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D Tweed

Publications and source records attributed to D Tweed.

At least 37 records · Page 2Linked to original sources
PubMed1994

Testing models of the oculomotor velocity-to-position transformation.

1. Do neural computations in premotor circuits mirror the physical properties of the systems they control? In 1987, Tweed and Vilis showed that oculomotor theories where a neural integrator converts eye angular velocity commands into position commands cannot be correct, because angular position is not the integral of angular velocity. Recently Schnabolk and Raphan proposed that an angular velocity integrator is nevertheless used to generate tonic commands in the oculomotor system. Here we test the Schnabolk-Raphan (S-R) model against Tweed and Vilis's quaternion (Q) model of the velocity to position transformation. 2. The S-R model predicts large (up to 7 degrees) transient (approximately 700 ms) deviations ("blips") in torsional eye position during attempted horizontal and vertical saccades. The Q model predicts no blips. Search coil recordings of saccades by 7 normal human subjects showed no large blips. 3. For approximately 200 saccades by each subject, we plotted the area under the torsional blip versus the product of saccade eccentricity and magnitude. According to the S-R model, this graph should form a straight line with slope 1.00. According to the Q model, the slope should be zero. Measured slopes averaged 0.016 (range -0.073 to 0.061) for saccade targets at 20 degrees eccentricity and 0.040 (range 0.004-0.076) for targets at 40 degrees. 4. No parameter change can significantly improve the S-R model, but lowering one parameter eradicates the tiny inaccuracy in the Q model. We show that the fundamental reason for the S-R model's failure is its use of a commutative controller to steer a noncommutative plant.

Attention↗
PubMed1994

Rotational kinematics of the human vestibuloocular reflex. I. Gain matrices.

1. This series of three papers aims to describe the three-dimensional, kinematic input-output relations of the rotational vestibuloocular reflex (VOR) in humans, and to identify the functional advantages of these relations. In this first paper the response to sinusoidal rotation in darkness at 0.3 Hz, maximum speed 37.5%/s, was quantified by the use of the three-dimensional analogue of VOR gain: a 3 x 3 matrix where each element describes the dependence of one component (torsional, vertical, or horizontal) of eye velocity on one component of head velocity. 2. The three matrix elements indicating collinear gains (i.e., dependence of torsional eye velocity on torsional head velocity, vertical on vertical, and horizontal on horizontal) were smaller than the -1's required for optimal retinal image stabilization. Of these three the torsional gain was weakest: -0.37 for rotation about an earth-vertical axis, versus -0.73 and -0.64 for vertical and horizontal gains. Matrix elements indicating cross talk were mostly negligible. There was a tendency to leftward eye rotation in response to clockwise head motion, but this was not statistically significant. 3. VOR responses were compared for rotation about earth-vertical and earth-horizontal axes. The varying otolith input due to the rotation of the gravity vector relative to the head during earth-horizontal axis rotation made no difference to the collinear gains. 4. There were no consistent phase leads or lags except for a torsional phase lead of up to 10 degrees, usually more marked for clock-wise head rotation versus counterclockwise, and for oblique axis rotations versus purely torsional. 5. Torsional gain was magnified, averaging -0.52, when the torsional component of head rotation was only a small part of a predominantly vertical or horizontal rotation, i.e., when the axis of head rotation was near the frontal plane. Because most natural head rotations occur about such axes, the torsional VOR is probably somewhat stronger than the response to pure torsion would suggest. 6. The speed of eye rotation in response to a given stimulus varied widely among subjects, but the direction of rotation was much more uniform. For head rotations about oblique axes out of the frontal plane, there was a systematic misalignment of eye and head axes, with eye axes tilted toward the frontal plane. These findings can be explained on the basis of a strategy where the VOR balances the muscular effort of rotating the eyes against the cost of retinal slip.

Acceleration↗
PubMed1994

Rotational kinematics of the human vestibuloocular reflex. II. Velocity steps.

1. Gain matrices were used to quantify the three-dimensional vestibuloocular reflex (VOR) in five human subjects who were accelerated over 1 s and then spun at a constant 150 degrees/s for 29 s in darkness. Rotations were torsional, vertical and horizontal, about earth-vertical and earth-horizontal axes. 2. Elements on the main diagonal of the gain matrices were much smaller than the optimal value of -1, and torsional gain was weaker than vertical or horizontal. Off-diagonal elements, indicating cross talk, were minimal except for a small but consistent horizontal response to torsional head rotation. 3. Downward slow phases were more than twice as fast as upward at the start of rotation about both earth-vertical and earth-horizontal axes, but the asymmetry vanished later in the rotation. 4. During earth-vertical-axis rotation, all matrix elements decayed to zero. The main-diagonal torsional and vertical gains waned with time constants close to that of the cupula (6.7 and 7.3 s). Velocity storage prolonged the horizontal response to horizontal head rotation (time constant 14.2 s) but not the horizontal response to torsion (7.7 s). A simple explanation is that velocity storage acts on a central estimate of head motion that accurately distinguishes horizontal from torsional and that the inappropriate horizontal eye velocity response to torsion occurs because of cross talk downstream from velocity storage. 5. During earth-horizontal-axis rotation, the torsional, vertical, and horizontal main-diagonal elements declined, with time constants of 7.6, 8.2, and 7.9 s, to maintained nonzero values, all equal to about -0.1. Off-diagonal elements, including the horizontal response to torsion, decayed to zero, so that the otolith-driven reflex, late in the rotation, was equally strong in all dimensions and almost free of detectable cross talk. 6. The difference between gain curves over the course of earth-vertical- and earth-horizontal-axis rotations was not constant but increased with time, suggesting that the VOR response to earth-horizontal-axis rotation is not a simple sum of canal and otolith reflexes.

Acceleration↗
PubMed1994

Rotational kinematics of the human vestibuloocular reflex. III. Listing's law.

1. Do slow phase eye velocities generated by the vestibuloocular reflex (VOR) depend on eye position? If the purpose of the VOR is simply to stabilize the retinal image, there can be no such dependence, because eye velocity must always be equal and opposite to head velocity. But if the VOR tolerates some retinal slip to achieve other goals, such as reducing eye velocity or following Listing's law, then one should see specific patterns of dependence. We examined VOR responses of human subjects to yaw, pitch, and roll rotation looking in various directions to quantify how the input-output properties of the VOR vary with eye position. 2. Eye rotation axes during yaw and pitch tilted in the same direction as the gaze line but only one-quarter as far on average. Thus, during yaw head rotation, the axis of eye rotation was roughly aligned with the head axis when the subject looked straight ahead, but tilted up when the gaze direction was up, and down when gaze was down. The amount of tilt varied between subjects, but on average a 30 degrees change in eye position caused a 7.5 degrees tilt in the eye rotation axis. During pitch, the eye axis tilted right when gaze was right and left when gaze was left, also moving 7.5 degrees on average for a 30 degrees change in the gaze direction. 3. During roll stimulation, the axis of eye rotation tilted in the opposite direction to the gaze line, and about one-half as far. On average, when the gaze line moved 30 degrees down, the eye rotation axis tilted 12.0 degrees up; when the gaze moved 30 degrees left, the eye axis tilted 15.3 degrees right. 4. It is often argued that the torsional VOR is weak because head rotation about the line of sight causes little image displacement on the fovea. But the line of sight is collinear with the torsional axis only when the subject looks straight ahead. Does the "weak axis" of the VOR stay collinear with the gaze line when the subject looks eccentrically? We calculated the axis of head rotation for which the VOR response is weakest and found that it does vary with eye position, but does not stay parallel with the gaze direction. When subjects looked straight ahead, the weak axis was roughly collinear with the gaze line; when gaze shifted eccentrically, the weak axis shifted in the same direction but only about one-half as far.(ABSTRACT TRUNCATED AT 400 WORDS)

Acceleration↗
PubMed1994

Three-dimensional eye, head, and chest orientations after large gaze shifts and the underlying neural strategies.

1. The fixation orientations adopted by the eye, head, and chest were examined when all three were allowed to participate in gaze shifts to visual targets. The objective was to discover whether there are invariant, neurally determined laws governing these orientations that might provide clues to the processes of perception and motor control. This is an extension of the classical studies of eye-only saccades that determined that there is only one eye orientation for each gaze direction (Donders' law) and that the rotations necessary to take the eye from a reference orientation to all other orientations adopted are about axes that lie in a plane (Listing's law). 2. The three-dimensional orientations of the static eyes, head, and chest were measured after each gaze shift to a visual target, the targets having been fixed at positions ranging from 0 to 135 degrees to the left and right of center and 45 degrees up and down. These measurements were taken of seven human subjects by means of the search coil technique with coils attached to the sternum, head, and right eye. Orientations were plotted as quaternion vectors so that those orientations obeying Donders' law formed a surface and those obeying Listing's law formed a plane. 3. The orientations adopted by the eye, head, and chest were found to be a small subset of those possible under the biomechanical and task-imposed constraints. Thus there is a neurally implemented restriction, specifically of the rotation of the eye relative to space (i.e., the orientation variable es) and to the head (eh); also of the rotation of the head relative to space (hs) and to the chest (hc), and the rotation of the chest relative to space (cs). Plotted as quaternion vectors, the data for each orientation variable formed a characteristic surfacelike shape. In the case of es, hs, and hc these were twisted surfaces, whereas for eh the surface was planar and for cs it was nearly linear. Thus to a first approximation each of the orientation variables conformed to Donders' law. 4. The eye adopted a pointing (gaze) direction that has the ratio of vertical to horizontal components generally greater than one when fixating each of the corner targets. The chest, by contrast, moved almost entirely in the horizontal direction, whereas the head performed an intermediate role. 5. The es-, hs-, and hc-fitted surfaces and cs-fitted lines were titled remarkably little from the vertical axis (i.e., the gravity direction) despite larger tilts being possible.(ABSTRACT TRUNCATED AT 400 WORDS)

Adult↗
PubMed1994

Head position dependent adjustment of the three-dimensional human vestibuloocular reflex.

We studied the influence of static head position relative to the rotation axis on the three-dimensional (3-D) vestibuloocular reflex (VOR). By means of a 3-D rotating chair and a 3-D magnetic search-coil system, eye movements were recorded in 6 normal human subjects during sinusoidal rotation about an earth-vertical axis (yaw) with the head positioned at different pitch angles and about an earth-horizontal axis (pitch) with the head positioned at different yaw angles. We confirmed that torsional VOR gain is about 2/3 of horizontal and vertical VOR gain leading to non-collinear axes of eye and head rotation whenever torsional head movement components were present with eye movement axes tilting away from the torsional direction. Despite this non-collinearity of stimulus and eye movement rotation axes there was close to perfect adjustment of the different VOR components depending on the angle between gaze direction and stimulation axis, indicating a vectorial summation of gains obtained for rotations in the major body axes (roll, pitch and yaw). The horizontal and vertical eye movement components followed a cosine function of the angle between the plane of rotation and gaze direction. The torsional component followed a sine function.

Adult↗
PubMed1993

The influence of gravity on vestibular nystagmus in humans.

Traditionally the human vestibular system is tested by accelerations and decelerations in a rotating chair, stimulating the horizontal semicircular canals. This kind of testing provides no information about the performance or the two pairs of vertical (anterior and posterior) canals and the two pairs of otoliths. Testing the vestibulo-ocular reflex (VOR) in its entirety requires rotations around the 3 axis of the head (yaw, pitch and roll) as well as rotations where the axis is not aligned with gravity. The data presented here are, to our knowledge, the first measurements of the VOR in normal humans obtained with 3-dimensional high resolution recording techniques.

Eye Movements↗
PubMed1992

The influence of head position and head reorientation on the axis of eye rotation and the vestibular time constant during postrotatory nystagmus.

Reorienting the head with respect to gravity during the postrotatory period alters the time course of postrotatory nystagmus (PRN), hastening its decline and thereby reducing the calculated vestibular time constant. One explanation for this phenomenon is that the head reorientation results in a corresponding reorientation of the axis of eye rotation with respect to head coordinates. This possibility was investigated in 10 human subjects whose eye movements were monitored with a three-dimensional magnetic field - search - coil technique using a variety of head reorientation paradigms in a randomized order during PRN following the termination of a 90 degrees/s rotation about earth vertical. Average eye velocities were calculated over two time intervals: from 1 s to 2 s and from 7 s to 8 s after cessation of head rotation. The time constant was estimated as one third of the duration of PRN. For most conditions, a reorientation of the head with respect to gravity 2 s after the rotation had stopped did not significantly alter the direction of the eye velocity vector of PRN with respect to head coordinates. This strongly indicates that, in humans, PRN is mainly stabilized in head coordinates and not in space coordinates, even if the otolith input changes. This finding invalidates the notion that the shortening of PRN due to reorientation of the head could be due to a change of the eye velocity vector towards a direction (torsion), which is not detectable with the eye recording methods (electrooculography) used in earlier studies.(ABSTRACT TRUNCATED AT 250 WORDS)

Adult↗
PubMed1992

Three-dimensional properties of human pursuit eye movements.

For any given location and velocity of a point target, there are infinitely many different eye velocities that the pursuit system could use to track the target perfectly. Three-dimensional recordings of eye position and velocity in 8 normal human subjects showed that the system chooses the unique tracking velocity that keeps eye position vectors (a particular mathematical representation of three-dimensional eye orientation) confined to a single plane, i.e. pursuit obeys Listing's law. One advantage of this strategy over other possible ones, such as choosing the smallest eye velocity compatible with perfect tracking, is that it permits continuous pursuit without accumulation of ocular torsion. For nonpoint targets, there is at most one eye velocity compatible with perfect retinal image stabilisation, and the optimal velocity may not fit Listing's law; we observed small but consistent deviations from the law during pursuit of rotating line targets.

Adult↗
PubMed1990

Computing three-dimensional eye position quaternions and eye velocity from search coil signals.

The four-component rotational operators called quaternions, which represent eye rotations in terms of their axes and angles, have several advantages over other representations of eye position (such as Fick coordinates): they provide easy computations, symmetry, a simple form for Listing's law, and useful three-dimensional plots of eye movements. In this paper we present algorithms for computing eye position quaternions and eye angular velocity (not the derivative of position in three dimensions) from two search coils (not necessarily orthogonal) on one eye in two or three magnetic fields, and for locating primary position using quaternions. We show how differentiation of eye position signals yields poor estimates of all three components of eye velocity.

Adult↗
PubMed1990

Geometric relations of eye position and velocity vectors during saccades.

Measurements of angular position and velocity vectors of the eye in three human and three monkey subjects showed that: (1) position vectors lie roughly in a single plane, in accordance with Listing's law, between and during saccades; (2) primary position of the eye is often far from the centre of the oculomotor range. (3) saccades have nearly-fixed rotation axes, which tilt out of Listing's plane in a systematic way depending on current eye position. Findings 1 and 3 show that saccadic control signals accurately reflect the properties of three-dimensional rotations, as predicted by a new quaternion model of the saccadic system; models that approximate rotational kinematics using vectorial addition and integration do not predict these findings.

Adult↗
PubMed1988

A matrix analysis for a conjugate vestibulo-ocular reflex.

The technique of matrix analysis is used to compare the connectivity between vestibular neurons and oculomotor neurons of the two eyes that would generate a conjugate vestibulo-ocular reflex (VOR). The technique shows that the connectivity is normally anatomically symmetric. The technique is also used to determine the types and loci of adaptation within the VOR that will maintain conjugacy. Adaptation is divided into 1) that evoked by changes in visual feedback, which requires VOR or system-specific changes and 2) that produced by changes in the canals or muscles, which requires deficit-specific adaptation. In the former case, the adaptation could best be achieved by an additive alteration of the vestibular-motoneuron projections. In the latter case, the appropriate adaptations would be serial, multiplicative changes, applied at the level of the vestibular neurons when the canals are at fault or at the level of the motoneurons of the eye whose muscles are impaired. The analysis thus suggests multiple loci of plasticity within the VOR, specialized for adapting to different deficits.

Adaptation, Physiological↗
PubMed1987

Implications of rotational kinematics for the oculomotor system in three dimensions.

1. This paper develops three-dimensional models for the vestibuloocular reflex (VOR) and the internal feedback loop of the saccadic system. The models differ qualitatively from previous, one-dimensional versions, because the commutative algebra used in previous models does not apply to the three-dimensional rotations of the eye. 2. The hypothesis that eye position signals are generated by an eye velocity integrator in the indirect path of the VOR must be rejected because in three dimensions the integral of angular velocity does not specify angular position. Computer simulations using eye velocity integrators show large, cumulative gaze errors and post-VOR drift. We describe a simple velocity to position transformation that works in three dimensions. 3. In the feedback control of saccades, eye position error is not the vector difference between actual and desired eye positions. Subtractive feedback models must continuously adjust the axis of rotation throughout a saccade, and they generate meandering, dysmetric gaze saccades. We describe a multiplicative feedback system that solves these problems and generates fixed-axis saccades that accord with Listing's law. 4. We show that Listing's law requires that most saccades have their axes out of Listing's plane. A corollary is that if three pools of short-lead burst neurons code the eye velocity command during saccades, the three pools are not yoked, but function independently during visually triggered saccades. 5. In our three-dimensional models, we represent eye position using four-component rotational operators called quaternions. This is not the only algebraic system for describing rotations, but it is the one that best fits the needs of the oculomotor system, and it yields much simpler models than do rotation matrix or other representations. 6. Quaternion models predict that eye position is represented on four channels in the oculomotor system: three for the vector components of eye position and one inversely related to gaze eccentricity and torsion. 7. Many testable predictions made by quaternion models also turn up in models based on other mathematics. These predictions are therefore more fundamental than the specific models that generate them. Among these predictions are 1) to compute eye position in the indirect path of the VOR, eye or head velocity signals are multiplied by eye position feedback and then integrated; consequently 2) eye position signals and eye or head velocity signals converge on vestibular neurons, and their interaction is multiplicative.(ABSTRACT TRUNCATED AT 400 WORDS)

Computer Simulation↗
PubMed1986

A reexamination of the gain of the vestibuloocular reflex.

The properties of the vestibuloocular reflex (VOR) when the axis of rotation is behind the eyes and fixation of a near target is required were studied in the monkey. The magnitude of VOR gain in each eye was found to be above 1.0 and near the ideal value for stabilizing a retinal image. Evidence that this large VOR gain was not visually mediated was provided by the observations that no reduction in gain and no phase lag were observed at high frequencies of head rotation (2 Hz), large gain was observed in the dark, and large gain was observed within 10-20 ms of the start of head rotation. The magnitude of VOR gain was found to increase with increasing radius of head rotation and also to increase with decreasing target distance. When the distances from the two eyes to the target were different the instantaneous velocities and VOR gains of the eyes were also different. The dependence on radius of rotation indicates that the VOR is mediated by a combination of otolith and canal inputs. A general model for otolith-canal interaction is proposed in which VOR gain is based on a computation of target location relative to the head. This model simplifies to the classical VOR reflex when a cyclopean eye is subjected only to angular displacement.

Adaptation, Ocular↗
PubMed1985

A two dimensional model for saccade generation.

A model for the generation of oblique saccades is constructed by extending and modifying the one dimensional local feedback model. It is proposed that the visual system stores target location in inertial coordinates, but that the feedback loop which guides saccades works in retinotopic coordinates. To achieve straight trajectories for centripetal and centrifugal saccades in all meridians, a comparator computes motor error as a vector and uses the vectorial error signal to drive two orthogonally-acting burst generators. The generation of straight saccade trajectories when the extraocular muscles are of unequal strengths requires the introduction of a burst-tonic cell input to motor neurons. The model accounts for the results of two-site stimulation of the superior colliculus and frontal eye fields by allowing simultaneous activation of more than one comparator. The postulated existence of multiple comparators suggests that motor error may be computed topographically.

Animals↗