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# An Efficient Probabilistic Methodology for Incorporating Uncertainty in Body Segment Parameters and Anatomical Landmarks in Joint Loadings Estimated From Inverse Dynamics

[+] Author and Article Information
Joseph E. Langenderfer

Computational Biomechanics Laboratory, Department of Mechanical and Materials Engineering, University of Denver, Denver, CO 80208jlangend@du.edu

Peter J. Laz, Paul J. Rullkoetter

Computational Biomechanics Laboratory, Department of Mechanical and Materials Engineering, University of Denver, Denver, CO 80208

Anthony J. Petrella

DePuy, a Johnson and Johnson Company, Warsaw, IN 46581

http://www.isbweb.org/data

J Biomech Eng 130(1), 014502 (Feb 05, 2008) (7 pages) doi:10.1115/1.2838037 History: Received November 02, 2006; Revised May 11, 2007; Published February 05, 2008

## Abstract

Inverse dynamics is a standard approach for estimating joint loadings in the lower extremity from kinematic and ground reaction data for use in clinical and research gait studies. Variability in estimating body segment parameters and uncertainty in defining anatomical landmarks have the potential to impact predicted joint loading. This study demonstrates the application of efficient probabilistic methods to quantify the effect of uncertainty in these parameters and landmarks on joint loading in an inverse-dynamics model, and identifies the relative importance of the parameters and landmarks to the predicted joint loading. The inverse-dynamics analysis used a benchmark data set of lower-extremity kinematics and ground reaction data during the stance phase of gait to predict the three-dimensional intersegmental forces and moments. The probabilistic analysis predicted the 1–99 percentile ranges of intersegmental forces and moments at the hip, knee, and ankle. Variabilities, in forces and moments of up to 56% and 156% of the mean values were predicted based on coefficients of variation less than 0.20 for the body segment parameters and standard deviations of $2mm$ for the anatomical landmarks. Sensitivity factors identified the important parameters for the specific joint and component directions. Anatomical landmarks affected moments to a larger extent than body segment parameters. Additionally, for forces, anatomical landmarks had a larger effect than body segment parameters, with the exception of segment masses, which were important to the proximal-distal joint forces. The probabilistic modeling approach predicted the range of possible joint loading, which has implications in gait studies, clinical assessments, and implant design evaluations.

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## Figures

Figure 1

Uncertainties in BSPs and ALs were simulated with a probabilistic analysis of inverse dynamics. Deterministic inputs were (a) kinematics calculated from the motion of ALs attached to the lower-extremity and (b) ground reaction data (18). Probabilistic inputs were (c) BSPs: segment masses, moments of inertia, and proximal-distal locations of centers of mass, as well as (d) nine lower-extremity ALs. Inverse-dynamics analysis (e) was conducted using Newton’s and Euler’s equations. Outputs of the probabilistic analysis were (f) distributions of intersegmental forces and moments for the hip, knee, and ankle, and (g) sensitivities of forces and moments to inputs.

Figure 2

Bounds (1–99 percentile) of intersegmental forces predicted for gait stance phase with probabilistic simulation of ALs locations and BSPs input to the inverse-dynamics model. Results shown for magnitudes and components.

Figure 3

Bounds (1–99 percentile) of intersegmental moments predicted for gait stance phase with probabilistic simulation of AL locations and BSPs input to the inverse-dynamics model. Results shown for magnitudes and components.

Figure 4

Sensitivities of intersegmental forces at the (a) ankle, (b) knee, and (c) hip to BSPs: mass of foot (Mfoot), mass of shank (Mshank), mass of thigh (Mthigh), and location ratio of the foot center of mass (Lc.m. foot) and ALs: fifth metatarsal head (Metatarsal Head), heel (Heel), lateral malleolus (Lat. Malleolus), tibial tubercle (Tib. Tubercle), femoral epicondyle (Fem. Epi.), greater trochanter (Great. Troch.), right anterior superior iliac spine (R.ASIS), and the sacrum (Sacrum). The levels of sensitivities are only presented when any one component demonstrates a sensitivity of greater than 0.20 to a given input parameter.

Figure 5

Sensitivities of inter-segmental moments at the (a) ankle, (b) knee, and (c) hip to BSPs: thigh moment of inertia (Ithigh) and ALs: fifth metatarsal head (Metatarsal Head), heel (Heel), lateral malleolus (Lat. Malleolus), tibial tubercle (Tib. Tubercle), femoral epicondyle (Fem. Epi.), greater trochanter (Great. Troch.), right anterior superior iliac spine (R.ASIS) and the sacrum (Sacrum). The levels of sensitivities are only presented when any one component demonstrates a sensitivity of greater than 0.20 to a given input parameter.

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