Analyzing synergistic and antagonistic muscle behavior during elbow planar flexion-extension: Entropy-assisted vs. shift-parameter criterion

Providing a capable musculoskeletal model for predicting antagonistic muscle forces has been dramatically flourished in recent decades. To reach this destiny, many researchers have struggled to modify objective functions in optimization-based models. The purpose of this paper is to compare two objective functions (Entropy-assisted and shift parameter objective function) exhibited in the literature for predicting muscle co-contraction. Furthermore, the effect of these objective functions in forecasting synergic muscles pattern was taken into account. To do so, a 2 DOF upper limb skeletal model actuated with 15 muscles, has been developed. A phenomenological Hill-based model in accompanied with a rigid tendon was employed to represent musculotendon units. While performing a flexion/extension in the elbow, the upper arm was held stationary in a vertical pose. Exploiting the kinematic data and considering different values (range 0 to 1 with step of 0.1) for entropy weight and shift parameter in the objective function of the static optimization problems, activation level of muscles spanning the elbow was obtained. The results showed that by increasing either of these parameters activation level of agonist and antagonist muscles rise. Besides, inspecting the results, it was clear that both of the optimization problems led to a same trend in the results and by choosing proper weight and shift parameter it was possible to minimize the difference between the obtained results from these two objective functions. Furthermore, considering a graphical approach it was showed that the entropy-assisted problem was a convex one which tried to obtain a minimum state of total activation. Contemplating this fact and utilizing each muscle's moment generation capacity, synergic behavior of muscles spanning elbow was discussed. We also examined the validity of the results, using EMG signals of Brachioradialis (BRD) and lateral head of Triceps (TRILAT). Although EMG signal of BRD was somehow consistent with activation level of this muscle, EMG signal of TRILAT was in conflict with the results of static optimization problem.