Modelling of the Skeletal Muscle under Functional Electrical Stimulation

Mathematical muscle models are required to better understand biomechanical behaviour and to develop strategies for simulation, motion synthesis or motor control during clinical restoration of movement for paralysed limbs through functional electrical stimulation (FES). A muscle model has to predict accurately the force output under physiological operating conditions. But very few models are able to describe the muscle response to controlled electrical activation. A common problem is the lack of direct control input. They only attempt to exhibit the microscopic [2] or macroscopic [1] functional behaviour. Firstly, the classical twoelements model of Hill [1], which is the basis of almost all current practical muscle models, described its macroscopic dynamics. After, Huxley [2] proposed an explanation of the interaction cross bridge in a sarcomere. Finally, Zahalak [3] assigned with the moment function models a bridge between the microscopic and the macroscopic levels. These models represent quite properly the muscle properties under specific operational conditions (isometric contraction, isotonic contraction). But none of them considers a control input. In Bestel [4], they introduced a model of the heart with a controllable input. In this paper, we will focus on the extension of this model to muscle involved in lower limb motion. It is organized as follows: section 2 is dedicated to dynamic modelling, section 3 presents the static model; section 4 exhibits the identification protocol and finally we will give experimental results.