A general approach for modelling and mathematical investigation of the human upper limb.

This paper is an attempt to systematize and solve the problems connected with biomechanical modelling and mathematical investigation of the upper limb, when all muscles acting on the shoulder, elbow and wrist joint are included. The basic problem is the assumption of a hypothesis for the unit vectors, collinear with muscle forces. The so-called segment-lines modelling of the muscle force direction is proposed for solving this problem. This approach combines the simplicity of the straight line joining the muscle tendon origin to the insertion point, its application for the analytical description of the model and the real description of the muscle anatomical functions. The principle of the anatomically adequate moment is the general criterion for choosing the segments (straight and curvilinear sections) by which the direction of the muscle action is replaced. The different optimization techniques which are used for solving the statically indeterminate problem, formulated for musculoskeletal biomechanical models, are considered. Aiming to obtain strictly positive and continuous solutions for the muscle forces moduli, the application of the Lagrange multipliers method is proposed. The possibility of applying different optimization criteria is explored. A general conclusion may be formulated: if there exists any criterion which is independent of the joint angles, it follows than that it must be dependent on the joint reactions and, in addition, it must be nonlinearly dependent on the muscle forces moduli.