Solution of Redundant Muscle Forces in Human Locomotion with Multibody Dynamics and Optimization Tools

Abstract

The analysis of human motion using inverse dynamics approaches allows for the evaluation of the muscle forces based on the knowledge of the kinematics of the human subject and the applied external forces. Owing to the redundant nature of the muscle arrangement, the system of equations available for the solution of the inverse dynamics problem has more unknown muscle forces than available equations. Therefore static optimization techniques are required to obtain a solution of the problem. Emphasizing applications to gait analysis and normal sports activities a whole-body, three-dimensional, biomechanical model of the human muscle-skeletal system is purposed to support the inverse dynamic analysis. In its current state of development, the biomechanical model includes a detailed description of the principal muscles of the locomotion apparatus for the lower limbs while net moments-of-force are used to represent the lumped muscle action about each other anatomical joint of the model. The muscles used in the biomechanical model include point-to-point and wrap-around muscles, depending in their nature and function, which results in a geometrically realistic muscle arrangement. A solution procedure for the redundant problem based on the static optimization is proposed here. Different types of objective functions representing the muscle forces, joint reaction forces, energy, or combinations of these are used in alternative. The muscle contraction dynamics is included in the optimization problem through the application of the Hill's muscle model. The methodology developed is applied to a case of gait analysis with normal cadence. The results obtained are discussed in face of the modeling assumptions used in the biomechanical model and muscle system representation.