Cost Function in Muscle Redundancy Problems: Computational Aspects

Abstract

Several methods have been proposed to solve the “redundancy problem in biomechanics,” optimization techniques that are being most widely used. In posing the optimization problem, a variety of cost functions can be found in the literature, designed to meet various criteria, whether to minimize muscle fatigue, active or passive instant muscle strength, the level of muscle activation, or metabolic cost. The aim of this paper is to compare muscles forces generated by different cost functions. We have studied the forces produced by the muscles of the human leg during flexion, using a static optimization algorithm, accounting for the dynamics of muscle contraction.

Keywords:

• Biomechanics
• Muscle
• Redundancy problem

ACKNOWLEDGMENTS

This work was funded by the Spanish Ministry of Education and Science as a part of project DPI2009-11-792 and by the Junta de Andalucía as a part of Excellence Project TEP03115.

Notes

Optimal length of the CE (Gerritsen and van den Bogert, 1998), width (Gerritsen and van den Bogert, 1998), maximal isometric muscle strength (Gerritsen and van den Bogert, 1998), tendon slack length l _slack (Gerritsen and van den Bogert, 1998), pennation angle α _p of muscle fibers (Menegaldo and Fleury, 2006), and muscle length in the anatomical position (Gerritsen and van den Bogert, 1998) for the muscle groups considered: iliopsoas (Ilio), rectus femoris (RF), gluteus (Glu), hamstrings (Hams), vastus (Vas), gastrocnemius (Gas), tibialis anterior (TA) and soleus (Sol).