Neural control of three-dimensional eye and head movements

Decoding spatial locations from primate lateral prefrontal cortex neural activity during virtual navigation

Objective. Decoding the intended trajectories from brain signals using a brain-computer interface system could be used to improve the mobility of patients with disabilities.Approach. Neuronal activity associated with spatial locations was examined while macaques performed a navigation task within a virtual environment.Main results.Here, we provide proof of principle that multi-unit spiking activity recorded from the lateral prefrontal cortex (LPFC) of non-human primates can be used to predict the location of a subject in a virtual maze during a navigation task. The spatial positions within the maze that require a choice or are associated with relevant task events can be better predicted than the locations where no relevant events occur. Importantly, within a task epoch of a single trial, multiple locations along the maze can be independently identified using a support vector machine model.Significance. Considering that the LPFC of macaques and humans share similar properties, our results suggest that this area could be a valuable implant location for an intracortical brain-computer interface system used for spatial navigation in patients with disabilities.

Reduced Facilitation of Parietal-Motor Functional Connections in Older Adults

Age-related changes in cortico-cortical connectivity in the human motor network in older adults are associated with declines in hand dexterity. Posterior parietal cortex (PPC) is strongly interconnected with motor areas and plays a critical role in many aspects of motor planning. Functional connectivity measures derived from dual-site transcranial magnetic stimulation (dsTMS) studies have found facilitatory inputs from PPC to ipsilateral primary motor cortex (M1) in younger adults. In this study, we investigated whether facilitatory inputs from PPC to M1 are altered by age. We used dsTMS in a conditioning-test paradigm to characterize patterns of functional connectivity between the left PPC and ipsilateral M1 and a standard pegboard test to assess skilled hand motor function in 13 young and 13 older adults. We found a PPC-M1 facilitation in young adults but not older adults. Older adults also showed a decline in motor performance compared to young adults. We conclude that the reduced PPC-M1 facilitation in older adults may be an early marker of age-related decline in the neural control of movement.

A Geometric Theory Integrating Human Binocular Vision With Eye Movement

A theory of the binocular system with asymmetric eyes (AEs) is developed in the framework of bicentric perspective projections. The AE accounts for the eyeball's global asymmetry produced by the foveal displacement from the posterior pole, the main source of the eye's optical aberrations, and the crystalline lens' tilt countering some of these aberrations. In this theory, the horopter curves, which specify retinal correspondence of binocular single vision, are conic sections resembling empirical horopters. This advances the classic model of empirical horopters as conic sections introduced in an ad hoc way by Ogle in 1932. In contrast to Ogle's theory, here, anatomically supported horopteric conics vary with the AEs' position in the visual plane of bifoveal fixations and their transformations are visualized in a computer simulation. Integrating horopteric conics with eye movements can help design algorithms for maintaining a stable perceptual world from visual information captured by a mobile robot's camera head. Further, this paper proposes a neurophysiologically meaningful definition for the eyes' primary position, a concept which has remained elusive despite its theoretical importance to oculomotor research. Finally, because the horopteric conic's shape is dependent on the AE's parameters, this theory allows for changes in retinal correspondence, which is usually considered preformed and stable.

Advances in the pathophysiology of adult-onset focal dystonias: recent neurophysiological and neuroimaging evidence

Focal dystonia is a movement disorder characterized by involuntary muscle contractions that determine abnormal postures. The traditional hypothesis that the pathophysiology of focal dystonia entails a single structural dysfunction (i.e. basal ganglia) has recently come under scrutiny. The proposed network disorder model implies that focal dystonias arise from aberrant communication between various brain areas. Based on findings from animal studies, the role of the cerebellum has attracted increased interest in the last few years. Moreover, it has been increasingly reported that focal dystonias also include nonmotor disturbances, including sensory processing abnormalities, which have begun to attract attention. Current evidence from neurophysiological and neuroimaging investigations suggests that cerebellar involvement in the network and mechanisms underlying sensory abnormalities may have a role in determining the clinical heterogeneity of focal dystonias.

The Influence of a Memory Delay on Spatial Coding in the Superior Colliculus: Is Visual Always Visual and Motor Always Motor?

The memory-delay saccade task is often used to separate visual and motor responses in oculomotor structures such as the superior colliculus (SC), with the assumption that these same responses would sum with a short delay during immediate "reactive" saccades to visual stimuli. However, it is also possible that additional signals (suppression, delay) alter visual and/or motor response in the memory delay task. Here, we compared the spatiotemporal properties of visual and motor responses of the same SC neurons recorded during both the reactive and memory-delay tasks in two head-unrestrained monkeys. Comparing tasks, visual (aligned with target onset) and motor (aligned on saccade onset) responses were highly correlated across neurons, but the peak response of visual neurons and peak motor responses (of both visuomotor (VM) and motor neurons) were significantly higher in the reactive task. Receptive field organization was generally similar in both tasks. Spatial coding (along a Target-Gaze (TG) continuum) was also similar, with the exception that pure motor cells showed a stronger tendency to code future gaze location in the memory delay task, suggesting a more complete transformation. These results suggest that the introduction of a trained memory delay alters both the vigor and spatial coding of SC visual and motor responses, likely due to a combination of saccade suppression signals and greater signal noise accumulation during the delay in the memory delay task.

Control of redundant pointing movements involving the wrist and forearm

The musculoskeletal system can move in more ways than are strictly necessary, allowing many tasks to be accomplished with a variety of limb configurations. Why some configurations are preferred has been a focus of motor control research, but most studies have focused on shoulder-elbow or whole arm movements. This study focuses on movements involving forearm pronation-supination (PS), wrist flexion-extension (FE), and wrist radial-ulnar deviation (RUD) and elucidates how these three degrees of freedom (DOF) combine to perform the common task of pointing, which only requires two DOF. Although pointing is more sensitive to FE and RUD than to PS and could be easily accomplished with FE and RUD alone, subjects tend to involve a small amount of PS. However, why we choose this behavior has been unknown and is the focus of this paper. With the use of a second-order model with lumped parameters, we tested a number of plausible control strategies involving minimization of work, potential energy, torque, and path length. None of these control schemes robustly predicted the observed behavior. However, an alternative control scheme, hypothesized to control the DOF that were most important to the task (FE and RUD) and ignore the less important DOF (PS), matched the observed behavior well. In particular, the behavior observed in PS appears to be a mechanical side effect caused by unopposed interaction torques. We conclude that moderately sized pointing movements involving the wrist and forearm are controlled by ignoring forearm rotation even though this strategy does not robustly minimize work, potential energy, torque, or path length. NEW & NOTEWORTHY Many activities require us to point our hands in a given direction using wrist and forearm rotations. Although there are infinitely many ways to do this, we tend to follow a stereotyped pattern. Why we choose this pattern has been unknown and is the focus of this paper. After testing a variety of hypotheses, we conclude that the pattern results from a simplifying strategy in which we focus on wrist rotations and ignore forearm rotation.

An Extended Passive Motion Paradigm for Human-Like Posture and Movement Planning in Redundant Manipulators

A major challenge in robotics and computational neuroscience is relative to the posture/movement problem in presence of kinematic redundancy. We recently addressed this issue using a principled approach which, in conjunction with nonlinear inverse optimization, allowed capturing postural strategies such as Donders' law. In this work, after presenting this general model specifying it as an extension of the Passive Motion Paradigm, we show how, once fitted to capture experimental postural strategies, the model is actually able to also predict movements. More specifically, the passive motion paradigm embeds two main intrinsic components: joint damping and joint stiffness. In previous work we showed that joint stiffness is responsible for static postures and, in this sense, its parameters are regressed to fit to experimental postural strategies. Here, we show how joint damping, in particular its anisotropy, directly affects task-space movements. Rather than using damping parameters to fit a posteriori task-space motions, we make the a priori hypothesis that damping is proportional to stiffness. This remarkably allows a postural-fitted model to also capture dynamic performance such as curvature and hysteresis of task-space trajectories during wrist pointing tasks, confirming and extending previous findings in literature.

Sampling rate influences saccade detection in mobile eye tracking of a reading task

The purpose of this study was to compare saccade detection characteristics in two mobile eye trackers with different sampling rates in a natural task. Gaze data of 11 participants were recorded in one 60 Hz and one 120 Hz mobile eye tracker and compared directly to the saccades detected by a 1000 HZ stationary tracker while a reading task was performed. Saccades and fixations were detected using a velocity based algorithm and their properties analyzed. Results showed that there was no significant difference in the number of detected fixations but mean fixation durations differed between the 60 Hz mobile and the stationary eye tracker. The 120 Hz mobile eye tracker showed a significant increase in the detection rate of saccades and an improved estimation of the mean saccade duration, compared to the 60 Hz eye tracker. To conclude, for the detection and analysis of fast eye movements, such as saccades, it is better to use a 120 Hz mobile eye tracker.

Cervical dystonia: a neural integrator disorder

Ocular motor neural integrators ensure that eyes are held steady in straight-ahead and eccentric positions of gaze. Abnormal function of the ocular motor neural integrator leads to centripetal drifts of the eyes with consequent gaze-evoked nystagmus. In 2002 a neural integrator, analogous to that in the ocular motor system, was proposed for the control of head movements. Recently, a counterpart of gaze-evoked eye nystagmus was identified for head movements; in which the head could not be held steady in eccentric positions on the trunk. These findings lead to a novel pathophysiological explanation in cervical dystonia, which proposed that the abnormalities of head movements stem from a malfunctioning head neural integrator, either intrinsically or as a result of impaired cerebellar, basal ganglia, or peripheral feedback. Here we briefly recapitulate the history of the neural integrator for eye movements, then further develop the idea of a neural integrator for head movements, and finally discuss its putative role in cervical dystonia. We hypothesize that changing the activity in an impaired head neural integrator, by modulating feedback, could treat dystonia.

Accuracy and re-test reliability of mobile eye-tracking in Parkinson's disease and older adults

Mobile eye-tracking is important for understanding the role of vision during real-world tasks in older adults (OA) and people with Parkinson's disease (PD). However, accuracy and reliability of such devices have not been established in these populations. We used a novel protocol to quantify accuracy and reliability of a mobile eye-tracker in OA and PD. A mobile eye-tracker (Dikablis) measured the saccade amplitudes of 20 OA and 14 PD on two occasions. Participants made saccades between targets placed 5°, 10° and 15° apart. Impact of visual correction (glasses) on saccadic amplitude measurement was also investigated in 10 OA. Saccade amplitude accuracy (median bias) was -1.21° but a wide range of bias (-7.73° to 5.81°) was seen in OA and PD, with large vertical saccades (15°) being least accurate. Reliability assessment showed a median difference between sessions of <1° for both groups, with poor to good relative agreement (Spearman rho: 0.14 to 0.85). Greater accuracy and reliability was observed in people without visual correction. Saccade amplitude can be measured with variable accuracy and reliability using a mobile eye-tracker in OA and PD. Human, technological and study-specific protocol factors may introduce error and are discussed along with methodological recommendations.

A kinematic model for 3-D head-free gaze-shifts

Rotations of the line of sight are mainly implemented by coordinated motion of the eyes and head. Here, we propose a model for the kinematics of three-dimensional (3-D) head-unrestrained gaze-shifts. The model was designed to account for major principles in the known behavior, such as gaze accuracy, spatiotemporal coordination of saccades with vestibulo-ocular reflex (VOR), relative eye and head contributions, the non-commutativity of rotations, and Listing's and Fick constraints for the eyes and head, respectively. The internal design of the model was inspired by known and hypothesized elements of gaze control physiology. Inputs included retinocentric location of the visual target and internal representations of initial 3-D eye and head orientation, whereas outputs were 3-D displacements of eye relative to the head and head relative to shoulder. Internal transformations decomposed the 2-D gaze command into 3-D eye and head commands with the use of three coordinated circuits: (1) a saccade generator, (2) a head rotation generator, (3) a VOR predictor. Simulations illustrate that the model can implement: (1) the correct 3-D reference frame transformations to generate accurate gaze shifts (despite variability in other parameters), (2) the experimentally verified constraints on static eye and head orientations during fixation, and (3) the experimentally observed 3-D trajectories of eye and head motion during gaze-shifts. We then use this model to simulate how 2-D eye-head coordination strategies interact with 3-D constraints to influence 3-D orientations of the eye-in-space, and the implications of this for spatial vision.

Computations underlying the visuomotor transformation for smooth pursuit eye movements

Smooth pursuit eye movements are driven by retinal motion and enable us to view moving targets with high acuity. Complicating the generation of these movements is the fact that different eye and head rotations can produce different retinal stimuli but giving rise to identical smooth pursuit trajectories. However, because our eyes accurately pursue targets regardless of eye and head orientation (Blohm G, Lefèvre P. J Neurophysiol 104: 2103-2115, 2010), the brain must somehow take these signals into account. To learn about the neural mechanisms potentially underlying this visual-to-motor transformation, we trained a physiologically inspired neural network model to combine two-dimensional (2D) retinal motion signals with three-dimensional (3D) eye and head orientation and velocity signals to generate a spatially correct 3D pursuit command. We then simulated conditions of 1) head roll-induced ocular counterroll, 2) oblique gaze-induced retinal rotations, 3) eccentric gazes (invoking the half-angle rule), and 4) optokinetic nystagmus to investigate how units in the intermediate layers of the network accounted for different 3D constraints. Simultaneously, we simulated electrophysiological recordings (visual and motor tunings) and microstimulation experiments to quantify the reference frames of signals at each processing stage. We found a gradual retinal-to-intermediate-to-spatial feedforward transformation through the hidden layers. Our model is the first to describe the general 3D transformation for smooth pursuit mediated by eye- and head-dependent gain modulation. Based on several testable experimental predictions, our model provides a mechanism by which the brain could perform the 3D visuomotor transformation for smooth pursuit.

The visual representation of 3D object orientation in parietal cortex

An accurate representation of three-dimensional (3D) object orientation is essential for interacting with the environment. Where and how the brain visually encodes 3D object orientation remains unknown, but prior studies suggest the caudal intraparietal area (CIP) may be involved. Here, we develop rigorous analytical methods for quantifying 3D orientation tuning curves, and use these tools to the study the neural coding of surface orientation. Specifically, we show that single neurons in area CIP of the rhesus macaque jointly encode the slant and tilt of a planar surface, and that across the population, the distribution of preferred slant-tilts is not statistically different from uniform. This suggests that all slant-tilt combinations are equally represented in area CIP. Furthermore, some CIP neurons are found to also represent the third rotational degree of freedom that determines the orientation of the image pattern on the planar surface. Together, the present results suggest that CIP is a critical neural locus for the encoding of all three rotational degrees of freedom specifying an object's 3D spatial orientation.

Frames of reference for eye-head gaze shifts evoked during frontal eye field stimulation

The frontal eye field (FEF), in the prefrontal cortex, participates in the transformation of visual signals into saccade motor commands and in eye-head gaze control. The FEF is thought to show eye-fixed visual codes in head-restrained monkeys, but it is not known how it transforms these inputs into spatial codes for head-unrestrained gaze commands. Here, we tested if the FEF influences desired gaze commands within a simple eye-fixed frame, like the superior colliculus (SC), or in more complex egocentric frames like the supplementary eye fields (SEFs). We electrically stimulated 95 FEF sites in two head-unrestrained monkeys to evoke 3D eye-head gaze shifts and then mathematically rotated these trajectories into various reference frames. In theory, each stimulation site should specify a specific spatial goal when the evoked gaze shifts are plotted in the appropriate frame. We found that these motor output frames varied site by site, mainly within the eye-to-head frame continuum. Thus, consistent with the intermediate placement of the FEF within the high-level circuits for gaze control, its stimulation-evoked output showed an intermediate trend between the multiple reference frame codes observed in SEF-evoked gaze shifts and the simpler eye-fixed reference frame observed in SC-evoked movements. These results suggest that, although the SC, FEF and SEF carry eye-fixed information at the level of their unit response fields, this information is transformed differently in their output projections to the eye and head controllers.

Experimental test of spatial updating models for monkey eye-head gaze shifts

How the brain maintains an accurate and stable representation of visual target locations despite the occurrence of saccadic gaze shifts is a classical problem in oculomotor research. Here we test and dissociate the predictions of different conceptual models for head-unrestrained gaze-localization behavior of macaque monkeys. We adopted the double-step paradigm with rapid eye-head gaze shifts to measure localization accuracy in response to flashed visual stimuli in darkness. We presented the second target flash either before (static), or during (dynamic) the first gaze displacement. In the dynamic case the brief visual flash induced a small retinal streak of up to about 20 deg at an unpredictable moment and retinal location during the eye-head gaze shift, which provides serious challenges for the gaze-control system. However, for both stimulus conditions, monkeys localized the flashed targets with accurate gaze shifts, which rules out several models of visuomotor control. First, these findings exclude the possibility that gaze-shift programming relies on retinal inputs only. Instead, they support the notion that accurate eye-head motor feedback updates the gaze-saccade coordinates. Second, in dynamic trials the visuomotor system cannot rely on the coordinates of the planned first eye-head saccade either, which rules out remapping on the basis of a predictive corollary gaze-displacement signal. Finally, because gaze-related head movements were also goal-directed, requiring continuous access to eye-in-head position, we propose that our results best support a dynamic feedback scheme for spatial updating in which visuomotor control incorporates accurate signals about instantaneous eye- and head positions rather than relative eye- and head displacements.

Three-dimensional visuo-motor control of saccades

Although the motion of the line of sight is a straightforward consequence of a particular rotation of the eye, it is much trickier to predict the rotation underlying a particular motion of the line of sight in accordance with Listing's law. Helmholtz's notion of the direction-circle together with the notion of primary and secondary reference directions in visual space provide an elegant solution to this reverse engineering problem, which the brain is faced with whenever generating a saccade. To test whether these notions indeed apply for saccades, we analyzed three-dimensional eye movements recorded in four rhesus monkeys. We found that on average saccade trajectories closely matched with the associated direction-circles. Torsional, vertical, and horizontal eye position of saccades scattered around the position predicted by the associated direction-circles with standard deviations of 0.5°, 0.3°, and 0.4°, respectively. Comparison of saccade trajectories with the likewise predicted fixed-axis rotations yielded mean coefficients of determinations (±SD) of 0.72 (±0.26) for torsion, 0.97 (±0.10) for vertical, and 0.96 (±0.11) for horizontal eye position. Reverse engineering of three-dimensional saccadic rotations based on visual information suggests that motor control of saccades, compatible with Listing's law, not only uses information on the fixation directions at saccade onset and offset but also relies on the computation of secondary reference positions that vary from saccade to saccade.

Relationships between neck muscle electromyography and three-dimensional head kinematics during centrally induced torsional head perturbations

The relationship between neck muscle electromyography (EMG) and torsional head rotation (about the nasooccipital axis) is difficult to assess during normal gaze behaviors with the head upright. Here, we induced acute head tilts similar to cervical dystonia (torticollis) in two monkeys by electrically stimulating 20 interstitial nucleus of Cajal (INC) sites or inactivating 19 INC sites by injection of muscimol. Animals engaged in a simple gaze fixation task while we recorded three-dimensional head kinematics and intramuscular EMG from six bilateral neck muscle pairs. We used a cross-validation-based stepwise regression to quantitatively examine the relationships between neck EMG and torsional head kinematics under three conditions: 1) unilateral INC stimulation (where the head rotated torsionally toward the side of stimulation); 2) corrective poststimulation movements (where the head returned toward upright); and 3) unilateral INC inactivation (where the head tilted toward the opposite side of inactivation). Our cross-validated results of corrective movements were slightly better than those obtained during unperturbed gaze movements and showed many more torsional terms, mostly related to velocity, although some orientation and acceleration terms were retained. In addition, several simplifying principles were identified. First, bilateral muscle pairs showed similar, but opposite EMG-torsional coupling terms, i.e., a change in torsional kinematics was associated with increased muscle activity on one side and decreased activity on the other side. s, whenever torsional terms were retained in a given muscle, they were independent of the inputs we tested, i.e., INC stimulation vs. corrective motion vs. INC inactivation, and left vs. right INC data. These findings suggest that, despite the complexity of the head-neck system, the brain can use a single, bilaterally coupled inverse model for torsional head control that is valid across different behaviors and movement directions. Combined with our previous data, these new data provide the terms for a more complete three-dimensional model of EMG: head rotation coupling for the muscles and gaze behaviors that we recorded.

Neural mechanisms for predictive head movement strategies during sequential gaze shifts

Humans adopt very different head movement strategies for different gaze behaviors, for example, when playing sports versus watching sports on television. Such strategy switching appears to depend on both context and expectation of future gaze positions. Here, we explored the neural mechanisms for such behaviors by training three monkeys to make head-unrestrained gaze shifts toward eccentric radial targets. A randomized color cue provided predictive information about whether that target would be followed by either a return gaze shift to center or another, more eccentric gaze shift, but otherwise animals were allowed to develop their own eye-head coordination strategy. In the first two animals we then stimulated the frontal eye fields (FEF) in conjunction with the color cue, and in the third animal we recorded from neurons in the superior colliculus (SC). Our results show that 1) monkeys can optimize eye-head coordination strategies from trial to trial, based on learned associations between color cues and future gaze sequences, 2) these cue-dependent coordination strategies were preserved in gaze saccades evoked during electrical stimulation of the FEF, and 3) two types of SC responses (the saccade burst and a more prolonged response related to head movement) modulated with these cue-dependent strategies, although only one (the saccade burst) varied in a predictive fashion. These data show that from one moment to the next, the brain can use contextual sensory cues to set up internal "coordination states" that convert fixed cortical gaze commands into the brain stem signals required for predictive head motion.

Cross-validated models of the relationships between neck muscle electromyography and three-dimensional head kinematics during gaze behavior

The object of this study was to model the relationship between neck electromyography (EMG) and three-dimensional (3-D) head kinematics during gaze behavior. In two monkeys, we recorded 3-D gaze, head orientation, and bilateral EMG activity in the sternocleidomastoid, splenius capitis, complexus, biventer cervicis, rectus capitis posterior major, and occipital capitis inferior muscles. Head-unrestrained animals fixated and made gaze saccades between targets within a 60° × 60° grid. We performed a stepwise regression in which polynomial model terms were retained/rejected based on their tendency to increase/decrease a cross-validation-based measure of model generalizability. This revealed several results that could not have been predicted from knowledge of musculoskeletal anatomy. During head holding, EMG activity in most muscles was related to horizontal head orientation, whereas fewer muscles correlated to vertical head orientation and none to small random variations in head torsion. A fourth-order polynomial model, with horizontal head orientation as the only independent variable, generalized nearly as well as higher order models. For head movements, we added time-varying linear and nonlinear perturbations in velocity and acceleration to the previously derived static (head holding) models. The static models still explained most of the EMG variance, but the additional motion terms, which included horizontal, vertical, and torsional contributions, significantly improved the results. Several coordinate systems were used for both static and dynamic analyses, with Fick coordinates showing a marginal (nonsignificant) advantage. Thus, during gaze fixations, recruitment within the neck muscles from which we recorded contributed primarily to position-dependent horizontal orientation terms in our data set, with more complex multidimensional contributions emerging during the head movements that accompany gaze shifts. These are crucial components of the late neuromuscular transformations in a complete model of 3-D head-neck system and should help constrain the study of premotor signals for head control during gaze behaviors.

Quick phases control ocular torsion during smooth pursuit

One of the open questions in oculomotor control of visually guided eye movements is whether it is possible to smoothly track a target along a curvilinear path across the visual field without changing the torsional stance of the eye. We show in an experimental study of three-dimensional eye movements in subhuman primates (Macaca mulatta) that although the pursuit system is able to smoothly change the orbital orientation of the eye's rotation axis, the smooth ocular motion was interrupted every few hundred milliseconds by a small quick phase with amplitude <1.5° while the animal tracked a target along a circle or ellipse. Specifically, during circular pursuit of targets moving at different angular eccentricities (5°, 10°, and 15°) relative to straight ahead at spatial frequencies of 0.067 and 0.1 Hz, the torsional amplitude of the intervening quick phases was typically around 1° or smaller and changed direction for clockwise vs. counterclockwise tracking. Reverse computations of the eye rotation based on the recorded angular eye velocity showed that the quick phases facilitate the overall control of ocular orientation in the roll plane, thereby minimizing torsional disturbances of the visual field. On the basis of a detailed kinematic analysis, we suggest that quick phases during curvilinear smooth tracking serve to minimize deviations from Donders' law, which are inevitable due to the spherical configuration space of smooth eye movements.

Revealing the kinematics of the oculomotor plant with tertiary eye positions and ocular counterroll

Retinal information is two-dimensional, whereas eye movements are three-dimensional. The oculomotor system solves this degrees-of-freedom problem by constraining eye positions to zero torsion (Listing's law) and determining how eye velocities change with eye position (half-angle rule). Here we test whether the oculomotor plant, in the absence of well-defined neural commands, can implement these constrains mechanically, not just in a primary position but for all eye and head orientations. We stimulated the abducens nerve at tertiary eye positions and when ocular counterroll was induced at tilted head orientations. Stimulation-induced eye velocities follow the half-angle rule, even for tertiary eye positions, and microstimulation at tilted head orientations elicits eye positions that adhere to torsionally shifted planes, similar to naturally occurring eye movements. These results support the notion that oculomotor plant can continuously apply these three-dimensional rules correctly and appropriately for all eye and head orientations that obey Listing's law, demonstrating a major role of peripheral biomechanics in motor control.

Visuomotor Velocity Transformations for Smooth Pursuit Eye Movements

Smooth pursuit eye movements are driven by retinal motion signals. These retinal motion signals are converted into motor commands that obey Listing's law (i.e., no accumulation of ocular torsion). The fact that smooth pursuit follows Listing's law is often taken as evidence that no explicit reference frame transformation between the retinal velocity input and the head-centered motor command is required. Such eye-position-dependent reference frame transformations between eye- and head-centered coordinates have been well-described for saccades to static targets. Here we suggest that such an eye (and head)-position-dependent reference frame transformation is also required for target motion (i.e., velocity) driving smooth pursuit eye movements. Therefore we tested smooth pursuit initiation under different three-dimensional eye positions and compared human performance to model simulations. We specifically tested if the ocular rotation axis changed with vertical eye position, if the misalignment of the spatial and retinal axes during oblique fixations was taken into account, and if ocular torsion (due to head roll) was compensated for. If no eye-position-dependent velocity transformation was used, the pursuit initiation should follow the retinal direction, independently of eye position; in contrast, a correct visuomotor velocity transformation would result in spatially correct pursuit initiation. Overall subjects accounted for all three components of the visuomotor velocity transformation, but we did observe differences in the compensatory gains between individual subjects. We concluded that the brain does perform a visuomotor velocity transformation but that this transformation was prone to noise and inaccuracies of the internal model.

Electrical stimulation of the frontal eye fields in the head-free macaque evokes kinematically normal 3D gaze shifts

The frontal eye field (FEF) is a region of the primate prefrontal cortex that is central to eye-movement generation and target selection. It has been shown that neurons in this area encode commands for saccadic eye movements. Furthermore, it has been suggested that the FEF may be involved in the generation of gaze commands for the eye and the head. To test this suggestion, we systematically stimulated (with pulses of 300 Hz frequency, 200 ms duration, 30-100 μA intensity) the FEF of two macaques, with the head unrestrained, while recording three-dimensional (3D) eye and head rotations. In a total of 95 sites, the stimulation consistently elicited gaze-orienting movements ranging in amplitude from 2 to 172°, directed contralateral to the stimulation site, and with variable vertical components. These movements were typically a combination of eye-in-head saccades and head-in-space movements. We then performed a comparison between the stimulation-evoked movements and gaze shifts voluntarily made by the animal. The kinematics of the stimulation-evoked movements (i.e., their spatiotemporal properties, their velocity-amplitude relationships, and the relative contributions of the eye and the head as a function of movement amplitude) were very similar to those of natural gaze shifts. Moreover, they obeyed the same 3D constraints as the natural gaze shifts (i.e., modified Listing's law for eye-in-head movements). As in natural gaze shifts, saccade and vestibuloocular reflex torsion during stimulation-evoked movements were coordinated so that at the end of the head movement the eye-in-head ended up in Listing's plane. In summary, movements evoked by stimulation of the FEF closely resembled those of naturally occurring eye-head gaze shifts. Thus we conclude that the FEF explicitly encodes gaze commands and that the kinematic aspects of eye-head coordination are likely specified by downstream mechanisms.

Somatosensory comparison during haptic tracing

Active sensing involves memory retrieval and updating as well as mechanisms that trigger corrections to the ongoing exploratory movement. The present study examined this process in a task where human subjects moved the index fingertip clockwise around the circumference of a virtual sphere created by a robotic device. The fingertip pressed into the sphere during the movement, and the subjects were to report slight differences in sphere size (or surface curvature), which occurred from trial to trial. During each 2- to 3-s trial, subjects gradually adjusted their speed and pressure according to the current surface curvature, achieving a consistent level of contact force in the last half of the exploration. The results demonstrate that subjects were gradually accumulating haptic information about curvature and, at the same time, gradually changing the motor commands for the movement. When subjects encountered an unexpected transition in curvature (from circular to flat), they reacted by abruptly decreasing contact force at a latency of about 50 ms. This short latency indicates that spinally mediated corrections are engaged during this task. The results support the hypothesis that during haptic exploration, the neural comparison between expected and actual somatosensory feedback takes places at multiple levels, including the spinal cord.

3-Dimensional eye-head coordination in gaze shifts evoked during stimulation of the lateral intraparietal cortex

Coordinated eye-head gaze shifts have been evoked during electrical stimulation of the frontal cortex (supplementary eye field (SEF) and frontal eye field (FEF)) and superior colliculus (SC), but less is known about the role of lateral intraparietal cortex (LIP) in head-unrestrained gaze shifts. To explore this, two monkeys (M1 and M2) were implanted with recording chambers and 3-D eye+ head search coils. Tungsten electrodes delivered trains of electrical pulses (usually 200 ms duration) to and around area LIP during head-unrestrained gaze fixations. A current of 200 muA consistently evoked small, short-latency contralateral gaze shifts from 152 sites in M1 and 243 sites in M2 (Constantin et al., 2007). Gaze kinematics were independent of stimulus amplitude and duration, except that subsequent saccades were suppressed. The average amplitude of the evoked gaze shifts was 8.46 degrees for M1 and 8.25 degrees for M2, with average head components of only 0.36 and 0.62 degrees respectively. The head's amplitude contribution to these movements was significantly smaller than in normal gaze shifts, and did not increase with behavioral adaptation. Stimulation-evoked gaze, eye and head movements qualitatively obeyed normal 3-D constraints (Donders' law and Listing's law), but with less precision. As in normal behavior, when the head was restrained LIP stimulation evoked eye-only saccades in Listing's plane, whereas when the head was not restrained, stimulation evoked saccades with position-dependent torsional components (driving the eye out of Listing's plane). In behavioral gaze-shifts, the vestibuloocular reflex (VOR) then drives torsion back into Listing's plane, but in the absence of subsequent head movement the stimulation-induced torsion was "left hanging". This suggests that the position-dependent torsional saccade components are preprogrammed, and that the oculomotor system was expecting a head movement command to follow the saccade. These data show that, unlike SEF, FEF, and SC stimulation in nearly identical conditions, LIP stimulation fails to produce normally-coordinated eye-head gaze shifts.

Neural correlates of forward and inverse models for eye movements: evidence from three-dimensional kinematics

Inverse and forward dynamic models have been conceptually important in computational motor control. In particular, inverse models are thought to convert desired action into appropriate motor commands. In parallel, forward models predict the consequences of the motor command on behavior by constructing an efference copy of the actual movement. Despite theoretical appeal, their neural representation has remained elusive. Here, we provide evidence supporting the notion that a group of premotor neurons called burst-tonic (BT) cells represent the output of the inverse model for eye movements. We show that BT neurons, like extraocular motoneurons but different from the evoked eye movement, do not carry signals appropriate for the half-angle rule of ocular kinematics during smooth-pursuit eye movements from eccentric positions. Along with findings of identical response dynamics as motoneurons, these results strongly suggest that BT cells carry a replica of the motor command. In contrast, eye-head (EH) neurons, a premotor cell type that is the target of Purkinje cell inhibition from the cerebellar flocculus/ventral paraflocculus, exhibit properties that could be consistent with the half-angle rule. Therefore, EH cells may be functionally related to the output of a forward internal model thought to construct an efference copy of the actual eye movement.

Noncommutative control in the rotational vestibuloocular reflex

To investigate the role of noncommutative computations in the oculomotor system, three-dimensional (3D) eye movements were measured in seven healthy subjects using a memory-contingent vestibulooculomotor paradigm. Subjects had to fixate a luminous point target that appeared briefly at an eccentricity of 20 degrees in one of four diagonal directions in otherwise complete darkness. After a fixation period of approximately 1 s, the subject was moved through a sequence of two rotations about mutually orthogonal axes in one of two orders (30 degrees yaw followed by 30 degrees pitch and vice versa in upright and 30 degrees yaw followed by 20 degrees roll and vice versa in both upright and supine orientations). We found that the change in ocular torsion induced by consecutive rotations about the yaw and the pitch axis depended on the order of rotations as predicted by 3D rotation kinematics. Similarly, after rotations about the yaw and roll axis, torsion depended on the order of rotations but now due to the change in final head orientation relative to gravity. Quantitative analyses of these ocular responses revealed that the rotational vestibuloocular reflexes (VORs) in far vision closely matched the predictions of 3D rotation kinematics. We conclude that the brain uses an optimal VOR strategy with the restriction of a reduced torsional position gain. This restriction implies a limited oculomotor range in torsion and systematic tilts of the angular eye velocity as a function of gaze direction.

Rotation Axes of the Head During Positioning, Head Shaking, and Locomotion

Static head orientations obey Donders’ law and are postulated to be rotations constrained by a Fick gimbal. Head oscillations can be voluntary or generated during natural locomotion. Whether the rotation axes of the voluntary oscillations or during locomotion are constrained by the same gimbal is unknown and is the subject of this study. Head orientation was monitored with an Optotrak (Northern Digital). Human subjects viewed visual targets wearing pin-hole goggles to achieve static head positions with the eyes centered in the orbit. Incremental rotation axes were determined for pitch and yaw by computing the velocity vectors during head oscillation and during locomotion at 1.5 m/s on a treadmill. Static head orientation could be described by a generalization of the Fick gimbal by having the axis of the second rotation rotate by a fraction, k, of the angle of the first rotation without a third rotation. We have designated this as a k-gimbal system. Incremental rotation axes for both pitch and yaw oscillations were functions of the pitch but not the yaw head positions. The pivot point for head oscillations was close to the midpoint of the interaural line. During locomotion, however, the pivot point was considerably lower. These findings are well explained by an implementation of the k-gimbal model, which has a rotation axis superimposed on a Fick-gimbal system. This could be realized physiologically by the head interface with the dens and occipital condyles during head oscillation with a contribution of the lower spine to pitch during locomotion.

Fascicular specialization in human and monkey rectus muscles: evidence for anatomic independence of global and orbital layers

PURPOSE

Connective tissue pulleys inflect the extraocular muscles (EOMs) and receive insertions from some fibers. The authors investigated insertions and anatomic relationships of fiber fascicles within rectus EOMs to clarify the relationship to their pulleys.

METHODS

Two human and two monkey orbits were removed intact, serially sectioned in the coronal plane, histologically stained, and digitally photographed. The authors traced representative fascicles in the human medial rectus (MR) and inferior rectus and monkey lateral rectus and superior rectus muscles. In the human MR, the authors computed average collagen fractions in the orbital layer (OL) and the global layer (GL).

RESULTS

In human and monkey, OL fascicles remained distinct from each other and from the GL throughout. Most OL fascicles were inserted into the pulley through short tendons. Most GL fascicles bypassed the pulley without insertion. Collagen content in the human MR OL increased from 29% +/- 5% (SD) in midorbit to 65% +/- 9% in the anterior orbit but slightly decreased from 26% +/- 6% to 23% +/- 1% in the GL. Tracing of every fiber in a human MR OL fascicle demonstrated terminations on pulley tendons without myomyous junctions.

CONCLUSIONS

Fibers in the primate rectus OL lack myomyous or GL junctions, but nearly all insert on the pulley through a broad distribution of short tendons and dense intercalated collagen. Fibers in the GL generally do not insert on pulley tissues and are associated with less collagen. These features support the distinct role of the OL in anteroposterior positioning of connective tissues proposed in the active pulley hypothesis and substantial mechanical independence of the OL and GL.

Kinematics of the Rotational Vestibuloocular Reflex: Role of the Cerebellum

We studied the effect of cerebellar lesions on the 3-D control of the rotational vestibuloocular reflex (RVOR) to abrupt yaw-axis head rotation. Using search coils, three-dimensional (3-D) eye movements were recorded from nine patients with cerebellar disease and seven normal subjects during brief chair rotations (200°/s2 to 40°/s) and manual head impulses. We determined the amount of eye-position dependent torsion during yaw-axis rotation by calculating the torsional-horizontal eye-velocity axis for each of three vertical eye positions (0°, ±15°) and performing a linear regression to determine the relationship of the 3-D velocity axis to vertical eye position. The slope of this regression is the tilt angle slope. Overall, cerebellar patients showed a clear increase in the tilt angle slope for both chair rotations and head impulses. For chair rotations, the effect was not seen at the onset of head rotation when both patients and normal subjects had nearly head-fixed responses (no eye-position-dependent torsion). Over time, however, both groups showed an increasing tilt-angle slope but to a much greater degree in cerebellar patients. Two important conclusions emerge from these findings: the axis of eye rotation at the onset of head rotation is set to a value close to head-fixed (i.e., optimal for gaze stabilization during head rotation), independent of the cerebellum and once the head rotation is in progress, the cerebellum plays a crucial role in keeping the axis of eye rotation about halfway between head-fixed and that required for Listing's Law to be obeyed.

Dissociation of eye and head components of gaze shifts by stimulation of the omnipause neuron region

Natural movements often include actions integrated across multiple effectors. Coordinated eye-head movements are driven by a command to shift the line of sight by a desired displacement vector. Yet because extraocular and neck motoneurons are separate entities, the gaze shift command must be separated into independent signals for eye and head movement control. We report that this separation occurs, at least partially, at or before the level of pontine omnipause neurons (OPNs). Stimulation of the OPNs prior to and during gaze shifts temporally decoupled the eye and head components by inhibiting gaze and eye saccades. In contrast, head movements were consistently initiated before gaze onset, and ongoing head movements continued along their trajectories, albeit with some characteristic modulations. After stimulation offset, a gaze shift composed of an eye saccade, and a reaccelerated head movement was produced to preserve gaze accuracy. We conclude that signals subject to OPN inhibition produce the eye-movement component of a coordinated eye-head gaze shift and are not the only signals involved in the generation of the head component of the gaze shift.

Computation of gaze orientation under unrestrained head movements

Given the high relevance of visual input to human behavior, it is often important to precisely monitor the spatial orientation of the visual axis. One popular and accurate technique for measuring gaze orientation is based on the dual search coil. This technique does not allow for very large displacements of the subject, however, and is not robust with respect to translations of the head. More recently, less invasive procedures have been developed that record eye movements with camera-based systems attached to a helmet worn by the subject. Computational algorithms have also been developed that can calibrate eye orientation when the head's position is fixed. Given that camera-based systems measure the eye's position in its orbit, however, the reconstruction of gaze orientation is not as straightforward when the head is allowed to move. In this paper, we propose a new algorithm and calibration method to compute gaze orientation under unrestrained head conditions. Our method requires only the accurate measurement of orbital eye position (for instance, with a camera-based system), and the position of three points on the head. The calculations are expressed in terms of linear algebra, so can easily be interpreted and related to the geometry of the human body. Our calibration method has been tested experimentally and validated against independent data, proving that is it robust even under large translations, rotations, and torsions of the head.

Contribution of the Frontal Eye Field to Gaze Shifts in the Head-Unrestrained Monkey: Effects of Microstimulation

The role of the primate frontal eye field (FEF) has been inferred primarily from experiments investigating saccadic eye movements with the head restrained. Three recent reports investigating head-unrestrained gaze shifts disagree on whether head movements are evoked with FEF stimulation and thus whether the FEF participates in gaze movement commands. We therefore examined the eye, head, and overall gaze movement evoked by low-intensity microstimulation of the low-threshold region of the FEF in two head-unrestrained monkeys. Microstimulation applied at 200 or 350 Hz for 200 ms evoked large gaze shifts with substantial head movement components from most sites in the dorsomedial FEF, but evoked small, predominantly eye-only gaze shifts from ventrolateral sites. The size and direction of gaze and eye movements were strongly affected by the eye position before stimulation. Head movements exhibited little position dependency, but at some sites and initial eye positions, head-only movements were evoked. Stimulus-evoked gaze shifts and their eye and head components resembled those elicited naturally by visual targets. With stimulus train durations >200 ms, the evoked gaze shifts were more likely to be accomplished with a substantial head movement, which often continued for the entire stimulus duration. The amplitude, duration and peak velocity of the evoked head movement were more strongly correlated with stimulus duration than were those of the gaze or eye movements. We conclude that the dorsomedial FEF generates a gaze command signal that can produce eye, head, or combined eye–head movement depending on the initial orbital position of the eye.

Functional organization within a neural network trained to update target representations across 3-D saccades

The goal of this study was to understand how neural networks solve the 3-D aspects of updating in the double-saccade task, where subjects make sequential saccades to the remembered locations of two targets. We trained a 3-layer, feed-forward neural network, using back-propagation, to calculate the 3-D motor error the second saccade. Network inputs were a 2-D topographic map of the direction of the second target in retinal coordinates, and 3-D vector representations of initial eye orientation and motor error of the first saccade in head-fixed coordinates. The network learned to account for all 3-D aspects of updating. Hidden-layer units (HLUs) showed retinal-coordinate visual receptive fields that were remapped across the first saccade. Two classes of HLUs emerged from the training, one class primarily implementing the linear aspects of updating using vector subtraction, the second class implementing the eye-orientation-dependent, non-linear aspects of updating. These mechanisms interacted at the unit level through gain-field-like input summations, and through the parallel "tweaking" of optimally-tuned HLU contributions to the output that shifted the overall population output vector to the correct second-saccade motor error. These observations may provide clues for the biological implementation of updating.

Evidence supporting extraocular muscle pulleys: refuting the platygean view of extraocular muscle mechanics

BACKGROUND

Late in the 20th century, it was recognized that connective tissue structures in the orbit influence the paths of the extraocular muscles and constitute their functional origins. Targeted investigations of these connective tissue "pulleys" led to the formulation of the active pulley hypothesis, which proposes that pulling directions of the rectus extraocular muscles are actively controlled via connective tissues.

PURPOSE

This review rebuts a series of criticisms of the active pulley hypothesis published by Jampel, and Jampel and Shi, in which these authors have disputed the existence and function of the pulleys.

METHODS

This article reviews published evidence for the existence of orbital pulleys, the active pulley hypothesis, and physiological tests of the active pulley hypothesis. Magnetic resonance imaging in a living subject and histological examination of a human cadaver directly illustrate the relationship of pulleys to extraocular muscles.

RESULTS

Strong scientific evidence is cited that supports the existence of orbital pulleys and their role in ocular motility. The criticisms of the hypothesis have ignored mathematical truisms and strong scientific evidence.

CONCLUSIONS

Actively control led orbital pulleys play a fundamental role in ocular motility. Pulleys profoundly influence the neural commands required to control eye movements and binocular alignment. Familiarity with the anatomy and physiology of the pulleys is requisite for a rational approach to diagnosing and treating strabismus using emerging methods. Conversely, approaches that deny or ignore the pulleys risk the sorts of errors that arise in geography and navigation from incorrect assumptions such as those of a flat ("platygean") earth.

On the barn owl's visual pre-attack behavior: I. Structure of head movements and motion patterns

Barn owls exhibit a rich repertoire of head movements before taking off for prey capture. These movements occur mainly at light levels that allow for the visual detection of prey. To investigate these movements and their functional relevance, we filmed the pre-attack behavior of barn owls. Off-line image analysis enabled reconstruction of all six degrees of freedom of head movements. Three categories of head movements were observed: fixations, head translations and head rotations. The observed rotations contained a translational component. Head rotations did not follow Listing's law, but could be well described by a second-order surface, which indicated that they are in close agreement with Donder's law. Head translations did not contain any significant rotational components. Translations were further segmented into straight-line and curved paths. Translations along an axis perpendicular to the line of sight were similar to peering movements observed in other animals. We suggest that these basic motion elements (fixations, head rotations, translations along a straight line, and translation along a curved trajectory) may be combined to form longer and more complex behavior. We speculate that these head movements mainly underlie estimation of distance during prey capture.

Current concepts of mechanical and neural factors in ocular motility

PURPOSE OF REVIEW

The oculomotor periphery was classically regarded as a simple mechanism executing complex behaviors specified explicitly by neural commands. A competing view has emerged that many important aspects of ocular motility are properties of the extraocular muscles and their associated connective tissue pulleys. This review considers current concepts regarding aspects of ocular motility that are mechanically determined versus those that are specified explicitly as innervation.

RECENT FINDINGS

While it was established several years ago that the rectus extraocular muscles have connective tissue pulleys, recent functional imaging and histology has suggested that the rectus pulley array constitutes an inner mechanism, analogous to a gimbal, that is rotated torsionally around the orbital axis by an outer mechanism driven by the oblique extraocular muscles. This arrangement may account mechanically for several commutative aspects of ocular motor control, including Listing's Law, yet permits implementation of non-commutative motility. Recent human behavioral studies, as well as neurophysiology in monkeys, are consistent with implementation of Listing's Law in the oculomotor periphery, rather than centrally.

SUMMARY

Varied evidence now strongly supports the conclusion that Listing's Law and other important ocular kinematics are mechanically determined. This finding implies more limited possibilities for neural adaptation to some ocular motor pathologies, but indicates possibilities for surgical treatments.

Temporal dynamics of ocular position dependence of the initial human vestibulo-ocular reflex

PURPOSE

While an ideal vestibulo-ocular reflex (VOR) generates ocular rotations compensatory for head motion, during visually guided movements, Listing's Law (LL) constrains the eye to rotational axes lying in Listing's Plane (LP). The present study was conducted to explore the recent proposal that the VOR's rotational axis is not collinear with the head's, but rather follows a time-dependent strategy intermediate between LL and an ideal VOR.

METHODS

Binocular LPs were defined during visual fixation in eight normal humans. The VOR was evoked by a highly repeatable transient whole-body yaw rotation in darkness at a peak acceleration of 2800 deg/s2. Immediately before rotation, subjects regarded targets 15 or 500 cm distant located at eye level, 20 degrees up, or 20 degrees down. Eye and head responses were compared with LL predictions in the position and velocity domains.

RESULTS

LP orientation varied both among subjects and between individual subject's eyes, and rotated temporally with convergence by 5 +/- 5 degrees (+/-SEM). In the position domain, the eye compensated for head displacement even when the head rotated out of LP. Even within the first 20 ms from onset of head rotation, the ocular velocity axis tilted relative to the head axis by 30% +/- 8% of vertical gaze position. Saccades increased this tilt. Regardless of vertical gaze position, the ocular rotation axis tilted backward 4 degrees farther in abduction than in adduction. There was also a binocular vertical eye velocity transient and lateral tilt of the ocular axis.

CONCLUSIONS

These disconjugate, short-latency axis perturbations appear intrinsic to the VOR and may have neural or mechanical origins.

Three-dimensional kinematics at the level of the oculomotor plant

Motor systems often require that superfluous degrees of freedom be constrained. For the oculomotor system, a redundancy in the degrees of freedom occurs during visually guided eye movements and is solved by implementing Listing's law and the half-angle rule, kinematic constraints that limit the range of eye positions and angular velocities used by the eyes. These constraints have been attributed either to neurally generated commands or to the physical mechanics of the eye and its surrounding muscles and tissues (i.e., the ocular plant). To directly test whether the ocular plant implements the half-angle rule, critical to the maintenance of Listing's law, we microstimulated the abducens nerve with the eye at different initial vertical eye positions. We report that the electrically evoked eye velocity exhibits the same eye position dependence as seen in visually guided smooth-pursuit eye movements. These results support an important role for the ocular plant in providing a solution to the degrees-of-freedom problem during eye movements.

Present concepts of oculomotor organization

This chapter gives an introduction to the oculomotor system, thus providing a framework for the subsequent chapters. This chapter describes the characteristics, and outlines the structures involved, of the five basic types of eye movements, for gaze holding ("neural integrator") and eye movements in three dimensions (Listing's law, pulleys).

Magnetic Resonance Imaging of Human Extraocular Muscles During Static Ocular Counter-Rolling

The rectus extraocular muscle (EOM) pulleys constrain EOM paths. During visual fixation with head immobile, actively controlled pulleys are known to maintain positions causing EOM pulling directions to change by one-half the change in eye position. This pulley behavior is consistent with Listing's law (LL) of ocular torsion as observed during fixation, saccades, and pursuit. However, pulley behavior during the vestibulo-ocular reflex (VOR) has been unstudied. This experiment studied ocular counter-rolling (OCR), a static torsional VOR that violates LL but can be evoked during MRI. Tri-planar MRI was performed in 10 adult humans during central target fixation while positioned in right and left side down positions known to evoke static OCR. EOM cross-sections and paths were determined from area centroids. Paths were used to locate pulleys in three dimensions. Significant ( P < 0.025) counter-rotational repositioning of the rectus pulley arrays of both orbits was observed in the coronal plane averaging 4.1° (maximum, 8.7°) from right to left side down positions for the inferior, medial, and superior rectus pulleys. There was a trend for the lateral rectus averaging 1.4°. Torsional shift of the rectus pulley array was associated with significant contractile cross-section changes in the superior and inferior oblique muscles. Torsional rectus pulley shift during OCR, which changes pulling directions of the rectus EOMs, correlates with known insertions of the oblique EOM orbital layers on rectus pulleys. The amount of pulley reconfiguration is roughly one-half of published values of ocular torsion during static OCR, an arrangement that would cause rectus pulling directions to change by less than one-half the amount of ocular torsion.

Noncommutativity of eye rotations and the half-angle rule

In order to produce kinematically efficient behavior when dealing with the noncommutativity of rotations, the oculomotor system has developed strategies such as the half-angle rule. In this issue of Neuron, Ghasia and Angelaki demonstrate that during smooth pursuit eye movements the half-angle rule is implemented by the mechanical properties of the eye plant.