Author(s): M Clark
Optimal control theory takes into account constraints such as energy and time economies which are relevant to the understanding of biological design. The versional eye tracking system responsible for the extremely rapid and precise movements called saccades, which occur, for example, during reading, seemed a likely biological system in which to test for time optimality. A homeomorphic detailed physiological model was constructed based on quantitative muscle, neuronal and oculomotor characteristcs. It is a sixth-order nonlinear representation which considers reciprocal innervation and the asymmetrical force-velocity relationship of the agonist-antagonist muscle pair that moves the eye. Simulations were done by digital computer, and responses of the model to first-, second-, and third-order time optimal control signals were observed; the major portions of the response trajectories were essentially the same. The model response was then compared with measured human saccadic eye movements, and it was found that this experimental data agreed most completely with the model driven by first-order time optimal control signals. Additionally, electromyographic studies in man and neurophysiological experiments in animals agree in showing that the nervous controller signals during saccades are also of the first-order type. Thus, we can conclude that the saccadic eye movements studied are accurately depicted by a model that yields time optimal responses.