The optimisation of the energy-related cost function for the Delft Shoulder & Elbow Model

Abstract

For inverse-dynamic models cost functions account for the load sharing problem that arises when modelling the musculoskeletal system. This study focuses on the optimisation of the energy-related cost function integrated in the Delft Shoulder & Elbow Model and compares the translation of the obtained representation to results from in vitro measurements. An existing data set containing electromyography (EMG) recordings of elbow flexors (m. biceps brachii, m. brachialis and m. brachioradialis) and extensors (m. triceps brachii and m. anconeus) was used. A grid search was performed over a range of [1, 120] for b¬1 and [1, 60] for b2. The overall explained variance was calculated for each cost function, classifying the particular muscles in flexion and/or extension tasks where activity is expected. For the comparison to in vitro measurements the ratio of contraction dynamics and activation dynamics described by the cost function was determined under varying degree of force production over all muscles used for the analysis. Optimal weight factors were obtained for b1 = 3 and b2 = 50. The contribution of the contraction dynamics compared to the activation dynamics was 60% at 50% of its maximal force generation and 78% at maximal force generation which compares to the in vitro measurements.