A window moving inverse dynamics optimization for biomechanics of motion

The application of musculoskeletal models to estimate muscle and joint reaction forces usually requires optimization strategies, regardless of using inverse or forward dynamics approaches. Most studies combined inverse dynamics and Static Optimization (SO) to solve the redundant muscle force distribution problem. However, the SO does not allow the simulation of time-dependent physiological criteria or of the time-dependent physiological nature of muscles. The Extended Inverse Dynamics (EID), which solves all instants of time simultaneously, was proposed to overcome these limitations of the SO, but the feasibility of this procedure is limited by the size of the optimization problem that can be realistically considered. This work proposes a new method that overcomes the aforementioned limitations of the SO and EID, i.e., that is able to handle time-dependent physiological criteria and has no limitations on the size of the problem to be solved. The proposed procedure, named here Window Moving Inverse Dynamics Optimization (WMIDO), consists in considering a moving window with the size of k instants of time in which the muscle force distribution problem is solved. The window moves iteratively across all instants of time until the muscle force distribution problem has been solved. The SO, EID, and WMIDO are applied to solve an upper limb abduction in the frontal plane, for which results are widely available in the literature, to demonstrate that similar optimal solutions are obtained for a time-independent physiological criterion if the redundant problem is not too large. Although the WMIDO is not as efficient as the SO for the type of problem tested, it is significantly faster than the EID. Moreover, the WMIDO is able to solve the motion under analysis regardless of the discretization level considered, whereas the EID fails due to memory limitations. Overall, the results show the WMIDO as a viable alternative to the current optimization procedures based on inverse dynamics.