Deficits in torsional and vertical rapid eye movements and shift of Listing's plane after uni- and bilateral lesions of the rostral interstitial nucleus of the medial longitudinal fasciculus

Loss of torsional quick eye movements during head roll in progressive supranuclear palsy: a new diagnostic marker

BACKGROUND AND OBJECTIVES

Even though impaired horizontal and vertical saccades are well-known features of progressive supranuclear palsy (PSP), abnormalities of torsional quick phases of eye movements have not been defined in PSP and other Parkinsonian syndromes. This study aims to determine the diagnostic value of decreased torsional quick phases during head oscillations in the roll plane in patients with PSP.

METHODS

Using video-oculography, we recorded the head and eye motion during passive head oscillations in the roll plane and determined the decrease of torsional quick phases in patients with PSP (n = 13) in comparison to normal controls (n = 13) and those with multiple system atrophy (MSA, n = 17) or idiopathic Parkinson's disease (PD, n = 6).

RESULTS

Torsional quick phases were absent during the torsional vestibulo-ocular reflex (VOR) in 78.6% (11/13) of the patients with PSP, but only in 11.8% (2/17) of those with MSA and none with idiopathic PD or of normal controls (Chi-square tests, p < 0.001) while gains of the torsional VOR did not differ among the groups (Chi-square tests, p > 0.05). Furthermore, the torsional quick phases were smaller even when observed in patients with PSP.

CONCLUSION

Loss of torsional quick phases is an early biological marker for diagnosis of PSP, and may be ascribed to degeneration of the rostral interstitial nucleus of the medial longitudinal fasciculus that contains the burst neurons for torsional as well as vertical saccades.

Accuracy of clinical versus oculographic detection of pathological saccadic slowing

Saccadic slowing as a component of supranuclear saccadic gaze palsy is an important diagnostic sign in multiple neurologic conditions, including degenerative, inflammatory, genetic, or ischemic lesions affecting brainstem structures responsible for saccadic generation. Little attention has been given to the accuracy with which clinicians correctly identify saccadic slowing. We compared clinician (n = 19) judgements of horizontal and vertical saccade speed on video recordings of saccades (from 9 patients with slow saccades, 3 healthy controls) to objective saccade peak velocity measurements from infrared oculographic recordings. Clinician groups included neurology residents, general neurologists, and fellowship-trained neuro-ophthalmologists. Saccades with normal peak velocities on infrared recordings were correctly identified as normal in 57% (91/171; 171 = 9 videos × 19 clinicians) of clinician decisions; saccades determined to be slow on infrared recordings were correctly identified as slow in 84% (224/266; 266 = 14 videos × 19 clinicians) of clinician decisions. Vertical saccades were correctly identified as slow more often than horizontal saccades (94% versus 74% of decisions). No significant differences were identified between clinician training levels. Reliable differentiation between normal and slow saccades is clinically challenging; clinical performance is most accurate for detection of vertical saccade slowing. Quantitative analysis of saccade peak velocities enhances accurate detection and is likely to be especially useful for detection of mild saccadic slowing.

Neuro-Ophthalmologic Features and Outcomes of Thalamic Infarction: A Single-Institutional 10-Year Experience

BACKGROUND

Neuro-ophthalmologic deficit after thalamic infarction has been of great concern to ophthalmologists because of its debilitating impacts on patients' daily living. We aimed to describe the visual and oculomotor features of thalamic infarction and to delineate clinical outcomes and prognostic factors of the oculomotor deficits from an ophthalmologic point of view.

METHODS

Clinical and neuroimaging data of all participants were retrospectively reviewed. Among the 12,755 patients with first-ever ischemic stroke, who were registered in our Stroke Data Bank between January 2009 and December 2018, 342 were found to have acute thalamic infarcts on MRI, from whom we identified the patients exhibiting neuro-ophthalmologic manifestations including visual, oculomotor, pupillary, and eyelid anomalies.

RESULTS

Forty (11.7%) of the 342 patients with thalamic infarction demonstrated neuro-ophthalmologic manifestations, consisting of vertical gaze palsy (n = 19), skew deviation with an invariable hypotropia of the contralesional eye (n = 18), third nerve palsy (n = 11), pseudoabducens palsy (n = 9), visual field defects (n = 7), and other anomalies such as isolated ptosis and miosis (n = 7). Paramedian infarct was the most predominant lesion of neuro-ophthalmologic significance, accounting for 84.8% (n = 28) of all patients sharing the oculomotor features. Although most of the patients with oculomotor abnormalities rapidly improved without sequelae, 6 (18.2%) patients showed permanent oculomotor deficits. Common clinical features of patients with permanent oculomotor deficits included the following: no improvement within 3 months, combined upgaze and downgaze palsy, and the involvement of the paramedian tegmentum of the rostral midbrain.

CONCLUSIONS

Thalamic infarction, especially in paramedian territory, can cause a wide variety of neuro-ophthalmologic manifestations, including vertical gaze palsy, skew deviation, and third nerve palsy. Although most oculomotor abnormalities resolve spontaneously within a few months, some may persist for years when the deficits remain unimproved for more than 3 months after stroke.

An alternative mechanism of crossed vertical gaze palsy in unilateral mesodiencephalic infarction

Crossed vertical gaze palsy refers to a rare combination of elevation paresis in one eye and depression palsy in the fellow eye. It was once reported in a patient with unilateral infarction involving the mesodiencephalic junction, and was ascribed to selective disruption of the fibers projecting from the rostral interstitial nucleus of the medial longitudinal fasciculus (riMLF) to the oculomotor nuclear complex. Cerebral autosomal dominant arteriopathy with subcortical infarcts and leukoencephalopathy (CADASIL) is a rare cause of ophthalmoplegia and crossed vertical gaze palsy has not been described in this disorder. Our patient with a circumscribed acute infarction involving the left mesodiencephalic junction due to CADASIL showed both upward and downward gaze palsy in both eyes, but more marked depression paresis in the ipsilesional eye and more conspicuous elevation deficit in the contralesional eye, which was consistent with crossed vertical gaze palsy. We provide alternate explanation for this rare phenotype of vertical gaze palsy. Selective disruption of riMLF fibers may cause crossed vertical gaze palsy in unilateral mesodiencephalic lesion.

Ocular Motor Dysfunction Due to Brainstem Disorders

BACKGROUND

The brainstem contains numerous structures including afferent and efferent fibers that are involved in generation and control of eye movements.

EVIDENCE ACQUISITION

These structures give rise to distinct patterns of abnormal eye movements when damaged. Defining these ocular motor abnormalities allows a topographic diagnosis of a lesion within the brainstem.

RESULTS

Although diverse patterns of impaired eye movements may be observed in lesions of the brainstem, medullary lesions primarily cause various patterns of nystagmus and impaired vestibular eye movements without obvious ophthalmoplegia. By contrast, pontine ophthalmoplegia is characterized by abnormal eye movements in the horizontal plane, while midbrain lesions typically show vertical ophthalmoplegia in addition to pupillary and eyelid abnormalities.

CONCLUSIONS

Recognition of the patterns and characteristics of abnormal eye movements observed in brainstem lesions is important in understanding the roles of each neural structure and circuit in ocular motor control as well as in localizing the offending lesion.

Neurons in the Nucleus papilio contribute to the control of eye movements during REM sleep

Rapid eye movements (REM) are characteristic of the eponymous phase of sleep, yet the underlying motor commands remain an enigma. Here, we identified a cluster of Calbindin-D28K-expressing neurons in the Nucleus papilio (NP^Calb), located in the dorsal paragigantocellular nucleus, which are active during REM sleep and project to the three contralateral eye-muscle nuclei. The firing of opto-tagged NP^Calb neurons is augmented prior to the onset of eye movements during REM sleep. Optogenetic activation of NP^Calb neurons triggers eye movements selectively during REM sleep, while their genetic ablation or optogenetic silencing suppresses them. None of these perturbations led to a change in the duration of REM sleep episodes. Our study provides the first evidence for a brainstem premotor command contributing to the control of eye movements selectively during REM sleep in the mammalian brain.

Rapid eye movement (REM) sleep is a sleep phase characterised by random eye movements for which the underlying motor commands are yet to be revealed. The authors describe that a cluster of medulla oblongata neurons in the Nucleus papiliocontributes to the control of eye movements during REM sleep.

Pendular Seesaw Nystagmus in a Patient With a Giant Pituitary Macroadenoma: Pathophysiology and the Role of the Accessory Optic System

Seesaw nystagmus is characterized by cyclic eye movements with a conjugate torsional component and a dissociated vertical component. In the first half of the cycle, one eye elevates and intorts, whereas the other eye depresses and extorts. The pattern is reversed in the remaining half of the cycle. We describe a patient with a giant pituitary adenoma who developed pendular seesaw nystagmus. Disturbance in the visuovestibular system is postulated to contribute to this form of seesaw nystagmus. Lesions compressing the optic chiasm and the accessory optic system could interrupt the transmission of retinal error signals to the inferior olivary nucleus and the interstitial nucleus of Cajal, thus interfering with the adaptive mechanism of the vestibulo-ocular reflex and leading to pendular seesaw nystagmus.

Brain Stem Neural Circuits of Horizontal and Vertical Saccade Systems and their Frame of Reference

Sensory signals for eye movements (visual and vestibular) are initially coded in different frames of reference but finally translated into common coordinates, and share the same final common pathway, namely the same population of extraocular motoneurons. From clinical studies in humans and lesion studies in animals, it is generally accepted that voluntary saccadic eye movements are organized in horizontal and vertical Cartesian coordinates. However, this issue is not settled yet, because neural circuits for vertical saccades remain unidentified. We recently determined brainstem neural circuits from the superior colliculus to ocular motoneurons for horizontal and vertical saccades with combined electrophysiological and neuroanatomical techniques. Comparing well-known vestibuloocular pathways with our findings of commissural excitation and inhibition between both superior colliculi, we proposed that the saccade system uses the same frame of reference as the vestibuloocular system, common semicircular canal coordinate. This proposal is mainly based on marked similarities (1) between output neural circuitry from one superior colliculus to extraocular motoneurons and that from a respective canal to its innervating extraocular motoneurons, (2) of patterns of commissural reciprocal inhibitions between upward saccade system on one side and downward system on the other, and between anterior canal system on one side and posterior canal system on the other, and (3) between the neural circuits of saccade and quick phase of vestibular nystagmus sharing brainstem burst neurons. In support of the proposal, commissural excitation of the superior colliculi may help to maintain Listing's law in saccades in spite of using semicircular canal coordinate.

Clinical Approach to Supranuclear Brainstem Saccadic Gaze Palsies

Failure of brainstem supranuclear centers for saccadic eye movements results in the clinical presence of a brainstem-mediated supranuclear saccadic gaze palsy (SGP), which is manifested as slowing of saccades with or without range of motion limitation of eye movements and as loss of quick phases of optokinetic nystagmus. Limitation in the range of motion of eye movements is typically worse with saccades than with smooth pursuit and is overcome with vestibular–ocular reflexive eye movements. The differential diagnosis of SGPs is broad, although acute-onset SGP is most often from brainstem infarction and chronic vertical SGP is most commonly caused by the neurodegenerative condition progressive supranuclear palsy. In this review, we discuss the brainstem anatomy and physiology of the brainstem saccade-generating network; we discuss the clinical features of SGPs, with an emphasis on insights from quantitative ocular motor recordings; and we consider the broad differential diagnosis of SGPs.

Basic and translational neuro-ophthalmology of visually guided saccades: disorders of velocity

Introduction

Saccades are rapid, yoked eye movements in an effort to direct a target over fovea. The complex circuitry of saccadic eye movements has been exhaustively described. As a result clinicians can elegantly localize the pathology if it falls on the neuraxis responsible for saccades. Traditionally saccades are studied with their quantitative characteristics such as amplitude, velocity, duration, direction, latency and accuracy.

Areas covered

Amongst all subtypes, the physiology of the visually guided saccades is most extensively studied. Here we will review the basic and pertinent neuro-anatomy and physiology of visually guided saccade and then discuss common or classic disorders affecting the velocity of visually guided saccades. We will then discuss the basic mechanism for saccade slowing in these disorders.

Expert commentary

Prompt appreciation of disorders of saccade velocity is critical to reach appropriate diagnosis. Disorders of midbrain, cerebellum, or basal ganglia can lead to prolonged transition time during gaze shift and decreased saccade velocity.

Saccadic Palsy following Cardiac Surgery: Possible Role of Perineuronal Nets

Objective

Perineuronal nets (PN) form a specialized extracellular matrix around certain highly active neurons within the central nervous system and may help to stabilize synaptic contacts, promote local ion homeostasis, or play a protective role. Within the ocular motor system, excitatory burst neurons and omnipause neurons are highly active cells that generate rapid eye movements – saccades; both groups of neurons contain the calcium-binding protein parvalbumin and are ensheathed by PN. Experimental lesions of excitatory burst neurons and omnipause neurons cause slowing or complete loss of saccades. Selective palsy of saccades in humans is reported following cardiac surgery, but such cases have shown normal brainstem neuroimaging, with only one clinicopathological study that demonstrated paramedian pontine infarction. Our objective was to test the hypothesis that lesions of PN surrounding these brainstem saccade-related neurons may cause saccadic palsy.

Methods

Together with four controls we studied the brain of a patient who had developed a permanent selective saccadic palsy following cardiac surgery and died several years later. Sections of formalin-fixed paraffin-embedded brainstem blocks were applied to double-immunoperoxidase staining of parvalbumin and three different components of PN. Triple immunofluorescence labeling for all PN components served as internal controls. Combined immunostaining of parvalbumin and synaptophysin revealed the presence of synapses.

Results

Excitatory burst neurons and omnipause neurons were preserved and still received synaptic input, but their surrounding PN showed severe loss or fragmentation.

Interpretation

Our findings support current models and experimental studies of the brainstem saccade-generating neurons and indicate that damage to PN may permanently impair the function of these neurons that the PN ensheathe. How a postulated hypoxic mechanism could selectively damage the PN remains unclear. We propose that the well-studied saccadic eye movement system provides an accessible model to evaluate the role of PN in health and disease.

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.

Vestibular responses in the macaque pedunculopontine nucleus and central mesencephalic reticular formation

The pedunculopontine nucleus (PPN) and central mesencephalic reticular formation (cMRF) both send projections and receive input from areas with known vestibular responses. Noting their connections with the basal ganglia, the locomotor disturbances that occur following lesions of the PPN or cMRF, and the encouraging results of PPN deep brain stimulation in Parkinson's disease patients, both the PPN and cMRF have been linked to motor control. In order to determine the existence of and characterize vestibular responses in the PPN and cMRF, we recorded single neurons from both structures during vertical and horizontal rotation, translation, and visual pursuit stimuli. The majority of PPN cells (72.5%) were vestibular-only (VO) cells that responded exclusively to rotation and translation stimuli but not visual pursuit. Visual pursuit responses were much more prevalent in the cMRF (57.1%) though close to half of cMRF cells were VO cells (41.1%). Directional preferences also differed between the PPN, which was preferentially modulated during nose-down pitch, and cMRF, which was preferentially modulated during ipsilateral yaw rotation. Finally, amplitude responses were similar between the PPN and cMRF during rotation and pursuit stimuli, but PPN responses to translation were of higher amplitude than cMRF responses. Taken together with their connections to the vestibular circuit, these results implicate the PPN and cMRF in the processing of vestibular stimuli and suggest important roles for both in responding to motion perturbations like falls and turns.

Simulating the cortical 3D visuomotor transformation of reach depth

We effortlessly perform reach movements to objects in different directions and depths. However, how networks of cortical neurons compute reach depth from binocular visual inputs remains largely unknown. To bridge the gap between behavior and neurophysiology, we trained a feed-forward artificial neural network to uncover potential mechanisms that might underlie the 3D transformation of reach depth. Our physiologically-inspired 4-layer network receives distributed 3D visual inputs (1^st layer) along with eye, head and vergence signals. The desired motor plan was coded in a population (3^rd layer) that we read out (4^th layer) using an optimal linear estimator. After training, our network was able to reproduce all known single-unit recording evidence on depth coding in the parietal cortex. Network analyses predict the presence of eye/head and vergence changes of depth tuning, pointing towards a gain-modulation mechanism of depth transformation. In addition, reach depth was computed directly from eye-centered (relative) visual distances, without explicit absolute depth coding. We suggest that these effects should be observable in parietal and pre-motor areas.

A neural model for cyclovertical eye movements and their disorders

Both see-saw nystagmus and dissociated vertical divergence are cyclovertical eye movements characterized by vertical disconjugation and torsional conjugation. See-saw nystagmus is known to occur with chiasmal disorders and bitemporal hemianopia. Dissociated vertical divergence is commonly encountered in the infantile strabismus syndrome. A hypothetical model is presented in which both conditions are explained. The basic organization of the oculomotor system is most likely monocular and synchronous eye movements may have developed by neuronal coupling of the symmetrical oculomotor structures. The vertical dissociation of both eye movement disorders is explained by insufficiently developed neuronal coupling between the superior colliculi. A functional differentiation between crossed and uncrossed retinal ganglion cells fibers is assumed to cause this diminished binocular coupling in the case of see-saw nystagmus. The interstitial nucleus of Cajal may well play a pivotal role in explaining the distinct torsional eye movements in both conditions.

Influence of orbital eye position on vertical saccades in progressive supranuclear palsy

Disturbance of vertical saccades is a cardinal feature of progressive supranuclear palsy (PSP). We investigated whether the amplitude and peak velocity (PV) of saccades are affected by the orbital position from which movements start in PSP patients and age-matched control subjects. Subjects made vertical saccades in response to ±5° vertical target jumps with their heads in one of three positions: head "center," head pitched forward ∼15°, and head pitched back ∼15°. All patients showed some effect of starting eye position, whether beginning in the upward or downward field of gaze, on saccade amplitude, PV, and net range of movement. Generally, reduction of amplitude and PV were commensurate and bidirectional in the affected hemifield of gaze. Such findings are unlikely to be because of orbital factors and could be explained by varying degrees of involvement of rostral midbrain nuclei in the pathological process.

The anatomy and physiology of the ocular motor system

Accurate diagnosis of abnormal eye movements depends upon knowledge of the purpose, properties, and neural substrate of distinct functional classes of eye movement. Here, we summarize current concepts of the anatomy of eye movement control. Our approach is bottom-up, starting with the extraocular muscles and their innervation by the cranial nerves. Second, we summarize the neural circuits in the pons underlying horizontal gaze control, and the midbrain connections that coordinate vertical and torsional movements. Third, the role of the cerebellum in governing and optimizing eye movements is presented. Fourth, each area of cerebral cortex contributing to eye movements is discussed. Last, descending projections from cerebral cortex, including basal ganglionic circuits that govern different components of gaze, and the superior colliculus, are summarized. At each stage of this review, the anatomical scheme is used to predict the effects of lesions on the control of eye movements, providing clinical-anatomical correlation.

Selective saccadic palsy after cardiac surgery

We report a patient who showed a selective deficit of voluntary saccades and quick phases of nystagmus after cardiac surgery. Voluntary saccades in the horizontal plane were very slow, while vertical saccades, vestibular and optokinetic nystagmus, were absent. However, smooth pursuit, the vestibulo-ocular reflex, and the ability to hold steady eccentric gaze were preserved.

The disturbance of gaze in progressive supranuclear palsy: implications for pathogenesis

Progressive supranuclear palsy (PSP) is a disease of later life that is currently regarded as a form of neurodegenerative tauopathy. Disturbance of gaze is a cardinal clinical feature of PSP that often helps clinicians to establish the diagnosis. Since the neurobiology of gaze control is now well understood, it is possible to use eye movements as investigational tools to understand aspects of the pathogenesis of PSP. In this review, we summarize each disorder of gaze control that occurs in PSP, drawing on our studies of 50 patients, and on reports from other laboratories that have measured the disturbances of eye movements. When these gaze disorders are approached by considering each functional class of eye movements and its neurobiological basis, a distinct pattern of eye movement deficits emerges that provides insight into the pathogenesis of PSP. Although some aspects of all forms of eye movements are affected in PSP, the predominant defects concern vertical saccades (slow and hypometric, both up and down), impaired vergence, and inability to modulate the linear vestibulo-ocular reflex appropriately for viewing distance. These vertical and vergence eye movements habitually work in concert to enable visuomotor skills that are important during locomotion with the hands free. Taken with the prominent early feature of falls, these findings suggest that PSP tauopathy impairs a recently evolved neural system concerned with bipedal locomotion in an erect posture and frequent gaze shifts between the distant environment and proximate hands. This approach provides a conceptual framework that can be used to address the nosological challenge posed by overlapping clinical and neuropathological features of neurodegenerative tauopathies.

Ocular motor abnormalities in Parkinsonian syndromes

Oculomotor abnormalities can be observed in all Parkinsonian syndromes (PS). Nevertheless, due to the considerable overlap of oculomotor pathology in Parkinsonism, oculomotor changes are not generally considered to contribute substantially to the differential diagnosis of PS. Here we review the characteristics of oculomotor disturbances in the major PS, we provide a survey of the current concepts of the underlying neural physiology of oculomotor control and a summary of the major recording techniques for eye movements. The main focus of this review is to outline the subtle differences between apparently similar oculomotor alterations in Parkinson's disease (PD) and atypical neurodegenerative PS that can contribute to the early differential diagnosis of these entities.

Influence of saccade efference copy on the spatiotemporal properties of remapping: a neural network study

Remapping of gaze-centered target-position signals across saccades has been observed in the superior colliculus and several cortical areas. It is generally assumed that this remapping is driven by saccade-related signals. What is not known is how the different potential forms of this signal (i.e., visual, visuomotor, or motor) might influence this remapping. We trained a three-layer recurrent neural network to update target position (represented as a "hill" of activity in a gaze-centered topographic map) across saccades, using discrete time steps and backpropagation-through-time algorithm. Updating was driven by an efference copy of one of three saccade-related signals: a transient visual response to the saccade-target in two-dimensional (2-D) topographic coordinates (Vtop), a temporally extended motor burst in 2-D topographic coordinates (Mtop), or a 3-D eye velocity signal in brain stem coordinates (EV). The Vtop model produced presaccadic remapping in the output layer, with a "jumping hill" of activity and intrasaccadic suppression. The Mtop model also produced presaccadic remapping with a dispersed moving hill of activity that closely reproduced the quantitative results of Sommer and Wurtz. The EV model produced a coherent moving hill of activity but failed to produce presaccadic remapping. When eye velocity and a topographic (Vtop or Mtop) updater signal were used together, the remapping relied primarily on the topographic signal. An analysis of the hidden layer activity revealed that the transient remapping was highly dispersed across hidden-layer units in both Vtop and Mtop models but tightly clustered in the EV model. These results show that the nature of the updater signal influences both the mechanism and final dynamics of remapping. Taken together with the currently known physiology, our simulations suggest that different brain areas might rely on different signals and mechanisms for updating that should be further distinguishable through currently available single- and multiunit recording paradigms.

Torsional deviations with voluntary saccades caused by a unilateral midbrain lesion

Three dimensional eye rotations were measured using the magnetic search coil technique in a patient with a lesion of the right rostral interstitial nucleus of the medial longitudinal fasciculus (RIMLF) and in four control subjects. Up to 10° contralesional torsional deviations with each voluntary saccade were revealed, which also could be seen during bedside examination. There was no spontaneous nystagmus. Based on MRI criteria, the lesion involved the RIMLF but spared the interstitial nucleus of Cajal. To date, this deficit has not been described in patients. Our results support the hypothesis that the vertical-torsional saccade generator in humans is organised similarly as in monkeys: each RIMLF encodes torsional saccades in one direction, while both participate in vertical saccades.

Decoding the cortical transformations for visually guided reaching in 3D space

To explore the possible cortical mechanisms underlying the 3-dimensional (3D) visuomotor transformation for reaching, we trained a 4-layer feed-forward artificial neural network to compute a reach vector (output) from the visual positions of both the hand and target viewed from different eye and head orientations (inputs). The emergent properties of the intermediate layers reflected several known neurophysiological findings, for example, gain field-like modulations and position-dependent shifting of receptive fields (RFs). We performed a reference frame analysis for each individual network unit, simulating standard electrophysiological experiments, that is, RF mapping (unit input), motor field mapping, and microstimulation effects (unit outputs). At the level of individual units (in both intermediate layers), the 3 different electrophysiological approaches identified different reference frames, demonstrating that these techniques reveal different neuronal properties and suggesting that a comparison across these techniques is required to understand the neural code of physiological networks. This analysis showed fixed input-output relationships within each layer and, more importantly, within each unit. These local reference frame transformation modules provide the basic elements for the global transformation; their parallel contributions are combined in a gain field-like fashion at the population level to implement both the linear and nonlinear elements of the 3D visuomotor transformation.

Saccadic palsy after cardiac surgery: characteristics and pathogenesis

OBJECTIVE

To characterize the syndrome of saccadic palsy that may follow cardiac surgery, and to interpret the findings using current concepts of the neurobiology of fast eye movements.

METHODS

Using the magnetic search coil technique, we measured eye, eyelid, and head movements of 10 patients who developed selective palsy of saccades after cardiac surgery.

RESULTS

Patients showed varying degrees of slowing and hypometria of saccades in the vertical plane or both horizontal and vertical planes, with complete loss of all saccades in one patient. Quick phases of nystagmus were also affected, but smooth pursuit, vergence, and the vestibuloocular reflex were usually spared. The smallest saccades were less slowed than larger saccades. Affected patients were visually disabled by loss of ability to voluntarily shift their direction of gaze. Blinks and head thrusts modestly improved the range and speed of voluntary movement. The syndrome usually followed aortic valve replacement. Common accompanying features included dysarthria, labile emotions, and unsteady gait. The saccadic palsy either improved during the early part of the course or remained static.

INTERPRETATION

Selective loss of all forms of saccades, with sparing of other eye movements, indicates malfunction of the brainstem machinery that generates saccades. A current model of brainstem circuits could account for both hypometria and slowing. This syndrome and the visual disability it causes often go unrecognized unless saccades are systematically tested at the bedside.

Vestibular signals in primate thalamus: properties and origins

Vestibular activation is found in diverse cortical areas. To characterize the pathways and types of signals supplied to cortex, we recorded responses to rotational and/or translational stimuli in the macaque thalamus. Few cells responded to rotation alone, with most showing convergence between semicircular canal and otolith signals. During sinusoidal rotation, thalamic responses lead head velocity by approximately 30 degrees on average at frequencies between 0.01-4 Hz. During translation, neurons encoded combinations of linear acceleration and velocity. In general, thalamic responses were similar to those recorded in the vestibular and cerebellar nuclei using identical testing paradigms, but differed from those of vestibular afferents. Thalamic responses represented a biased continuum: most cells more strongly encoded translation and fewer cells modulated primarily in response to net gravitoinertial acceleration. Responsive neurons were scattered within a large area that included regions of the ventral posterior and ventral lateral nuclei, and so were not restricted to the known vestibular nuclei projection zones. To determine the origins of these responses, a retrograde tracer was injected into a dorsolateral thalamic site where rotation/translation-sensitive cells were encountered. This injection labeled neurons in the rostral contralateral anterior interposed and fastigial nuclei, but did not label cells within the vestibular nuclei. Examination of thalamic terminations after tracer injections into the cerebellar and vestibular nuclei indicated that most vestibular responsive units fall within the thalamic terminal zones of these nuclei. Thus, vestibular signals, which are supplied to the thalamus from both vestibular and cerebellar nuclei, are positioned for distribution to widespread cortical areas.

Torsional deviations with voluntary saccades caused by a unilateral midbrain lesion

Three dimensional eye rotations were measured using the magnetic search coil technique in a patient with a lesion of the right rostral interstitial nucleus of the medial longitudinal fasciculus (RIMLF) and in four control subjects. Up to 10 degree contralesional torsional deviations with each voluntary saccade were revealed, which also could be seen during bedside examination. There was no spontaneous nystagmus. Based on MRI criteria, the lesion involved the RIMLF but spared the interstitial nucleus of Cajal. To date, this deficit has not been described in patients. Our results support the hypothesis that the vertical-torsional saccade generator in humans is organised similarly as in monkeys: each RIMLF encodes torsional saccades in one direction, while both participate in vertical saccades.

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.

Truncal contrapulsion in pretectal syndrome

Truncal contrapulsion in association with pretectal syndrome has not been described previously. We report a patient with vertical-gaze palsy and severe truncal contrapulsion due to an infarction in the mesodiencephalic junction. Truncal contrapulsion in this patient may have resulted from the disruption of the ascending fibers in the crossed cerebellothalamic tract.

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).

The mammalian superior colliculus: laminar structure and connections

The superior colliculus is a laminated midbrain structure that acts as one of the centers organizing gaze movements. This review will concentrate on sensory and motor inputs to the superior colliculus, on its internal circuitry, and on its connections with other brainstem gaze centers, as well as its extensive outputs to those structures with which it is reciprocally connected. This will be done in the context of its laminar arrangement. Specifically, the superficial layers receive direct retinal input, and are primarily visual sensory in nature. They project upon the visual thalamus and pretectum to influence visual perception. These visual layers also project upon the deeper layers, which are both multimodal, and premotor in nature. Thus, the deep layers receive input from both somatosensory and auditory sources, as well as from the basal ganglia and cerebellum. Sensory, association, and motor areas of cerebral cortex provide another major source of collicular input, particularly in more encephalized species. For example, visual sensory cortex terminates superficially, while the eye fields target the deeper layers. The deeper layers are themselves the source of a major projection by way of the predorsal bundle which contributes collicular target information to the brainstem structures containing gaze-related burst neurons, and the spinal cord and medullary reticular formation regions that produce head turning.

The reticular formation

The reticular formation of the brainstem contains functional cell groups that are important for the control of eye, head, or lid movements. The mesencephalic reticular formation is primarily involved in the control of vertical gaze, the paramedian pontine reticular formation in horizontal gaze, and the medullary pontine reticular formation in head movements and gaze holding. In this chapter, the locations, connections, and histochemical properties of the functional cell groups are reviewed and correlated with specific subdivisions of the reticular formation.

Do motoneurons encode the noncommutativity of ocular rotations?

As we look around, the orientation of our eyes depends on the order of the rotations that are carried out, a mathematical feature of rotatory motions known as noncommutativity. Theorists and experimentalists continue to debate how biological systems deal with this property when generating kinematically appropriate movements. Some believe that this is always done by neural commands to a simplified eye plant. Others have postulated that noncommutativity is implemented solely by the mechanical properties of the eyeball. Here we directly examined what the brain tells the muscles, by recording motoneuron activities as monkeys made eye movements. We found that vertical recti and superior/inferior oblique motoneurons, which drive sensory-generated torsional eye movements, do not modulate their firing rates according to the noncommutative-driven torsion during pursuit. We conclude that part of the solution for kinematically appropriate eye movements is found in the mechanical properties of the eyeball, although neural computations remain necessary and become increasingly important during head movements.

Distributed population mechanism for the 3-D oculomotor reference frame transformation

Human saccades require a nonlinear, eye orientation-dependent reference frame transformation to transform visual codes to the motor commands for eye muscles. Primate neurophysiology suggests that this transformation is performed between the superior colliculus and brain stem burst neurons, but provides little clues as to how this is done. To understand how the brain might accomplish this, we trained a 3-layer neural net to generate accurate commands for kinematically correct 3-D saccades. The inputs to the network were a 2-D, eye-centered, topographic map of Gaussian visual receptive fields and an efference copy of eye position in 6-dimensional, push-pull "neural integrator" coordinates. The output was an eye orientation displacement command in similar coordinates appropriate to drive brain stem burst neurons. The network learned to generate accurate, kinematically correct saccades, including the eye orientation-dependent tilts in saccade motor error commands required to match saccade trajectories to their visual input. Our analysis showed that the hidden units developed complex, eye-centered visual receptive fields, widely distributed fixed-vector motor commands, and "gain field"-like eye position sensitivities. The latter evoked subtle adjustments in the relative motor contributions of each hidden unit, thereby rotating the population motor vector into the correct correspondence with the visual target input for each eye orientation: a distributed population mechanism for the visuomotor reference frame transformation. These findings were robust; there was little variation across networks with between 9 and 49 hidden units. Because essentially the same observations have been reported in the visuomotor transformations of the real oculomotor system, as well as other visuomotor systems (although interpreted elsewhere in terms of other models) we suggest that the mechanism for visuomotor reference frame transformations identified here is the same solution used in the real brain.

Using saccades as a research tool in the clinical neurosciences

Saccades are rapid eye movements that move the line of sight between successive points of fixation; they are among the best understood of movements, possessing dynamic properties that are easily measured. Saccades have become a popular means to study motor control, cognition and memory, and are often used in conjunction with techniques such as functional imaging and transcranial magnetic stimulation. It has been possible to identify several, distinct populations of neurons, from brainstem to cerebral cortex, that contribute to behaviours ranging from reflexive glances to memorized sequences of saccades during learned tasks. This progress has led to the development of schemes for the neurobiology of saccades that imply an equivalence of a region of the brain with specific behaviours (e.g. prefrontal cortex with memory-guided saccades). In fact, multiple neuronal populations contribute to each type of saccadic behaviour, be it 'reflexive' or 'complex'. Furthermore, an important difference exists between cortical areas that encode visual stimuli or desired saccades over a population of neurons as 'place maps', and motoneurons in oculomotor, trochlear and abducens nuclei that dictate eye rotations in terms of their discharge rates. This dichotomy implies that a 'spatial-temporal transformation' of saccadic signals must occur between cerebral cortex and ocular motoneurons, to which the superior colliculus and cerebellum contribute. Consideration of such factors may broaden the value of saccades, which can be used to test a range of hypotheses, and provide a simple scheme for understanding clinical disorders of saccades; some illustrative video clips are available as supplementary material at Brain Online.

Static ocular counterroll is implemented through the 3-D neural integrator

Static head roll about the naso-occipital axis is known to produce an opposite ocular counterroll with a gain of approximately 10%, but the purpose and neural mechanism of this response remain obscure. In theory counterroll could be maintained either by direct tonic vestibular inputs to motoneurons, or by a neurally integrated pulse, as observed in the saccade generator and vestibulo-ocular reflex. When simulated together with ocular drift related to torsional integrator failure, the direct tonic input model predicted that the pattern of drift would shift torsionally as in ordinary counterroll, but the integrated pulse model predicted that the equilibrium position of torsional drift would be unaffected by head roll. This was tested experimentally by measuring ocular counterroll in 2 monkeys after injection of muscimol into the mesencephalic interstitial nucleus of Cajal. Whereas 90 degrees head roll produced a mean ocular counterroll of 8.5 degrees (+/-0.7 degrees SE) in control experiments, the torsional equilibrium position observed during integrator failure failed to counterroll, showing a torsional shift of only 0.3 degrees (+/-0.6 degrees SE). This result contradicted the direct tonic input model, but was consistent with models that implement counterroll by a neurally integrated pulse.

Resets of torsional eye position errors in different lighting conditions

To investigate a resetting mechanism of torsional eye position errors, spontaneous scanning eye movements and visually guided eye movements in different lighting conditions were recorded three dimensionally. Two monkeys (Macaca fuscata, TS, MI) were engaged in this experiment. A dual scleral search coil method was used for three-dimensional (3-D) eye movement recordings. In complete darkness, the thickness of Listing's plane at the onset of spontaneous saccades (0.51/0.37 degrees (TS/MI)) and that at the end of spontaneous fixation periods (0.47/0.34 degrees (TS/MI)) were significantly (P<0.001) smaller than that at the end of spontaneous saccades (0.59/0.45 degrees (TS/MI)) and that at the onset of spontaneous fixation periods (0.58/0.44 degrees (TS/MI)). Such differences in the thickness of Listing's plane were not observed in the light (P>0.10). Amplitude of torsional drift during post-saccadic fixation period was correlated with the amount of torsional position error at the end of saccade (P<0.001). The slope of regressed line in the dark or dim light (-0.40 to -0.50/-0.32 to -0.33 (TS/MI)) was steeper than that in the light (-0.04/-0.03 to -0.09 (TS/MI)). A resetting mechanism for torsional eye position errors during post-saccadic fixation periods is active in the dark but inactive in the light.

Orientation of Listing's plane during static tilt in young and older human subjects

Three-dimensional eye positions, when expressed as rotation vectors, are constrained to lie in a head-fixed Listing's plane. The offset and orientation of Listing's plane changes when the head is tilted. To assess the influence of age on this phenomenon, young (less than 30 years old) and older (>65 years old) human subjects were seated upright, pitched nose up and nose down, and rolled right ear down and left ear down. Listing's plane was computed from eye movements recorded using a dual scleral search coil while subjects scanned a complex visual scene. During pitch, Listing's plane counterpitched with respect to the head, while during roll, it translated in a manner consistent with "ocular counterrolling". There was no significant difference in this reorientation of Listing's plane between the young and older subjects. The only obvious difference between the two age groups was that the "thickness" of Listing's plane was greater in the older subjects. This suggests that aging has a small, but definite, influence on Listing's law.

The contribution of midbrain circuits in the control of gaze

The midbrain contains several structures important for the generation of torsional and vertical eye movements including the rostral interstitial nucleus of the MLF (riMLF) and the interstitial nucleus of Cajal (iC). While the riMLF is the immediate premotor structure for the generation of torsional and vertical saccades, the iC is considered a major part of the neural integrator for torsional and vertical eye movements. Experiments in monkeys show that a unilateral inactivation of the riMLF with muscimol leads to spontaneous contralesional torsional nystagmus, whereas an iC inactivation causes ipsilesional torsional nystagmus. In addition, inactivation of either structure leads to a tonic ocular torsion to the contralesional side. While the deficits after a riMLF lesion are thought to result from an imbalance of the saccade generator, a vestibular imbalance probably causes the deficits after an iC lesion. Contralesional and ipsilesional torsional nystagmus is also found in patients with unilateral mesencephalic lesions. A detailed analysis of the lesions from MRI scans shows a preferential involvement of the riMLF for patients with contralesional torsional nystagmus, and a major involvement of iC in cases with ipsilesional torsional nystagmus. Thus, the direction of torsional nystagmus appears to be a valuable topodiagnostic sign for patients with midbrain lesions.

Overlap of saccadic and pursuit eye movement systems in the brain stem reticular formation

Recent physiological studies have suggested that there are several sites of interaction between the neural pathways that control saccadic eye movements and those that control visual pursuit movements. To address the question of saccade/pursuit interaction from a neuroanatomical point of view, we have studied the connections from the smooth and saccadic eye movement subregions of the frontal eye field (FEFsem and FEFsac, respectively) to the rostral interstitial nucleus of the medial longitudinal fasciculus (riMLF) in four Cebus apella monkeys. The riMLF has traditionally been considered to be a premotor center for vertical saccadic eye movements on the basis of single neuron recording experiments, microstimulation experiments, and surgical or chemical lesion experiments. We localized the functional subregions of the FEF with the use of low-threshold (< or =50 microA) intracortical microstimulation. Biotinylated dextran amine or lectin from triticum vulgaris (wheat germ), peroxidase labeled, was placed into these functionally defined subregions to label anterogradely the terminals of axons that originated in the FEF. Our results demonstrate that both the FEFsem and FEFsac send direct projections to the ipsilateral riMLF. The distribution and density of labeling from the FEFsem are comparable to those from the FEFsac. The direct FEFsem-to-riMLF projection suggests a possible role of the riMLF in smooth pursuit eye movements and supports the hypothesis that there is interaction between the saccadic and pursuit subsystems at the brain stem level.

Convergence retraction nystagmus: a disorder of vergence?

The pathological mechanism of convergence retraction nystagmus (CRN) is not known. To determine whether CRN is a disorder of vergence or of the saccadic system, the scleral search coil technique was used to record binocularly the three-dimensional components of CRN in a patient with a left mesencephalic infarction involving the nucleus of the posterior commissure and the rostral interstitial nucleus of the medial longitudinal fascicle. CRN had disconjugate horizontal and torsional components. The horizontal amplitude/velocity relationship of CRN aligned with the main sequence of vergence responses of normal control subjects but not with that of saccades. Vergence responses of the right eye and left eye were not asynchronous. The slow phases of CRN showed an exponential decay with a time constant of 70 milliseconds. Thus, CRN is probably a disorder of vergence rather than of opposing adducting saccades.

Central positional nystagmus simulated by a mathematical ocular motor model of otolith-dependent modification of Listing's plane

To find an explanation of the mechanisms of central positional nystagmus in neurological patients with posterior fossa lesions, we developed a three-dimensional (3-D) mathematical model to simulate head position-dependent changes in eye position control relative to gravity. This required a model implementation of saccadic burst generation, of the neural velocity to eye position integrator, which includes the experimentally demonstrated leakage in the torsional component, and of otolith-dependent neural control of Listing's plane. The validity of the model was first tested by simulating saccadic eye movements in different head positions. Then the model was used to simulate central positional nystagmus in off-vertical head positions. The model simulated lesions of assumed otolith inputs to the burst generator or the neural integrator, both of which resulted in different types of torsional-vertical nystagmus that only occurred during head tilt in roll plane. The model data qualitatively fit clinical observations of central positional nystagmus. Quantitative comparison with patient data were not possible, since no 3-D analyses of eye movements in various head positions have been reported in the literature on patients with positional nystagmus. The present model, prompted by an open clinical question, proposes a new hypothesis about the generation of pathological nystagmus and about neural control of Listing's plane.

Effect of light sleep on three-dimensional eye position in static roll and pitch

We examined three-dimensional eye positions in alertness and light sleep when monkeys were placed in different roll and pitch body orientations. In alertness, eye positions were confined to a fronto-parallel (Listing's) plane, torsional variability was small and static roll or pitch induced a torsional shift or vertical rotation of these planes. In light sleep, the planes rotated temporally by about 10 degrees, torsional variability increased by a factor of two and the static otolith-ocular reflexes were reduced by about 70%. These data support the importance of a neural control of the thickness and orientation of Listing's plane, and suggest that part of the vestibular input underlying otolith-ocular reflexes depend on polysynaptic neural processing.

Effects of reversible inactivation of the primate mesencephalic reticular formation. II. Hypometric vertical saccades

Electrical microstimulation and single-unit recording have suggested that a group of long-lead burst neurons (LLBNs) in the mesencephalic reticular formation (MRF) just lateral to the interstitial nucleus of Cajal (INC) (the peri-INC MRF, piMRF) may play a role in the generation of vertical rapid eye movements. Inactivation of this region with muscimol (a GABA(A) agonist) rapidly produced vertical saccade hypometria (6 injections). In three of six injections, there was a marked reduction in the velocity of vertical saccades out of proportion to saccade amplitude (i.e., saccades fell below the main sequence). This was associated with a moderate increase in saccade duration. Inadvertent inactivation of the INC could not account for these observations because vertical, postsaccadic drift was not observed. Similarly, pure downward saccade hypometria, the hallmark of rostral interstitial nucleus of the medial longitudinal fasciculus (riMLF) inactivation, was always preceded by loss of upward saccades in our experiments. We also found a downward and ipsiversive displacement of initial eye position and evidence of a contraversive head tilt following piMRF injections. Saccade latency was shorter after two of six injections. Simulation of a local feedback model provided three possible explanations for vertical saccade hypometria: 1) a shift in the input to the model to request smaller saccades, 2) a reduction of LLBN input to the vertical saccade medium lead burst neurons (MLBNs), or 3) an increase in the gain of the feedback pathway. However, when the second hypothesis was coupled to a shortened duration of the saccade trigger (i.e., the discharge of the omnipause neurons), the physiological observations of piMRF inactivation could be replicated. This suggested that muscimol had targeted structures that provided both long-lead burst activity to the MLBNs in the riMLF and were critical for reactivation of the omnipause neurons. Evidence of markedly reduced vertical saccade amplitude, curved saccade trajectories, increased saccade duration, and saccades that fall below the amplitude/velocity main sequence in these monkeys closely parallels the oculomotor findings of patients with progressive supranuclear palsy (PSP).

Three-dimensional kinematics of ocular drift in humans with cerebellar atrophy

One of the signs of the cerebellar ocular motor syndrome is the inability to maintain horizontal and vertical fixation. Typically, in the presence of cerebellar atrophy, the eyes show horizontal gaze-evoked and vertical downbeat nystagmus. We investigated whether or not the cerebellar ocular motor syndrome also includes a torsional drift and, specifically, if it is independent from the drift in the horizontal-vertical plane. The existence of such a torsional drift would suggest that the cerebellum is critically involved in maintaining the eyes in Listing's plane. Eighteen patients with cerebellar atrophy (diagnosis confirmed by magnetic resonance imaging) were tested and compared with a group of normal subjects. Three-dimensional eye movements (horizontal, vertical, and torsional) during attempted fixations of targets at different horizontal and vertical eccentricities were recorded by dual search coils in a three-field magnetic frame. The overall ocular drift was composed of an upward drift that increased during lateral gaze, a horizontal centripetal drift that appeared during lateral gaze, and a torsional drift that depended on horizontal eye position. The vertical drift consisted of two subcomponents: a vertical gaze-evoked drift and a constant vertical velocity bias. The increase of upward drift velocity with eccentric horizontal gaze was caused by an increase of the vertical velocity bias; this component did not comply with Listing's law. The horizontal-eye-position-dependent torsional drift was intorsional in abduction and extorsional in adduction, which led to an additional violation of Listing's law. The existence of torsional drift that is eye-position-dependent suggests that the cerebellum is critically involved in the implementation of Listing's law, perhaps by mapping a tonic torsional signal that depends on the direction of the line of sight. The magnitude of this signal might reflect the difference in torsional eye position between the torsional resting position determined by the mechanics of the eye plant and the torsional position required by Listing's law.