Modeling three-dimensional velocity-to-position transformation in oculomotor control

1994 ◽  
Vol 71 (2) ◽  
pp. 623-638 ◽  
Author(s):  
C. Schnabolk ◽  
T. Raphan
Keyword(s):  
Dynamical System ◽  
Eye Movements ◽  
Orientation Relationship ◽  
Shortest Path ◽  
Three Dimensional ◽  
Three Dimensions ◽  
Oculomotor Control ◽  
Applied Torque ◽  
Orbital Tissue ◽  
Primary Orientation

1. A considerable amount of attention has been devoted to understanding the velocity-position transformation that takes place in the control of eye movements in three dimensions. Much of the work has focused on the idea that rotations in three dimensions do not commute and that a "multiplicative quaternion model" of velocity-position integration is necessary to explain eye movements in three dimensions. Our study has indicated that this approach is not consistent with the physiology of the types of signals necessary to rotate the eyes. 2. We developed a three-dimensional dynamical system model for movement of the eye within its surrounding orbital tissue. The main point of the model is that the eye muscles generate torque to rotate the eye. When the eye reaches an orientation such that the restoring torque of the orbital tissue counterbalances the torque applied by the muscles, a unique equilibrium point is reached. The trajectory of the eye to reach equilibrium may follow any path, depending on the starting eye orientation and eye velocity. However, according to Euler's theorem, the equilibrium reached is equivalent to a rotation about a fixed axis through some angle from a primary orientation. This represents the shortest path that the eye could take from the primary orientation in reaching equilibrium. Consequently, it is also the shortest path for returning the eye to the primary orientation. Thus the restoring torque developed by the tissue surrounding the eye was approximated as proportional to the product of this angle and a unit vector along this axis. The relationship between orientation and restoring torque gives a unique torque-orientation relationship. 3. Once the appropriate torque-orientation relationship for eye rotation is established the velocity-position integrator can be modeled as a dynamical system that is a direct extension of the one-dimensional velocity-position integrator. The linear combination of the integrator state and a direct pathway signal is converted to a torque signal that activates the muscles to rotate the eyes. Therefore the output of the integrator is related to a torque signal that positions the eyes. It is not an eye orientation signal. The applied torque signal drives the eye to an equilibrium orientation such that the restoring torque equals the applied torque but in the opposite direction. The eye orientation reached at equilibrium is determined by the unique torque-orientation relation. Because torque signals are vectors, they commute.(ABSTRACT TRUNCATED AT 400 WORDS)

Monkey superior colliculus represents rapid eye movements in a two-dimensional motor map

1993 ◽  
Vol 69 (3) ◽  
pp. 965-979 ◽  
Author(s):  
K. Hepp ◽  
A. J. Van Opstal ◽  
D. Straumann ◽  
B. J. Hess ◽  
V. Henn
Keyword(s):  
Eye Movements ◽  
Superior Colliculus ◽  
Degrees Of Freedom ◽  
Three Dimensional ◽  
Three Dimensions ◽  
Eye Position ◽  
Two Dimensional ◽  
Vestibular Nystagmus ◽  
Rapid Eye Movements ◽  
Q Model

1. Although the eye has three rotational degrees of freedom, eye positions, during fixations, saccades, and smooth pursuit, with the head stationary and upright, are constrained to a plane by ListingR's law. We investigated whether Listing's law for rapid eye movements is implemented at the level of the deeper layers of the superior colliculus (SC). 2. In three alert rhesus monkeys we tested whether the saccadic motor map of the SC is two dimensional, representing oculocentric target vectors (the vector or V-model), or three dimensional, representing the coordinates of the rotation of the eye from initial to final position (the quaternion or Q-model). 3. Monkeys made spontaneous saccadic eye movements both in the light and in the dark. They were also rotated about various axes to evoke quick phases of vestibular nystagmus, which have three degrees of freedom. Eye positions were measured in three dimensions with the magnetic search coil technique. 4. While the monkey made spontaneous eye movements, we electrically stimulated the deeper layers of the SC and elicited saccades from a wide range of initial positions. According to the Q-model, the torsional component of eye position after stimulation should be uniquely related to saccade onset position. However, stimulation at 110 sites induced no eye torsion, in line with the prediction of the V-model. 5. Activity of saccade-related burst neurons in the deeper layers of the SC was analyzed during rapid eye movements in three dimensions. No systematic eye-position dependence of the movement fields, as predicted by the Q-model, could be detected for these cells. Instead, the data fitted closely the predictions made by the V-model. 6. In two monkeys, both SC were reversibly inactivated by symmetrical bilateral injections of muscimol. The frequency of spontaneous saccades in the light decreased dramatically. Although the remaining spontaneous saccades were slow, Listing's law was still obeyed, both during fixations and saccadic gaze shifts. In the dark, vestibularly elicited fast phases of nystagmus could still be generated in three dimensions. Although the fastest quick phases of horizontal and vertical nystagmus were slower by about a factor of 1.5, those of torsional quick phases were unaffected. 7. On the basis of the electrical stimulation data and the properties revealed by the movement field analysis, we conclude that the collicular motor map is two dimensional. The reversible inactivation results suggest that the SC is not the site where three-dimensional fast phases of vestibular nystagmus are generated.(ABSTRACT TRUNCATED AT 400 WORDS)

The Brain Stem Saccadic Burst Generator Encodes Gaze in Three-Dimensional Space

2008 ◽  
Vol 99 (5) ◽  
pp. 2602-2616 ◽  
Author(s):  
Marion R. Van Horn ◽  
Pierre A. Sylvestre ◽  
Kathleen E. Cullen
Keyword(s):  
Eye Movements ◽  
Brain Stem ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Saccadic Eye Movements ◽  
Three Dimensions ◽  
Related Information ◽  
Computer Based ◽  
Different Depths ◽  
The Brain

When we look between objects located at different depths the horizontal movement of each eye is different from that of the other, yet temporally synchronized. Traditionally, a vergence-specific neuronal subsystem, independent from other oculomotor subsystems, has been thought to generate all eye movements in depth. However, recent studies have challenged this view by unmasking interactions between vergence and saccadic eye movements during disconjugate saccades. Here, we combined experimental and modeling approaches to address whether the premotor command to generate disconjugate saccades originates exclusively in “vergence centers.” We found that the brain stem burst generator, which is commonly assumed to drive only the conjugate component of eye movements, carries substantial vergence-related information during disconjugate saccades. Notably, facilitated vergence velocities during disconjugate saccades were synchronized with the burst onset of excitatory and inhibitory brain stem saccadic burst neurons (SBNs). Furthermore, the time-varying discharge properties of the majority of SBNs (>70%) preferentially encoded the dynamics of an individual eye during disconjugate saccades. When these experimental results were implemented into a computer-based simulation, to further evaluate the contribution of the saccadic burst generator in generating disconjugate saccades, we found that it carries all the vergence drive that is necessary to shape the activity of the abducens motoneurons to which it projects. Taken together, our results provide evidence that the premotor commands from the brain stem saccadic circuitry, to the target motoneurons, are sufficient to ensure the accurate control shifts of gaze in three dimensions.

Quick phases control ocular torsion during smooth pursuit

2011 ◽  
Vol 106 (5) ◽  
pp. 2151-2166 ◽  
Author(s):  
Bernhard J. M. Hess ◽  
Jakob S. Thomassen
Keyword(s):  
Eye Movements ◽  
Visual Field ◽  
Rotation Axis ◽  
Three Dimensional ◽  
Oculomotor Control ◽  
Visually Guided ◽  
Open Questions ◽  
Spatial Frequencies ◽  
Eye Rotation ◽  
Smooth Tracking

One of the open questions in oculomotor control of visually guided eye movements is whether it is possible to smoothly track a target along a curvilinear path across the visual field without changing the torsional stance of the eye. We show in an experimental study of three-dimensional eye movements in subhuman primates ( Macaca mulatta) that although the pursuit system is able to smoothly change the orbital orientation of the eye's rotation axis, the smooth ocular motion was interrupted every few hundred milliseconds by a small quick phase with amplitude <1.5° while the animal tracked a target along a circle or ellipse. Specifically, during circular pursuit of targets moving at different angular eccentricities (5°, 10°, and 15°) relative to straight ahead at spatial frequencies of 0.067 and 0.1 Hz, the torsional amplitude of the intervening quick phases was typically around 1° or smaller and changed direction for clockwise vs. counterclockwise tracking. Reverse computations of the eye rotation based on the recorded angular eye velocity showed that the quick phases facilitate the overall control of ocular orientation in the roll plane, thereby minimizing torsional disturbances of the visual field. On the basis of a detailed kinematic analysis, we suggest that quick phases during curvilinear smooth tracking serve to minimize deviations from Donders' law, which are inevitable due to the spherical configuration space of smooth eye movements.

Three-Dimensional Shortest Path Planning in the Presence of Polyhedral Obstacles

1996 ◽  
Vol 210 (4) ◽  
pp. 373-381 ◽  
Author(s):  
K Jiang ◽  
L D Seneviratne ◽  
S W E Earles
Keyword(s):  
Computational Complexity ◽  
Path Planning ◽  
Shortest Path ◽  
Turning Points ◽  
Three Dimensional ◽  
Two Dimensions ◽  
Visibility Graph ◽  
Three Dimensions ◽  
View Point ◽  
Polyhedral Obstacles

A new algorithm is presented for solving the three-dimensional shortest path planning (3DSP) problem for a point object moving among convex polyhedral obstacles. It is the first non-approximate three-dimensional path planing algorithm that can deal with more than two polyhedral obstacles. The algorithm extends the visibility graph concept from two dimensions to three dimensions. The two main problems with 3DSP are identifying the edge sequence the shortest path passes through and the turning points of the shortest path. A technique based on projective relationships is presented for identifying the set of visible boundary edges (VBE) corresponding to a given view point over which the shortest path, from the view point to the goal, will pass. VBE are used to construct an initial reduced visibility graph (RVG). Optimization is used to revise the position of the turning points and hence the three-dimensional RVG (3DRVG) and the global shortest path is then selected from the 3DRVG. The algorithm is of computational complexity O(n3vk), where n is the number of verticles, v is the maximum number of vertices on any one obstacle and k is the number of obstacles. The algorithm is applicable only with polyhedral obstacles, as the theorems developed for searching for the turning points of the three-dimensional shortest path are based on straight edges of the obstacles. It needs to be further developed for dealing with arbitrary-shaped obstacles and this would increase the computational complexity. The algorithm is tested using computer simulations and some results are presented.

An Efficient Algorithm for Shortest Path in Three Dimensions With Polyhedral Obstacles

1989 ◽  
Vol 111 (3) ◽  
pp. 433-436 ◽  
Author(s):  
J. Khouri ◽  
K. A. Stelson
Keyword(s):  
Shortest Path ◽  
Efficient Algorithm ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Three Dimensions ◽  
Minimum Length ◽  
Precise Location ◽  
Computer Storage ◽  
Polyhedral Obstacles ◽  
Three Dimensional Space

An algorithm to find the shortest path between two specified points in three-dimensional space in the presence of polyhedral obstacles is described. The proposed method iterates for the precise location of the minimum length path on a given sequence of edges on the obstacles. The iteration procedure requires solving a tri-diagonal matrix at each step. Both the computer storage and the number of computations are proportional to n, the number of edges in the sequence. The algorithm is stable and converges for the general case of any set of lines, intersecting, parallel or skew.

Three Dimensional Eye Movements of Squirrel Monkeys Following Postrotatory Tilt

1993 ◽  
Vol 3 (2) ◽  
pp. 123-139 ◽  
Author(s):  
Daniel M. Merfeld ◽  
Laurence R. Young ◽  
Gary D. Paige ◽  
David L. Tomko
Keyword(s):  
Eye Movements ◽  
Time Course ◽  
Three Dimensional ◽  
Three Dimensions ◽  
Head Orientation ◽  
Ocular Reflex ◽  
Eye Rotation ◽  
Acceleration And Deceleration ◽  
Vestibulo Ocular Reflex ◽  
Vertical Nystagmus

Three-dimensional squirrel monkey eye movements were recorded during and immediately following rotation around an earth-vertical yaw axis (160∘/s steady state, 100∘/s2 acceleration and deceleration). To study interactions between the horizontal angular vestibulo-ocular reflex (VOR) and head orientation, postrotatory VOR alignment was changed relative to gravity by tilting the head out of the horizontal plane (pitch or roll tilt between 15∘ and 90∘) immediately after cessation of motion. Results showed that in addition to post rotatory horizontal nystagmus, vertical nystagmus followed tilts to the left or right (roll), and torsional nystagmus followed forward or backward (pitch) tilts. When the time course and spatial orientation of eye velocity were considered in three dimensions, the axis of eye rotation always shifted toward alignment with gravity, and the postrotatory horizontal VOR decay was accelerated by the tilts. These phenomena may reflect a neural process that resolves the sensory conflict induced by this postrotatory tilt paradigm.

convergent-beam diffraction from surfaces

1987 ◽  
Vol 45 ◽  
pp. 30-33
Author(s):  
J. A. Eades ◽  
A. E. Smith ◽  
D. F. Lynch
Keyword(s):  
Reciprocal Lattice ◽  
Three Dimensional ◽  
Grazing Incidence ◽  
Three Dimensions ◽  
Plane Figure ◽  
Transmission Electron ◽  
Convergent Beam ◽  
Beam Patterns ◽  
Beam Diffraction

It is quite simple (in the transmission electron microscope) to obtain convergent-beam patterns from the surface of a bulk crystal. The beam is focussed onto the surface at near grazing incidence (figure 1) and if the surface is flat the appropriate pattern is obtained in the diffraction plane (figure 2). Such patterns are potentially valuable for the characterization of surfaces just as normal convergent-beam patterns are valuable for the characterization of crystals.There are, however, several important ways in which reflection diffraction from surfaces differs from the more familiar electron diffraction in transmission.GeometryIn reflection diffraction, because of the surface, it is not possible to describe the specimen as periodic in three dimensions, nor is it possible to associate diffraction with a conventional three-dimensional reciprocal lattice.

Tire Modeling by Finite Elements

1992 ◽  
Vol 20 (1) ◽  
pp. 33-56 ◽  
Author(s):  
L. O. Faria ◽  
J. T. Oden ◽  
B. Yavari ◽  
W. W. Tworzydlo ◽  
J. M. Bass ◽  
...  
Keyword(s):  
Three Dimensional ◽  
Rolling Contact ◽  
Test Problems ◽  
State Behavior ◽  
Normal Contact ◽  
New Developments ◽  
Applied Torque ◽  
Dimensional Finite Element ◽  
Tire Modeling ◽  
Three Dimensional Finite Element

Abstract Recent advances in the development of a general three-dimensional finite element methodology for modeling large deformation steady state behavior of tire structures is presented. The new developments outlined here include the extension of the material modeling capabilities to include viscoelastic materials and a generalization of the formulation of the rolling contact problem to include special nonlinear constraints. These constraints include normal contact load, applied torque, and constant pressure-volume. Several new test problems and examples of tire analysis are presented.

Extension of the Spatial PDI Model to Three Dimensions

1997 ◽  
Vol 84 (1) ◽  
pp. 176-178
Author(s):  
Frank O'Brien
Keyword(s):  
Population Density ◽  
Dimensional Space ◽  
Finite Lattice ◽  
Three Dimensional ◽  
Upper Bounds ◽  
Three Dimensions ◽  
Lower And Upper Bounds ◽  
Density Index ◽  
Three Dimensional Space

The author's population density index ( PDI) model is extended to three-dimensional distributions. A derived formula is presented that allows for the calculation of the lower and upper bounds of density in three-dimensional space for any finite lattice.

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