In this research, a homeomorphic model of the human ocular system pertaining to horizontal saccadic movements has been developed. Using this model simulations of typical saccadic movement are produced which are in good agreement with existing physiological data for such phenomena. Musculotendon physiology is modeled in part by using common phenomenological Hill-based models as well as non-linear tendon and muscle dynamics. Most of the system parameters are empirically established from clinical research, while other parameters are approximated by means of derived analytical expressions. The ability of the model schema presented here to realistically simulate typical saccades is suggestive of the validity of the approach used. As mentioned in the previous chapter, an important qualitative observation based on the comparative results of the two models presented is that inclusion of muscle mass in the model is both convenient mathematically and helpful for maintaining realistic model behavior. Mathematically, exclusion of the muscle mass necessitates a laborious development of analytical expressions for tendon length and muscle length and velocity. The inversion of the force-velocity curve in the development of a muscle velocity expression could pose stability problems in the presence of passive muscle. The concern of realism arises in that exclusion of mass necessitates exclusion of muscle viscosity. Consequently, globe viscosity must be increased by some arbitrary factor to account for muscle viscosity, with the end result being a system which tends to be overdamped. Certainly the eye movement system is one of the simpler muscle movement systems in the human body, and the horizontal saccades considered here involve only a part of this system. However, the ability to accurately and realistically model such a system is the first step in achieving realistic biomechanical models of the more complicated systems. The next step would be to include the remaining ocular muscles into the model with the intent of modeling the full range of eye motions. Although each of
the remaining sets of ocular muscles work in reciprocal pairs as detailed in this thesis, presumably there would be additional subtleties encountered related to the geometry of the system. Another pending area of research is a thorough mathematical development of the issues of controllability and optimization of the human eye movement system. In this thesis the basis has been laid for a state space description of the eye system that accurately reflects known mechanical and structural behavior. Using the equations provided in this work, the mathematical analysis can be pursued with a view to predicting the controls, i.e., neural inputs, which would generate the desired range of movements. Moving beyond the scope of eye movement itself, models of the sort provided in this work can be expected to be crucial components of wider systems being modeled in the human body. In particular, the apparatus behind saccadic movement is but one component of the biomechanical complex involved in head-eye movement and co-ordination. Head movements are closely coupled to movements of the eyes, assisting in visual stabilization of images as well as vestibular function and postural concerns. It is generally accepted that the large number of receptors in the head-neck-eye sys-tem provide physiological evidence that the closed-loop effects are vital in achieving coordinated movements required in tracking. These sensors provide feedback derived from kinetic as well as kinematic information. Consequently, accurate predictions of trajectories, velocities, accelerations, and musculotendon force such as those provided by this model would be integral to the development of a realistic closed-loop model of head-eye movement.