INVERSE OPTIMIZATION - FUNCTIONAL AND PHYSIOLOGICAL CONSIDERATIONS RELATED TO THE FORCE-SHARING PROBLEM

This paper is a review of the optimization techniques used for the sol ution of the force-sharing problem in biomechanics; that is, the distr ibution of the net joint moment to the force generating structures suc h as muscles and ligaments. The solution to this problem is achieved b y the minimization (or maximization) of an objective function that inc ludes the design variables !usually muscle forces) that are subject to certain constraints, and it is generally related to physiological or mechanical properties such as muscle stress, maximum force or moment, activation level, etc. The usual constraints require the sum of the ex erted moments to be equal to the net joint moment and certain boundary conditions restrict the force solutions within physiologically accept able limits. Linear optimization (objective and constraint functions a re both linear relationships) has limited capabilities for the solutio n of the force sharing problem, although the use of appropriate constr aints and physiologically realistic boundary conditions can improve th e solution and lead to reasonable and functionally acceptable muscle f orce predictions. Nonlinear optimization provides more physiologically acceptable results, especially when the criteria used are related to the dynamics of the movement (e.g., instantaneous maximum force derive d from muscle: modeling based on length and velocity histories). The e valuation of predicted forces can be performed using direct measuremen ts of forces (usually in animals), relationship with EMG patterns, com parisons with forces obtained from optimized forward dynamics, and by evaluating the results using analytical solutions of the optimal probl em to highlight muscle synergism for example. Global objective functio ns are more restricting compared to local ones that are related to the specific objective of the movement at its different phases (e.g., max imize speed or minimize pain). In complex dynamic activities multiobje ctive optimization is likely to produce more realistic results.