Force-dependent kinematics: a new analysis method for non-conforming joints

INTRODUCTION In traditional inverse dynamic analysis of musculoskeletal models [1,2], kinematics and kinetics are treated separately. Kinematic analysis is performed to compute the position, velocity and accelerations of the segments in the model from a description of the joints and the motion. This is formulated through the solution of a set of nonlinear constraint equations. Subsequently, the computed segment positions, velocities and accelerations are substituted into the dynamic equilibrium equations to obtain a set of equations with only unknown reaction and muscle forces. This set of equations is solved through muscle recruitment by assuming a criterion for the distribution of the internal forces between the muscles and the reactions. This approach requires that the joints and motion of the model can be completely described through these constraint equations without consideration of the forces that created the motion. However, several anatomical and prosthetic joints, such as spinal disks, knees and many shoulders are nonconforming to such an extent that the forces significantly influence the detailed joint kinematics and the joint’s internal force equilibrium. For instance, in the knee, the internal motions occurring are due to a complex interaction between the muscle actions, cartilage contact mechanics, and soft tissue stiffness and deformations. Forward dynamics approaches have the potential to address these phenomena, but they do not handle complex muscle systems well and often require careful tuning and long computation times to simulate vibrations and damping which in many cases are not very relevant to orthopaedic problems.