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1.  The nonlinearity of passive extraocular muscles 
Passive extraocular muscles (EOMs), like most biological tissues, are hyper-elastic, i.e., their stiffness increases as they are stretched. It has always been assumed, and in a few occasions argued, that this is their only nonlinearity and that it can be ignored in central gaze. However, using novel measurement techniques in anesthetized paralyzed monkeys, we have recently demonstrated that EOMs are characterized by another prominent nonlinearity: the forces induced by sequences of stretches do not sum. Thus, superposition, a central tenet of linear and quasi-linear models, does not hold in passive EOMs. Here, we outline the implications of this finding, especially in light of the common assumption that it is easier for the brain to control a linear than a nonlinear plant. We argue against this common belief: the specific nonlinearity of passive EOMs may actually make it easier for the brain to control the plant than if muscles were linear.
doi:10.1111/j.1749-6632.2011.06111.x
PMCID: PMC3187914  PMID: 21950971
viscoelasticity; model; control; quasilinear; superposition
2.  Pharmacological tests of hypotheses for acquired pendular nystagmus 
Acquired pendular nystagmus (APN) occurs with multiple sclerosis (MS) and oculopalatal tremor (OPT); distinct features of the nystagmus have led to the development of separate models for the pathogenesis. APN in MS has been attributed to instability in the neural integrator, which normally ensures steady gaze. APN in OPT may result from electrotonic coupling between neurons in the hypertrophied inferior olivary nucleus, which induces maladaptive learning in cerebellar cortex. We tested these two hypotheses by analyzing the effects of gabapentin, memantine, and baclofen on both forms of nystagmus. No drug changed the dominant frequency of either form of APN, but the variability of frequency was affected with gabapentin and memantine in patients with OPT. The amplitude of APN in both MS and OPT was reduced with gabapentin and memantine, but not baclofen. Analyzing the effects of drug therapies on ocular oscillations provides a novel approach to test models of nystagmus.
doi:10.1111/j.1749-6632.2011.06118.x
PMCID: PMC3187918  PMID: 21951011
cerebellum; inferior olive; plasticity; learning; Guillain–Mollaret triangle; multiple sclerosis
3.  Hierarchical control of two-dimensional gaze saccades 
Coordinating the movements of different body parts is a challenging process for the central nervous system because of several problems. Four of these main difficulties are: first, moving one part can move others; second, the parts can have different dynamics; third, some parts can have different motor goals; and fourth, some parts may be perturbed by outside forces. Here, we propose a novel approach for the control of linked systems with feedback loops for each part. The proximal parts have separate goals, but critically the most distal part has only the common goal. We apply this new control policy to eye-head coordination in two-dimensions, specifically head-unrestrained gaze saccades. Paradoxically, the hierarchical structure has controllers for the gaze and the head, but not for the eye (the most distal part). Our simulations demonstrate that the proposed control structure reproduces much of the published empirical data about gaze movements, e.g., it compensates for perturbations, accurately reaches goals for gaze and head from arbitrary initial positions, simulates the nine relationships of the head-unrestrained main sequence, and reproduces observations from lesion and single-unit recording experiments. We conclude by showing how our model can be easily extended to control structures with more linked segments, such as the control of coordinated eye on head on trunk movements.
doi:10.1007/s10827-013-0477-1
PMCID: PMC4190094  PMID: 24062206
Gaze saccades; Eye; Head; Feedback control; Superior colliculus; VOR suppression
4.  Terminator Disparity Contributes to Stereo Matching for Eye Movements and Perception 
The Journal of Neuroscience  2013;33(48):18867-18879.
In the context of motion detection, the endings (or terminators) of 1-D features can be detected as 2-D features, affecting the perceived direction of motion of the 1-D features (the barber-pole illusion) and the direction of tracking eye movements. In the realm of binocular disparity processing, an equivalent role for the disparity of terminators has not been established. Here we explore the stereo analogy of the barber-pole stimulus, applying disparity to a 1-D noise stimulus seen through an elongated, zero-disparity, aperture. We found that, in human subjects, these stimuli induce robust short-latency reflexive vergence eye movements, initially in the direction orthogonal to the 1-D features, but shortly thereafter in the direction predicted by the disparity of the terminators. In addition, these same stimuli induce vivid depth percepts, which can only be attributed to the disparity of line terminators. When the 1-D noise patterns are given opposite contrast in the two eyes (anticorrelation), both components of the vergence response reverse sign. Finally, terminators drive vergence even when the aperture is defined by a texture (as opposed to a contrast) boundary. These findings prove that terminators contribute to stereo matching, and constrain the type of neuronal mechanisms that might be responsible for the detection of terminator disparity.
doi:10.1523/JNEUROSCI.3332-13.2013
PMCID: PMC3841453  PMID: 24285893
5.  Oculopalatal tremor explained by a model of inferior olivary hypertrophy and cerebellar plasticity 
Brain  2010;133(3):923-940.
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 ∼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.
doi:10.1093/brain/awp323
PMCID: PMC2842510  PMID: 20080879
vestibular; gap junction; connexin; motor disorders; eye movement
6.  pyElectrode: an open-source tool using structural MRI for electrode positioning and neuron mapping 
Journal of neuroscience methods  2012;213(1):123-131.
Neurophysiogists want to place the tip of an electrode in a specific area of the brain. The coordinates of this area can be obtained from standard stereotaxic atlases. However, individual brains may not align with the atlas exactly. Additionally, for chronic recordings, electrodes are placed through a chamber attached to the animal's skull. Thus, the user wants to know where the area of interest is in chamber coordinates, not stereotaxic coordinates. After the chamber has been attached an MRI is often made. This assists in electrode placement, as the location of a target relative to the chamber can be determined based on the atlas. However, doing this in practice requires rough estimation or cumbersome calculations. pyElectrode provides a graphical display and performs calculations necessary to convert between stereotaxic and chamber coordinates, thus facilitating MR-based targeting from an implanted chamber. It also allows the experimenter to visualize recording or stimulation sites during experiments. Finally, it can display and output those sites on an MRI slice background in a format suitable for publication.
doi:10.1016/j.jneumeth.2012.12.012
PMCID: PMC3570753  PMID: 23261658
brain; atlas; stereotaxic; 3D; slice
7.  Temporal evolution of pattern disparity processing in humans 
Stereo matching, i.e., the matching by the visual system of corresponding parts of the images seen by the two eyes, is inherently a 2-D problem. To gain insights into how this operation is carried out by the visual system, we measured, in human subjects, the reflexive vergence eye movements elicited by the sudden presentation of stereo plaids. We found compelling evidence that the 2-D pattern disparity is computed by combining disparities first extracted within orientation selective channels. This neural computation takes 10–15 ms, and is carried out even when subjects perceive not a single plaid but rather two gratings in different depth planes (transparency). However, we found that 1-D disparities are not always effectively combined: When spatial frequency and contrast of the gratings are sufficiently different pattern disparity is not computed, a result that cannot be simply attributed to the transparency of such stimuli. Based on our results, we propose that a narrow-band implementation of the Intersection Of Constraints (IOC) rule (Fennema and Thompson, 1979; Adelson and Movshon, 1982), preceded by cross-orientation suppression, underlies the extraction of pattern disparity.
doi:10.1523/JNEUROSCI.4318-12.2013
PMCID: PMC3711760  PMID: 23426674
8.  Neuromimetic model of saccades for localizing deficits in an atypical eye-movement pathology 
Background
When patients with ocular motor deficits come to the clinic, in numerous situations it is hard to relate their behavior to one or several deficient neural structures. We sought to demonstrate that neuromimetic models of the ocular motor brainstem could be used to test assumptions of the neural deficits linked to a patient’s behavior.
Methods
Eye movements of a patient with unexplained neurological pathology were recorded. We analyzed the patient’s behavior in terms of a neuromimetic saccadic model of the ocular motor brainstem to formulate a pathophysiological hypothesis.
Results
Our patient exhibited unusual ocular motor disorders including increased saccadic peak velocities (up to ≈1000 deg/s), dynamic saccadic overshoot, left-right asymmetrical post-saccadic drift and saccadic oscillations. We show that our model accurately reproduced the observed disorders allowing us to hypothesize that those disorders originated from a deficit in the cerebellum.
Conclusion
Our study suggests that neuromimetic models could be a good complement to traditional clinical tools. Our behavioral analyses combined with the model simulations localized four different features of abnormal eye movements to cerebellar dysfunction. Importantly, this assumption is consistent with clinical symptoms.
doi:10.1186/1479-5876-11-125
PMCID: PMC3672089  PMID: 23694702
9.  Eye movement sequence generation in humans: Motor or goal updating? 
Journal of vision  2010;10(14):10.1167/10.14.28 28.
Saccadic eye movements are often grouped in pre-programmed sequences. The mechanism underlying the generation of each saccade in a sequence is currently poorly understood. Broadly speaking, two alternative schemes are possible: first, after each saccade the retinotopic location of the next target could be estimated, and an appropriate saccade could be generated. We call this the goal updating hypothesis. Alternatively, multiple motor plans could be pre-computed, and they could then be updated after each movement. We call this the motor updating hypothesis. We used McLaughlin’s intra-saccadic step paradigm to artificially create a condition under which these two hypotheses make discriminable predictions. We found that in human subjects, when sequences of two saccades are planned, the motor updating hypothesis predicts the landing position of the second saccade in two-saccade sequences much better than the goal updating hypothesis. This finding suggests that the human saccadic system is capable of executing sequences of saccades to multiple targets by planning multiple motor commands, which are then updated by serial subtraction of ongoing motor output.
doi:10.1167/10.14.28
PMCID: PMC3610575  PMID: 21191134
eye movements; memory; plasticity
10.  Role of Cerebellum in Motion Perception and Vestibulo-ocular Reflex—Similarities and Disparities 
Cerebellum (London, England)  2013;12(1):97-107.
Vestibular velocity storage enhances the efficacy of the angular vestibulo-ocular reflex (VOR) during relatively low-frequency head rotations. This function is modulated by GABA-mediated inhibitory cerebellar projections. Velocity storage also exists in perceptual pathway and has similar functional principles as VOR. However, it is not known whether the neural substrate for perception and VOR overlap. We propose two possibilities. First, there is the same velocity storage for both VOR and perception; second, there are nonoverlapping neural networks: one might be involved in perception and the other for the VOR. We investigated these possibilities by measuring VOR and perceptual responses in healthy human subjects during whole-body, constant-velocity rotation steps about all three dimensions (yaw, pitch, and roll) before and after 10 mg of 4-aminopyridine (4-AP). 4-AP, a selective blocker of inward rectifier potassium conductance, can lead to increased synchronization and precision of Purkinje neuron discharge and possibly enhance the GABAergic action. Hence 4-AP could reduce the decay time constant of the perceived angular velocity and VOR. We found that 4-AP reduced the decay time constant, but the amount of reduction in the two processes, perception and VOR, was not the same, suggesting the possibility of nonoverlapping or partially overlapping neural substrates for VOR and perception. We also noted that, unlike the VOR, the perceived angular velocity gradually built up and plateau prior to decay. Hence, the perception pathway may have additional mechanism that changes the dynamics of perceived angular velocity beyond the velocity storage. 4-AP had no effects on the duration of build-up of perceived angular velocity, suggesting that the higher order processing of perception, beyond the velocity storage, might not occur under the influence of mechanism that could be influenced by 4-AP.
doi:10.1007/s12311-012-0401-7
PMCID: PMC3510326  PMID: 22777507
Vestibular; Eye movements; GABA; Brainstem; Velocity storage; Cerebellum
11.  OrbitView: Eye movement visualization software 
Journal of neuroscience methods  2011;200(2):181-184.
Measurement of eye movements often helps to diagnose ocular motor disorders in the clinic, and is also used as a research tool in ocular motor, vision and vestibular research. Eye movements, however, are usually recorded without simultaneous video recordings, making offline interpretation difficult. We developed a tool that converts the measured eye movement data into a three-dimensional (3D) movie of eye movements. Having useful functions such as slow-play, pause and exaggeration of the movements, this new software provides a research and teaching tool to aid interpretation of the recorded eye movements.
doi:10.1016/j.jneumeth.2011.06.002
PMCID: PMC3156268  PMID: 21689683
Data visualization; Emulation of eye movements; Clinical tool; Research tool; Teaching tool
12.  Do brainstem omnipause neurons terminate saccades? 
Saccade-generating burst neurons (BN) are inhibited by omnipause neurons (OPN), except during saccades. OPN activity pauses before saccade onset and resumes at the saccade end. Microstimulation of OPN stops saccades in mid-flight, which shows that OPN can end saccades. However, OPN pause duration does not correlate well with saccade duration, and saccades are normometric after OPN lesions. We tested whether OPN were responsible for stopping saccades both in late-onset Tay–Sachs, which causes premature saccadic termination, and in individuals with cerebellar hypermetria. We studied gaze shifts between two targets at different distances aligned on one eye, which consist of a disjunctive saccade followed by vergence. High-frequency conjugate oscillations during the vergence movements that followed saccades were present in all subjects studied, indicating OPN silence. Thus, mechanisms other than OPN discharge (e.g., cerebellar caudal fastigial nucleus–promoting inhibitory BN discharge) must contribute to saccade termination.
doi:10.1111/j.1749-6632.2011.06170.x
PMCID: PMC3438674  PMID: 21950975
Tay–Sachs disease; saccades; omnipause neurons; fastigial nucleus; Müller paradigm
13.  Ocular following in humans: Spatial properties 
Journal of vision  2012;12(4):10.1167/12.4.13 13.
Ocular following responses (OFRs) are tracking eye movements elicited at ultrashort latency by the sudden movement of a textured pattern. Here we report the results of our study of their dependency on the spatial arrangement of the motion stimulus. Unlike previous studies that looked at the effect of stimulus size, we investigated the impact of stimulus location and how two distinct stimuli, presented together, collectively determine the OFR. We used as stimuli vertical gratings that moved in the horizontal direction and that were confined to either one or two 0.58° high strips, spanning the width of the screen. We found that the response to individual strips varied as a function of the location and spatial frequency (SF) of the stimulus. The response decreased as the stimulus eccentricity increased, but this relationship was more accentuated at high than at low spatial frequencies. We also found that when pairs of stimuli were presented, nearby stimuli interacted strongly, so that the response to the pair was barely larger than the response to a single strip in the pair. This suppressive effect faded away as the separation between the strips increased. The variation of the suppressive interaction with strip separation, paired with the dependency on eccentricity of the responses to single strips, caused the peak response for strip pairs to be achieved at a specific separation, which varied as a function of SF.
doi:10.1167/12.4.13
PMCID: PMC3438696  PMID: 22523400
ocular following; spatial frequency; stimulus
14.  The effects of ion channel blockers validate the conductance-based model of saccadic oscillations 
Conductance-based models of reciprocally inhibiting burst neurons suggest that intrinsic membrane properties and postinhibitory rebound (PIR) determine the amplitude and frequency of saccadic oscillations. Reduction of the low-threshold calcium currents (IT) in the model decreased the amplitude but increased the frequency of the simulated oscillations. Combined reduction of hyperpolarization-activated cation current (Ih) and IT in the model abolished the simulated oscillations. We measured the effects of a selective blocker of IT (ethosuximide) in healthy subjects on the amplitude and frequency of saccadic oscillations evoked by eye closure and of a nonselective blocker of Ih and IT (propronolol) in a patient with microsaccadic oscillation and limb tremor syndrome (mSOLT). Ethosuximide significantly reduced the amplitude but increased the frequency of the saccadic oscillations during eye closure in healthy subjects. Propranolol abolished saccadic oscillations in the mSOLT patient. These results support the hypothetical role of postinhibitory rebound, Ih, and IT, in generation of saccadic oscillations and determining their kinematic properties.
doi:10.1111/j.1749-6632.2011.06130.x
PMCID: PMC3431800  PMID: 21950976
burst neurons; hyperpolarization-activated cation current; low-threshold calcium current; reciprocal innervations
15.  Sustained eye closure slows saccades 
Vision research  2010;50(17):1665-1675.
Saccadic eye movements rapidly orient the line of sight towards the object of interest. Pre-motor burst neurons (BNs) controlling saccades receive excitation from superior colliculus and cerebellum, but inhibition by omnipause neurons (OPNs) prevents saccades. When the OPNs pause, BNs begin to fire. It has been presumed that part of the BN burst comes from post-inhibitory rebound (PIR). We hypothesized that in the absence of prior inhibition from OPNs there would be no PIR, and thus the increase in initial firing rate of BNs would be reduced. Consequently, saccade acceleration would be reduced. We measured eye movements and showed that sustained eye closure, which inhibits the activity of OPNs and thus hypothetically should weaken PIR, reduced the peak velocity, acceleration, and deceleration of saccades in healthy human subjects. Saccades under closed eyelids also had irregular trajectories; the frequency of the oscillations underlying this irregularity was similar to that of high-frequency ocular flutter (back-to-back saccades) often seen in normal subjects during attempted fixation at straight ahead while eyes are closed. Saccades and quick phases of nystagmus are generated by the same pre-motor neurons, and we found that the quick-phase velocity of nystagmus was also reduced by lid closure. These changes were not due to a mechanical hindrance to the eyes, because lid closure did not affect the peak velocities or accelerations of the eyes in the “slow-phase” response to rapid head movements of comparable speeds to those of saccades. These results indicate a role for OPNs in generating the abrupt onset and high velocities of saccades. We hypothesize that the mechanism involved is PIR in pre-motor burst neurons.
doi:10.1016/j.visres.2010.05.019
PMCID: PMC2929924  PMID: 20573593
Omnipause neurons; Burst neurons; Oscillations; Ballistic movement; Post-inhibitory rebound
16.  The Viscoelastic Properties of Passive Eye Muscle in Primates. III: Force Elicited by Natural Elongations 
PLoS ONE  2010;5(3):e9595.
We have recently shown that in monkey passive extraocular muscles the force induced by a stretch does not depend on the entire length history, but to a great extent is only a function of the last elongation applied. This led us to conclude that Fung's quasi-linear viscoelastic (QLV) model, and more general nonlinear models based on a single convolution integral, cannot faithfully mimic passive eye muscles. Here we present additional data about the mechanical properties of passive eye muscles in deeply anesthetized monkeys. We show that, in addition to the aforementioned failures, previous models also grossly overestimate the force exerted by passive eye muscles during smooth elongations similar to those experienced during normal eye movements. Importantly, we also show that the force exerted by a muscle following an elongation is largely independent of the elongation itself, and it is mostly determined by the final muscle length. These additional findings conclusively rule out the use of classical viscoelastic models to mimic the mechanical properties of passive eye muscles. We describe here a new model that extends previous ones using principles derived from research on thixotropic materials. This model is able to account reasonably well for our data, and could thus be incorporated into models of the eye plant.
doi:10.1371/journal.pone.0009595
PMCID: PMC2833209  PMID: 20221406
17.  Ocular motor anatomy in a case of interrupted saccades 
Progress in brain research  2008;171:563-566.
Saccades normally place the eye on target with one smooth movement. In late-onset Tay—Sachs (LOTS), intrasaccadic transient decelerations occur that may result from (1) premature omnipause neuron (OPN) re-activation due to malfunction of the latch circuit that inhibits OPNs for the duration of the saccade or (2) premature inhibitory burst neuron (IBN) activation due to fastigial nucleus (FN) dysregulation by the dorsal cerebellar vermis. Neuroanatomic analysis of a LOTS brain was performed. Purkinje cells were absent and gliosis of the granular cell layer was present in the dorsal cerebellar vermis. Deep cerebellar nuclei contained large inclusions. IBNs were present with small inclusions. The sample did not contain the complete OPN region; however, neurons in the OPN region contained massive inclusions. Pathologic findings suggest that premature OPN re-activation and/or inappropriate firing of IBNs may be responsible for interrupted saccades in LOTS. Cerebellar clinical dysfunction, lack of saccadic slowing, and significant loss of cerebellar cells suggest that the second cause is more likely.
doi:10.1016/S0079-6123(08)00680-8
PMCID: PMC2752380  PMID: 18718354
fastigial nucleus; omnipause neurons; burst neurons; latch circuit; brainstem
18.  Mechanism of interrupted saccades in patients with late-onset Tay-Sachs disease 
Progress in brain research  2008;171:567-570.
In late-onset Tay-Sachs disease (LOTS), saccades are interrupted by one or more transient decelerations. Some saccades reaccelerate and continue on before eye velocity reaches zero, even in darkness. Intervals between successive decelerations are not regularly spaced. Peak decelerations of horizontal and vertical components of oblique saccades in LOTS is more synchronous than those in control subjects. We hypothesize that these decelerations are caused by dysregulation of the fastigial nuclei (FN) of the cerebellum, which fire brain stem inhibitory burst neurons (IBNs).
doi:10.1016/S0079-6123(08)00681-X
PMCID: PMC2750844  PMID: 18718355
fastigial nucleus; omnipause neurons; burst neurons; latch circuit
19.  The role of omnipause neurons 
Progress in brain research  2008;171:115-121.
The anatomy and neurophysiology of the saccadic eye movement system have been well studied, but the roles of certain key neurons in this system are not fully appreciated. Important clues about the functional interactions in the saccadic system can be gleaned from the histochemistry of different saccadic neurons. The most prominent inhibitory neurons in the circuit are the omnidirectional pause neurons (OPN), which inhibit the premotor burst neurons that drive the eye. Most inhibitory neurons in the brain transmit γ-aminobutyric acid (GABA), but OPN transmit glycine (Gly). It is interesting to ask whether the saccadic system would work any differently if OPN were GABA-ergic. Gly and GABA receptors both provide a channel for a hyperpolarizing Cl- current that inhibits its target neuron. Depolarizing currents that excite the neurons come through several channels, including the NMDA receptor (NMDAR). The NMDAR is unique among receptors in that it has active sites for two different neurotransmitters, glutamate (Glu) and Gly. Gly is a co-agonist that acts to amplify the current produced by Glu. We have proposed a model of the saccadic brain stem circuitry that exploits this dual role of Gly to produce both inhibition of the saccadic circuit during fixation, and to increase its responsiveness, or gain, during movements. This suggests that OPNs act more as a regulator of the saccadic circuit’s gain, rather than as a gate for allowing saccades. We propose a new hypothesis: the OPNs play a general role as a modulator of arousal in orienting subsystems, such as saccades, pursuit, head movements, etc.
doi:10.1016/S0079-6123(08)00615-8
PMCID: PMC2750832  PMID: 18718289
glycine; burst neurons; brainstem; saccades
20.  Saccadic Burst Cell Membrane Dysfunction Is Responsible for Saccadic Oscillations 
Saccadic oscillations threaten clear vision by causing image motion on the retina. They are either purely horizontal (ocular flutter) or multidimensional (opsoclonus). We propose that ion channel dysfunction in the burst cell membrane is the underlying abnormality. We have tested this hypothesis by simulating a neuromimetic computational model of the burst neurons. This biologically realistic model mimics the physiologic properties and anatomic connections in the brainstem saccade generator. A rebound firing after sustained inhibition, called post-inhibitory rebound (PIR), and reciprocal inhibition between premotor saccadic burst neurons are the key features of this conceptual scheme. PIR and reciprocal inhibition make the circuits that generate the saccadic burst inherently unstable and can lead to oscillations unless stabilized by external inhibition. Our simulations suggest that alterations in membrane properties that lead to an increase in PIR, a reduction in external glycinergic inhibition, or both can cause saccadic oscillations.
doi:10.1097/WNO.0b013e31818eb3a5
PMCID: PMC2752370  PMID: 19145136
21.  The Viscoelastic Properties of Passive Eye Muscle in Primates. II: Testing the Quasi-Linear Theory 
PLoS ONE  2009;4(8):e6480.
We have extensively investigated the mechanical properties of passive eye muscles, in vivo, in anesthetized and paralyzed monkeys. The complexity inherent in rheological measurements makes it desirable to present the results in terms of a mathematical model. Because Fung's quasi-linear viscoelastic (QLV) model has been particularly successful in capturing the viscoelastic properties of passive biological tissues, here we analyze this dataset within the framework of Fung's theory.
We found that the basic properties assumed under the QLV theory (separability and superposition) are not typical of passive eye muscles. We show that some recent extensions of Fung's model can deal successfully with the lack of separability, but fail to reproduce the deviation from superposition.
While appealing for their elegance, the QLV model and its descendants are not able to capture the complex mechanical properties of passive eye muscles. In particular, our measurements suggest that in a passive extraocular muscle the force does not depend on the entire length history, but to a great extent is only a function of the last elongation to which it has been subjected. It is currently unknown whether other passive biological tissues behave similarly.
doi:10.1371/journal.pone.0006480
PMCID: PMC2715107  PMID: 19649257
22.  The Effect of Acute Superior Oblique Palsy on Torsional Optokinetic Nystagmus in Monkeys 
Purpose
To investigate the effects of acquired superior oblique palsy (SOP) and corrective strabismus surgery on torsional optokinetic nystagmus (tOKN) in monkeys.
Methods
The trochlear nerve was severed intracranially in two rhesus monkeys (M1 and M2). For each monkey, more than 4 months after the SOP, the ipsilateral inferior oblique muscle was denervated and extirpated. For M2, 4 months later, the contralateral inferior rectus muscle was recessed by 2 mm. tOKN was elicited during monocular viewing of a rotating stimulus that was rear projected onto a screen 43.5 cm in front of the animal. Angular rotation of the stimulus about the center was 40 deg/s clockwise or counterclockwise.
Results
The main findings after trochlear nerve sectioning were (1) the amplitude and peak velocity of torsional quick and slow phases of the paretic eye was less than that in the normal eye for both intorsion and extorsion, and (2) the vertical motion of the paretic eye increased during both torsional slow and quick phases. After corrective inferior oblique surgery, both of these effects were even greater.
Conclusions
Acquired SOP and corrective inferior oblique–weakening surgery create characteristic patterns of change in tOKN that reflect alterations in the dynamic properties of the extraocular muscles involved in eye torsion. tOKN also provides information complementary to that provided by the traditional Bielschowsky head-tilt test and potentially can help distinguish among different causes of vertical ocular misalignment.
doi:10.1167/iovs.07-0989
PMCID: PMC2367221  PMID: 18385059
23.  The Viscoelastic Properties of Passive Eye Muscle in Primates. I: Static Forces and Step Responses 
PLoS ONE  2009;4(4):e4850.
The viscoelastic properties of passive eye muscles are prime determinants of the deficits observed following eye muscle paralysis, the root cause of several types of strabismus. Our limited knowledge about such properties is hindering the ability of eye plant models to assist in formulating a patient's diagnosis and prognosis. To investigate these properties we conducted an extensive in vivo study of the mechanics of passive eye muscles in deeply anesthetized and paralyzed monkeys. We describe here the static length-tension relationship and the transient forces elicited by small step-like elongations. We found that the static force increases nonlinearly with length, as previously shown. As expected, an elongation step induces a fast rise in force, followed by a prolonged decay. The time course of the decay is however considerably more complex than previously thought, indicating the presence of several relaxation processes, with time constants ranging from 1 ms to at least 40 s. The mechanical properties of passive eye muscles are thus similar to those of many other biological passive tissues. Eye plant models, which for lack of data had to rely on (erroneous) assumptions, will have to be updated to incorporate these properties.
doi:10.1371/journal.pone.0004850
PMCID: PMC2660417  PMID: 19337381
24.  Hypothetical membrane mechanisms in essential tremor 
Background
Essential tremor (ET) is the most common movement disorder and its pathophysiology is unknown. We hypothesize that increased membrane excitability in motor circuits has a key role in the pathogenesis of ET. Specifically, we propose that neural circuits controlling ballistic movements are inherently unstable due to their underlying reciprocal innervation. Such instability is enhanced by increased neural membrane excitability and the circuit begins to oscillate. These oscillations manifest as tremor.
Methods
Postural limb tremor was recorded in 22 ET patients and then the phenotype was simulated with a conductance-based neuromimetic model of ballistic movements. The model neuron was Hodgkin-Huxley type with added hyperpolarization activated cation current (Ih), low threshold calcium current (IT), and GABA and glycine mediated chloride currents. The neurons also featured the neurophysiological property of rebound excitation after release from sustained inhibition (post-inhibitory rebound). The model featured a reciprocally innervated circuit of neurons that project to agonist and antagonist muscle pairs.
Results
Neural excitability was modulated by changing Ih and/or IT. Increasing Ih and/or IT further depolarized the membrane and thus increased excitability. The characteristics of the tremor from all ET patients were simulated when Ih was increased to ~10× the range of physiological values. In contrast, increasing other membrane conductances, while keeping Ih at a physiological value, did not simulate the tremor. Increases in Ih and IT determined the frequency and amplitude of the simulated oscillations.
Conclusion
These simulations support the hypothesis that increased membrane excitability in potentially unstable, reciprocally innervated circuits can produce oscillations that resemble ET. Neural excitability could be increased in a number of ways. In this study membrane excitability was increased by up-regulating Ih and IT. This approach suggests new experimental and clinical ways to understand and treat common tremor disorders.
doi:10.1186/1479-5876-6-68
PMCID: PMC2613385  PMID: 18990221
25.  Interaction between Purkinje Cells and Inhibitory Interneurons May Create Adjustable Output Waveforms to Generate Timed Cerebellar Output 
PLoS ONE  2008;3(7):e2770.
We develop a new model that explains how the cerebellum may generate the timing in classical delay eyeblink conditioning. Recent studies show that both Purkinje cells (PCs) and inhibitory interneurons (INs) have parallel signal processing streams with two time scales: an AMPA receptor-mediated fast process and a metabotropic glutamate receptor (mGluR)-mediated slow process. Moreover, one consistent finding is an increased excitability of PC dendrites (in Larsell's lobule HVI) in animals when they acquire the classical delay eyeblink conditioning naturally, in contrast to in vitro studies, where learning involves long-term depression (LTD). Our model proposes that the delayed response comes from the slow dynamics of mGluR-mediated IP3 activation, and the ensuing calcium concentration change, and not from LTP/LTD. The conditioned stimulus (tone), arriving on the parallel fibers, triggers this slow activation in INs and PC spines. These excitatory (from PC spines) and inhibitory (from INs) signals then interact at the PC dendrites to generate variable waveforms of PC activation. When the unconditioned stimulus (puff), arriving on the climbing fibers, is coupled frequently with this slow activation the waveform is amplified (due to an increased excitability) and leads to a timed pause in the PC population. The disinhibition of deep cerebellar nuclei by this timed pause causes the delayed conditioned response. This suggested PC-IN interaction emphasizes a richer role of the INs in learning and also conforms to the recent evidence that mGluR in the cerebellar cortex may participate in slow motor execution. We show that the suggested mechanism can endow the cerebellar cortex with the versatility to learn almost any temporal pattern, in addition to those that arise in classical conditioning.
doi:10.1371/journal.pone.0002770
PMCID: PMC2474676  PMID: 18648667

Results 1-25 (26)