Muscle models: what is gained and what is lost by varying model complexity.

Three structurally different types of models have evolved over the years to describe muscle-joint systems. The first, based on an input-output analysis of a given task, results in a simple second-order differential equation description that is adequate over a certain movement operating range. The second, based on the classic structural model of Hill (1938), results in a higher-order nonlinear model described by ordinary differential equations. The third, based on an analysis of the biophysical contractile mechanism, results in a complex partial differential equation description. The advantages and disadvantages of each type of model are considered, based on the criteria of identifying the simplest model that can adequately simulate any fundamental type of human movement without modifying model parameters for different tasks. It is shown that an eighth-order Hill-based antagonistic muscle-joint model is able to satisfy these criteria for a given joint if each of the four basic mechanically-significant non-linearities of the system are included in the model. This same model structure has been used successfully for eight different muscle-joint systems, ranging in size from knee flexion-extension to eye rotation--the only difference between the models is in the parameter values. Second-order models are shown to be task-specific special cases of the input-output behavior of the eighth-order model, while the more complex biophysical models are hypothesized to have insignificant advantages and many disadvantages over the Hill-based model during normal human movement.