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

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.

Download Full-text

Visual-Motor Transformations Required for Accurate and Kinematically Correct Saccades

Journal of Neurophysiology ◽

10.1152/jn.1997.78.3.1447 ◽

1997 ◽

Vol 78 (3) ◽

pp. 1447-1467 ◽

Cited By ~ 65

Author(s):

J. Douglas Crawford ◽

Daniel Guitton

Keyword(s):

Reference Frame ◽

Eye Position ◽

Target Displacement ◽

Listing's Law ◽

Listing's Plane ◽

Listing’S Law ◽

Reference Frame Transformation ◽

Visual Motor ◽

Frame Transformation ◽

Listing’S Plane

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.

Download Full-text

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.

Download Full-text

Implications of rotational kinematics for the oculomotor system in three dimensions

Journal of Neurophysiology ◽

10.1152/jn.1987.58.4.832 ◽

1987 ◽

Vol 58 (4) ◽

pp. 832-849 ◽

Cited By ~ 181

Author(s):

D. Tweed ◽

T. Vilis

Keyword(s):

Three Dimensional ◽

Oculomotor System ◽

Three Dimensions ◽

Eye Position ◽

Head Velocity ◽

Listing’S Law ◽

Indirect Path ◽

Dimensional Models ◽

Three Dimensional Models ◽

Eye Velocity

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)

Download Full-text

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

Download Full-text

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.

Download Full-text

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.

Download Full-text