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A Probabilistic Model of Glenohumeral External Rotation Strength for Healthy Normals and Rotator Cuff Tear Cases

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The reigning paradigm of musculoskeletal modeling is to construct deterministic models from parameters of an “average” subject and make predictions for muscle forces and joint torques with this model. This approach is limited because it does not perform well for outliers, and it does not model the effects of population parameter variability. The purpose of this study was to simulate variability in musculoskeletal parameters on glenohumeral external rotation strength in healthy normals, and in rotator cuff tear case using a Monte Carlo model. The goal was to determine if variability in musculoskeletal parameters could quantifiably explain variability in glenohumeral external rotation strength. Multivariate Gamma distributions for musculoskeletal architecture and moment arm were constructed from empirical data. Gamma distributions of measured joint strength were constructed. Parameters were sampled from the distributions and input to the model to predict muscle forces and joint torques. The model predicted measured joint torques for healthy normals, subjects with supraspinatus tears, and subjects with infraspinatus–supraspinatus tears with small error. Muscle forces for the three conditions were predicted and compared. Variability in measured torques can be explained by differences in parameter variability.

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ACKNOWLEDGMENTS

We thank the reviewers for many constructive comments which added to the quality of this paper. This study was supported by grants from the Whitaker Foundation and the National Institutes of Health (AR048540, AR41171 and HD07447).

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Authors and Affiliations

  1. MedSport and Orthopaedic Research Laboratories, University of Michigan, Ann Arbor, MI, USA

    Joseph E. Langenderfer, James E. Carpenter & Richard E. Hughes PhD

  2. Department of Biomedical Engineering, University of Michigan, Ann Arbor, MI, USA

    Joseph E. Langenderfer & Richard E. Hughes PhD

  3. Department of Orthopaedic Surgery, University of Michigan, Ann Arbor, MI, USA

    James E. Carpenter & Richard E. Hughes PhD

  4. Department of Physical Therapy and Human Movement Sciences, Northwestern University, Evanston, IL, USA

    Marjorie E. Johnson

  5. Orthopaedic Biomechanics Laboratory, Division of Orthopaedic Research, Mayo Clinic and Mayo Foundation, Rochester, MN, USA

    Kai-nan An

  6. MedSport, University of Michigan, 24 Frank Lloyd Wright Drive, POB 391, Ann Arbor, MI, 48106-0391, USA

    Richard E. Hughes PhD

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  1. Joseph E. Langenderfer
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Langenderfer, J.E., Carpenter, J.E., Johnson, M.E. et al. A Probabilistic Model of Glenohumeral External Rotation Strength for Healthy Normals and Rotator Cuff Tear Cases. Ann Biomed Eng 34, 465–476 (2006). https://doi.org/10.1007/s10439-005-9045-9

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