Inverse Dynamics and the Immeasurable Motions

Motion capture technology is a set of experimental methods with finite accuracy. The current golden standard in the field is synchronized hi-speed infrared camera systems based on passive markers attached to the skin of the test subject. Due to skin artefacts and the tolerance of registering the precise 3-D marker locations, certain movements are inherently difficult to register, for instance the movement of the scapula relative to the thorax or glenohumeral superior migration. This paper, however, focuses on the knee. Knee flexion/extension is a large articulation in most practical cases, typically gait, and a well-conducted experiment with a good-quality motion capture system will register this degree-of-freedom with sufficient accuracy for most applications. However, it is known from bone pin studies (Benoit et al. 2006) that the knee has significant movements additional to flexion/extension, and these movements cannot be registered reliably with skin-mounted markers. Motion and forces are related by the laws of mechanics, so knowledge of the acting forces in the system and the inherent elasticity in the knee could theoretically lead to estimation of the immeasurable motions. One of the primary complications of this scheme is that a large part of the acting forces are due to muscle contractions, which in this case also must be simulated. The ability to predict muscle contraction in complex movements has improved significantly in recent years, but the simultaneous prediction of movement and force remains extremely computationally challenging. In this paper, we attempt prediction of forces as well as small movements in the knee based upon knowledge of large movements, i.e. flexion/extension, from camera-based motion capture. The applied method, force-dependent kinematics, is rooted in a reformulation of the underdeterminate inverse dynamics-type equilibrium equations to allow certain degrees of freedom to be governed by elastic equilibrium rather than measured movements. We briefly outline the method and compare predicted movements during overground gait on a treadmill measured using fluoroscopy on the same subject using the dataset from the first Grand Challenge to predict in vivo knee kinematics and kinetics. We show that several of the immeasurable degrees-of-freedom in the knee can be accurately predicted, while others are more challenging. The figure shows abduction/adduction in the knee as a function of the knee flexion angle. Benoit, D.L., Ramsey, D.K., Lamontagne, M., Xu, L., Wretenberg, P. & Renström, P. 2006, "Effect of skin movement artifact on knee kinematics during gait and cutting motions measured in vivo", Gait & posture, vol. 24, no. 2, pp. 152-164.