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A Model of the Lower Limb for Analysis of Human Movement

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Abstract

Computer models that estimate the force generation capacity of lower limb muscles have become widely used to simulate the effects of musculoskeletal surgeries and create dynamic simulations of movement. Previous lower limb models are based on severely limited data describing limb muscle architecture (i.e., muscle fiber lengths, pennation angles, and physiological cross-sectional areas). Here, we describe a new model of the lower limb based on data that quantifies the muscle architecture of 21 cadavers. The model includes geometric representations of the bones, kinematic descriptions of the joints, and Hill-type models of 44 muscle–tendon compartments. The model allows calculation of muscle–tendon lengths and moment arms over a wide range of body positions. The model also allows detailed examination of the force and moment generation capacities of muscles about the ankle, knee, and hip and is freely available at www.simtk.org.

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References

  1. Anderson, D. E., M. L. Madigan, and M. A. Nussbaum. Maximum voluntary joint torque as a function of joint angle and angular velocity: model development and application to the lower limb. J. Biomech. 40:3105–3113, 2007.

    Article  PubMed  Google Scholar 

  2. Arnold, A. S., D. J. Asakawa, and S. L. Delp. Do the hamstrings and adductors contribute to excessive internal rotation of the hip in persons with cerebral palsy? Gait Posture 11:181–190, 2000.

    Article  CAS  PubMed  Google Scholar 

  3. Arnold, A. S., S. S. Blemker, and S. L. Delp. Evaluation of a deformable musculoskeletal model for estimating muscle-tendon lengths during crouch gait. Ann. Biomed. Eng. 29:263–274, 2001.

    Article  CAS  PubMed  Google Scholar 

  4. Arnold, A. S., S. Salinas, D. J. Asakawa, and S. L. Delp. Accuracy of muscle moment arms estimated from MRI-based musculoskeletal models of the lower extremity. Comput. Aided Surg. 5:108–119, 2000.

    Article  CAS  PubMed  Google Scholar 

  5. Blemker, S. S., and S. L. Delp. Rectus femoris and vastus intermedius fiber excursions predicted by three-dimensional muscle models. J. Biomech. 39:1383–1391, 2006.

    Article  PubMed  Google Scholar 

  6. Brand, R. A., R. D. Crowninshield, C. E. Wittstock, D. R. Pedersen, C. R. Clark, and F. M. van Krieken. A model of lower extremity muscular anatomy. J. Biomech. Eng. 104:304–310, 1982.

    Article  CAS  PubMed  Google Scholar 

  7. Buford, Jr., W. L., F. M. Ivey, Jr., J. D. Malone, R. M. Patterson, G. L. Peare, D. K. Nguyen, and A. A. Stewart. Muscle balance at the knee–moment arms for the normal knee and the ACL-minus knee. IEEE Trans. Rehabil. Eng. 5:367–379, 1997.

    Article  PubMed  Google Scholar 

  8. Cahalan, T. D., M. E. Johnson, S. Liu, and E. Y. Chao. Quantitative measurements of hip strength in different age groups. Clin. Orthop. Relat. Res. 246:136–145, 1989.

    PubMed  Google Scholar 

  9. Crowninshield, R. D., and R. A. Brand. A physiologically based criterion of muscle force prediction in locomotion. J. Biomech. 14:793–801, 1981.

    Article  CAS  PubMed  Google Scholar 

  10. Delp, S. L. Surgery Simulation: A Computer Graphics System to Analyze and Design Musculoskeletal Reconstructions of the Lower Limb. Ph.D., Department of Mechanical Engineering. Stanford, CA: Stanford University, 1990.

    Google Scholar 

  11. Delp, S. L., F. C. Anderson, A. S. Arnold, P. Loan, A. Habib, C. T. John, E. Guendelman, and D. G. Thelen. OpenSim: open-source software to create and analyze dynamic simulations of movement. IEEE Trans. Biomed. Eng. 54:1940–1950, 2007.

    Article  PubMed  Google Scholar 

  12. Delp, S. L., and J. P. Loan. A graphics-based software system to develop and analyze models of musculoskeletal structures. Comput. Biol. Med. 25:21–34, 1995.

    Article  CAS  PubMed  Google Scholar 

  13. 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.

    Article  CAS  PubMed  Google Scholar 

  14. Delp, S. L., D. A. Ringwelski, and N. C. Carroll. Transfer of the rectus femoris: effects of transfer site on moment arms about the knee and hip. J. Biomech. 27:1201–1211, 1994.

    Article  CAS  PubMed  Google Scholar 

  15. Friederich, J. A., and R. A. Brand. Muscle fiber architecture in the human lower limb. J. Biomech. 23:91–95, 1990.

    Article  CAS  PubMed  Google Scholar 

  16. Fukunaga, T., R. R. Roy, F. G. Shellock, J. A. Hodgson, and V. R. Edgerton. Specific tension of human plantar flexors and dorsiflexors. J. Appl. Physiol. 80:158–165, 1996.

    CAS  PubMed  Google Scholar 

  17. Gordon, C. C., T. Churchill, C. E. Clauser, B. Cradtmillser, J. T. McConville, I. Tebbets, and R. A. Walker. 1988 Anthropometric Survey of U.S. Army Personnel: Methods and Summary Statistics. Natick, MA: United States Army Natick Research, Development, and Engineering Center, 1989.

    Google Scholar 

  18. Grood, E. S., W. J. Suntay, F. R. Noyes, and D. L. Butler. Biomechanics of the knee-extension exercise. Effect of cutting the anterior cruciate ligament. J. Bone Joint Surg. Am. 66:725–734, 1984.

    CAS  PubMed  Google Scholar 

  19. Herzog, W., E. Hasler, and S. K. Abrahamse. A comparison of knee extensor strength curves obtained theoretically and experimentally. Med. Sci. Sports Exerc. 23:108–114, 1991.

    CAS  PubMed  Google Scholar 

  20. Horsman, M. D. K. The Twente Lower Extremity Model: Consistent Dynamic Simulation of the Human Locomotor Apparatus. Ph.D., Department of Engineering Technology. Enschede, The Netherlands: University of Twente, 2007.

    Google Scholar 

  21. Horsman, M. D. K., H. F. J. M. Koopman, F. C. T. van der Helm, L. P. Prose, and H. E. J. Veeger. Morphological muscle and joint parameters for musculoskeletal modelling of the lower extremity. Clin. Biomech. 22:239–247, 2007.

    Article  Google Scholar 

  22. Inman, V. T. The Joints of the Ankle. Baltimore: Williams & Wilkins, 1976.

    Google Scholar 

  23. Inman, V. T., H. J. Ralston, and F. Todd. Human Walking. Baltimore: Williams & Wilkins, 1981.

    Google Scholar 

  24. Klein, C. S., C. L. Rice, and G. D. Marsh. Normalized force, activation, and coactivation in the arm muscles of young and old men. J. Appl. Physiol. 91:1341–1349, 2001.

    CAS  PubMed  Google Scholar 

  25. Lexell, J., C. C. Taylor, and M. Sjostrom. What is the cause of the ageing atrophy? Total number, size and proportion of different fiber types studied in whole vastus lateralis muscle from 15- to 83-year-old men. J. Neurol. Sci. 84:275–294, 1988.

    Article  CAS  PubMed  Google Scholar 

  26. Lieber, R. L., and J. Friden. Functional and clinical significance of skeletal muscle architecture. Muscle Nerve 23:1647–1666, 2000.

    Article  CAS  PubMed  Google Scholar 

  27. Liu, M. Q., F. C. Anderson, M. G. Pandy, and S. L. Delp. Muscles that support the body also modulate forward progression during walking. J. Biomech. 39:2623–2630, 2006.

    Article  PubMed  Google Scholar 

  28. Lu, T.-W., J. J. O’Connor, S. J. G. Taylor, and P. S. Walker. Validation of a lower limb model with in vivo femoral forces telemetered from two subjects. J. Biomech. 31:63–69, 1998.

    Article  CAS  PubMed  Google Scholar 

  29. Marsh, E., D. Sale, A. J. McComas, and J. Quinlan. Influence of joint position on ankle dorsiflexion in humans. J. Appl. Physiol. 51:160–167, 1981.

    CAS  PubMed  Google Scholar 

  30. Morse, C. I., J. M. Thom, K. M. Birch, and M. V. Narici. Changes in triceps surae muscle architecture with sarcopenia. Acta Physiol. Scand. 183:291–298, 2005.

    Article  CAS  PubMed  Google Scholar 

  31. Murray, M. P., G. M. Gardner, L. A. Mollinger, and S. B. Sepic. Strength of isometric and isokinetic contractions: knee muscles of men aged 20 to 86. Phys. Ther. 60:412–419, 1980.

    CAS  PubMed  Google Scholar 

  32. Neptune, R. R., S. A. Kautz, and F. E. Zajac. Contributions of the individual ankle plantar flexors to support, forward progression and swing initiation during walking. J. Biomech. 34:1387–1398, 2001.

    Article  CAS  PubMed  Google Scholar 

  33. Olson, V. L., G. L. Smidt, and R. C. Johnston. The maximum torque generated by the eccentric, isometric, and concentric contractions of the hip abductor muscles. Phys. Ther. 52:149–158, 1972.

    CAS  PubMed  Google Scholar 

  34. Piazza, S. J., and S. L. Delp. Three-dimensional dynamic simulation of total knee replacement motion during a step-up task. J. Biomech. Eng. 123:599–606, 2001.

    Article  CAS  PubMed  Google Scholar 

  35. Powell, P. L., R. R. Roy, P. Kanim, M. A. Bello, and V. R. Edgerton. Predictability of skeletal muscle tension from architectural determinations in guinea pig hindlimbs. J. Appl. Physiol. 57:1715–1721, 1984.

    CAS  PubMed  Google Scholar 

  36. Raasch, C. C., F. E. Zajac, B. Ma, and W. S. Levine. Muscle coordination of maximum-speed pedaling. J. Biomech. 30:595–602, 1997.

    Article  CAS  PubMed  Google Scholar 

  37. Riener, R., and T. Edrich. Identification of passive elastic joint moments in the lower extremities. J. Biomech. 32:539–544, 1999.

    Article  CAS  PubMed  Google Scholar 

  38. Sale, D., J. Quinlan, E. Marsh, A. J. McComas, and A. Y. Belanger. Influence of joint position on ankle plantarflexion in humans. J. Appl. Physiol. 52:1636–1642, 1982.

    CAS  PubMed  Google Scholar 

  39. Seireg, A., and R. J. Arvikar. A mathematical model for evaluation of forces in lower extremities of the musculo-skeletal system. J. Biomech. 6:313–326, 1973.

    Article  CAS  PubMed  Google Scholar 

  40. Spoor, C. W., and J. L. van Leeuwen. Knee muscle moment arms from MRI and from tendon travel. J. Biomech. 25:201–206, 1992.

    Article  CAS  PubMed  Google Scholar 

  41. van den Bogert, A. J., K. G. Gerritsen, and G. K. Cole. Human muscle modelling from a user’s perspective. J. Electromyogr. Kinesiol. 8:119–124, 1998.

    Article  PubMed  Google Scholar 

  42. van Eijden, T. M., W. A. Weijs, E. Kouwenhoven, and J. Verburg. Forces acting on the patella during maximal voluntary contraction of the quadriceps femoris muscle at different knee flexion/extension angles. Acta Anat (Basel) 129:310–314, 1987.

    Article  Google Scholar 

  43. Walker, P. S., J. S. Rovick, and D. D. Robertson. The effects of knee brace hinge design and placement on joint mechanics. J. Biomech. 21:965–974, 1988.

    Article  CAS  PubMed  Google Scholar 

  44. Ward, S. R., C. M. Eng, L. H. Smallwood, and R. L. Lieber. Are current measurements of lower extremity muscle architecture accurate? Clin. Orthop. Relat. Res. 467:1074–1082, 2009.

    Article  PubMed  Google Scholar 

  45. Waters, R. L., J. Perry, J. M. McDaniels, and K. House. The relative strength of the hamstrings during hip extension. J. Bone Joint Surg. Am. 56:1592–1597, 1974.

    CAS  PubMed  Google Scholar 

  46. Wickiewicz, T. L., R. R. Roy, P. L. Powell, and V. R. Edgerton. Muscle architecture of the human lower limb. Clin. Orthop. 179:275–283, 1983.

    PubMed  Google Scholar 

  47. Young, A., M. Stokes, and M. Crowe. Size and strength of the quadriceps muscles of old and young women. Eur. J. Clin. Invest. 14:282–287, 1984.

    Article  CAS  PubMed  Google Scholar 

  48. Zajac, F. E. Muscle and tendon: properties, models, scaling, and application to biomechanics and motor control. Crit. Rev. Biomed. Eng. 17:359–411, 1989.

    CAS  PubMed  Google Scholar 

  49. Zajac, F. E. Muscle coordination of movement: a perspective. J. Biomech. 26(Suppl 1):109–124, 1993.

    Article  PubMed  Google Scholar 

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Acknowledgments

We thank Carolyn Eng, Trevor Kingsbury, Kristin Lieber, Jaqueline Braun, Laura Smallwood, and Taylor Winters and the Anatomical Services Department at the University of California San Diego for their work collecting this cadaver data. Funding for this work was provided by the National Institutes of Health Grants HD048501, HD050837, EB006735, U54 GM072970 and a Stanford Bio-X Graduate Student Fellowship.

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Correspondence to Scott L. Delp.

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Arnold, E.M., Ward, S.R., Lieber, R.L. et al. A Model of the Lower Limb for Analysis of Human Movement. Ann Biomed Eng 38, 269–279 (2010). https://doi.org/10.1007/s10439-009-9852-5

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  • DOI: https://doi.org/10.1007/s10439-009-9852-5

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