Dynamic eye plant models and the control of eye movements

Models of the oculomotor plant (globe, muscles, pulleys, and orbital tissues) fall into three categories: 1). one-dimensional dynamic with lumped plant elements, 2). three-dimensional dynamic with lumped plant elements, or 3). three-dimensional static with distinct plant elements. The second class of models is most often used when studying the neural control of 3-D eye movement, because they best represent the plant dynamics. However, they are often faulted because they make two unrealistic assumptions: 1). muscle pairs act along the three orthogonal axes (symmetry assumption); and 2). the force generated by the muscles depends only on their innervation (force assumption). It turns out that the symmetry assumption is quite benign, because in a realistic model of the plant the deviations from orthogonal axes can be easily accounted for by simple adjustments to the innervation. In contrast, the force assumption introduces some serious problems. In the present paper, the authors show that a realistic, dynamic model of the geometry of the orbit, with independent muscles, makes different predictions than a similar model with lumped muscles. This difference arises because muscle force is a function of both innervation and muscle length.