Geometric relations of eye position and velocity vectors during saccades

doi:10.1016/0042-6989(90)90131-4

Vision Research

Volume 30, Issue 1, 1990, Pages 111-127

https://doi.org/10.1016/0042-6989(90)90131-4 Get rights and content

Abstract

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.

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Citation Excerpt :
However, this is not true for saccades, because saccadic eye movements from the primary position do not have torsional components and only have horizontal and vertical components (Listing’s law) (Helmholtz, 1867). Listing’s law holds during fixation, saccades, and smooth pursuit, but not during VOR and rapid eye movement sleep (Tweed and Vilis, 1990; Haslwaner et al., 1991; Tweed et al., 1992) (see an excellent review of van Opstal (1998) for 3D eye movements). The crucial feature of vertical saccade, when compared to horizontal saccade, is as follows.
Sensory signals for eye movements (visual and vestibular) are initially coded in different frames of reference but finally translated into common coordinates, and share the same final common pathway, namely the same population of extraocular motoneurons. From clinical studies in humans and lesion studies in animals, it is generally accepted that voluntary saccadic eye movements are organized in horizontal and vertical Cartesian coordinates. However, this issue is not settled yet, because neural circuits for vertical saccades remain unidentified. We recently determined brainstem neural circuits from the superior colliculus to ocular motoneurons for horizontal and vertical saccades with combined electrophysiological and neuroanatomical techniques. Comparing well-known vestibuloocular pathways with our findings of commissural excitation and inhibition between both superior colliculi, we proposed that the saccade system uses the same frame of reference as the vestibuloocular system, common semicircular canal coordinate. This proposal is mainly based on marked similarities (1) between output neural circuitry from one superior colliculus to extraocular motoneurons and that from a respective canal to its innervating extraocular motoneurons, (2) of patterns of commissural reciprocal inhibitions between upward saccade system on one side and downward system on the other, and between anterior canal system on one side and posterior canal system on the other, and (3) between the neural circuits of saccade and quick phase of vestibular nystagmus sharing brainstem burst neurons. In support of the proposal, commissural excitation of the superior colliculi may help to maintain Listing’s law in saccades in spite of using semicircular canal coordinate.
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In previous work, we showed that two degree of freedom oscillators can be advantageously applied to horological time bases since they can be used to eliminate the escapement mechanism. We subsequently examined planar two degree of freedom oscillators based on parallel flexure stages. We noted that these oscillators are strongly affected by the orientation of gravity so are not directly suitable for portable timekeepers such as wristwatches. In this paper we examine the design and performance of two degree of freedom spherical oscillators. By spherical oscillator, we mean a spherical mass having purely rotational kinematics and subject to elastic restoring torque. As opposed to our previously examined oscillators, the oscillation period of spherical oscillators is relatively insensitive to the effect of tilting the mechanism in the presence of gravity. In order to restrict spherical rotation to two degrees of freedom, we restrict the kinematics to obey Listing's law, a well-known constraint occurring in human eye movement. We show that a particular central restoring force we call the scissors law is best suited for chronometric performance and propose a number of theoretical mechanisms producing it. We then design an actual spherical oscillator based on our theoretical results. The design uses flexure springs to restrict kinematics to Listing's law, produce the scissors law and provide the necessary suspension. Finally, we present experimental data based on a physical realization indicating promising chronometric performance.
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Geometric relations of eye position and velocity vectors during saccades

Abstract

Vector and tensor analysis

Beitrag zur Lehre von den Bewegungen des menschlichen Auges

Human gaze stability in the horizontal, vertical and torsional direction during voluntary head movements, evaluated with a three-dimensional scleral induction coil technique

Vision Research

A direct test of Listing's law—I. Human ocular torsion in static tertiary positions

Vision Research

A direct test of Listing's law—II. Human ocular torsion measured under dynamic conditions

Vision Research

Treatise on physiological optics

On the generation of rapid eye movements in three dimensions

Die Lehre vom Binocularen Sehen

Reticular control of vertical saccadic eye movements by mesencephalic burst neurons

Journal of Neurophysiology

Vertical eye movement-related responses of neurons in midbrain near interstitial nucleus of Cajal

Journal of Neurophysiology