A kinematic model for 3-D head-free gaze-shifts

Rotations of the line of sight are mainly implemented by coordinated motion of the eyes and head. Here, we propose a model for the kinematics of three-dimensional (3-D) head-unrestrained gaze-shifts. The model was designed to account for major principles in the known behavior, such as gaze accuracy, spatiotemporal coordination of saccades with vestibulo-ocular reflex (VOR), relative eye and head contributions, the non-commutativity of rotations, and Listing's and Fick constraints for the eyes and head, respectively. The internal design of the model was inspired by known and hypothesized elements of gaze control physiology. Inputs included retinocentric location of the visual target and internal representations of initial 3-D eye and head orientation, whereas outputs were 3-D displacements of eye relative to the head and head relative to shoulder. Internal transformations decomposed the 2-D gaze command into 3-D eye and head commands with the use of three coordinated circuits: (1) a saccade generator, (2) a head rotation generator, (3) a VOR predictor. Simulations illustrate that the model can implement: (1) the correct 3-D reference frame transformations to generate accurate gaze shifts (despite variability in other parameters), (2) the experimentally verified constraints on static eye and head orientations during fixation, and (3) the experimentally observed 3-D trajectories of eye and head motion during gaze-shifts. We then use this model to simulate how 2-D eye-head coordination strategies interact with 3-D constraints to influence 3-D orientations of the eye-in-space, and the implications of this for spatial vision.