Abstract
Although variability of anthropometric measures within a population is a well established phenomenon, most biomechanical models are based on average parameter values. For example, optimisation models for predicting muscle forces from net joint reaction moments typically use average muscle moment arms. However, understanding the distribution of musculoskeletal morbidity within a population requires information about the variation of tissue loads within the population. This study investigated the use of Monte Carlo simulation techniques to predict the statistical distribution of deltoid and rotator cuff muscle forces during static arm elevation. Muscle moment arms were modelled either as independent random variables or jointly distributed random variables. Moment arm data was collected on 22 cadaver specimens. The results demonstrated the use of Monte Carlo techniques to describe the statistical distribution of muscle forces. Although assuming statistically independent moment arms did affect the statistical distribution shape, that assumption did not affect the median predicted forces. The standard deviations of muscle forces predicted using Monte Carlo techniques were similar to the standard deviation of muscle force predictions using the whole sample of specimens. It is concluded that Monte Carlo simulation techniques are a useful tool to analyse the interindividual variability of rotator cuff muscle forces.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
An, K.N., Kwak, B.M., Chao, E.Y. andMorrey, B.F. (1984a): ‘Determination of muscle and joint forces: a new technique to solve the indeterminacy problem’,J. Biomech. Eng.,106, pp. 364–367
An, K.N., Takahashi, K., Harrigan, T.P.I. andChao, E.Y. (1984b): ‘Determination of muscle orientations and moment arms’,J. Biomech. Eng.,106, pp. 280–282
An, K.N., Kaufman, K.R. andChao, E.Y.S. (1989): ‘Physiological considerations of muscle force through the elbow joint’,J. Biomechanics,22, pp. 1249–1256
Bassett, R.W., Browne, A.O., Morrey, B.F. andAn, K.N. (1990): ‘Glenohumeral muscle force and moment mechanics in a position of shoulder instability’,J. Biomechanics,23, pp. 405–415
Brook, N., Mizrahi, J., Shoham, M. andDayan, J. (1995): ‘A biomechanical model of index finger dynamics’,Med. Eng. Phys.,17, pp. 54–63
Chaffin, D.B. andAndersson, G.B.J. (1984): ‘Occupational biomechanics’ (John Wiley, New York, USA)
Cholewicki, J., McGill, S.M. andNorman, R.W. (1995): ‘Comparison of muscle forces and joint load from an optimization and EMG assisted lumbar spine model: Towards development of a hybrid approach’,J. Biomechanics,28, pp. 321–331
Collins, J.J. (1995): ‘The redundant nature of locomotor optimization laws’,J. Biomechanics,28, pp. 251–267
Herzog, W. (1996): ‘Force-sharing among synergistic muscles: theoretical considerations and experimental approaches’,Exercise Sport Sci. Rev.,24, pp. 173–203
Högfors, C., Karlsson, D. andPeterson, B. (1995): ‘Structure and internal consistency of a shoulder model’,J. Biomechanics,28, 767–777
Johnson, M.E. (1987): ‘Multivariate statistical simulation’ (John Wiley, New York, USA).
Karlsson, D. andPeterson, B. (1992): ‘Towards a model for force predictions in the human shoulder’,J. Biomechanics,25, 189–199.
Kronberg, M., Németh, G. andBroström, L.-A. (1990): ‘Muscle activity and coordination in the normal shoulder’,Clin. Orthop.,257, pp. 76–85
Kuechle, D.K. (1994): ‘Shoulder muscle moment arm during horizontal flexion, rotation, and elevation, MS Thesis, Department of Biomedical Sciences—Orthopedics, Mayo Graduate School, Rochester, MN, USA
Liu, J., Hughes, R., Smutz, P., Neibur, G., An, K.N. (1997): ‘Roles of deltoid and rotator cuff muscles in shoulder elevation’,Clin. Biomech.,12, pp. 32–38
McCann, P.D., Wootten, M.E., Kadaba, M.P. andBigliani, L.U. (1993): ‘A kinematic and electromyographic study of shoulder rehabilitation exercises’,Clin. Orthop.,288, pp. 179–188
Mirka, G.A. andMarras, W.S. (1993): ‘A stochastic model of trunk muscle coactivation during trunk bending’,Spine,18, pp. 1396–1409
Morrey, B.F. andAn, K.N. (1990): ‘Biomechanics of the shoulder’,in Rockwood, C.A. andMatsen, F.A. (Eds.): ‘The Shoulder’ (Saunders Co., Philadelphia, USA)
Nieminen, H., Niemi, J., Takala, E.-P., Viikari-Juntura, E. (1995): ‘Load sharing patterns in the shoulder during isometric flexion tasks’,J. Biomechanics,28, pp. 555–566
Poppen, N.K. andWalker, P.S. (1978): ‘Forces at the glenohumeral joint in abduction’,Clin. Orthop.,135, pp. 165–170
Rubenstein, R.Y. (1981): ‘Simulation and the Monte Carlo method’ (John Wiley, New York, USA)
Sanders, M.S. andMcCormick, E.J. (1987): ‘Human factors in engineering and design’ (McGraw-Hill, New York, USA)
van der Helm, F.C.T., Veeger, H.E.J., Pronk, G.M., van der Woude, L.H.V. andRozendal, R.H. (1992): ‘Geometry parameters for musculoskeletal modelling of the shoulder system’,J. Biomechanics,25, pp. 129–144
van der Helm, F.C.T. (1994): ‘A finite element musculoskeletal model of the shoulder mechanism’,J. Biomechanics,27, pp. 551–569
Veeger, H.E.J., van der Helm, F.C.T., van der Woude, L.H.V., Pronk, G.M., Rozendal, R.H. (1991): ‘Inertia and muscle contraction parameters for musculoskeletal modelling of the shoulder mechanism’,J. Biomechanics,24, pp. 615–629
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Hughes, R.E., An, K.N. Monte Carlo simulation of a planar shoulder model. Med. Biol. Eng. Comput. 35, 544–548 (1997). https://doi.org/10.1007/BF02525538
Received:
Accepted:
Issue Date:
DOI: https://doi.org/10.1007/BF02525538