Annals of Biomedical Engineering

, Volume 31, Issue 2, pp 207–220 | Cite as

Estimation of Musculotendon Properties in the Human Upper Limb

  • Brian A. Garner
  • Marcus G. Pandy


The purpose of this study was to develop and apply a general method for estimating the architectural properties of human muscles in vivo. The method consists of a two-phase, nested optimization procedure in which the values of peak isometric force, optimal muscle-fiber length, and tendon slack length are calculated for each musculotendon actuator, knowing muscle volume and the minimum and maximum physiological lengths of the actuator. In phase I, the positions of the bones and the activation levels of the muscles are found by maximizing the isometric torque developed for each degree of freedom at each joint. In phase II, the architectural properties of each musculotendon actuator are found by matching the strength profile of the model to that measured for subjects. The method is used to estimate the architectural properties of 26 major muscle groups crossing the shoulder, elbow, and wrist. Wherever possible, the model calculations are compared against measurements obtained from anatomical studies reported in the literature. Architectural data obtained from our work should be useful to researchers interested in developing musculoskeletal models of the upper limb. © 2003 Biomedical Engineering Society.

PAC2003: 8719Rr, 8710+e, 8719Ff

Musculoskeletal Modeling Muscle Tendon Parameter optimization Joint torque 


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  1. 1.
    Amis, A. A., D. Dowson, and V. Wright. Elbow joint force predictions for some strenuous isomeric actions. J. Biomech.13:765–775, 1980.Google Scholar
  2. 2.
    Amis, A. A., D. Dowson, and V. Wright. Muscle strengths and musculoskeletal geometry of the upper limb. Eng. Med. (Berlin)8:41–48, 1979.Google Scholar
  3. 3.
    An, K. N., F. C. Hui, B. G. Morrey, R. L. Linscheid, and E. Y. Chao. Muscles across the elbow joint: A biomechanical analysis. J. Biomech.14:659–669, 1981.Google Scholar
  4. 4.
    Anderson, F. C., and M. G. Pandy. Dynamic optimization of human walking. J. Biomech. Eng.123:381–390, 2001.Google Scholar
  5. 5.
    Anderson, F. C., and M. G. Pandy. Storage and utilization of elastic strain energy during jumping. J. Biomech.26:1413–1427, 1993.Google Scholar
  6. 6.
    Bassett, R. W., A. O. Browne, B. F. Morrey, and K. N. An. Glenohumeral muscle force and moment mechanics in a position of shoulder instability. J. Biomech.14:659–669, 1990.Google Scholar
  7. 7.
    Brand, P. W., R. B. Beach, and D. E. Thompson. Relative tension and potential excursion of muscles in the forearm and hand. J. Hand Surgery6:209–219, 1981.Google Scholar
  8. 8.
    Chen, J. J. Quantitative architectural analysis of human upper-extremity muscles. PhD dissertation, University of Virginia, 1988.Google Scholar
  9. 9.
    Cutts, A., R. M. Alexander, and R. F. Ker. Ratios of cross-sectional areas of muscles and their tendons in a healthy human forearm. J. Anatomy176:133–137, 1991.Google Scholar
  10. 10.
    Delp, S. L., A. E. Grierson, and T. S. Buchanan. Maximum isometric movements generated by the wrist muscles in flexion-extension and radial-ulnar deviation. J. Biomech.29:1371–1375, 1996.Google Scholar
  11. 11.
    Delp, S. L., J. P. Loan, M. G. Hoy, F. E. Zajac, E. L. Topp, and J. M. Rosen. An interactive graphics-based model of the lower extremity to study orthopaedic surgical procedures. IEEE Trans. Biomed. Eng.37:757–767, 1990.Google Scholar
  12. 12.
    Engin, A. E., and I. Kaleps. Active muscle torques about long-bone axes of major human joints. Aviat., Space Environ. Med.51:551–555, 1980.Google Scholar
  13. 13.
    Engin, A. E., and S. M. Chen. Statistical data base for the biomechanical properties of the human shoulder complex—I: Kinematics of the shoulder complex. J. Biomech. Eng.108:215–225, 1986.Google Scholar
  14. 14.
    Garner, B. A., and M. G. Pandy. Musculoskeletal model of the human arm based on the visible human male dataset. Comput. Methods Biomech. Biomed. Eng.4:93–126, 2001.Google Scholar
  15. 15.
    Garner, B. A., and M. G. Pandy. The obstacle set method for representing muscle paths in musculoskeletal models. Comput. Methods Biomech. Biomed. Eng.3:1–30, 2000.Google Scholar
  16. 16.
    Garner, B. A., and M. G. Pandy. A kinematic model of the upper limb based on the visible human project (VHP) image dataset. Comput. Methods Biomech. Biomed. Eng.2:107–124, 1999.Google Scholar
  17. 17.
    Gonzalez, R. V., E. L. Hutchins, R. E. Barr, and L. D. Abraham. Development and evaluation of a musculoskeletal model of the elbow joint complex. J. Biomech. Eng.118:32–40, 1996.Google Scholar
  18. 18.
    Gordon, A. M., A. F. Huxley, and F. J. Julian. The variation in isometric tension with sarcomere length in vertebrate muscle fibres. J. Physiol. (London)184:170–192, 1966.Google Scholar
  19. 19.
    Hatze, H.. Estimation of myodynamic parameter values from observations on isometrically contracting muscle groups. Appl. Phys. (Berlin)46:325–338, 1981.Google Scholar
  20. 20.
    Hoy, M. G., F. E. Zajac, and M. E. Gordon. A musculoskeletal model of the human lower extremity: The effect of muscle, tendon, and moment arm on the moment-angle relationship of musculotendon actuators at the hip, knee, and ankle. J. Biomech.23:157–169, 1990.Google Scholar
  21. 21.
    Hutchins, E. L. The musculoskeletal geometry of the human elbow and wrist: An analysis using torque-angle relationships. Masters thesis, The University of Texas at Austin, 1993.Google Scholar
  22. 22.
    Johnson, G. R., D. Spalding, A. Nowitzke, and N. Bogduk. Modelling the muscles of the scapula: Morphometric and coordinate data and functional implications. J. Biomech.29:1039–1051, 1996.Google Scholar
  23. 23.
    Karlsson, D., and B. Peterson. Towards a model for force predictions in the human shoulder. J. Biomech.25:189–192, 1992.Google Scholar
  24. 24.
    Keating, J. F., P. Waterworth, J. Shaw-Dunn, and J. Crossan. The relative strengths of the rotator cuff muscles. J. Bone Jt. Surg., Br. Vol.75B:137–140, 1993.Google Scholar
  25. 25.
    Klein-Breteler, M. D., C. W. Spoor, and F. C. T. Van der Helm. Measuring muscle and joint geometry parameters of a shoulder for modeling purposes. J. Biomech.32:1191–1197, 1999.Google Scholar
  26. 26.
    Knapik, J. J., J. E. Wright, R. H. Mawdsley, and J Braun. Isometric, isotonic, and isokinetic torque variations in four muscle groups through a range of joint motion. Physical Therapy63:938–947, 1983.Google Scholar
  27. 27.
    Lemay, M. A., and P. E. Crago. A dynamic model for simulating movements of the elbow, forearm, and wrist. J. Biomech.29:1319–1330, 1996.Google Scholar
  28. 28.
    Lieber, R. L., M. D. Jacobson, B. M. Fazeli, R. A. Abrams, and M. J. Botte. Architecture of selected muscles of the arm and forearm: Anatomy and implications for tendon transfer. J. Hand Surgery17A:787–798, 1992.Google Scholar
  29. 29.
    Loren, G. J., S. D. Shoemaker, T. J. Burkholder, M. D. Jacobson, J. Friden, and R. L. Lieber. Human wrist motors: Biomechanical design and application to tendon transfers. J. Biomech.29:331–342, 1996.Google Scholar
  30. 30.
    Otis, J. C., R. F. Warren, S. I. Backus, T. J. Santner, and J. D. Mabrey. Torque production in the shoulder of the normal young adult male. Am. J. Sports Med.18:119–123, 1990.Google Scholar
  31. 31.
    Pandy, M. G.. Computer modeling and simulation of human movement. Annu. Rev. Biomed. Eng.3:245–273, 2001.Google Scholar
  32. 32.
    Pandy, M. G., F. E. Zajac, E. Sim, and W. S. Levine. An optimal control model for maximum-height human jumping. J. Biomech.23:1185–1198, 1990.Google Scholar
  33. 33.
    Raasch, C. C., F. E. Zajac, B. Ma, and W. S. Levine. Muscle coordination of maximum-speed pedaling. J. Biomech.30:595–602, 1997.Google Scholar
  34. 34.
    Reiser, R. F. Development of geometric and muscle-specific parameter values for musculoskeletal modeling of the shoulder joint. Masters thesis, The University of Texas at Austin, 1993.Google Scholar
  35. 35.
    Spector, S. A., P. F. Gardiner, R. F. Zernicke, R. R. Roy, and V. R. Edgerton. Muscle architecture and force-velocity characteristics of cat soleus and medial gastrocnemius: Implications for motor control. J. Neurophysiol.44:951–960, 1980.Google Scholar
  36. 36.
    Steindler, A. Postgraduate lectures in orthopedics, diagnosis, and indications. Springfield, Illinois: Charles C. Thomas, 1950.Google Scholar
  37. 37.
    Veeger, H. E., Y. Bing, K. N. An, and R. H. Rozendal. Parameters for modeling the upper extremity. J. Biomech.30:647–652, 1997.Google Scholar
  38. 38.
    Veeger, H. E., F. C. van der Helm, L. H. van der Woulde, G. M. Pronk, and R. H. Rozendal. Inertia and muscle contraction parameters for musculoskeletal modeling of the shoulder mechanism. J. Biomech.24:615–629, 1991.Google Scholar
  39. 39.
    Weijs, W. A., and B. Hillen. Cross-sectional areas and estimated intrinsic strength of the human jaw muscles. Acta Morphology Aeerl.Scand23:267–274, 1985.Google Scholar
  40. 40.
    Winters, J. M., and D. J. Kleweno. Effect of initial upper limb alignment on muscle contributions to isometric strength curves. J. Biomech.26:143–153, 1993.Google Scholar
  41. 41.
    Winters, J. M., and L. Stark. Estimated mechanical properties of synergistic muscles involved in movements of a variety of human joints. J. Biomech.21:1027–1041, 1988.Google Scholar
  42. 42.
    Wood, J. E., S. G. Meek, and S. C. Jacobsen. Quantitation of human shoulder anatomy for prosthetic arm control—I. Surface modelling. J. Biomech.22:273–292, 1989.Google Scholar
  43. 43.
    Zajac, F. E. Muscle and tendon: Properties, models, scaling, and application to biomechanics and motor control. In: CRC Critical Reviews in Biomedical Engineering, edited by J. R. Bourne. Baltimore; Williams & Wilkins, 1989, Vol. 17, pp. 359–411.-Google Scholar

Copyright information

© Biomedical Engineering Society 2003

Authors and Affiliations

  • Brian A. Garner
    • 1
  • Marcus G. Pandy
    • 2
  1. 1.Department of EngineeringBaylor UniversityWaco
  2. 2.Department of Biomedical EngineeringUniversity of TexasAustin

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