Three-dimensional visuo-motor control of saccades

V1 neurons encode the perceptual compensation of false torsion arising from Listing's law

We try to deploy the retinal fovea to optimally scrutinize an object of interest by directing our eyes to it. The horizontal and vertical components of eye positions acquired by goal-directed saccades are determined by the object's location. However, the eccentric eye positions also involve a torsional component, which according to Donder's law is fully determined by the two-dimensional (2D) eye position acquired. According to von Helmholtz, knowledge of the amount of torsion provided by Listing's law, an extension of Donder's law, alleviates the perceptual interpretation of the image tilt that changes with 2D eye position, a view supported by psychophysical experiments he pioneered. We address the question of where and how Listing's law is implemented in the visual system and we show that neurons in monkey area V1 use knowledge of eye torsion to compensate the image tilt associated with specific eye positions as set by Listing's law.

Three-dimensional ocular kinematics underlying binocular single vision

We have analyzed the binocular coordination of the eyes during far-to-near refixation saccades based on the evaluation of distance ratios and angular directions of the projected target images relative to the eyes' rotation centers. By defining the geometric point of binocular single vision, called Helmholtz point, we found that disparities during fixations of targets at near distances were limited in the subject's three-dimensional visual field to the vertical and forward directions. These disparities collapsed to simple vertical disparities in the projective binocular image plane. Subjects were able to perfectly fuse the vertically disparate target images with respect to the projected Helmholtz point of single binocular vision, independent of the particular location relative to the horizontal plane of regard. Target image fusion was achieved by binocular torsion combined with corrective modulations of the differential half-vergence angles of the eyes in the horizontal plane. Our findings support the notion that oculomotor control combines vergence in the horizontal plane of regard with active torsion in the frontal plane to achieve fusion of the dichoptic binocular target images.

The kinematics of far-near re-fixation saccades

We have analyzed the three-dimensional spatiotemporal characteristics of saccadic refixations between far and near targets in three behaviorally trained rhesus monkeys. The kinematics underlying these rapid eye movements can be accurately described by rotations of the eyes in four different planes, namely, first disconjugate rotations in the horizontal plane of regard converging the eyes toward the near target, followed by rotations in each eye's vertical direction plane, and finally, disconjugate rotations in a common frontoparallel plane. This compounded rotation of the eye was underlying an initially fast-rising variable torsion that typically overshot the final torsion, which the eyes attained at the time of target acquisition. The torsion consisted of a coarse, widely varying component of opposite polarity in the two eyes, which contained a more robust, much smaller modulation that sharply increased toward the end of saccades. The reorientation of the eyes in torsion depended on each eye's azimuth, elevation, and target distance. We conclude that refixation saccades are generated by motor commands that control ocular torsion in concert with the saccade generator, which operates in Donders-Listing kinematics underlying Listing's law.