Physiological prediction of muscle forces—I. Theoretical formulation

A physiological model for predicting muscle forces is described. Rigid-body mechanics and musculoskeletal physiology are used to describe the dynamics of the segment model and muscle model. Unknown muscle and joint contact forces outnumber the equilibrium equations resulting in an indeterminate problem. Mathematical optimization is utilized to resolve the indeterminacy. The modeling procedure relies entirely on established physiological principles. Data describing the muscle anatomy and body structures are included. A model defining the force-length-velocity-activation relationship of a muscle is adopted. The force a muscle produces is assumed to be proportional to its maximum stress, physiological cross-sectional area, activation, and its functional configurations including the muscle architecture, muscle length, contracting velocity, and passive tension. These factors are incorporated into inequality equations which limit the force for each muscle. Minimal muscular activation is forwarded as the optimization criterion for muscle force determination.