An Analysis of Including the Evolution Law for the Serial Element in the Musculoskeletal Modelling

Abstract: In the classic Hill model for muscle contraction, the split between the muscle and tendon is arbitrary and the problem lacks a unique solution. Instead of reformulating the problem to a differential-algebraic equation and solving for a set of initial conditions, a constant tendon length is commonly assumed in musculoskeletal simulation tools. This assumption has not been thoroughly tested and introduces errors of unknown magnitude to the simulations. In this thesis, the contractile element of the Hill model is modelled as a friction clutch in parallel to a viscous damper. This provides an evolution law for the muscle length by which the muscle speed is numerically calculated taking into account a non-zero tendon speed. A simple biceps curl is simulated with the friction clutch model and compared to corresponding commercial musculoskeletal simulations. Overall, the results are similar, in particular for the muscle lengths which are almost identical in every simulation (0.00-0.42% difference). The difference in tendon speed is 0.00-3.26%, with upwards tendencies. In general, the error percentage of the tendon speed appears to decrease by the same amount that the contraction speed is reduced. Conclusively, it can be said that the introduced friction clutch model delivers comparative outcomes to a commercial musculoskeletal simulation software, while not assuming a constant tendon length. However, while presenting a relatively simple solution, an increased computation time is to be expected due to the need of a differential equation solver. Further investigation regarding implementation and computing times in more complex simulations may provide an alternative approach to conventional musculoskeletal simulations.