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Annals of Biomedical Engineering

, Volume 39, Issue 1, pp 147–160 | Cite as

An Optimization Approach to Inverse Dynamics Provides Insight as to the Function of the Biarticular Muscles During Vertical Jumping

  • Daniel J. CleatherEmail author
  • Jon E. Goodwin
  • Anthony M. J. Bull
Article

Abstract

Traditional inverse dynamics approaches to calculating the inter-segmental moments are limited in their ability to accurately reflect the function of the biarticular muscles. In particular they are based on the assumption that the net inter-segmental moment is zero and that total joint moments are independent of muscular activity. Traditional approaches to calculating muscular forces from the inter-segmental moments are based on a consideration of joint moments which do not encapsulate the potential moment asymmetry between segments. In addition, traditional approaches may artificially constrain the activity of the biarticular muscles. In this study, an optimization approach to the simultaneous inverse determination of inter-segmental moments and muscle forces (the 1-step method) based on a consideration of segmental rotations was employed to study vertical jumping and contrasted with the more traditional 2-step approach of determining inter-segmental moments from an inverse dynamics analysis then muscle forces using optimization techniques. The 1-step method resulted in significantly greater activation of both the monoarticular and biarticular musculature which was then translated into significantly greater joint contact forces, muscle powers, and inter-segmental moments. The results of this study suggest that traditional conceptions of inter-segmental moments do not completely encapsulate the function of the biarticular muscles and that joint function can be better understood by recognizing the asymmetry in inter-segmental moments.

Keywords

Musculoskeletal modeling Muscle force Joint contact force Muscle power Inter-segmental moments 

Abbreviations

AS

Anterior tibial shear

BI

Inverse optimization approach (biarticular muscles with standard upper bounds)

BIH

Inverse optimization approach (selected biarticular muscles have double the standard upper bound)

GCS

Global coordinate system

LCS

Local coordinate system

MONO

Inverse optimization approach (only monoarticular muscles)

PFJ

Patellofemoral joint contact force

PS

Posterior tibial shear

TFJ

Tibiofemoral joint contact force

TRAD

Traditional method of calculating joint moments

TRADB

Traditional method of calculating muscle forces (biarticular muscles with standard upper bounds)

TRADM

Traditional method of calculating muscle forces (only monoarticular muscles)

Notes

Acknowledgments

The authors would like to thank the anonymous reviewers for the clarity of their thoughts which greatly increased the transparency of this article.

References

  1. 1.
    Anderson, F. C., and M. G. Pandy. A dynamic optimization solution for vertical jumping in three dimensions. Comput. Methods Biomech. Biomed. Eng. 2:201–231, 1999.CrossRefGoogle Scholar
  2. 2.
    Bobbert, M. F., K. G. M. Gerritsen, M. C. A. Litjens, and A. J. VanSoest. Why is countermovement jump height greater than squat jump height? Med. Sci. Sports Exerc. 28:1402–1412, 1996.PubMedGoogle Scholar
  3. 3.
    Bobbert, M. F., and J. P. van Zandwijk. Dynamics of force and muscle stimulation in human vertical jumping. Med. Sci. Sports Exerc. 31:303–310, 1999.PubMedCrossRefGoogle Scholar
  4. 4.
    Cleather, D. J. Forces in the Knee During Vertical Jumping and Weightlifting. Ph.D. thesis, Imperial College London, 2010.Google Scholar
  5. 5.
    Cleather, D. J., and A. M. J. Bull. Lower extremity musculoskeletal geometry effects the calculation of patellofemoral forces in vertical jumping and weightlifting. Proc. IME H J. Eng. Med. 224:1073–1083, 2010.CrossRefGoogle Scholar
  6. 6.
    Crowninshield, R. D., and R. A. Brand. A physiologically based criterion of muscle force prediction in locomotion. J. Biomech. 14:793–801, 1981.PubMedCrossRefGoogle Scholar
  7. 7.
    de Leva, P. Adjustments to Zatsiorsky-Seluyanov’s segment inertia parameters. J. Biomech. 29:1223–1230, 1996.PubMedCrossRefGoogle Scholar
  8. 8.
    Dumas, R., R. Aissaoui, and J. A. de Guise. A 3D generic inverse dynamic method using wrench notation and quaternion algebra. Comput. Methods Biomech. Biomed. Eng. 7:159–166, 2004.CrossRefGoogle Scholar
  9. 9.
    Dumas, R., E. Nicol, and L. Cheze. Influence of the 3D inverse dynamic method on the joint forces and moments during gait. J. Biomech. Eng. 129:786–790, 2007.PubMedCrossRefGoogle Scholar
  10. 10.
    Fraysse, F., R. Dumas, L. Cheze, and X. Wang. Comparison of global and joint-to-joint methods for estimating the hip joint load and the muscle forces during walking. J. Biomech. 42:2357–2362, 2009.PubMedCrossRefGoogle Scholar
  11. 11.
    Gregoire, L., H. E. Veeger, P. A. Huijing, and G. J. van Ingen Schenau. Role of mono- and bi-articular muscles in explosive movements. Int. J. Sports Med. 5:301–305, 1984.PubMedCrossRefGoogle Scholar
  12. 12.
    Heise, G. D., D. W. Morgan, H. Hough, and M. Craib. Relationships between running economy and temporal EMG characteristics of bi-articular muscles. Int. J. Sports Med. 17:128–133, 1996.PubMedCrossRefGoogle Scholar
  13. 13.
    Heise, G. D., M. Shinohara, and L. Binks. Biarticular leg muscles and links to running economy. Int. J. Sports Med. 29:688–691, 2008.PubMedCrossRefGoogle Scholar
  14. 14.
    Horn, B. K. P. Closed form solution of absolute orientation using unit quaternions. J. Opt. Soc. Am. A 4:629–642, 1987.CrossRefGoogle Scholar
  15. 15.
    Horsman, M. D., H. F. J. M. Koopman, F. C. T. van der Helm, L. Poliacu Prose, and H. E. J. Veeger. Morphological muscle and joint parameters for musculoskeletal modelling of the lower extremity. Clin. Biomech. 22:239–247, 2007.CrossRefGoogle Scholar
  16. 16.
    Jacobs, R., M. F. Bobbert, and G. J. V. Schenau. Function of monoarticular and biarticular muscles in running. Med. Sci. Sports Exerc. 25:1163–1173, 1993.PubMedGoogle Scholar
  17. 17.
    Jacobs, R., M. F. Bobbert, and G. J. van Ingen Schenau. Mechanical output from individual muscles during explosive leg extensions: the role of biarticular muscles. J. Biomech. 29:513–523, 1996.PubMedCrossRefGoogle Scholar
  18. 18.
    Lees, A., J. Vanrenterghem, and D. de Clercq. The maximal and submaximal vertical jump: implications for strength and conditioning. J. Strength Cond. Res. 18:787–791, 2004.PubMedGoogle Scholar
  19. 19.
    Nha, K. W., R. Papannagari, T. J. Gill, S. K. Van de Velde, A. A. Freiberg, H. E. Rubash, and G. Li. In vivo patellar tracking: Clinical motions and patellofemoral indices. J. Orthop. Res. 26:1067–1074, 2008.PubMedCrossRefGoogle Scholar
  20. 20.
    Pandy, M. G., and F. E. Zajac. Optimal muscular coordination strategies for jumping. J. Biomech. 24:1–10, 1991.PubMedCrossRefGoogle Scholar
  21. 21.
    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.PubMedCrossRefGoogle Scholar
  22. 22.
    Pflum, M. A., K. B. Shelburne, M. R. Torry, M. J. Decker, and M. G. Pandy. Model prediction of anterior cruciate ligament force during drop-landings. Med. Sci. Sports Exerc. 36:1949–1958, 2004.PubMedCrossRefGoogle Scholar
  23. 23.
    Press, W. H., S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery. Numerical Recipes in C++: The Art of Scientific Computing. Cambridge, NY: Cambridge University Press, 1002 pp., 2002.Google Scholar
  24. 24.
    Prilutsky, B. I., T. Isaka, A. M. Albrecht, and R. J. Gregor. Is coordination of two-joint leg muscles during load lifting consistent with the strategy of minimum fatigue? J. Biomech. 31:1025–1034, 1998.PubMedCrossRefGoogle Scholar
  25. 25.
    Prilutsky, B. I., and V. M. Zatsiorsky. Tendon action of two-joint muscles: transfer of mechanical energy between joints during jumping, landing, and running. J. Biomech. 27:25–34, 1994.PubMedCrossRefGoogle Scholar
  26. 26.
    Raikova, R. Prediction of individual muscle forces using Lagrange multipliers method—a model of the upper human limb in the sagittal plane. 1. Theoretical considerations. Comput. Methods Biomech. Biomed. Eng. 3:95–107, 2000.CrossRefGoogle Scholar
  27. 27.
    Raikova, R. Investigation of the peculiarities of two-joint muscles using a 3 DOF model of the human upper limb in the sagittal plane: an optimization approach. Comput. Methods Biomech. Biomed. Eng. 4:463–490, 2001.CrossRefGoogle Scholar
  28. 28.
    Van Sint Jan, S. Skeletal Landmark Definitions: Guidelines for Accurate and Reproducible Palpation. Department of Anatomy, University of Brussels, 2005. www.Ulb.Ac.Be/~Anatemb.
  29. 29.
    Van Sint Jan, S., and U. D. Croce. Identifying the location of human skeletal landmarks: why standardized definitions are necessary—a proposal. Clin. Biomech. 20:659–660, 2005.CrossRefGoogle Scholar
  30. 30.
    van Soest, A. J., A. L. Schwab, M. F. Bobbert, and G. J. van Ingen Schenau. The influence of the biarticularity of the gastrocnemius muscle on vertical jumping achievement. J. Biomech. 26:1–8, 1993.PubMedCrossRefGoogle Scholar
  31. 31.
    Vanezis, A., and A. Lees. A biomechanical analysis of good and poor performers of the vertical jump. Ergonomics 48:1594–1603, 2005.PubMedCrossRefGoogle Scholar
  32. 32.
    Voronov, A. V. The roles of monoarticular and biarticular muscles of the lower limbs in terrestial locomotion. Hum. Physiol. 30:476–484, 2004.CrossRefGoogle Scholar
  33. 33.
    Winter, D. A. Biomechanics and Motor Control of Human Movement. Hoboken, NJ: John Wiley & Sons, 344 pp., 2005.Google Scholar
  34. 34.
    Woltring, H. J. A Fortran package for generalized, cross-validatory spline smoothing and differentiation. Adv. Eng. Softw. 8:104–113, 1986.Google Scholar
  35. 35.
    Yamaguchi, G. T. Dynamic Modeling of Musculoskeletal Motion: A Vectorized Approach for Biomechanical Analysis in Three Dimensions. New York, NY: Springer, 257 pp., 2001.Google Scholar
  36. 36.
    Zajac, F. E., R. R. Neptune, and S. A. Kautz. Biomechanics and muscle coordination of human walking. Part I. Introduction to concepts, power transfer, dynamics and simulations. Gait Posture 16:215–232, 2002.PubMedCrossRefGoogle Scholar
  37. 37.
    Zatsiorsky, V. M. Kinetics of Human Motion. Champaign, IL: Human Kinetics, 672 pp., 2002.Google Scholar

Copyright information

© Biomedical Engineering Society 2010

Authors and Affiliations

  • Daniel J. Cleather
    • 1
    • 2
    Email author
  • Jon E. Goodwin
    • 1
  • Anthony M. J. Bull
    • 2
  1. 1.St. Mary’s University CollegeTwickenhamUK
  2. 2.Department of BioengineeringImperial College LondonLondonUK

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