Ke Liao

Case Western Reserve University, Cleveland, OH, USA

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Publications (20)74.75 Total impact

  • Article: The human translational vestibulo-ocular reflex in response to complex motion.
    Mark Walker, Ke Liao
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    ABSTRACT: We studied the translational vestibulo-ocular reflex (tVOR) in four healthy human subjects during complex, unpredictable sum-of-sines head motion (combination of 0.73, 1.33, 1.93, and 2.93 Hz), while subjects viewed a target 15 cm away. Ideal eye velocity was calculated from recorded head motion; actual eye velocity was measured with scleral coils. The gain and phase for each frequency component was determined by least-squares optimization. Gain averaged approximately 40% and did not change with frequency; phase lag increased with frequency to a maximum of 66°. Fitting actual to ideal eye velocity predicted a tVOR latency of 48 m/s for vertical and 38 m/s for horizontal translation. These findings provide further evidence that the normal tVOR is considerably undercompensatory, even at low frequencies if the stimulus is not predictable. The similarity of this behavior to that of pursuit suggests that these two eye movements may share some aspects of neural processing.
    Annals of the New York Academy of Sciences 09/2011; 1233:242-8. · 3.15 Impact Factor
  • Article: Visual and vestibular determinants of the translational vestibulo-ocular reflex.
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    ABSTRACT: Prior studies indicate that the human translational vestibulo-ocular reflex (tVOR) generates eye rotations approximately half the magnitude required to keep the line of sight pointed at a stationary object--a compensation ratio (CR) of ∼0.5. We asked whether changes of visual or vestibular stimuli could increase the CR of tVOR. First, subjects viewed their environment through an optical device that required eye movements to increase by ∼50% to maintain fixation of a stationary visual target. During vertical translation, eye movements did increase, but tVOR CR remained at ∼0.5. Second, subjects viewed through LCD goggles providing 4 Hz strobe vision that minimized retinal image motion; this reduced tVOR CR. Finally, subjects were rotated in roll while they translated vertically; no increase in tVOR occurred. Taken with prior studies, we conclude that tVOR is optimally set to generate eye rotations that are about 50% of those required to stabilize the line of sight.
    Annals of the New York Academy of Sciences 09/2011; 1233:263-70. · 3.15 Impact Factor
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    Article: Oculopalatal tremor explained by a model of inferior olivary hypertrophy and cerebellar plasticity.
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    ABSTRACT: The inferior olivary nuclei clearly play a role in creating oculopalatal tremor, but the exact mechanism is unknown. Oculopalatal tremor develops some time after a lesion in the brain that interrupts inhibition of the inferior olive by the deep cerebellar nuclei. Over time the inferior olive gradually becomes hypertrophic and its neurons enlarge developing abnormal soma-somatic gap junctions. However, results from several experimental studies have confounded the issue because they seem inconsistent with a role for the inferior olive in oculopalatal tremor, or because they ascribe the tremor to other brain areas. Here we look at 3D binocular eye movements in 15 oculopalatal tremor patients and compare their behaviour to the output of our recent mathematical model of oculopalatal tremor. This model has two mechanisms that interact to create oculopalatal tremor: an oscillator in the inferior olive and a modulator in the cerebellum. Here we show that this dual mechanism model can reproduce the basic features of oculopalatal tremor and plausibly refute the confounding experimental results. Oscillations in all patients and simulations were aperiodic, with a complicated frequency spectrum showing dominant components from 1 to 3 Hz. The model's synchronized inferior olive output was too small to induce noticeable ocular oscillations, requiring amplification by the cerebellar cortex. Simulations show that reducing the influence of the cerebellar cortex on the oculomotor pathway reduces the amplitude of ocular tremor, makes it more periodic and pulse-like, but leaves its frequency unchanged. Reducing the coupling among cells in the inferior olive decreases the oscillation's amplitude until they stop (at approximately 20% of full coupling strength), but does not change their frequency. The dual-mechanism model accounts for many of the properties of oculopalatal tremor. Simulations suggest that drug therapies designed to reduce electrotonic coupling within the inferior olive or reduce the disinhibition of the cerebellar cortex on the deep cerebellar nuclei could treat oculopalatal tremor. We conclude that oculopalatal tremor oscillations originate in the hypertrophic inferior olive and are amplified by learning in the cerebellum.
    Brain 03/2010; 133(Pt 3):923-40. · 9.46 Impact Factor
  • Article: The disturbance of gaze in progressive supranuclear palsy: implications for pathogenesis.
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    ABSTRACT: 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.
    Frontiers in neurology. 01/2010; 1:147.
  • Article: The linear vestibulo-ocular reflex, locomotion and falls in neurological disorders.
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    ABSTRACT: During locomotion, head perturbations, consisting of rotations and translations (linear movements), occur with predominant frequencies of 0.5-5.0 Hz. The vestibular reflexes act at short latency to safeguard clear vision and stable posture during locomotion. Much is known about the angular vestibulo-ocular reflex (aVOR) in response to head rotations, which depend on the semicircular canals of the vestibular labyrinth. However, the means to test reliably the linear or translational vestibulo-ocular reflex (tVOR), which depends on the otolithic organs, has only become available more recently. We used a moving platform to translate normal human subjects vertically at frequencies similar to those occurring during locomotion, under ambient illumination. Our findings suggested that, whereas aVOR is concerned with stabilizing images of visual targets on the retina to optimize visual acuity, tVOR seems best suited to minimize retinal image motion between objects lying in different depth planes, in order to optimize motion parallax information. We then asked whether the tVOR functioned abnormally in patients with two neurological disorders that often cause falls: progressive supranuclear palsy (PSP) and cerebellar ataxia. We found that patients with PSP cannot adjust tVOR responses appropriately during viewing of near objects, nor converge their eyes. Vestibular-evoked myogenic potentials (VEMPs), an otolith-spinal reflex, are also impaired in PSP patients. Patients with cerebellar ataxia also lack the ability to adjust tVOR for near viewing, even though they may be able to converge. Taken together, our studies suggest that abnormal otolithic vestibular reflexes contribute to postural instability in PSP and cerebellar ataxia, and deserve further investigation.
    Restorative neurology and neuroscience 01/2010; 28(1):91-103. · 2.51 Impact Factor
  • Article: The human vertical translational vestibulo-ocular reflex. Normal and abnormal responses.
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    ABSTRACT: Geometric considerations indicate that the human translational vestibulo-ocular reflex (tVOR) should have substantially different properties than the angular vestibulo-ocular reflex (aVOR). Specifically, tVOR cannot simultaneously stabilize images of distant and near objects on the retina. Most studies make the tacit assumption that tVOR acts to stabilize foveal images even though, in humans, tVOR is reported to compensate for less than 60% of foveal image motion. We have determined that the compensation gain (eye rotational velocity/required eye rotational velocity to maintain foveal target fixation) of tVOR is held steady at approximately 0.6 during viewing of either near or distant targets during vertical (bob) translations in ambient illumination. We postulate that tVOR evolved not to stabilize the image of the target on the fovea, but rather to minimize retinal image motion between objects lying in different depth planes, in order to optimize motion parallax information. Such behavior is optimized when binocular visual cues of both near and distant targets are available in ambient light. Patients with progressive supranuclear palsy or cerebellar ataxia show impaired ability to increase tVOR responses appropriately when they view near targets. In cerebellar patients, impaired ability to adjust tVOR responses to viewing conditions occurs despite intact ability to converge at near. Loss of the ability to adjust tVOR according to viewing conditions appears to represent a distinct disorder of vestibular function.
    Annals of the New York Academy of Sciences 06/2009; 1164:68-75. · 3.15 Impact Factor
  • Article: The Human Vertical Translational Vestibulo‐ocular Reflex
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    ABSTRACT: Geometric considerations indicate that the human translational vestibulo-ocular reflex (tVOR) should have substantially different properties than the angular vestibulo-ocular reflex (aVOR). Specifically, tVOR cannot simultaneously stabilize images of distant and near objects on the retina. Most studies make the tacit assumption that tVOR acts to stabilize foveal images even though, in humans, tVOR is reported to compensate for less than 60% of foveal image motion. We have determined that the compensation gain (eye rotational velocity/required eye rotational velocity to maintain foveal target fixation) of tVOR is held steady at ∼0.6 during viewing of either near or distant targets during vertical (bob) translations in ambient illumination. We postulate that tVOR evolved not to stabilize the image of the target on the fovea, but rather to minimize retinal image motion between objects lying in different depth planes, in order to optimize motion parallax information. Such behavior is optimized when binocular visual cues of both near and distant targets are available in ambient light. Patients with progressive supranuclear palsy or cerebellar ataxia show impaired ability to increase tVOR responses appropriately when they view near targets. In cerebellar patients, impaired ability to adjust tVOR responses to viewing conditions occurs despite intact ability to converge at near. Loss of the ability to adjust tVOR according to viewing conditions appears to represent a distinct disorder of vestibular function.
    Annals of the New York Academy of Sciences 05/2009; 1164(1):68 - 75. · 3.15 Impact Factor
  • Article: Diagnosing disconjugate eye movements: phase-plane analysis of horizontal saccades.
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    ABSTRACT: Saccades are fast eye movements that conjugately shift the point of fixation between distant features of interest in the visual environment. Several disorders, affecting sites from brainstem to extraocular muscle, may cause horizontal saccades to become disconjugate. Prior techniques for detection of saccadic disconjugacy, especially in internuclear ophthalmoparesis (INO), have compared only one point in abducting vs adducting saccades, such as peak velocity. We applied a phase-plane technique that compared each eye's velocity as a function of change in position (normalized displacement) in 22 patients with disease variously affecting the brainstem reticular formation, the abducens nucleus, the medial longitudinal fasciculus, the oculomotor nerve, the abducens nerve, the neuromuscular junction, or the extraocular muscles; 10 age-matched subjects served as controls. We found three different patterns of disconjugacy throughout the course of horizontal saccades: early abnormal velocity disconjugacy during the first 10% of the displacement in patients with INO, oculomotor or abducens nerve palsy, and advanced extraocular muscle disease; late disconjugacy in patients with disease affecting the neuromuscular junction; and variable middle-course disconjugacy in patients with pontine lesions. When normal subjects made disconjugate saccades between two targets aligned on one eye, the initial part of the movement remained conjugate. Along with conventional measures of saccades, such as peak velocity, phase planes provide a useful tool to determine the site, extent, and pathogenesis of disconjugacy. We hypothesize that the pale global extraocular muscle fibers, which drive the high-acceleration component of saccades, receive a neural command that ensures initial ocular conjugacy.
    Neurology 11/2008; 71(15):1167-75. · 8.31 Impact Factor
  • Article: Abnormal vestibular responses to vertical head motion in cerebellar ataxia.
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    ABSTRACT: Falls pose an important problem to neurologists caring for patients with cerebellar disorders. Normal human gait is characterized by prominent up-and-down linear head movements (vertical translations). Thus, we asked whether patients with cerebellar gait ataxia showed abnormal responses of otolithic vestibuloocular reflexes to this motion. Compared with healthy subjects, all cerebellar patients showed impaired otolith-ocular responses. Neurologists often test the rotational vestibuloocular reflexes in cerebellar patients, but our results indicate that vestibular responses to vertical linear motion are severely affected. Impairment of the corresponding otolith-spinal reflexes may contribute substantially to falls.
    Annals of Neurology 09/2008; 64(2):224-7. · 11.09 Impact Factor
  • Article: Vestibulo-ocular responses to vertical translation in normal human subjects.
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    ABSTRACT: Prior studies of the human translational vestibulo-ocular reflex (tVOR) report that eye rotations amount to less than 60% of those required to keep the eyes pointed at a stationary visual target, unlike the angular VOR (aVOR) which is optimized to maintain stable gaze. Our first goal was to determine if the performance of the tVOR improves when head translations are combined with head rotations in ambient lighting. A second goal was to measure tVOR during vertical head translations (bob), which has not received systematic study. We measured tVOR alone and in combination with the aVOR in 20 normal human subjects, aged 25-72 years, as they sat on a moving platform that bobbed at 2.0 Hz while rotating horizontally (yaw) at 1.0 Hz. When subjects viewed a visual target at 2 m, median "compensation gain" (eye rotational velocity/required eye rotational velocity to maintain foveal target fixation) was 0.52 during pure bob and 0.59 during combined bob-yaw; during viewing of a near target at approximately 17 cm, compensation gain was 0.58 for pure bob and 0.60 for combined bob-yaw. Mean phase lag of eye-in-head velocity for the tVOR was approximately 19 degrees with respect to the ideal compensatory response, irrespective of whether translation was accompanied by rotation. Thus, the tVOR changed only slightly during translation-rotation versus pure translation, and our subjects' ocular rotations remained at about 60% of those required to point the eyes at the target. Comparison of response during binocular or monocular viewing, and ambient or reduced illumination, indicated that relative image motion between the target and background was an important determinant of tVOR behavior. We postulate that tVOR evolved not to stabilize the image of the target on the fovea, but rather to minimize retinal image motion between objects lying in different planes, in order to optimize motion parallax information.
    Experimental Brain Research 04/2008; 185(4):553-62. · 2.39 Impact Factor
  • Article: Conjugacy of horizontal saccades: application of binocular phase planes.
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    ABSTRACT: The goal of this study was to evaluate the ability of binocular phase planes to detect disconjugacy of horizontal saccades. We recorded horizontal saccades in 22 patients with disease affecting the brainstem reticular formation, medial longitudinal fasciculus (INO), abducens nerve, neuromuscular junction and extraocular muscles, and in 10 age-matched controls. We found that patients with disorders of the brainstem, including INO, or the cranial nerves, showed significant velocity disconjugacy in the first 10% of the displacement. Patients with myasthenia gravis did not show early disconjugacy, but might do so later in the course of the saccade. We conclude that binocular phase planes supplement conventional measures of saccades, such as peak velocity, and are useful to differentiate INO and cranial nerve palsies from myasthenia.
    Progress in brain research 02/2008; 171:571-4. · 3.04 Impact Factor
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    Article: Impulsive head rotation resets oculopalatal tremor: examination of a model.
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    ABSTRACT: We have described a neuromimetic model of the interaction between the inferior olive (IO) and the cerebellum that accounts for symptomatic oculopalatal tremor (OPT), a disorder characterized by oscillations of the eyes (nystagmus), palate and other branchial muscles. OPT develops months after some brainstem strokes, in association with hypertrophic degeneration of the inferior olivary nucleus (IO). We hypothesized that OPT requires both (1) a pulsatile oscillator created by tighter electrotonic coupling between cells in the IO, and (2) a learned response from the cerebellar cortex that combines with the IO pulses to generate the quasi-pendular oscillations. Since the vestibular nuclei project to both IO and vestibulocerebellum, one prediction of the model is that rapid head rotations could interrupt the oscillator, effectively resetting the timing of the ocular nystagmus. The ocular oscillations in OPT vary in amplitude and phase, making it difficult to determine by Fourier analysis whether head perturbations phase-shift the nystagmus. We applied complex wavelet analysis to data from four patients with OPT and checked whether vestibular stimuli induced a change in phase of the nystagmus. First we calculated a threshold for the spontaneous rate of change of phase of OPT by comparing many segments of nystagmus waveform with their time-shifted versions, bootstrapping these arrays, and computing 95% prediction intervals for each patient. Then we compared the rate of change of phase due to each head perturbation with the threshold for that patient. To minimize the effects of the head perturbation itself on the wavelet analysis, we measured effects in a plane orthogonal to the head rotation, e.g., effects of horizontal head rotations on the torsional component of OPT. In all four patients, the rate of change of phase shift increased sharply at the time of the head perturbation, and in three the change was judged to be statistically significant. Thus, the experimental tests supported the prediction of our model for OPT.
    Progress in brain research 02/2008; 171:227-34. · 3.04 Impact Factor
  • Article: A reinterpretation of the purpose of the translational vestibulo-ocular reflex in human subjects.
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    ABSTRACT: In a prior study we reported that the human translational vestibulo-ocular reflex (tVOR) in response to vertical (bob) 2 Hz oscillations generated eye rotations of only 60% of those required to keep the eyes pointed at a stationary visual target, whether located at near (approximately 17 cm) or far (2 m). Best responses occurred in ambient illumination and we concluded that relative image motion between the target and background was an important determinant of tVOR behaviour. To investigate further how visual conditions influenced tVOR, we measured responses as subjects binocularly viewed the bridge of their own nose in a mirror at approximately 8.5 cm, a visual condition that required similar convergence to viewing the near target, but cancellation of tVOR. Median tVOR cancellation gain [(near-viewing response-mirror viewing response)/near-viewing response] was 0.81 (range 0.55-0.97), which was substantially greater than the gain of smooth visual tracking of a large visual display moving at 2 Hz (median gain 0.27, range 0.09-0.42). Thus, visual inputs other than smooth tracking must contribute to tVOR cancellation. We then compared tVOR response to 2 Hz bob as subjects fixed upon a visual target at 17 cm and viewed a large textured background at 1.5 m that was either stationary or moving at 2.1 Hz. Vertical eye rotations waxed and waned as a function of the difference between platform and background oscillations. These findings support our hypothesis that tVOR evolved not to stabilize the image of the target on the fovea, but rather to minimize retinal image motion between objects lying in different planes, in order to optimize motion parallax information. A geometrically based optimization function is proposed to account for tVOR responses at different target distances.
    Progress in brain research 02/2008; 171:295-302. · 3.04 Impact Factor
  • Article: Ocular myasthenia revisited: insights from pseudo-internuclear ophthalmoplegia.
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    ABSTRACT: Ocular myasthenia can mimic central disorders of eye movements. We compared horizontal saccades in two patients with myasthenia gravis who presented as pseudo-internuclear ophthalmoplegia (pseudo-INO), two patients with true INO due to multiple sclerosis (MS), and five healthy subjects. In myasthenics, peak velocity of horizontal saccades was similar to, or greater than, controls; in MS patients, adducting saccades were slower than controls. Differences between the peak velocity of abducting and adducting eyes for each saccade were similar to controls for myasthenic pseudo-INO, but greater than controls for true INO. Using the technique of phase-plane analysis, in which eye velocity is plotted against eye position, we found that initial components of abducting and adducting saccades in the myasthenics were as conjugate as controls, even though later components of myasthenic saccades were highly and variably disjunctive. Conversely, phase planes of saccades in true INO showed disjunctive early components of abducting and adducting saccades. Two hypotheses have been offered to account for preservation of fast saccades despite reduced range of eye movements in ocular myasthenia. The first is intrasaccadic neuromuscular fatigue, which is variable over time. Our finding that initial components of saccades were consistently conjugate in the myasthenics gives support to a second hypothesis: selective sparing of pale global fibers, which are important for generating highspeed eye movements, and which are unique amongst extraocular fibers in possessing well developed synaptic folding.
    Journal of Neurology 12/2007; 254(11):1569-74. · 3.47 Impact Factor
  • Article: Comparison of Velocity Waveforms of Eye and Head Saccades
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    ABSTRACT: We compared the velocity waveforms of head and eye-in-head movements during eye-head saccades over a range 5-50 degrees. The velocity waveforms of eye-in-head saccades showed a skew ratio (acceleration period/saccade duration) that varied as a function of saccade size and duration. The velocity waveforms of head saccades showed a more constant skew of ∼0.5 for the range of movements tested. These results suggest independent system controllers for eye and head components of eye-head saccades.
    Annals of the New York Academy of Sciences 01/2006; 1039(1):477 - 479. · 3.15 Impact Factor
  • Article: Comparison of velocity waveforms of eye and head saccades.
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    ABSTRACT: We compared the velocity waveforms of head and eye-in-head movements during eye-head saccades over a range 5-50 degrees. The velocity waveforms of eye-in-head saccades showed a skew ratio (acceleration period/saccade duration) that varied as a function of saccade size and duration. The velocity waveforms of head saccades showed a more constant skew of approximately 0.5 for the range of movements tested. These results suggest independent system controllers for eye and head components of eye-head saccades.
    Annals of the New York Academy of Sciences 05/2005; 1039:477-9. · 3.15 Impact Factor
  • Article: Tests of Hering- and Helmholtz-type models for saccade-vergence interactions by comparing visually guided and memory-guided movements.
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    ABSTRACT: We compared the dynamic properties of memory-guided and visually-guided saccade-vergence movements. For memory-guided responses, convergence components were slowed proportionally more than corresponding saccadic components, compared with visually-guided responses. This result is consistent with independent saccadic and vergence systems, and supports a Hering-type model for saccade-vergence interactions.
    Annals of the New York Academy of Sciences 05/2005; 1039:466-9. · 3.15 Impact Factor
  • Article: Evaluating large saccades in patients with brain-stem or cerebellar disorders.
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    ABSTRACT: Clinicians conventionally test saccades at the bedside by noting the accuracy, initiation time, and speed of large movements, with the patient's head stationary. Partly for methodological reasons, laboratory analysis of saccades has mainly focused on movements of 20 degrees or less. By measuring the velocity waveform of large saccades, it is possible to examine more closely the way in which brain stem and cerebellum guide the eye to the target. Large saccades made by healthy humans show a positively skewed velocity profile. Slow saccades made by patients with brain-stem disorders show a prolonged plateau of low velocity. Some patients with cerebellar disorders may show increased acceleration and deceleration of saccades. Each of these velocity waveforms can be modeled by changing the parameters that describe medium-lead burst neuron firing. In certain other brain-stem and cerebellar disorders, transient decelerations or premature terminations of saccades occur; such velocity waveforms cannot be modeled solely by changing the parameters that describe burst neuron firing. Instead, it is necessary to postulate dysfunction of the mechanism that normally inhibits pontine omnipause neurons, thereby permitting burst neurons to discharge until the saccade is completed. Analysis of large, abnormal saccades calls for application of novel techniques to identify the beginning and end of the saccadic pulse command.
    Annals of the New York Academy of Sciences 05/2005; 1039:404-16. · 3.15 Impact Factor
  • Article: Tests of Hering‐ and Helmholtz‐Type Models for Saccade‐Vergence Interactions by Comparing Visually Guided and Memory‐Guided Movements
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    ABSTRACT: We compared the dynamic properties of memory-guided and visually-guided saccade-vergence movements. For memory-guided responses, convergence components were slowed proportionally more than corresponding saccadic components, compared with visually-guided responses. This result is consistent with independent saccadic and vergence systems, and supports a Hering-type model for saccade-vergence interactions.
    Annals of the New York Academy of Sciences 03/2005; 1039(1):466 - 469. · 3.15 Impact Factor
  • Article: Impulsive head rotation resets oculopalatal tremor: examination of a model
    [show abstract] [hide abstract]
    ABSTRACT: We have described a neuromimetic model of the interaction between the inferior olive (IO) and the cerebellum that accounts for symptomatic oculopalatal tremor (OPT), a disorder characterized by oscillations of the eyes (nystagmus), palate and other branchial muscles. OPT develops months after some brainstem strokes, in association with hypertrophic degeneration of the inferior olivary nucleus (IO). We hypothesized that OPT requires both (1) a pulsatile oscillator created by tighter electrotonic coupling between cells in the IO, and (2) a learned response from the cerebellar cortex that combines with the IO pulses to generate the quasi-pendular oscillations. Since the vestibular nuclei project to both IO and vestibulocerebellum, one prediction of the model is that rapid head rotations could interrupt the oscillator, effectively resetting the timing of the ocular nystagmus. The ocular oscillations in OPT vary in amplitude and phase, making it difficult to determine by Fourier analysis whether head perturbations phase-shift the nystagmus. We applied complex wavelet analysis to data from four patients with OPT and checked whether vestibular stimuli induced a change in phase of the nystagmus. First we calculated a threshold for the spontaneous rate of change of phase of OPT by comparing many segments of nystagmus waveform with their time-shifted versions, bootstrapping these arrays, and computing 95% prediction intervals for each patient. Then we compared the rate of change of phase due to each head perturbation with the threshold for that patient. To minimize the effects of the head perturbation itself on the wavelet analysis, we measured effects in a plane orthogonal to the head rotation, e.g., effects of horizontal head rotations on the torsional component of OPT. In all four patients, the rate of change of phase shift increased sharply at the time of the head perturbation, and in three the change was judged to be statistically significant. Thus, the experimental tests supported the prediction of our model for OPT.
    Progress in Brain Research.