Producing physiologically realistic individual muscle force estimations by imposing constraints when using optimization techniques

Abstract

Static optimization techniques have been used to estimate individual muscle forces in order to assess joint loads and muscle function. This study examined the validity of such techniques. Forces in the individual muscles, causing elbow flexion, were estimated using four different objective functions: minimizing the sum of the muscle stress either squared or cubed, and minimizing the sum of the relative muscle forces either squared or cubed. Constraints were placed on the maximum muscle forces based on physiological considerations. The resulting force estimates were compared with those from a validated muscle model that took account of the physiological properties of the muscles. The objective functions produced physiologically unrealistic muscle force estimations, unless the maximum muscle forces were constrained. By imposing constraints, individual muscle force predictions were restricted to those that were within physiologically realistic bounds. Using this procedure for sub-maximal activity resulted in some muscle activity being equal to the constraint, which, whilst possible, is still unrealistic. Therefore, by imposing constraints, the muscle forces can be kept within physiological boundaries, but the inferred recruitment is not necessarily the solution that the ‘body’ selects, but reflects a set of muscle forces that meet the solution to the optimization problem.