Eye mechanics and their implications for eye movement control

The topic of this thesis is the investigation of the mechanical properties of the oculomotor system and the implications of these properties for eye movement control. The investigation was conducted by means of computer models and simulations. This allowed us to combine data from anatomy, physiology and psychophysics with basic principles of physics (mechanics) and mathematics (geometry). In chapter 2 we investigate the degree to which mechanical and neural non-linearities contribute to the kinematic differences between centrifugal and centripetal saccades. On the basis of the velocity profiles of centrifugal and centripetal saccades we calculate the forces and muscle innervations during these eye movements. This was done using an inverted model of the eye plant. Our results indicate that the non-linear force-velocity relationship (i.e. muscle viscosity) of the muscles is probably the cause of the kinematic differences between centrifugal and centripetal saccades. In chapter 3 we calculate the adjustment of the saccadic command that is necessary to compensate for the eye plant non-linearities. These calculations show that the agonist and antagonist muscles require different net saccade signal gain changes. In order to better understand how this gain change is accomplished we use the inverted model of the eye plant (chapter 2) to calculate the muscle innervation profiles of saccades with different starting orientations. Based on these calculations we conclude that the saccade signal gain changes are accomplished primarily by changes in the magnitude of the saccade signal. In chapter 4 we examine the requirements that the oculomotor system must meet for the eye to be able to make desired gaze changes and fixate at various eye orientations. We first determine how the axes of action (i.e. unit moment vectors) of the muscles are related to eye orientation and the location of the effective muscle origin (i.e. the muscle pulleys). Next we show how this relation constrains muscle pulley locations if the eye movements are controlled by specific rules. The two control theories we investigate are: 1. Eye movements that obey Listing's law, and the binocular extension of Listing's law, actively use only the horizontal and vertical muscle pairs. 2. Oculomotor control involves perfect agonist-antagonist muscle alignment. In chapter 5 we test two assumptions that are commonly made in models of the oculomotor plant. The first is the assumption that the antagonistic muscles can be viewed as a single bi-directional muscle. The second is the assumption that the three muscle pairs act in orthogonal directions. On the basis of the geometrical properties governing the muscle paths we show how these assumptions give rise to incorrect predictions for the oculomotor control signals. Using the same muscle activation patterns for eye plant models with and without these assumptions we calculate the eye orientations that are reached. Finally in chapter 6 we discuss some general conclusions concerning the consequences of the mechanics of the eye for oculomotor control