Development of a Musculotendon Model Within the Framework of Multibody Systems Dynamics

Human movement is the result of a complex and synergistic interaction between the musculoskeletal and the central nervous system. As result, muscles contract coordinately to produce forces that are transmitted by tendons to the skeletal system, causing its movement or keeping its pose. Often neglected in current muscle models, the elastic properties of tendons play a significant role in the dynamic interaction between the muscular and skeletal systems, influencing the force transmission, energy storage and transfer, and joint control. The aim of this work is to present in detail the necessary steps to incorporate a musculotendon model in the framework of a multibody systems dynamics formulation. A methodology to compute the musculotendon forces and activations is presented based on the use of a Hill-type muscle model assembled in series with a spring-like element defined according to the elastic properties of the tendon. The proposed methodology can be applied, without significant changes, to both inverse and forward dynamic analyses of biomechanical systems. Three daily activities with different levels of musculotendon recruitment are analyzed from an inverse dynamics perspective. The selected activities are walking, running and jumping. The movement data characterizing these activities were acquired experimentally in a movement laboratory. A 3D biomechanical model of the human body, described with natural coordinates and encompassing 43 musculotendon actuators per leg, is proposed to assess the performance of the presented musculotendon model and of its incorporation on the referred multibody dynamics framework. The influence of the introduction of a compliant tendon model on the produced muscle forces and activation patterns is analyzed in face of those same results produced by the same biomechanical model defined with infinitely stiff (or rigid) tendons. Results revealed that the introduction of the tendon model allows muscles to work, predominantly, on their optimal configuration as the dynamic equilibrium generated between muscle and tendon prevents the muscle from support all musculotendon deformation. This not only reduces the activations needed to perform the required contractile forces but it also considerably prevents the development of non-physiological passive forces.