Do motoneurons encode the noncommutativity of ocular rotations?

Eyeball translations affect saccadic eye movements beyond brainstem control

Vision requires that we rotate our eyes frequently to look at informative structures in the scene. Eye movements are planned by the brain but their execution depends on the mechanical properties of the oculomotor plant, that is, the arrangement of eyeball position, muscle insertions, and pulley locations. Therefore, the biomechanics of rotations is sensitive to eyeball translation because it changes muscle levers. Eyeball translations are little researched as they are difficult to measure with conventional techniques. Here, we investigated the effects of eyeball translation on the coordination of eyeball rotation by high-speed MRI recordings of saccadic eye movements during blinks, which are known to produce strong translations. We found that saccades during blinks massively overshoot their targets and that these overshoots occur in a transient fashion such that the gaze is back on target at the time the blink ends. These dynamic overshoots were tightly coupled to the eyeball translation, both in time and in size. Saccades made without blinks were also accompanied by small amounts of transient eyeball retraction, the size of which scaled with saccade amplitude. These findings demonstrate a complex combination of rotation and translation of the eye. The mechanical consequences of eyeball translation on oculomotor control should be considered along with the neural implementation in the brainstem to understand the generation of eye movements and their disorders.NEW & NOTEWORTHY We found that saccades during blinks can massively overshoot their target when the eyeball is retracted. Our data imply that the overshoots are not part of the saccade plan prepared in the brainstem, but instead a consequence of the altered biomechanics resulting from concurrent eyeball translation and rotation. To our best knowledge, this is the first direct observation of dynamic properties of the oculomotor plant altering the execution of rotational eye movements.

Biomechanical modeling of actively controlled rectus extraocular muscle pulleys

The Active Pulley Hypothesis (APH) is based on modern functional anatomical descriptions of the oculomotor plant, and postulates behaviors of the orbital pulleys proposed to be positioned by the extraocular muscles (EOMs). A computational model is needed to understand this schema quantitatively. We developed and evaluated a novel biomechanical model of active horizontal rectus pulleys. The orbital (OL) and global (GL) layers of the horizontal rectus EOMs were implemented as separate musculoskeletal strands. Pulley sleeves were modeled as tube-like structures receiving the OL insertion and suspended by elastic strands. Stiffnesses and orientations of pulley suspensions were determined empirically to limit horizontal rectus EOM side-slip while allowing anteroposterior pulley travel. Independent neural drives of the OL greater than GL were assumed. The model was iteratively refined in secondary gazes to implement realistic behavior using the simplest mechanical configuration and neural control strategy. Simulated horizontal rectus EOM paths and pulley positions during secondary gazes were consistent with published MRI measurements. Estimated EOM tensions were consistent with the range of experimentally measured tensions. This model is consistent with postulated bilaminar activity of the EOMs, and the separate roles of the GL in ocular rotation, and OL in pulley positioning.

Statics of plant mechanics

David A. Robinson took all that was known in his time about ocular anatomy, extraocular muscle force generation, and neural control of extraocular muscles, and integrated this information into a quantitative model of the static behavior of the ocular motor plant suitable for application to strabismus, the pathological misalignment of the eyes. Robinson's comprehensive mathematical descriptions of the essential details he knew to be the properties of the ocular motor plant highlighted the critical gaps in the state of knowledge that he very explicitly bridged by quantitative assumptions that later motivated focused research that ultimately revealed many missing pieces of the puzzle. Robinson suggested that it should be possible, in principle, to account (in a computational model) for all the mechanical factors and neural drives that regulate binocular alignment and strabismus, and that such modeling could assist in diagnosis and treatment of this common ophthalmic disorder.

Extraocular Motoneurons and Neurotrophism

Extraocular motoneurons are located in three brainstem nuclei: the abducens, trochlear and oculomotor. They control all types of eye movements by innervating three pairs of agonistic/antagonistic extraocular muscles. They exhibit a tonic-phasic discharge pattern, demonstrating sensitivity to eye position and sensitivity to eye velocity. According to their innervation pattern, extraocular muscle fibers can be classified as singly innervated muscle fiber (SIF), or the peculiar multiply innervated muscle fiber (MIF). SIF motoneurons show anatomical and physiological differences with MIF motoneurons. The latter are smaller and display lower eye position and velocity sensitivities as compared with SIF motoneurons.

Modelling 3D saccade generation by feedforward optimal control

An interesting problem for the human saccadic eye-movement system is how to deal with the degrees-of-freedom problem: the six extra-ocular muscles provide three rotational degrees of freedom, while only two are needed to point gaze at any direction. Measurements show that 3D eye orientations during head-fixed saccades in far-viewing conditions lie in Listing’s plane (LP), in which the eye’s cyclotorsion is zero (Listing’s law, LL). Moreover, while saccades are executed as single-axis rotations around a stable eye-angular velocity axis, they follow straight trajectories in LP. Another distinctive saccade property is their nonlinear main-sequence dynamics: the affine relationship between saccade size and movement duration, and the saturation of peak velocity with amplitude. To explain all these properties, we developed a computational model, based on a simplified and upscaled robotic prototype of an eye with 3 degrees of freedom, driven by three independent motor commands, coupled to three antagonistic elastic muscle pairs. As the robotic prototype was not intended to faithfully mimic the detailed biomechanics of the human eye, we did not impose specific prior mechanical constraints on the ocular plant that could, by themselves, generate Listing’s law and the main-sequence. Instead, our goal was to study how these properties can emerge from the application of optimal control principles to simplified eye models. We performed a numerical linearization of the nonlinear system dynamics around the origin using system identification techniques, and developed open-loop controllers for 3D saccade generation. Applying optimal control to the simulated model, could reproduce both Listing’s law and and the main-sequence. We verified the contribution of different terms in the cost optimization functional to realistic 3D saccade behavior, and identified four essential terms: total energy expenditure by the motors, movement duration, gaze accuracy, and the total static force exerted by the muscles during fixation. Our findings suggest that Listing’s law, as well as the saccade dynamics and their trajectories, may all emerge from the same common mechanism that aims to optimize speed-accuracy trade-off for saccades, while minimizing the total muscle force during eccentric fixation.

Saccades are rapid eye movements that humans and other animals perform three to four times per second to scan and perceive the environment around them. These movements orient the eye in space with high precision and in a highly stereotyped fashion. Existing studies on animal models advocate that both mechanical and neuronal functions play an important role in the control of the saccades, but some facts are still not fully understood due to difficulties in experimenting and measuring the variables in living animals. Instead, robots are computational and physical models of reality that expose all its variables and can be programmed in interpretable ways. We have built a robotic model of an artificial eye containing the basic ingredients of human eyes: full 3D rotations, viscous friction and 6 muscle-like actuators connected to the eyeball in a geometry similar to the biological system. By synthesizing robotic eye control systems we found that important characteristics of the movements become similar to human saccades when the control relies on few simple fundamental principles: the maximization of saccade accuracy and the minimization of saccade duration, energy in control, and force in the muscles during fixation.

Non-commutative, nonlinear, and non-analytic aspects of the ocular motor plant

The ocular motor plant, consisting of the globe, extraocular muscles (EOMs), and connective tissue suspension, constitutes an intricate and non-linear actuator of eye movements. The pulley system of the rectus EOMs constitutes a non-linear inner gimbal actuated by the orbital layers of these EOMs that renders the sequence of ocular rotations effectively commutative to the central controller, and can be rotated by the outer gimbal driven by the oblique EOMs. Optic nerve (ON) length is insufficient to permit large angle adduction without tethering by the ON and sheath, creating at and beyond this threshold a large additional load on the medial rectus muscle. Finite element modeling suggests that adduction may eventually cause repetitive strain injury to the ON and glaucomatous optic nerve damage.

The Macaque Cerebellar Flocculus Outputs a Forward Model of Eye Movement

The central nervous system (CNS) achieves fine motor control by generating predictions of the consequences of the motor command, often called forward models of the movement. These predictions are used centrally to detect not-self generated sensations, to modify ongoing movements, and to induce motor learning. However, finding a neuronal correlate of forward models has proven difficult. In the oculomotor system, we can identify neuronal correlates of forward models vs. neuronal correlates of motor commands by examining neuronal responses during smooth pursuit at eccentric eye positions. During pursuit, torsional eye movement information is not present in the motor command, but it is generated by the mechanic of the orbit. Importantly, the directionality and approximate magnitude of torsional eye movement follow the half angle rule. We use this rule to investigate the role of the cerebellar flocculus complex (FL, flocculus and ventral paraflocculus) in the generation of forward models of the eye. We found that mossy fibers (input elements to the FL) did not change their response to pursuit with eccentricity. Thus, they do not carry torsional eye movement information. However, vertical Purkinje cells (PCs; output elements of the FL) showed a preference for counter-clockwise (CCW) eye velocity [corresponding to extorsion (outward rotation) of the ipsilateral eye]. We hypothesize that FL computes an estimate of torsional eye movement since torsion is present in PCs but not in mossy fibers. Overall, our results add to those of other laboratories in supporting the existence in the CNS of a predictive signal constructed from motor command information.

An alignment maximization method for the kinematics of the eye and eye-head fixations

The orientation of human eyes is uniquely defined with respect to their gaze direction, known as Donders' law. Further, the manner in which the eyes follow Donders' law varies as a function of the situation. When the head is stationary, the Donders' surfaces are flat planes but they tilt when eye fixation distance changes. These planes also shift and rotate when head orientation changes with respect to the direction of gravito-inertial acceleration. When the head is free to rotate, the Donders' surfaces are twisted. In this paper, we present a systematic method to analyze the kinematics of the eye under different gaze situations utilizing the measurement of alignment between various coordinate frames. Kinematic equations are presented for various eye movements ranging from simple head-fixed monocular shifts of eye gaze to complex eye-head shifts of gaze. At each stage, we show that simulated eye orientations that derived from our equations are able to capture the variations of Donders' surfaces and they are comparable with experimental results in the literature. The final equations we propose provide the unified kinematics of head-upright far gaze, head-upright binocular fixation, head static tilted monocular gaze and head-free monocular gaze.

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.

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.

Compartmentalization of extraocular muscle function

Ocular motor diversity exceeds capabilities of only six extraocular muscles (EOMs), but this deficiency is overcome by the plethora of fibers within individual EOMs surpassing requirements of homogeneous actuators. This paper reviews emerging evidence that regions of individual EOMs can be differentially innervated to exert independent oculorotary torques, broadening the oculomotor repertoire, and potentially explaining diverse strabismus pathophysiology. Parallel structure characterizes EOM and tendon fibers, with little transverse coupling of experimentally imposed or actively generated tension. This arrangement enables arbitrary groupings of tendon and muscle fibers to act relatively independently. Coordinated force generation among EOM fibers occurs only upon potentially mutable coordination of innervational commands, whose central basis is suggested by preliminary findings of apparent compartmental segregation of abducens motor neuron pools. Humans, monkeys, and other mammals demonstrate separate, nonoverlapping intramuscular nerve arborizations in the superior vs inferior compartments of the medial rectus (MR) and lateral rectus (LR) EOMs that could apply force at the superior vs inferior portions of scleral insertions, and in the medial vs lateral compartments of the superior oblique that act at the equatorial vs posterior scleral insertions that might preferentially implement incycloduction vs infraduction. Magnetic resonance imaging of the MR during several physiological ocular motor behaviors indicates differential compartmental function. Differential compartmental pathology can influence clinical strabismus. Partial abducens palsy commonly affects the superior LR compartment more than the inferior, inducing vertical strabismus that might erroneously be attributed to cyclovertical EOM pathology. Surgery may selectively manipulate EOM compartments.

The Apt Lecture. Connective tissues reflect different mechanisms of strabismus over the life span

BACKGROUND

Connective tissue pulleys determine extraocular muscle force directions and pulley heterotopy can induce strabismus. The etiology and type of pulley abnormalities vary with patient age, resulting in different but predictable types presentations of strabismus.

METHODS

Magnetic resonance imaging (MRI) was obtained in 95 patients with pulley heterotopy, of whom 56 had childhood-onset pattern strabismus, and was compared with published data on 28 patients aged 69 ± 12 years who had sagging eye syndrome. Control data were from age-matched normal controls with no strabismus.

RESULTS

Patients with childhood-onset strabismus had intact lateral rectus-superior rectus band ligaments and straight extraocular muscle paths but exhibited pulley array A pattern-associated incyclorotation or V pattern-associated excyclorotation. Rectus transposition surgery collapsed patterns. Patients with sagging eye syndrome exhibited blepharoptosis, superior sulcus defect, and inferolateral displacement of rectus pulleys with elongation of extraocular muscles that followed curved paths. Symmetrical lateral rectus pulley sag was associated with divergence paralysis esotropia; asymmetrical sag > 1 mm, with cyclovertical strabismus. Both lateral rectus resection and medial rectus recession treated divergence paralysis esotropia. Partial vertical rectus tenotomy treated cyclovertical strabismus.

CONCLUSIONS

Childhood onset pulley abnormalities are associated with A or V pattern strabismus and external anatomical features suggest that these pulley defects are probably congenital. Adult onset pulley defects commonly result from age-related tissue involution and external features such as adnexal laxity are also helpful in recognizing involution as a possible etiology of strabismus.

Pattern Strabismus: Where Does the Brain's Role End and the Muscle's Begin?

Vertically incomitant pattern strabismus comprises 50% of infantile horizontal strabismus. The oblique muscle dysfunction has been associated with pattern strabismus. High-resolution orbit imaging and contemporary neurophysiology studies in non-human primate models of strabismus have shed light into the mechanisms of pattern strabismus. In this review, we will examine our current understanding of etiologies of pattern strabismus. Speculated pathophysiology includes oblique muscle dysfunction, loss of fusion with altered recti muscle pull, displacements and instability in connective tissue pulleys of the recti muscles, vestibular hypofunction, and abnormal neural connections. Orbital mechanical factors, such as abnormal pulleys, were reported as a cause of pattern strabismus in patients with craniofacial anomalies, connective tissue disorders, and late-onset strabismus. In contrast, abnormal neural connections could be responsible for the development of a pattern in infantile-onset strabismus. Pattern strabismus is likely multifactorial. Understanding the mechanisms of pattern strabismus is pivotal to determine an appropriate surgical treatment strategy for these patients.

Reaching the limit of the oculomotor plant: 3D kinematics after abducens nerve stimulation during the torsional vestibulo-ocular reflex

Accumulating evidence shows that the oculomotor plant is capable of implementing aspects of three-dimensional kinematics such as Listing's law and the half-angle rule. But these studies have only examined the eye under static conditions or with movements that normally obey these rules (e.g., saccades and pursuit). Here we test the capability of the oculomotor plant to rearrange itself as necessary for non-half-angle behavior. Three monkeys (Macaca mulatta) fixated five vertically displaced targets along the midsagittal plane while sitting on a motion platform that rotated sinusoidally about the naso-occipital axis. This activated the torsional, rotational vestibulo-ocular reflex, which exhibits a zero-angle or negative-angle rule (depending on the visual stimulus). On random sinusoidal cycles, we stimulated the abducens nerve and observed the resultant eye movements. If the plant has rearranged itself to implement this non-half-angle behavior, then stimulation should reveal this behavior. On the other hand, if the plant is only capable of half-angle behavior, then stimulation should reveal a half-angle rule. We find the latter to be true and therefore additional neural signals are likely necessary to implement non-half-angle behavior.

Differential lateral rectus compartmental contraction during ocular counter-rolling

PURPOSE

The lateral rectus (LR) and medial rectus (MR) extraocular muscles (EOMs) have largely nonoverlapping superior and inferior innervation territories, suggesting functional compartmental specialization. We used magnetic resonance imaging (MRI) in humans to investigate differential compartmental activity in the rectus EOMs during head tilt, which evokes ocular counter-rolling, a torsional vestibulo-ocular reflex (VOR).

METHODS

MRI in quasi-coronal planes was analyzed during target-controlled central gaze in 90° right and left head tilts in 12 normal adults. Cross sections and posterior partial volumes of the transverse portions of the four rectus EOMs were compared in contiguous image planes 2 mm thick spanning the orbit from origins to globe equator, and used as indicators of contractility.

RESULTS

Horizontal rectus EOMs had significantly greater posterior volumes and maximum cross sections in their inferior compartments (P < 10(-8)). In orbit tilt up (extorted) compared with orbit tilt down (intorted) head tilts, contractile changes in LR maximum cross section (P < 0.0001) and posterior partial volume (P < 0.05) were significantly greater in the inferior but not in the superior compartment. These changes were not explainable by horizontal or vertical eye position changes. A weaker compartmental effect was suggested for MR. The vertical rectus EOMs did not exhibit significant compartmental contractile changes during head tilt. Mechanical modeling suggests that differential LR contraction may contribute to physiological cyclovertical effects.

CONCLUSIONS

Selective activation of the two LR, and possibly MR, compartments correlates with newly recognized segregation of intramuscular innervation into distinct compartments, and probably contributes to noncommutative torsion during the VOR.

Three-dimensional transformations for goal-directed action

Much of the central nervous system is involved in visuomotor transformations for goal-directed gaze and reach movements. These transformations are often described in terms of stimulus location, gaze fixation, and reach endpoints, as viewed through the lens of translational geometry. Here, we argue that the intrinsic (primarily rotational) 3-D geometry of the eye-head-reach systems determines the spatial relationship between extrinsic goals and effector commands, and therefore the required transformations. This approach provides a common theoretical framework for understanding both gaze and reach control. Combined with an assessment of the behavioral, neurophysiological, imaging, and neuropsychological literature, this framework leads us to conclude that (a) the internal representation and updating of visual goals are dominated by gaze-centered mechanisms, but (b) these representations must then be transformed as a function of eye and head orientation signals into effector-specific 3-D movement commands.

Expanding repertoire in the oculomotor periphery: selective compartmental function in rectus extraocular muscles

Since connective tissue pulleys implement Listing's law by systematically changing rectus extraocular muscle (EOM) pulling directions, non-Listing's law gaze dependence of the vestibulo-ocular reflex is currently inexplicable. Differential activation of compartments within rectus EOMs may endow the ocular motor system with more behavioral diversity than previously supposed. Innervation to horizontal, but not vertical, rectus EOMs of mammals is segregated into superior and inferior compartments. Magnetic resonance imaging in normal subjects demonstrates contractile changes in the lateral rectus (LR) inferior, but not superior, compartment during ocular counter-rolling (OCR) induced by head tilt. In human orbits ipsilesional to unilateral superior oblique palsy, neither LR compartment exhibits contractile change during head tilt, although the inferior compartment contracts normally in contralesional orbits. This suggests that differential compartmental LR contraction assists normal OCR. Computational simulation suggests that differential compartmental action in horizontal rectus EOMs could achieve more force than required by vertical fusional vergence.

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.

Compartmentalized innervation of primate lateral rectus muscle

PURPOSE

Skeletal and craniofacial muscles are frequently composed of multiple neuromuscular compartments that serve different physiological functions. Evidence of possible regional selectivity in LR intramuscular innervation was sought in a study of the anatomic potential of lateral rectus (LR) muscle compartmentalization.

METHODS

Whole orbits of two humans and five macaque monkeys were serially sectioned at 10-microm thickness and stained with Masson trichrome. The abducens nerve (CN6) was traced anteriorly from the deep orbit as it branched to enter the LR and arborized among extraocular muscle (EOM) fibers. Three-dimensional reconstruction was performed in human and monkey orbits.

RESULTS

Findings were in concordance in the monkey and human orbits. External to the LR global surface, CN6 bifurcated into approximately equal-sized trunks before entering the global layer. Subsequent arborization showed a systematic topography, entering a well-defined inferior zone 0.4 to 2.5 mm more posteriorly than branches entering the largely nonoverlapping superior zone. Zonal innervation remained segregated anteriorly and laterally within the LR.

CONCLUSIONS

Consistent segregation of intramuscular CN6 arborization in humans and monkeys suggests functionally distinct superior and inferior zones for the LR. Since the LR is shaped as a broad vertical strap, segregated control of the two zones could activate them separately, potentially mediating previously unappreciated but substantial torsional and vertical oculorotary LR actions.

Internal models and neural computation in the vestibular system

The vestibular system is vital for motor control and spatial self-motion perception. Afferents from the otolith organs and the semicircular canals converge with optokinetic, somatosensory and motor-related signals in the vestibular nuclei, which are reciprocally interconnected with the vestibulocerebellar cortex and deep cerebellar nuclei. Here, we review the properties of the many cell types in the vestibular nuclei, as well as some fundamental computations implemented within this brainstem-cerebellar circuitry. These include the sensorimotor transformations for reflex generation, the neural computations for inertial motion estimation, the distinction between active and passive head movements, as well as the integration of vestibular and proprioceptive information for body motion estimation. A common theme in the solution to such computational problems is the concept of internal models and their neural implementation. Recent studies have shed new insights into important organizational principles that closely resemble those proposed for other sensorimotor systems, where their neural basis has often been more difficult to identify. As such, the vestibular system provides an excellent model to explore common neural processing strategies relevant both for reflexive and for goal-directed, voluntary movement as well as perception.

Internal models of eye movement in the floccular complex of the monkey cerebellum

Internal models are a key feature of most modern theories of motor control. Yet, it has been challenging to localize internal models in the brain, or to demonstrate that they are more than a metaphor. In the present review, I consider a large body of data on the cerebellar floccular complex, asking whether floccular output has features that would be expected of the output from internal models. I argue that the simple spike firing rates of a single group of floccular Purkinje cells could reflect the output of three different internal models. (1) An eye velocity positive feedback pathway through the floccular complex provides neural inertia for smooth pursuit eye movements, and appears to operate as a model of the inertia of real-world objects. (2) The floccular complex processes and combines input signals so that the dynamics of its average simple spike output are appropriate for the dynamics of the downstream brainstem circuits and eyeball. If we consider the brainstem circuits and eyeball as a more broadly conceived "oculomotor plant," then the output from the floccular complex could be the manifestation of an inverse model of "plant" dynamics. (3) Floccular output reflects an internal model of the physics of the orbit where head and eye motion sum to produce gaze motion. The effects of learning on floccular output suggest that it is modeling the interaction of the visually-guided and vestibular-driven components of eye and gaze motion. Perhaps the insights from studying oculomotor control provide groundwork to guide the analysis of internal models for a wide variety of cerebellar behaviors.

Functional anatomy of the extraocular muscles during vergence

Magnetic resonance imaging (MRI) now enables precise visualisation of the mechanical state of the living human orbit, enabling inferences about the effects of mechanical factors on ocular kinematics. We used 3-dimensional (3D) magnetic search coil recordings and MRI to investigate the mechanical state of the orbit during vergence in humans. Horizontal convergence of 23 degrees from a remote to a near target aligned on one eye was geometrically ideal, and was associated with lens thickening and extorsion of the rectus pulley array of the aligned eye with superior oblique muscle relaxation and inferior oblique muscle contraction. There was no rectus muscle co-contraction. Subjective fusion through a 1 degree vertical prism caused a clockwise (CW) torsion in both eyes, as well as variable vertical and horizontal vergences that seldom corresponded to prism amount or direction. MRI under these conditions did not show consistent torsion of the rectus pulley array, but a complex pattern of changes in rectus extraocular muscle (EOM) crossections, consistent with co-contraction. Binocular fusion during vergence is accomplished by complex, 3D eye rotations seldom achieving binocular retinal correspondence. Vergence eye movements are sometimes associated with changes in rectus EOM pulling directions, and may sometimes be associated with co-contraction. Thus, extraretinal information about eye position would appear necessary to interpret binocular correspondence, and to avoid diplopia.

Head stabilization by vestibulocollic reflexes during quadrupedal locomotion in monkey

Little is known about the three-dimensional characteristics of vestibulocollic reflexes during natural locomotion. Here we determined how well head stability is maintained by the angular and linear vestibulocollic reflexes (aVCR, lVCR) during quadrupedal locomotion in rhesus and cynomolgus monkeys. Animals walked on a treadmill at velocities of 0.4-1.25 m/s. Head rotations were represented by Euler angles (Fick convention). The head oscillated in yaw and roll at stride frequencies (approximately 1-2 Hz) and pitched at step frequencies (approximately 2-4 Hz). Head angular accelerations (100-2,500 degrees/s2) were sufficient to have excited the aVOR to stabilize gaze. Pitch and roll head movements were <7 degrees , peak to peak, and the amplitude was unrelated to stride frequency. Yaw movements were larger due to spontaneous voluntary head shifts and were smaller at higher walking velocities. Head translations were small (< or =4 cm). Cynomolgus monkeys positioned their heads more forward in pitch than the rhesus monkeys. None of the animals maintained a forward head fixation point, indicating that the lVCR contributed little to compensatory head movements in these experiments. Significantly, aVCR gains in roll and pitch were close to unity and phases were approximately 180 degrees over the full frequency range of natural walking, which is in contrast to previous findings using anesthesia or passive trunk rotation with body restraint. We conclude that the behavioral state associated with active body motion is necessary to maintain head stability in pitch and roll over the full range of stride/step frequencies encountered during walking.

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.

Adaptive neural mechanism for Listing's law revealed in patients with skew deviation caused by brainstem or cerebellar lesion

PURPOSE

Skew deviation is a vertical strabismus caused by damage to the otolithic-ocular reflex pathway and is associated with abnormal ocular torsion. This study was conducted to determine whether patients with skew deviation show the normal pattern of three-dimensional eye control called Listing's law, which specifies the eye's torsional angle as a function of its horizontal and vertical position.

METHODS

Ten patients with skew deviation caused by brain stem or cerebellar lesions and nine normal control subjects were studied. Patients with diplopia and neurologic symptoms less than 1 month in duration were designated as acute (n = 4) and those with longer duration were classified as chronic (n = 10). Serial recordings were made in the four patients with acute skew deviation. With the head immobile, subjects made saccades to a target that moved between straight ahead and eight eccentric positions, while wearing search coils. At each target position, fixation was maintained for 3 seconds before the next saccade. From the eye position data, the plane of best fit, referred to as Listing's plane, was fitted. Violations of Listing's law were quantified by computing the "thickness" of this plane, defined as the SD of the distances to the plane from the data points.

RESULTS

Both the hypertropic and hypotropic eyes in patients with acute skew deviation violated Listing's and Donders' laws-that is, the eyes did not show one consistent angle of torsion in any given gaze direction, but rather an abnormally wide range of torsional angles. In contrast, each eye in patients with chronic skew deviation obeyed the laws. However, in chronic skew deviation, Listing's planes in both eyes had abnormal orientations.

CONCLUSIONS

Patients with acute skew deviation violated Listing's law, whereas those with chronic skew deviation obeyed it, indicating that despite brain lesions, neural adaptation can restore Listing's law so that the neural linkage between horizontal, vertical, and torsional eye position remains intact. Violation of Listing's and Donders' laws during fixation arises primarily from torsional drifts, indicating that patients with acute skew deviation have unstable torsional gaze holding that is independent of their horizontal-vertical eye positions.

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.

Three dimensional kinematics of rapid compensatory eye movements in humans with unilateral vestibular deafferentation

Saccades executed with the head stationary have kinematics conforming to Listing's law (LL), confining the ocular rotational axis to Listing's plane (LP). In unilateral vestibular deafferentation (UVD), the vestibulo-ocular reflex (VOR), which does not obey LL, has at high head acceleration a slow phase that has severely reduced velocity during ipsilesional rotation, and mildly reduced velocity during contralesional rotation. Studying four subjects with chronic UVD using 3D magnetic search coils, we investigated kinematics of stereotypic rapid eye movements that supplement the impaired VOR. We defined LP with the head immobile, and expressed eye and head movements as quaternions in LP coordinates. Subjects underwent transient whole body yaw at peak acceleration 2,800 degrees /s(2) while fixating targets centered, or 20 degrees up or down prior to rotation. The VOR shifted ocular torsion out of LP. Vestibular catch-up saccades (VCUS) occurred with mean latency 90 +/- 44 ms (SD) from ipsilesional rotation onset, maintained initial non-LL torsion so that their quaternion trajectories paralleled LP, and had velocity axes changing by half of eye position. During contralesional rotation, rapid eye movements occurred at mean latency 135 +/- 36 ms that were associated with abrupt decelerations (ADs) of the horizontal slow phase correcting 3D deviations in its velocity axis, with quaternion trajectories not paralleling LP. Rapid eye movements compensating for UVD have two distinct kinematics. VCUS have velocity axis dependence on eye position consistent with LL, so are probably programmed in 2D by neural circuits subserving visual saccades. ADs have kinematics that neither conform to LL nor match the VOR axis, but appear instead programmed in 3D to correct VOR axis errors.

A reevaluation of the inverse dynamic model for eye movements

To construct an appropriate motor command from signals that provide a representation of desired action, the nervous system must take into account the dynamic characteristics of the motor plant to be controlled. In the oculomotor system, signals specifying desired eye velocity are thought to be transformed into motor commands by an inverse dynamic model of the eye plant that is shared for all types of eye movements and implemented by a weighted combination of eye velocity and position signals. Neurons in the prepositus hypoglossi and adjacent medial vestibular nuclei (PH-BT neurons) were traditionally thought to encode the "eye position" component of this inverse model. However, not only are PH-BT responses inconsistent with this theoretical role, but compensatory eye movement responses to translation do not show evidence for processing by a common inverse dynamic model. Prompted by these discrepancies between theoretical notions and experimental observations, we reevaluated these concepts using multiple-frequency rotational and translational head movements. Compatible with the notion of a common inverse model, we show that PH-BT responses are unique among all premotor cell types in bearing a consistent relationship to the motor output during eye movements driven by different sensory stimuli. However, because their responses are dynamically identical to those of motoneurons, PH-BT neurons do not simply represent an internal component of the inverse model, but rather its output. They encode and distribute an estimate of the motor command, a signal critical for accurate motor execution and learning.

Interstitial Nucleus of Cajal Encodes Three-Dimensional Head Orientations in Fick-Like Coordinates

Two central, related questions in motor control are 1) how the brain represents movement directions of various effectors like the eyes and head and 2) how it constrains their redundant degrees of freedom. The interstitial nucleus of Cajal (INC) integrates velocity commands from the gaze control system into position signals for three-dimensional eye and head posture. It has been shown that the right INC encodes clockwise (CW)-up and CW-down eye and head components, whereas the left INC encodes counterclockwise (CCW)-up and CCW-down components, similar to the sensitivity directions of the vertical semicircular canals. For the eyes, these canal-like coordinates align with Listing’s plane (a behavioral strategy limiting torsion about the gaze axis). By analogy, we predicted that the INC also encodes head orientation in canal-like coordinates, but instead, aligned with the coordinate axes for the Fick strategy (which constrains head torsion). Unilateral stimulation (50 μA, 300 Hz, 200 ms) evoked CW head rotations from the right INC and CCW rotations from the left INC, with variable vertical components. The observed axes of head rotation were consistent with a canal-like coordinate system. Moreover, as predicted, these axes remained fixed in the head, rotating with initial head orientation like the horizontal and torsional axes of a Fick coordinate system. This suggests that the head is ordinarily constrained to zero torsion in Fick coordinates by equally activating CW/CCW populations of neurons in the right/left INC. These data support a simple mechanism for controlling head orientation through the alignment of brain stem neural coordinates with natural behavioral constraints.

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.

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.

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.

Axis of eye rotation changes with head-pitch orientation during head impulses about earth-vertical

The goal of this study was to assess how the axis of head rotation, Listing's law, and eye position influence the axis of eye rotation during brief, rapid head rotations. We specifically asked how the axis of eye rotation during the initial angular vestibuloocular reflex (VOR) changed when the pitch orientation of the head relative to Earth-vertical was varied, but the initial position of the eye in the orbit and the orientation of Listing's plane with respect to the head were fixed. We measured three-dimensional eye and head rotation axes in eight normal humans using the search coil technique during head-and-trunk (whole-body) and head-on-trunk (head-only) "impulses" about an Earth-vertical axis. The head was initially oriented at one of five pitch angles (30 degrees nose down, 15 degrees nose down, 0 degrees, 15 degrees nose up, 30 degrees nose up). The fixation target was always aligned with the nasooccipital axis. Whole-body impulses were passive, unpredictable, manual, rotations with peak-amplitude of approximately 20 degrees , peak-velocity of approximately 80 degrees /s, and peak-acceleration of approximately 1000 degrees /s2. Head-only impulses were also passive, unpredictable, manual, rotations with peak-amplitude of approximately 20 degrees , peak-velocity of approximately 150 degrees /s, and peak-acceleration of approximately 3000 degrees /s2. During whole-body impulses, the axis of eye rotation tilted in the same direction, and by an amount proportional (0.51 +/- 0.09), to the starting pitch head orientation (P < 0.05). This proportionality constant decreased slightly to 0.39 +/- 0.08 (P < 0.05) during head-only impulses. Using the head-only impulse data, with the head pitched up, we showed that only 50% of the tilt in the axis of eye rotation could be predicted from vectorial summation of the gains (eye velocity/head velocity) obtained for rotations about the pure yaw and roll head axes. Thus, even when the orientation of Listing's plane and eye position in the orbit are fixed, the axis of eye rotation during the VOR reflects a compromise between the requirements of Listing's law and a perfectly compensatory VOR.

Magnetic resonance imaging of the effects of horizontal rectus extraocular muscle surgery on pulley and globe positions and stability

PURPOSE

Magnetic resonance imaging (MRI) was used to determine the effect of recessions and resections on horizontal extraocular muscle (EOM) paths and globe position.

METHODS

Four adults with horizontal strabismus underwent contrast-enhanced, surface-coil MRI in central, secondary, and tertiary gazes, before and after horizontal EOM recessions and/or resections. EOM paths were determined from 2-mm thickness, quasicoronal MRI by analysis of cross-sectional area centroids in a normalized, oculocentric coordinate system. Globe displacement was determined by measuring the apparent shift of the bony orbit in eccentric gaze.

RESULTS

In all subjects, the anteroposterior positions of the horizontal rectus pulleys shifted by less than 2 mm after surgery, indistinguishable from zero within measurement precision. In three subjects who underwent medial rectus (MR) recession or resection, postoperative globe position was similar in central gaze, but globe translation during vertical gaze shift changed markedly. There was no effect on globe translation in the subject who underwent only lateral rectus (LR) resection.

CONCLUSIONS

Recessions and resections of horizontal EOMs have minimal effect on anteroposterior EOM pulley positions. Because the pulley does not shift appreciably despite large alterations in the EOM insertion, the proximity of a recessed EOM to its pulley would be expected to introduce torsional and vertical actions in tertiary gazes. Connective tissue dissection during MR surgery may destabilize the globe's vertical translational stability within the orbit, potentially changing the effective pulling directions of the rectus EOMs in vertical gazes. These changes may mimic oblique muscle dysfunction. LR surgery may avoid globe destabilization.

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.