Improving Net Joint Torque Calculations Through a Two-Step Optimization Method for Estimating Body Segment Parameters

Abstract

Two main sources of error in inverse dynamics based calculations of net joint torques are inaccuracies in segmental motions and estimates of anthropometric body segment parameters (BSPs). Methods for estimating BSP (i.e., segmental moment of inertia, mass, and center of mass location) have been previously proposed; however, these methods are limited due to low accuracies, cumbersome use, need for expensive medical equipment, and∕or sensitivity of performance. This paper proposes a method for improving the accuracy of calculated net joint torques by optimizing for subject-specific BSP in the presence of characteristic and random errors in motion data measurements. A two-step optimization approach based on solving constrained nonlinear optimization problems was used. This approach minimized the differences between known ground reaction forces (GRFs), such as those measured by a force plate, and the GRF calculated via a top-down inverse dynamics approach. In step 1, a series of short calibration motions was used to compute first approximations of optimized segment motions and BSP for each motion. In step 2, refined optimal BSPs were derived from a combination of these motion profiles. We assessed the efficacy of this approach using a set of reference motions in which the true values for the BSP, segment motion, GRF, and net joint torques were known. To imitate real-world data, we introduced various noise conditions on the true motion and BSP data. We compared the root mean squared errors in calculated net joint torques relative to the true values due to the optimal BSP versus traditionally-derived BSP (from anthropometric tables derived from regression equations) and found that the optimized BSP reduced the error by 77%. These results suggest that errors in calculated net joint torques due to traditionally-derived BSP estimates could be reduced substantially using this optimization approach.