Effects of Introducing Fractional Dynamics in Hill's Model for Muscle Contraction

Abstract

Muscles can be conceived as distributed electro-mechanical-chemical systems that can be described by a set of coupled partial differential equations. Because of the difficulty of solving this kind of equations, these systems are usually approximated by a set of lumped elements leading to a set of coupled ordinary differential equations instead. Hill's model is the most popular of such models having four basic elements that describe the behavior of the muscle: contractile, damping, series elastic, and parallel elastic elements. The aim of this paper is to study the effects of introducing fractional dynamics into the Hill's model in order to characterize unhealthy muscles in spinal cord injured (SCI) subjects for control purposes. By doing so, more general dynamic behaviors can be obtained but keeping the simplicity of the lumped parameter models for control applications.