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A Probabilistic Approach to Quantify the Impact of Uncertainty Propagation in Musculoskeletal Simulations

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Abstract

Uncertainty that arises from measurement error and parameter estimation can significantly affect the interpretation of musculoskeletal simulations; however, these effects are rarely addressed. The objective of this study was to develop an open-source probabilistic musculoskeletal modeling framework to assess how measurement error and parameter uncertainty propagate through a gait simulation. A baseline gait simulation was performed for a male subject using OpenSim for three stages: inverse kinematics, inverse dynamics, and muscle force prediction. A series of Monte Carlo simulations were performed that considered intrarater variability in marker placement, movement artifacts in each phase of gait, variability in body segment parameters, and variability in muscle parameters calculated from cadaveric investigations. Propagation of uncertainty was performed by also using the output distributions from one stage as input distributions to subsequent stages. Confidence bounds (5–95%) and sensitivity of outputs to model input parameters were calculated throughout the gait cycle. The combined impact of uncertainty resulted in mean bounds that ranged from 2.7° to 6.4° in joint kinematics, 2.7 to 8.1 N m in joint moments, and 35.8 to 130.8 N in muscle forces. The impact of movement artifact was 1.8 times larger than any other propagated source. Sensitivity to specific body segment parameters and muscle parameters were linked to where in the gait cycle they were calculated. We anticipate that through the increased use of probabilistic tools, researchers will better understand the strengths and limitations of their musculoskeletal simulations and more effectively use simulations to evaluate hypotheses and inform clinical decisions.

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Acknowledgments

We thank Katie Thompson for her assistance in figure preparation. This work was funded in part by the Donald W. Gustafson Fellowship in Orthopaedic Biomechanics awarded by the Gustafson Family Foundation.

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There are no conflicts of interest to report in the preparation of this manuscript.

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Authors and Affiliations

  1. Center for Orthopaedic Biomechanics, Department of Mechanical and Materials Engineering, University of Denver, 2390 S. York St, Denver, CO, 80208, USA

    Casey A. Myers, Peter J. Laz, Kevin B. Shelburne & Bradley S. Davidson

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  1. Casey A. Myers
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Correspondence to Bradley S. Davidson.

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Associate Editor Michael R. Torry oversaw the review of this article.

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Myers, C.A., Laz, P.J., Shelburne, K.B. et al. A Probabilistic Approach to Quantify the Impact of Uncertainty Propagation in Musculoskeletal Simulations. Ann Biomed Eng 43, 1098–1111 (2015). https://doi.org/10.1007/s10439-014-1181-7

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  • DOI: https://doi.org/10.1007/s10439-014-1181-7

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