Visual-Motor Transformations Required for Accurate and Kinematically Correct Saccades

Crawford, J. Douglas and Daniel Guitton. Visual-motor transformations required for accurate and kinematically correct saccades. J. Neurophysiol. 78: 1447–1467, 1997. The goal of this study was to identify and model the three-dimensional (3-D) geometric transformations required for accurate saccades to distant visual targets from arbitrary initial eye positions. In abstract 2-D models, target displacement in space, retinal error (RE), and saccade vectors are trivially interchangeable. However, in real 3-D space, RE is a nontrivial function of objective target displacement and 3-D eye position. To determine the physiological implications of this, a visuomotor “lookup table” was modeled by mapping the horizontal/vertical components of RE onto the corresponding vector components of eye displacement in Listing's plane. This provided the motor error (ME) command for a 3-D displacement-feedback loop. The output of this loop controlled an oculomotor plant that mechanically implemented the position-dependent saccade axis tilts required for Listing's law. This model correctly maintained Listing's law but was unable to correct torsional position deviations from Listing's plane. Moreover, the model also generated systematic errors in saccade direction (as a function of eye position components orthogonal to RE), predicting errors in final gaze direction of up to 25° in the oculomotor range. Plant modifications could not solve these problems, because the intrisic oculomotor input-output geometry forced a fixed visuomotor mapping to choose between either accuracy or Listing's law. This was reflected internally by a sensorimotor divergence between input-defined visual displacement signals (inherently 2-D and defined in reference to the eye) and output-defined motor displacement signals (inherently 3-D and defined in reference to the head). These problems were solved by rotating RE by estimated 3-D eye position (i.e., a reference frame transformation), inputting the result into a 2-D–to–3-D “Listing's law operator,” and then finally subtracting initial 3-D eye position to yield the correct ME. This model was accurate and upheld Listing's law from all initial positions. Moreover, it suggested specific experiments to invasively distinguish visual and motor displacement codes, predicting a systematic position dependence in the directional tuning of RE versus a fixed-vector tuning in ME. We conclude that visual and motor displacement spaces are geometrically distinct such that a fixed visual-motor mapping will produce systematic and measurable behavioral errors. To avoid these errors, the brain would need to implement both a 3-D position-dependent reference frame transformation and nontrivial 2-D–to–3-D transformation. Furthermore, our simulations provide new experimental paradigms to invasively identify the physiological progression of these spatial transformations by reexamining the position-dependent geometry of displacement code directions in the superior colliculus, cerebellum, and various cortical visuomotor areas.

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Human Oculomotor System Accounts for 3-D Eye Orientation in the Visual-Motor Transformation for Saccades

Journal of Neurophysiology ◽

10.1152/jn.1998.80.5.2274 ◽

1998 ◽

Vol 80 (5) ◽

pp. 2274-2294 ◽

Cited By ~ 45

Author(s):

Eliana M. Klier ◽

J. Douglas Crawford

Keyword(s):

Reference Frame ◽

Oculomotor System ◽

Gaze Direction ◽

Eye Position ◽

Look Up Table ◽

Listing's Law ◽

Listing’S Law ◽

Reference Frame Transformation ◽

Visual Motor ◽

Frame Transformation

Klier, Eliana M. and J. Douglas Crawford. Human oculomotor system accounts for 3-D eye orientation in the visual-motor transformation for saccades. J. Neurophysiol. 80: 2274–2294, 1998. A recent theoretical investigation has demonstrated that three-dimensional (3-D) eye position dependencies in the geometry of retinal stimulation must be accounted for neurally (i.e., in a visuomotor reference frame transformation) if saccades are to be both accurate and obey Listing's law from all initial eye positions. Our goal was to determine whether the human saccade generator correctly implements this eye-to-head reference frame transformation (RFT), or if it approximates this function with a visuomotor look-up table (LT). Six head-fixed subjects participated in three experiments in complete darkness. We recorded 60° horizontal saccades between five parallel pairs of lights, over a vertical range of ±40° ( experiment 1), and 30° radial saccades from a central target, with the head upright or tilted 45° clockwise/counterclockwise to induce torsional ocular counterroll, under both binocular and monocular viewing conditions ( experiments 2 and 3). 3-D eye orientation and oculocentric target direction (i.e., retinal error) were computed from search coil signals in the right eye. Experiment 1: as predicted, retinal error was a nontrivial function of both target displacement in space and 3-D eye orientation (e.g., horizontally displaced targets could induce horizontal or oblique retinal errors, depending on eye position). These data were input to a 3-D visuomotor LT model, which implemented Listing's law, but predicted position-dependent errors in final gaze direction of up to 19.8°. Actual saccades obeyed Listing's law but did not show the predicted pattern of inaccuracies in final gaze direction, i.e., the slope of actual error, as a function of predicted error, was only −0.01 ± 0.14 (compared with 0 for RFT model and 1.0 for LT model), suggesting near-perfect compensation for eye position. Experiments 2 and 3: actual directional errors from initial torsional eye positions were only a fraction of those predicted by the LT model (e.g., 32% for clockwise and 33% for counterclockwise counterroll during binocular viewing). Furthermore, any residual errors were immediately reduced when visual feedback was provided during saccades. Thus, other than sporadic miscalibrations for torsion, saccades were accurate from all 3-D eye positions. We conclude that 1) the hypothesis of a visuomotor look-up table for saccades fails to account even for saccades made directly toward visual targets, but rather, 2) the oculomotor system takes 3-D eye orientation into account in a visuomotor reference frame transformation. This transformation is probably implemented physiologically between retinotopically organized saccade centers (in cortex and superior colliculus) and the brain stem burst generator.

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Axes of eye rotation and Listing's law during rotations of the head

Journal of Neurophysiology ◽

10.1152/jn.1991.65.3.407 ◽

1991 ◽

Vol 65 (3) ◽

pp. 407-423 ◽

Cited By ~ 138

Author(s):

J. D. Crawford ◽

T. Vilis

Keyword(s):

Head Rotation ◽

Three Dimensions ◽

Eye Position ◽

Gaze Stabilization ◽

Listing's Law ◽

Listing's Plane ◽

Listing’S Law ◽

Eye Rotation ◽

Indirect Path ◽

Listing’S Plane

1. The vestibuloocular reflex (VOR) was examined in four alert monkeys during rotations of the head about torsional, vertical, horizontal, and intermediate axes. Eye positions and axes were recorded in three dimensions (3-D). Visual targets were used to optimize gaze stabilization. 2. Axes of eye rotation during slow phases showed small but systematic deviations from collinearity with the axes of head rotation. These noncollinearities apparently resulted from vector summation of torsional, vertical, and horizontal VOR components with different gains. 3. VOR gain was lowest about a head-fixed torsional axis that was correlated with the primary gaze direction, as determined by Listing's law for saccades. As a result, rotation of the head about a partially torsional axis produced noncollinear slow phases, with axes that tilted toward Listing's plane. 4. During slow phases, eye position changed not only in the direction of rotation, but also systematically in other directions. Even axes of eye rotation within Listing's plane caused eye position to move out of the plane to a torsional position that was then held. Thus Listing's law for saccades cannot be a product of plant mechanics. 5. VOR slow phases were simulated with the use of a model that incorporated 3-D rotational kinematics into the indirect path and the oculomotor plant. This demonstrated that the observed pattern of position changes is the expected consequence of rotating the eye about a fixed axis and that to hold these positions the indirect path must employ a 3-D velocity-to-position transformation. 6. Quick phases not only corrected the violations of Listing's law produced by slow phases but anticipated them by directing the eye toward a plane rotated in the direction of head rotation. This was modeled by inputting the vestibular signal to a Listing's law operator that is shared by the quick phase and saccadic systems.

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Distributed Population Mechanism for the 3-D Oculomotor Reference Frame Transformation

Journal of Neurophysiology ◽

10.1152/jn.00306.2004 ◽

2005 ◽

Vol 93 (3) ◽

pp. 1742-1761 ◽

Cited By ~ 35

Author(s):

Michael A. Smith ◽

J. Douglas Crawford

Keyword(s):

Brain Stem ◽

Reference Frame ◽

Receptive Fields ◽

Eye Position ◽

The Real ◽

Burst Neurons ◽

Motor Commands ◽

Visual Receptive Fields ◽

Reference Frame Transformation ◽

Frame Transformation

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

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Introduction of Reference-Frame Transformation Through Interactive Simulation

2021 IEEE 25th International Conference on Intelligent Engineering Systems (INES) ◽

10.1109/ines52918.2021.9512905 ◽

2021 ◽

Author(s):

Istvan Halasz ◽

Tamas Orosz ◽

Jozsef Halasz ◽

Arpad Elekes

Keyword(s):

Reference Frame ◽

Interactive Simulation ◽

Reference Frame Transformation ◽

Frame Transformation

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Central Positional Nystagmus Simulated by a Mathematical Ocular Motor Model of Otolith-Dependent Modification of Listing's Plane

Journal of Neurophysiology ◽

10.1152/jn.2001.86.4.1546 ◽

2001 ◽

Vol 86 (4) ◽

pp. 1546-1554 ◽

Cited By ~ 30

Author(s):

S. Glasauer ◽

M. Dieterich ◽

Th. Brandt

Keyword(s):

Eye Movements ◽

Neural Control ◽

Position Control ◽

Three Dimensional ◽

Head Tilt ◽

Eye Position ◽

Positional Nystagmus ◽

Listing's Plane ◽

Head Positions ◽

Listing’S Plane

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

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Three-dimensional visuo-motor control of saccades

Journal of Neurophysiology ◽

10.1152/jn.00513.2012 ◽

2013 ◽

Vol 109 (1) ◽

pp. 183-192 ◽

Cited By ~ 5

Author(s):

Bernhard J. M. Hess

Keyword(s):

Motor Control ◽

Reverse Engineering ◽

Visual Information ◽

Three Dimensional ◽

Engineering Problem ◽

Line Of Sight ◽

Eye Position ◽

Listing's Law ◽

Saccade Onset ◽

Listing’S Law

Although the motion of the line of sight is a straightforward consequence of a particular rotation of the eye, it is much trickier to predict the rotation underlying a particular motion of the line of sight in accordance with Listing's law. Helmholtz's notion of the direction-circle together with the notion of primary and secondary reference directions in visual space provide an elegant solution to this reverse engineering problem, which the brain is faced with whenever generating a saccade. To test whether these notions indeed apply for saccades, we analyzed three-dimensional eye movements recorded in four rhesus monkeys. We found that on average saccade trajectories closely matched with the associated direction-circles. Torsional, vertical, and horizontal eye position of saccades scattered around the position predicted by the associated direction-circles with standard deviations of 0.5°, 0.3°, and 0.4°, respectively. Comparison of saccade trajectories with the likewise predicted fixed-axis rotations yielded mean coefficients of determinations (±SD) of 0.72 (±0.26) for torsion, 0.97 (±0.10) for vertical, and 0.96 (±0.11) for horizontal eye position. Reverse engineering of three-dimensional saccadic rotations based on visual information suggests that motor control of saccades, compatible with Listing's law, not only uses information on the fixation directions at saccade onset and offset but also relies on the computation of secondary reference positions that vary from saccade to saccade.

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Kinematic Principles of Primate Rotational Vestibulo-Ocular Reflex II. Gravity-Dependent Modulation of Primary Eye Position

Journal of Neurophysiology ◽

10.1152/jn.1997.78.4.2203 ◽

1997 ◽

Vol 78 (4) ◽

pp. 2203-2216 ◽

Cited By ~ 21

Author(s):

Bernhard J. M. Hess ◽

Dora E. Angelaki

Keyword(s):

Slow Phase ◽

Head Orientation ◽

Eye Position ◽

Single Plane ◽

Fast Phase ◽

Ocular Reflex ◽

Listing's Plane ◽

Vestibulo Ocular Reflex ◽

Torsional Component ◽

Listing’S Plane

Hess, Bernhard J. M. and Dora E. Angelaki. Kinematic principles of primate rotational vestibulo-ocular reflex. II. Gravity-dependent modulation of primary eye position. J. Neurophysiol. 78: 2203–2216, 1997. The kinematic constraints of three-dimensional eye positions were investigated in rhesus monkeys during passive head and body rotations relative to gravity. We studied fast and slow phase components of the vestibulo-ocular reflex (VOR) elicited by constant-velocity yaw rotations and sinusoidal oscillations about an earth-horizontal axis. We found that the spatial orientation of both fast and slow phase eye positions could be described locally by a planar surface with torsional variation of <2.0 ± 0.4° (displacement planes) that systematically rotated and/or shifted relative to Listing's plane. In supine/prone positions, displacement planes pitched forward/backward; in left/right ear-down positions, displacement planes were parallel shifted along the positive/negative torsional axis. Dynamically changing primary eye positions were computed from displacement planes. Torsional and vertical components of primary eye position modulated as a sinusoidal function of head orientation in space. The torsional component was maximal in ear-down positions and approximately zero in supine/prone orientations. The opposite was observed for the vertical component. Modulation of the horizontal component of primary eye position exhibited a more complex dependence. In contrast to the torsional component, which was relatively independent of rotational speed, modulation of the vertical and horizontal components of primary position depended strongly on the speed of head rotation (i.e., on the frequency of oscillation of the gravity vector component): the faster the head rotated relative to gravity, the larger was the modulation. Corresponding results were obtained when a model based on a sinusoidal dependence of instantaneous displacement planes (and primary eye position) on head orientation relative to gravity was fitted to VOR fast phase positions. When VOR fast phase positions were expressed relative to primary eye position estimated from the model fits, they were confined approximately to a single plane with a small torsional standard deviation (∼1.4–2.6°). This reduced torsional variation was in contrast to the large torsional spread (well >10–15°) of fast phase positions when expressed relative to Listing's plane. We conclude that primary eye position depends dynamically on head orientation relative to space rather than being fixed to the head. It defines a gravity-dependent coordinate system relative to which the torsional variability of eye positions is minimized even when the head is moved passively and vestibulo-ocular reflexes are evoked. In this general sense, Listing's law is preserved with respect to an otolith-controlled reference system that is defined dynamically by gravity.

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Reference Frames for Reach Planning in Macaque Dorsal Premotor Cortex

Journal of Neurophysiology ◽

10.1152/jn.00421.2006 ◽

2007 ◽

Vol 98 (2) ◽

pp. 966-983 ◽

Cited By ~ 80

Author(s):

Aaron P. Batista ◽

Gopal Santhanam ◽

Byron M. Yu ◽

Stephen I. Ryu ◽

Afsheen Afshar ◽

...

Keyword(s):

Reference Frame ◽

Reference Frames ◽

Premotor Cortex ◽

Visually Guided ◽

Electrode Arrays ◽

Reference Frame Transformation ◽

Frame Transformation ◽

Visual Reference Frame ◽

Reach Planning ◽

The Brain

When a human or animal reaches out to grasp an object, the brain rapidly computes a pattern of muscular contractions that can acquire the target. This computation involves a reference frame transformation because the target's position is initially available only in a visual reference frame, yet the required control signal is a set of commands to the musculature. One of the core brain areas involved in visually guided reaching is the dorsal aspect of the premotor cortex (PMd). Using chronically implanted electrode arrays in two Rhesus monkeys, we studied the contributions of PMd to the reference frame transformation for reaching. PMd neurons are influenced by the locations of reach targets relative to both the arm and the eyes. Some neurons encode reach goals using limb-centered reference frames, whereas others employ eye-centered reference fames. Some cells encode reach goals in a reference frame best described by the combined position of the eyes and hand. In addition to neurons like these where a reference frame could be identified, PMd also contains cells that are influenced by both the eye- and limb-centered locations of reach goals but for which a distinct reference frame could not be determined. We propose two interpretations for these neurons. First, they may encode reach goals using a reference frame we did not investigate, such as intrinsic reference frames. Second, they may not be adequately characterized by any reference frame.

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