Modeling dynamic contraction of muscle using the cross-bridge theory

During normal, voluntary movements, skeletal muscles typically contract in a highly dynamic manner; the length of the muscle and the speed of contraction change continuously. In this study, we present an approach to predict the accurate behavior of muscles for such dynamic contractions using Huxleyʹs cross-bridge model. A numerical procedure is proposed to solve, without any assumptions, the partial differential equation that governs the attachment distribution function in Huxleyʹs cross-bridge model. The predicted attachment distribution functions, and the corresponding force responses for shortening and stretching, were compared with those obtained using Zahalakʹs analytical solution and those obtained using the so-called “distribution moment model” in transient and steady-state contractions. Compared to the distribution moment model, the solutions obtained using our model are exact rather than approximate. The solutions obtained using the analytical approach and the present approach were virtually identical; however, in terms of CPU times, the present approach was 250–300 times faster than Zahalakʹs. From the results of this study, we concluded that the proposed solution is an exact and efficient way for solving the partial differential equation governing the cross-bridge model.