Investigation of the Peculiarities of Two-joint Muscles Using a 3 DOF Model of the Human Upper Limb in the Sagittal Plane: an Optimization Approach

INVESTIGATION OF THE INFLUENCE OF THE ELBOW JOINT REACTION ON THE PREDICTED MUSCLE FORCES USING DIFFERENT OPTIMIZATION FUNCTIONS

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.

An optimization approach to inverse dynamics provides insight as to the function of the biarticular muscles during vertical jumping

Traditional inverse dynamics approaches to calculating the inter-segmental moments are limited in their ability to accurately reflect the function of the biarticular muscles. In particular they are based on the assumption that the net inter-segmental moment is zero and that total joint moments are independent of muscular activity. Traditional approaches to calculating muscular forces from the inter-segmental moments are based on a consideration of joint moments which do not encapsulate the potential moment asymmetry between segments. In addition, traditional approaches may artificially constrain the activity of the biarticular muscles. In this study, an optimization approach to the simultaneous inverse determination of inter-segmental moments and muscle forces (the 1-step method) based on a consideration of segmental rotations was employed to study vertical jumping and contrasted with the more traditional 2-step approach of determining inter-segmental moments from an inverse dynamics analysis then muscle forces using optimization techniques. The 1-step method resulted in significantly greater activation of both the monoarticular and biarticular musculature which was then translated into significantly greater joint contact forces, muscle powers, and inter-segmental moments. The results of this study suggest that traditional conceptions of inter-segmental moments do not completely encapsulate the function of the biarticular muscles and that joint function can be better understood by recognizing the asymmetry in inter-segmental moments.