Huxley-type cross-bridge models in largeish-scale musculoskeletal models; an evaluation of computational cost

A Huxley-type cross-bridge model is attractive because it is inspired by our current understanding of the processes underlying muscle contraction, and because it provides a unified description of muscle's mechanical behavior and metabolic energy expenditure. In this study, we determined the computational cost for task optimization of a largeish-scale musculoskeletal model in which muscles are represented by a 2-state Huxley-type cross-bridge model. Parameter values defining the rate functions of the Huxley-type cross-bridge model could be chosen such that the steady-state force-velocity relation resembled that of a Hill-type model. Using these parameter values, maximum-height squat jumping was used as the example task to evaluate the computational cost of task optimization for a skeletal model driven by a Huxley-type cross-bridge model. The optimal solutions for the Huxley- and Hill-type muscle models were similar for all mechanical variables considered. Computational cost of the Huxley-type cross-bridge model was much higher than that of the Hill-type model. Compared to the Hill-type model, the number of state variables per muscle was large (2 vs about 18,000), the integration step size had to be about 100 times smaller, and the computational cost per integration step was about 100 times higher.