. We conclude that a nonvestibular signal with low-pass characteristics contributes to gaze during active head translations.

The subjective vertical and the sense of self orientation during active body tilt.

Previous testing of the ability to set a luminous line to the direction of gravity in passively-tilted subjects, in darkness, has revealed a remarkable pattern of systematic errors at tilts beyond 60 degrees, as if body tilt is undercompensated or underestimated (Aubert or A-effect). We investigated whether these consistent deviations from orientation constancy can be avoided during active body tilt, where more potential cues about body tilt (e.g. proprioception and efference copy) are available. The effects of active body tilt on the subjective vertical and on the perception of self tilt were studied in six subjects. After adopting a laterally-tilted posture, while standing in a dark room, they indicated the subjective vertical by adjusting a visual line and gave their verbal estimate of head orientation, expressed on a clock scale. Head roll tilts covered the range from -150 degrees to +150 degrees. The subjective vertical results showed no sign of improvement. Actively-tilted subjects still exhibited the same pattern of systematic errors that characterised their performance during passive tilt. Random errors in this task showed a steep monotonic increase with tilt angle, as in earlier passive tilt experiments. By contrast, verbal head-tilt estimates in the active experiments showed a clear improvement and were now almost devoid of systematic errors, but the noise level remained high. Various models are discussed in an attempt to clarify how these task-related differences and the selective improvement of the self-tilt estimates in the active experiments may have come about.

Context compensation in the vestibuloocular reflex during active head rotations.

The vestibuloocular reflex (VOR) needs to modulate its gain depending on target distance to prevent retinal slip during head movements. We investigated gain modulation (context compensation) for binocular gaze stabilization in human subjects during voluntary yaw and pitch head rotations. Movements of each eye were recorded, both when attempting to maintain gaze on a small visual target at straight-ahead in a darkened room and after its disappearance (remembered target). In the analysis, we relied on a binocular coordinate system yielding a version and a vergence component. We examined how frequency and target distance, approached here by using vergence angle, affected the gain and phase of the version component of the VOR and compared the results to the requirements for ideal performance. Linear regression analysis on the version gain-vergence relationship yielded a slope representing the influence of target proximity and an intercept corresponding to the response at zero vergence ("default gain"). The slope of the fitted relationship, divided by the geometrically required slope, provided a measure for the quality of version context compensation ("context gain"). In both yaw and pitch experiments, we found default version gains close to one even for the remembered target condition, indicating that the active VOR for far targets is already close to ideal without visual support. In near target experiments, the presence of visual feedback yielded near unity context gains, indicating close to optimal performance (retinal slip <0.4 degrees /s). For remembered targets, the context gain deteriorated but was still superior to performance in corresponding passive studies reported in the literature. In general, context compensation in the remembered target paradigm was better for vertical than for horizontal head rotations. The phase delay of version eye velocity relative to head velocity was small (approximately 2 degrees) for both horizontal and vertical head movements. Analysis of the vergence data from the near target experiments showed that context compensation took into account that the two eyes require slightly different VORs. In the DISCUSSION, comparison of the present default VOR gains and context gains with data from earlier passive studies has led us to propose a limited role for efference copies during self-generated movements. We also discuss how our analysis can provide a framework for evaluating two different hypotheses for the generation of binocular VOR eye movements.

Kinematic strategies for upper arm-forearm coordination in three dimensions.

This study addressed the question of how the three-dimensional (3-D) control strategy for the upper arm depends on what the forearm is doing. Subjects were instructed to point a laser-attached in line with the upper arm-toward various visual targets, such that two-dimensional (2-D) pointing directions of the upper arm were held constant across different tasks. For each such task, subjects maintained one of several static upper arm-forearm configurations, i. e., each with a set elbow angle and forearm orientation. Upper arm, forearm, and eye orientations were measured with the use of 3-D search coils. The results confirmed that Donders' law (a behavioral restriction of 3-D orientation vectors to a 2-D "surface") does not hold across all pointing tasks, i.e., for a given pointing target, upper arm torsion varied widely. However, for any one static elbow configuration, torsional variance was considerably reduced and was independent of previous arm position, resulting in a thin, Donders-like surface of orientation vectors. More importantly, the shape of this surface (which describes upper arm torsion as a function of its 2-D pointing direction) depended on both elbow angle and forearm orientation. For pointing with the arm fully extended or with the elbow flexed in the horizontal plane, a Listing's-law-like strategy was observed, minimizing shoulder rotations to and from center at the cost of position-dependent tilts in the forearm. In contrast, when the arm was bent in the vertical plane, the surface of best fit showed a Fick-like twist that increased continuously as a function of static elbow flexion, thereby reducing position-dependent tilts of the forearm with respect to gravity. In each case, the torsional variance from these surfaces remained constant, suggesting that Donders' law was obeyed equally well for each task condition. Further experiments established that these kinematic rules were independent of gaze direction and eye orientation, suggesting that Donders' law of the arm does not coordinate with Listing's law for the eye. These results revive the idea that Donders' law is an important governing principle for the control of arm movements but also suggest that its various forms may only be limited manifestations of a more general set of context-dependent kinematic rules. We propose that these rules are implemented by neural velocity commands arising as a function of initial arm orientation and desired pointing direction, calculated such that the torsional orientation of the upper arm is implicitly coordinated with desired forearm posture.

Properties of the internal representation of gravity inferred from spatial-direction and body-tilt estimates.

One of the key questions in spatial perception is whether the brain has a common representation of gravity that is generally accessible for various perceptual orientation tasks. To evaluate this idea, we compared the ability of six tilted subjects to indicate earth-centric directions in the dark with a visual and an oculomotor paradigm and to estimate their body tilt relative to gravity. Subjective earth-horizontal and -vertical data were collected, either by adjusting a visual line or by making saccades, at 37 roll-tilt angles across the entire range. These spatial perception responses and the associated body-tilt estimates were subjected to a principal-component analysis to describe their tilt dependence. This analysis allowed us to separate systematic and random errors in performance, to disentangle the effects of task (horizontal vs. vertical) and paradigm (visual vs. oculomotor) in the space-perception data, and to compare the veridicality of space perception and the sense of self-tilt. In all spatial-orientation tests, whether involving space-perception or body-tilt judgments, subjects made considerable systematic errors which mostly betrayed tilt underestimation [Aubert effect (A effect)] and peaked near 130 degrees tilt. However, the A effect was much smaller in body-tilt estimates than in spatial pointing, implying that the underlying signal processing must have been different. Pointing results obtained with the visual and the oculomotor paradigm were not identical either, but these differences, which were task-related (horizontal vs. vertical), were subtle in comparison. The tilt-dependent pattern of random errors (noisy scatter) was almost identical in visual and oculomotor pointing results, showing a steep monotonic increase with tilt angle, but was again clearly different in the body-tilt estimates. These findings are discussed in the context of a conceptual model in an attempt to explain how the different patterns of systematic and random errors in external-space and self-tilt perception may come about. The scheme proposes that basically similar computational mechanisms, working with different settings, may be responsible.

Stimulation in the rostral pole of monkey superior colliculus: effects on vergence eye movements.

Recent studies have indicated that the superior colliculus (SC), traditionally considered to be saccade-related, may play a role in the coding of eye movements in both direction and depth. Similarly, it has been suggested that omnidirectional pause neurons are not only involved in the initiation of saccades, but can also modulate vergence eye movements. These new developments provide a challenge for current oculomotor models that attempt to describe saccade-vergence coordination and the neural mechanisms that may be involved. In this paper, we have attempted to study these aspects further by investigating the role of the rostral pole of the SC in the control of vergence eye movements. It is well-known that, by applying long-duration electrical stimulation to rostral sites in the monkey SC, saccadic responses can be prevented and interrupted. We have made use of these properties to extend this paradigm to eye movements that contain a substantial depth component. We found that electrical intervention in the rostral region also has a clear effect on vergence. For an eye movement to a near target, stimulation leads to a significant suppression and change in dynamics of the pure vergence response during the period of stimulation, but the depth component cannot be prevented entirely. When these paradigms are implemented for 3D refixations, the saccade is inactivated, as expected, while the vergence component is often suppressed more than in the case of the pure vergence. The data lead us to conclude that the rostral SC, presumably indirectly via connections with the pause neurons, can affect vergence control for both pure vergence and combined 3D responses. Suppression of the depth component is incomplete, in contrast to the directional movement, and is often different in magnitude for 3D refixations and pure vergence responses. The results are discussed in connection with current models for saccade-vergence interaction.

Donders' law in torticollis.

We investigated head movements of patients with spasmodic torticollis toward targets in various directions. These patients, whose severe dystonia was reflected in an abnormal resting head position, appeared to retain a Donders'-type strategy for the control of the rotational degrees of freedom of the head. As in normals, rotation vectors, representing head orientation, were confined to a curved surface, which specifies how head torsion depends on gaze direction. The orientation of the surface in body coordinates, which was very stereotyped in normals, was different for patients. The same Donders surface was found for head movements and for stationary head postures, indicating that the same neural mechanism governs its implementation in both tasks. To interpret our results, we propose a conceptual scheme incorporating the basal ganglia, which are thought to be involved in the etiology of torticollis, and an implementation stage for Donders' law.

Perturbation of combined saccade-vergence movements by microstimulation in monkey superior colliculus.

Perturbation of combined saccade-vergence movements by microstimulation in monkey superior colliculus. This study investigated the role of the monkey superior colliculus (SC) in the control of visually (V)-guided combined saccade-vergence movements by assessing the perturbing effects of microstimulation. We elicited an electrical saccade (E) by stimulation (in 20% of trials) in the SC while the monkey was preparing a V-guided movement to a near target. The target was aligned such that E- and V-induced saccades had similar amplitudes but different directions and such that V-induced saccades had a significant vergence component (saccades to a near target). The onset of the E-stimulus was varied from immediately after V-target onset to after V-saccade onset. E-control trials, where stimulation was applied during fixation of a V-target, yielded the expected saccade but no vergence. By contrast, early perturbation trials, where the E-stimulus was applied soon after the onset of the V-target, caused an E-triggered response with a clear vergence component toward the V-target. Midflight perturbation, timed to occur just after the monkey initiated the movement toward the target, markedly curtailed the ongoing vergence component during the saccade. Examination of pooled responses from both types of perturbation trials showed weighted-averaging effects between E- and V-stimuli in both saccade and fast vergence components. Both components exhibited a progression from E- to V-dominance as the E-stimulus was delayed further. This study shows that artificial intervention in the SC, while a three-dimensional (3D) refixation is being prepared or is ongoing, can affect the timing (WHEN) and the metric specification (WHERE) of both saccades and vergence. To explain this we interpret the absence of overt vergence in the E-controls as being caused by a zero-vergence change command rather than reflecting the mere absence of a collicular vergence signal. In the perturbation trials, the E-evoked zero-vergence signal competes with the V-initiated saccade-vergence signal, thereby giving rise to a compromised 3D response. This effect would be expected if the population of movement cells at each SC site is tuned in 3D, combining the well-known topographical code for direction and amplitude with a nontopographical depth representation. On E-stimulation, the local population would yield a net saccade signal caused by the topography, but the cells coding for different depths would be excited equally, causing the vergence change to be zero.

Listing's plane dependence on alternating fixation in a strabismus patient.

Listing's law of the eye is one of the best studied findings in motor control, but its functional meaning is still incompletely understood and its status in neurological disorders and in strabismus is almost entirely unknown. We investigated the mechanisms underlying Listing's law and its possible clinical relevance. The dual magnetic search coil technique was used to record three-dimensional binocular eye movements in a stereoblind strabismic patient with good visual acuity in both eyes and capable of voluntarily alternating fixation. This technique yielded an accurate, objective and simultaneous measure of ocular misalignment in three dimensions and showed that the squint angle depended on which eye was fixating. Saccadic eye movement data throughout the oculomotor range were used to fit Listing's plane. Listing's primary position and the thickness of the plane for each eye were calculated for three different fixation conditions. For comparison, control measurements were taken from four normals. In the patient, no large deviations from normal values for the thickness of Listing's plane and the confidence limits of the Listing primary position were found. The most remarkable abnormality was that the orientation of Listing's plane depended on which eye was fixating. Both the change in ocular misalignment and the shift of Listing's primary positions observed when changing fixation are probably linked to accommodation-related vergence. Despite repeated surgery at early age, the patient had well-defined Listing planes for both eyes, but their alignment during left-eye fixation was abnormal. The obedience to Listing's law may reflect a strategy which minimizes muscular effort in each eye separately. The abnormal fixation-condition dependence is probably due to an aberrant coupling with vergence.