Three-dimensional analysis of strongly curved saccades elicited by double-step stimuli

Earlier recordings of eye position in three dimensions have revealed that Listing's law is obeyed in reasonable approximation, both statically and dynamically. This implies that all eye positions are confined to a plane when using a rotation vector or quaternion representation. The orientation of the angular velocity axis is crucial in order to preserve the law. For a single-axis rotation, the eye's angular velocity axis has to tilt out of Listing's plane, otherwise the law cannot be preserved in eccentric saccades. Experimental work has confirmed that normal, visually-guided saccades resemble single-axis rotations whose angular velocity axis tilts by the right amount. We investigated how well the saccadic system implements Listing's law when the trajectory of the eyes is more complicated, as in a non-single-axis rotation where the angular velocity vector depends on instantaneous eye position. Eye position was measured in three dimensions using the magnetic scleral search coil method for five subjects. Non-single-axis rotations of the eye were evoked with a double-step paradigm. We found that Listing's law is obeyed equally well during fixations, single-axis saccades and in non-single-axis saccades. Some deviations from the law were found in both curved and single-axis eye movements, but we demonstrated that the net torsional component of eye position of these saccades is negligible compared to that expected if the angular velocity axis did not tilt at all. In addition, analysis of the angular velocity signals in the curved movements showed strong similarity to the computed signal required for implementing Listing's law. Our results show that the observed deviations from Listing's law reflect only minor failures in the mechanism underlying its dynamic implementation. We conclude that single-axis rotations are not a necessary condition for the implementation of Listing's law in saccades. Our results are compatible with the notion that the implementation of Listing's law relies upon internal feedback. Various suggestions of how models can be reconciled with recent data on the three-dimensional control of saccades are discussed.