Behnoosh Parsa - Department of Biomedical Engineering Amirkabir University of Technology Tehran, Iran
Hossein Ehsani - Department of Biomedical Engineering Amirkabir University of Technology Tehran, Iran
Mostafa Rostami - Department of Biomedical Engineering Amirkabir University of Technology

Providing a capable musculoskeletal model for predicting antagonistic muscle forces has been dramatically flourished in recent decades. To reach this destiny, manyresearchers have struggled to modify objective functions in optimization-based models. The purpose of this paper is tocompare two objective functions (Entropy-assisted and shiftparameter objective function) exhibited in the literature for predicting muscle co-contraction. Furthermore, the effect ofthese objective functions in forecasting synergic muscles pattern was taken into account. To do so, a 2 DOF upper limb skeletalmodel 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 dataand considering different values (range 0 to 1 with step of 0.1) for entropy weight and shift parameter in the objective function ofthe static optimization problems, activation level of muscles spanning the elbow was obtained. The results showed that byincreasing either of these parameters activation level of agonistand antagonist muscles rise. Besides, inspecting the results, it was clear that both of the optimization problems led to a same trendin the results and by choosing proper weight and shift parameter it was possible to minimize the difference between the obtainedresults from these two objective functions. Furthermore, considering a graphical approach it was showed that the entropyassistedproblem was a convex one which tried to obtain a minimum state of total activation. Contemplating this fact andutilizing each muscle’s moment generation capacity, synergicbehavior of muscles spanning elbow was discussed. We also examined the validity of the results, using EMG signals ofBrachioradialis (BRD) and lateral head of Triceps (TRILAT). Although EMG signal of BRD was somehow consistent withactivation level of this muscle, EMG signal of TRILAT was in conflict with the results of static optimization problem.

Static Optimization , Co-contraction , Entropy assisted Optimization , Shift parameter , Musculoskeletal Modeling