Linearity in force – length Relation and Determination of Muscle Forces

Abstract

This paper examines the force–length relations of skeletal muscle actuators during normal human gait based on gait data analysis. Instead of time or gait cycle, the joint coordinates were taken as independent parameters in the study of force–length relations. Force–length relations are nonlinear and non-analytic functions in the domain of each gait cycle. We propose to carry out kinematic segmentation of each joint coordinate function into four kinematic states depending on its displacement, velocity and acceleration for studying the force–length relations. When considered segment-wise, linear fit to force–length curves were found statistically significant. Thus it was seen that the skeletal muscles behaved linearly when evaluated in terms of the kinematic segments in the gait cycle. Hence a method to evaluate muscle force distribution was proposed using linear equivalent static formulation based on strain energy minimization as a rapid procedure in comparison with static optimization algorithm. The method resulted in simplified modeling and analysis of musculo-skeletal system to draw interim conclusions before the fully fledged musculo-skeletal analysis is carried out. The proposed method was applied on a single degree of freedom case and was verified with established analysis procedure, namely static optimization using OpenSim, an open-source software system.