Annals of Biomedical Engineering

, Volume 37, Issue 7, pp 1342–1347 | Cite as

Optimization of Muscle Wrapping Objects Using Simulated Annealing

  • Christopher J. Gatti
  • Richard E. HughesEmail author


Musculoskeletal models use wrapping objects to constrain muscle paths from passing through anatomical obstacles; however, the selection of wrapping object parameters is typically a manual, iterative, and time-consuming process. The purpose of this study was to use a data-driven optimization algorithm to determine wrapping object parameters. Wrapping parameters were determined using simulated annealing for two cases: (1) modeling the triceps at the elbow using a cylindrical wrapping object, and (2) modeling the middle deltoid using a spherical wrapping object. It was found that an optimization algorithm could be used to determine wrapping object parameters which produced moment arms that were similar to experimental data. The greatest benefit of this method is the efficiency at which model parameters were determined, thus eliminating much of the time required to manually refine the wrapping objects. Model development could be further improved by extending this method to other model parameters and combining various optimization techniques.


Musculoskeletal model Moment arms Model parameters 



The authors would like to thank Dr. Barbara McCreadie, of Grizzly Moose LLC, for her insightful review of this manuscript, and Nick Flieg for his assistance in coding the shoulder model. Funding was provided to Grizzly Moose LLC, with subcontract to the University of Michigan, by grant R41HD53886 from the National Institutes of Health. Dr. Hughes is an unpaid scientific advisor to Grizzly Moose LLC and does not have equity in the company.


  1. 1.
    Ackland, D. C., P. Pak, M. Richardson, and M. G. Pandy. Moment arms of the muscles crossing the anatomical shoulder. J. Anat. 213(4):383-390, 2008. doi: 10.1111/j.1469-7580.2008.00965.x.PubMedCrossRefGoogle Scholar
  2. 2.
    An, K. N., F. C. Hui, B. F. Morrey, R. L. Linscheid, and E. Y. Chao. Muscles across the elbow joint: A biomechanical analysis. J. Biomech. 14(10):659-669, 1979. doi: 10.1016/0021-9290(81)90048-8.CrossRefGoogle Scholar
  3. 3.
    Delp, S. L., and J. P. Loan. A graphics-based software system to develop and analyze models of musculoskeletal structures. Comput. Biol. Med. 25(1):21-34, 1995. doi: 10.1016/0010-4825(95)98882-E.PubMedCrossRefGoogle Scholar
  4. 4.
    Ettema, G. J. C., G. Styles, and V. Kippers. The moment arms of 23 muscle segments of the upper limb with varying elbow and forearm positions: Implications for motor control. Hum. Movement Sci. 17(2):201-220, 1998. doi: 10.1016/S0167-9457(97)00030-4.CrossRefGoogle Scholar
  5. 5.
    Garner, B. A., and M. G. Pandy. The obstacle-set method for representing muscle paths in musculoskeletal models. Comput. Meth. Biomech. Biomed. Eng. 3(1):1-30, 2000. doi: 10.1080/10255840008915251.CrossRefGoogle Scholar
  6. 6.
    Gerbeaux, M., E. Turpin, and G. Lensel-Corbeil. Musculo-articular modelling of the triceps brachii. J. Biomech. 29(2):171-180, 1996. doi: 10.1016/0021-9290(95)00032-1.PubMedCrossRefGoogle Scholar
  7. 7.
    Holzbaur, K. R. S., W. M. Murray, and S. L. Delp. A model of the upper extremity for simulating musculoskeletal surgery and analyzing neuromuscular control. Ann. Biomed. Eng. 33(6):829-840, 2005. doi: 10.1007/s10439-005-3320-7.PubMedCrossRefGoogle Scholar
  8. 8.
    Inman, V. T., M. Saunders, and L. C. Abbott. Observations of the functional shoulder joint. J. Bone Joint Surg. Am. 26(1):1-30, 1944.Google Scholar
  9. 9.
    Kirkpatrick, S., C. D. Gelatt, and M. P. Veechi. Optimization by simulated annealing. Science 220(4598):671-680, 1983. doi: 10.1126/science.220.4598.671.PubMedCrossRefGoogle Scholar
  10. 10.
    Kuechle, D. K., S. R. Newman, E. Itoi, B. F. Morrey, and K. N. An. Shoulder muscle moment arms during horizontal flexion and elevation. J. Shoulder Elb. Surg. 6(5):429-439, 1997. doi: 10.1016/S1058-2746(97)70049-1.CrossRefGoogle Scholar
  11. 11.
    Liu, J., R. E. Hughes, W. P. Smutz, G. Neibur, and K. N. An. Roles of the deltoid and rotator cuff muscles in shoulder elevation. Clin. Biomech. 12(1):32-38, 1997. doi: 10.1016/S0268-0033(96)00047-2.CrossRefGoogle Scholar
  12. 12.
    Murray, W. M., T. S. Buchanan, and S. L. Delp. Scaling of peak moment arms of elbow muscles with upper extremity bone dimensions. J. Biomech. 35(1):19-26, 2002. doi: 10.1016/S0021-9290(01)00173-7.PubMedCrossRefGoogle Scholar
  13. 13.
    Petitti, D. B. Meta-Analysis, Decision Analysis, and Cost-Effectiveness Analysis: Methods for Quantitative Synthesis in Medicine. New York: Oxford University Press, pp. 120-123, 2000.Google Scholar
  14. 14.
    Pigeon, P., L. Yahia, and A. Feldman. Moment arms and lengths of human upper limb muscles as functions of joint angles. J. Biomech. 29(10):1365-1370, 1996. doi: 10.1016/0021-9290(96)00031-0.PubMedCrossRefGoogle Scholar
  15. 15.
    Santos, V. J., and F. J. Valero-Cuevas. A Bayesian approach to biomechanical modeling to optimize over large parameter spaces while considering anatomic variability. In: Proceedings of the 26th Annual International Conference of the IEEE EMBS, San Francisco, CA, 2004, pp. 4626–4629.Google Scholar
  16. 16.
    Sutton, A. J., K. R. Abrams, D. R. Jones, T. A. Sheldon, and F. Song. Methods for Meta-Analysis in Medical Research. New York: Wiley, 2000.Google Scholar
  17. 17.
    Valero-Cuevas, F. J., V. V. Anand, A. Saxena, and H. Lipson. Beyond parameters estimation: Extending biomechanical modeling by the explicit exploration of model toplogy. IEEE T. Biomed. Eng. 54(11):1951-1964, 2007. doi: 10.1109/TBME.2007.906494.PubMedCrossRefGoogle Scholar
  18. 18.
    Vandekerckhove, J. MATLAB Central File Exchange: general simulated annealing algorithm. Available at, 2008.
  19. 19.
    van der Helm, F. C. T. The shoulder mechanism: a dynamic approach. Ph.D. thesis, Delft University of Technology, Delft, The Netherlands, 1991.Google Scholar
  20. 20.
    Vasavada, A. N., R. A. Lasher, T. E. Meyer, and D. C. Lin. Defining and evaluating wrapping surfaces for MRI-based spinal muscle paths. J. Biomech. 41(7):1450-1457, 2008. doi: 10.1016/j.jbiomech.2008.02.027.PubMedCrossRefGoogle Scholar

Copyright information

© Biomedical Engineering Society 2009

Authors and Affiliations

  1. 1.Laboratory for Optimization and Computation in Orthopaedic Surgery, Department of Orthopaedic SurgeryUniversity of MichiganAnn ArborUSA

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