The problem of determining muscle forces in the leg during walking is addressed using mathematical optimization. This approach is necessi tated by the redundant arrangement of the muscles about the joints;​ but it also serves as a useful analog of the human adaptive motor control system. Minimum muscle energy, defined as the input chemical energy, is forwarded as the criterion of optimality, and a thermodynamic model of muscle is developed to allow implementation of this criterion.

This muscle energy model results from considering the chemico-mech anical dynamics of the energy transfers in muscle. Using bond graph models of these systems along with an existing model of actin and myosin dynamics, a simple static relationship between input chemical power and output mechanical power 18 established. (This relationship, however, applies only to muscle used in frequency ranges that are characteristic of walking). This chemical power is found to be a linear function of force and a non-linear, monotonic function of muscle contraction velocity.

Experiments are presented that measure lower limb kinematics and myoelectric signals from the surface muscles of the leg. The former are used to calculate the moments required at the joints for a specific subject's movements and these moments define the constraints on the force optimization.

Results of the minimum energy optimization, formulated as a linear program, indicate that the criterion selection affects only the relative load sharing between the active muscles whereas the basic temporal pattern of muscle activation is determined by the input joint moments. The agreement with MES's, which serve only as a temporal comparison, 18 acceptable, but several muscles that have distinct MES's are never used by the optimization. This problem is partially alleviated by introducing upper bounds on the muscle forces, which distributes the load among more of the muscles.

The validity of the minimum energy criterion 18 examined in a series of experiments with the subject walking at various age total muscle power is calculated using both a minimum energy and a minimum force optimal criterion and these results are compared to classical oxygen consumption - walking speed findings. Although the proper trend in average power with increasing speed 18 predicted with both criteria (a quadratic relationship) the slope of the predictions 18 too high. The minimum energy case does, however, have a lower slope than does the minimum force case.

Knowledge of individual muscle forces is essential to a basic understanding of the mechanics of movement, and it would also find immediate application in clinical areas reconstructive orthopedic surgery.