Less attention is paid to joint reactions when optimization tasks are solved aiming to predict individual muscle forces driving a biomechanical model. The reactions are important, however, for joint stability and for prevention from injuries, especially for fast motions and submaximal loading. The purpose of the paper is to investigate the influence of the joint reaction as a criterion in an objective function and to study the possibilities for prediction of antagonistic co-contraction. Planar elbow flexions in the sagittal plane with duration from 0.4 to 2 s are simulated, and muscle forces and elbow joint reaction are calculated solving numerically optimization tasks formulated for models with one (elbow moment equation only) and two (elbow and shoulder moment equations) degrees of freedom (DOF). The objective function is a weighted sum of muscle forces and joint reaction raised to different powers. The following conclusions can be made: (1) if the joint reaction is included in the objective function, antagonistic co-contraction can be predicted even for 1 DOF model; in some situations the use of such objective function can destroy the synergistic muscles' action; (2) the prediction of antagonistic muscles' co-contraction for 2 DOF model depends on the way the biarticular muscles are modeled, and this is valid for both dynamic and quasistatic conditions; if there are no biarticular muscles, antagonistic co-contraction cannot be predicted in one joint using popular objective functions, like minimum of sum of muscle forces or muscle stresses raised to a power.
Alternative objective function to predict reasonable muscle forces using a Hill-type muscle model
