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Research Papers

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

[+] Author and Article Information
Raziel Riemer

Department of Industrial Engineering and Management, Ben-Gurion University, Beer-Sheva 84105, Israel

Elizabeth T. Hsiao-Wecksler1

Department of Mechanical and Science Engineering, University of Illinois at Urbana-Champaign, MC-244, 1206 West Green Street, Urbana, IL 61801ethw@uiuc.edu

1

Corresponding author.

J Biomech Eng 131(1), 011007 (Nov 20, 2008) (7 pages) doi:10.1115/1.3005155 History: Received December 01, 2007; Revised September 22, 2008; Published November 20, 2008

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.

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Figures

Grahic Jump Location
Figure 1

The body represented by a three-segment model. Segment angles for the shank (θs), thigh (θt), and torso (θtr) were defined as shown.

Grahic Jump Location
Figure 2

Two step sequential optimization approach to determine optimal subject-specific body segment parameters (i.e., center of mass location, mass, and moment of inertia) in the presence of motion data error. Step 1 finds preliminary optimized BSPs and angular profiles that minimize the objective function; this step is done for the three different calibration motions. In step 2, the optimized angular profiles found in step 1 are concatenated together and BSPs from one of the three motions (BSP1) are used to find a refined second estimation (BSP2).

Grahic Jump Location
Figure 3

Framework for performance evaluation of the proposed method to determine the efficacy of optimized BSP estimates in calculating net joint torques. Note that the gray box corresponds to the sequential optimization described in Fig. 2.

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