Annals of Biomedical Engineering

, Volume 46, Issue 8, pp 1216–1227 | Cite as

Predictive Simulations of Neuromuscular Coordination and Joint-Contact Loading in Human Gait

  • Yi-Chung Lin
  • Jonathan P. Walter
  • Marcus G. Pandy


We implemented direct collocation on a full-body neuromusculoskeletal model to calculate muscle forces, ground reaction forces and knee contact loading simultaneously for one cycle of human gait. A data-tracking collocation problem was solved for walking at the normal speed to establish the practicality of incorporating a 3D model of articular contact and a model of foot–ground interaction explicitly in a dynamic optimization simulation. The data-tracking solution then was used as an initial guess to solve predictive collocation problems, where novel patterns of movement were generated for walking at slow and fast speeds, independent of experimental data. The data-tracking solutions accurately reproduced joint motion, ground forces and knee contact loads measured for two total knee arthroplasty patients walking at their preferred speeds. RMS errors in joint kinematics were < 2.0° for rotations and < 0.3 cm for translations while errors in the model-computed ground-reaction and knee-contact forces were < 0.07 BW and < 0.4 BW, respectively. The predictive solutions were also consistent with joint kinematics, ground forces, knee contact loads and muscle activation patterns measured for slow and fast walking. The results demonstrate the feasibility of performing computationally-efficient, predictive, dynamic optimization simulations of movement using full-body, muscle-actuated models with realistic representations of joint function.


Musculoskeletal model Dynamic optimization Collocation Knee contact model Foot–ground interaction 



This work was supported by a Discovery Projects Grant from the Australian Research Council (DP160104366).

Supplementary material

10439_2018_2026_MOESM1_ESM.pdf (368 kb)
Supplementary material 1 (PDF 369 kb)


  1. 1.
    Ackermann, M., and A. J. van den Bogert. Optimality principles for model-based prediction of human gait. J. Biomech. 43:1055–1060, 2010.CrossRefPubMedPubMedCentralGoogle Scholar
  2. 2.
    Akbarshahi, M., A. G. Schache, J. W. Fernandez, R. Baker, S. Banks, and M. G. Pandy. Non-invasive assessment of soft-tissue artifact and its effect on knee joint kinematics during functional activity. J. Biomech. 43:1292–1301, 2010.CrossRefPubMedGoogle Scholar
  3. 3.
    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
  4. 4.
    Anderson, F. C., and M. G. Pandy. Dynamic optimization of human walking. J. Biomech. Eng. Trans. ASME 123:381–390, 2001.CrossRefGoogle Scholar
  5. 5.
    Correa, T. A., R. Baker, H. K. Graham, and M. G. Pandy. Accuracy of generic musculoskeletal models in predicting the functional roles of muscles in human gait. J. Biomech. 44:2096–2105, 2011.CrossRefPubMedGoogle Scholar
  6. 6.
    De Groote, F., A. L. Kinney, A. V. Rao, and B. J. Fregly. Evaluation of direct collocation optimal control problem formulations for solving the muscle redundancy problem. Ann. Biomed. Eng. 44(10):2922–2936, 2016.CrossRefPubMedPubMedCentralGoogle Scholar
  7. 7.
    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. Trans. Biomed. Eng. 54:1940–1950, 2007.CrossRefGoogle Scholar
  8. 8.
    D’Lima, D. D., S. Patil, N. Steklov, S. Chien, and C. W. Colwell, Jr. In vivo knee moments and shear after total knee arthroplasty. J. Biomech. 40(Suppl 1):S11–S17, 2007.CrossRefPubMedGoogle Scholar
  9. 9.
    Fok, L. A., A. G. Schache, K. M. Crossley, Y. C. Lin, and M. G. Pandy. Patellofemoral joint loading during stair ambulation in people with patellofemoral osteoarthritis. Arthritis Rheum. 65:2059–2069, 2013.CrossRefPubMedGoogle Scholar
  10. 10.
    Fregly, B. J., T. F. Besier, D. G. Lloyd, S. L. Delp, S. A. Banks, M. G. Pandy, and D. D. D’Lima. Grand challenge competition to predict in vivo knee loads. J. Orthop. Res. 30:503–513, 2012.CrossRefPubMedGoogle Scholar
  11. 11.
    Guess, T. M., A. P. Stylianou, and M. Kia. Concurrent prediction of muscle and tibiofemoral contact forces during treadmill gait. J. Biomech. Eng. Trans. ASME 136(2):021032, 2014.CrossRefGoogle Scholar
  12. 12.
    Hatze, H. The complete optimization of a human motion. Math. Biosci. 28:99–135, 1976.CrossRefGoogle Scholar
  13. 13.
    Higginson, J. S., F. E. Zajac, R. R. Neptune, S. A. Kautz, and S. L. Delp. Muscle contributions to support during gait in an individual with post-stroke hemiparesis. J. Biomech. 39:1769–1777, 2006.CrossRefPubMedGoogle Scholar
  14. 14.
    Kaplan, M. L., and J. H. Heegaard. Predictive algorithms for neuromuscular control of human locomotion. J. Biomech. 34:1077–1083, 2001.CrossRefPubMedGoogle Scholar
  15. 15.
    Kim, H. J., J. W. Fernandez, M. Akbarshahi, J. P. Walter, B. J. Fregly, and M. G. Pandy. Evaluation of predicted knee-joint muscle forces during gait using an instrumented knee implant. J. Orthop. Res. 27:1326–1331, 2009.CrossRefPubMedGoogle Scholar
  16. 16.
    Kinney, A. L., T. F. Besier, D. D. D’Lima, and B. J. Fregly. Update on grand challenge competition to predict in vivo knee loads. J. Biomech. Eng. 135:021012, 2013.CrossRefPubMedGoogle Scholar
  17. 17.
    Kirking, B., J. Krevolin, C. Townsend, C. W. Colwell, and D. D. D’Lima. A multiaxial force-sensing implantable tibial prosthesis. J. Biomech. 39:1744–1751, 2006.CrossRefPubMedGoogle Scholar
  18. 18.
    Lai, A., A. G. Schache, Y. C. Lin, and M. G. Pandy. Tendon elastic strain energy in the human ankle plantar-flexors and its role with increased running speed. J. Exp. Biol. 217:3159–3168, 2014.CrossRefPubMedGoogle Scholar
  19. 19.
    Lim, Y. P., Y. C. Lin, and M. G. Pandy. Effects of step length and step frequency on lower-limb muscle function in human gait. J. Biomech. 57:1–7, 2017.CrossRefPubMedGoogle Scholar
  20. 20.
    Lin, Y. C., L. A. Fok, A. G. Schache, and M. G. Pandy. Muscle coordination of support, progression and balance during stair ambulation. J. Biomech. 48:340–347, 2015.CrossRefPubMedGoogle Scholar
  21. 21.
    Lin, Y. C., R. T. Haftka, N. V. Queipo, and B. J. Fregly. Two-dimensional surrogate contact modeling for computationally efficient dynamic simulation of total knee replacements. J. Biomech. Eng. Trans. ASME 131(4):041010, 2009.CrossRefGoogle Scholar
  22. 22.
    Lin, Y. C., R. T. Haftka, N. V. Queipo, and B. J. Fregly. Surrogate articular contact models for computationally efficient multibody dynamic simulations. Med. Eng. Phys. 32:584–594, 2010.CrossRefPubMedGoogle Scholar
  23. 23.
    Lin, Y. C., and M. G. Pandy. Three-dimensional data-tracking dynamic optimization simulations of human locomotion generated by direct collocation. J. Biomech. 59:1–8, 2017.CrossRefPubMedGoogle Scholar
  24. 24.
    Lu, T. W., and J. J. O’Connor. Bone position estimation from skin marker co-ordinates using global optimisation with joint constraints. J. Biomech. 32:129–134, 1999.CrossRefPubMedGoogle Scholar
  25. 25.
    Meyer, A. J., I. Eskinazi, J. N. Jackson, A. V. Rao, C. Patten, and B. J. Fregly. Muscle synergies facilitate computational prediction of subject-specific walking motions. Front. Bioeng. Biotechnol. 4:77, 2016.CrossRefPubMedPubMedCentralGoogle Scholar
  26. 26.
    Miller, R. H., and J. Hamill. Optimal footfall patterns for cost minimization in running. J. Biomech. 48:2858–2864, 2015.CrossRefPubMedGoogle Scholar
  27. 27.
    Moissenet, F., L. Cheze, and R. Dumas. A 3D lower limb musculoskeletal model for simultaneous estimation of musculo-tendon, joint contact, ligament and bone forces during gait. J. Biomech. 47:50–58, 2014.CrossRefPubMedGoogle Scholar
  28. 28.
    Ong, C. F., J. L. Hicks, and S. L. Delp. Simulation-based design for wearable robotic systems: an optimization framework for enhancing a standing long jump. IEEE Trans. Biomed. Eng. 63:894–903, 2016.CrossRefPubMedGoogle Scholar
  29. 29.
    Pandy, M. G. Computer modeling and simulation of human movement. Annu. Rev. Biomed. Eng. 3:245–273, 2001.CrossRefPubMedGoogle Scholar
  30. 30.
    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.CrossRefPubMedGoogle Scholar
  31. 31.
    Porsa, S., Y. C. Lin, and M. G. Pandy. Direct methods for predicting movement biomechanics based upon optimal control theory with implementation in OpenSim. Ann. Biomed. Eng. 44:2542–2557, 2016.CrossRefPubMedGoogle Scholar
  32. 32.
    Raasch, C. C., F. E. Zajac, B. M. Ma, and W. S. Levine. Muscle coordination of maximum-speed pedaling. J. Biomech. 30:595–602, 1997.CrossRefPubMedGoogle Scholar
  33. 33.
    Rajagopal, A., C. L. Dembia, M. S. DeMers, D. D. Delp, J. L. Hicks, and S. L. Delp. Full-body musculoskeletal model for muscle-driven simulation of human gait. IEEE Trans. Biomed. Eng. 63:2068–2079, 2016.CrossRefPubMedPubMedCentralGoogle Scholar
  34. 34.
    Sasaki, K., and R. R. Neptune. Individual muscle contributions to the axial knee joint contact force during normal walking. J. Biomech. 34:2780–2784, 2010.CrossRefGoogle Scholar
  35. 35.
    Serrancoli, G., A. L. Kinney, B. J. Fregly, and J. M. Font-Llagunes. Neuromusculoskeletal model calibration significantly affects predicted knee contact forces for walking. J. Biomech. Eng. 2016. Scholar
  36. 36.
    Seth, A., and M. G. Pandy. A neuromusculoskeletal tracking method for estimating individual muscle forces in human movement. J. Biomech. 40:356–366, 2007.CrossRefPubMedGoogle Scholar
  37. 37.
    Shelburne, K. B., M. R. Torry, and M. G. Pandy. Contributions of muscles, ligaments, and the ground-reaction force to tibiofemoral joint loading during normal gait. J. Orthop. Res. 24:1983–1990, 2006.CrossRefPubMedGoogle Scholar
  38. 38.
    Sritharan, P., Y. C. Lin, and M. G. Pandy. Muscles that do not cross the knee contribute to the knee adduction moment and tibiofemoral compartment loading during gait. J. Orthop. Res. 30:1586–1595, 2012.CrossRefPubMedGoogle Scholar
  39. 39.
    Sritharan, P., Y. C. Lin, S. E. Richardson, K. M. Crossley, T. B. Birmingham, and M. G. Pandy. Musculoskeletal loading in the symptomatic and asymptomatic knees of middle-aged osteoarthritis patients. J. Orthop. Res. 35:321–330, 2017.CrossRefPubMedGoogle Scholar
  40. 40.
    Stagni, R., S. Fantozzi, A. Cappello, and A. Leardini. Quantification of soft tissue artefact in motion analysis by combining 3D fluoroscopy and stereophotogrammetry: a study on two subjects. Clin. Biomech. 20:320–329, 2005.CrossRefGoogle Scholar
  41. 41.
    Steele, K. M., M. S. Demers, M. H. Schwartz, and S. L. Delp. Compressive tibiofemoral force during crouch gait. Gait Posture 35:556–560, 2012.CrossRefPubMedGoogle Scholar
  42. 42.
    Thelen, D. G., F. C. Anderson, and S. L. Delp. Generating dynamic simulations of movement using computed muscle control. J. Biomech. 36:321–328, 2003.CrossRefPubMedGoogle Scholar
  43. 43.
    Thelen, D. G., K. W. Choi, and A. M. Schmitz. Co-simulation of neuromuscular dynamics and knee mechanics during human walking. J. Biomech. Eng. 136:021033, 2014.CrossRefPubMedGoogle Scholar
  44. 44.
    Umberger, B. R. Stance and swing phase costs in human walking. J. R. Soc. Interface 7:1329–1340, 2010.CrossRefPubMedPubMedCentralGoogle Scholar
  45. 45.
    Vansoest, A. J., A. L. Schwab, M. F. Bobbert, and G. J. V. Schenau. The influence of the biarticularity of the gastrocnemius-muscle on vertical-jumping achievement. J. Biomech. 26:1–8, 1993.CrossRefGoogle Scholar
  46. 46.
    Walter, J. P., and M. G. Pandy. Dynamic simulation of knee-joint loading during gait using force-feedback control and surrogate contact modelling. Med. Eng. Phys. 48:196–205, 2017.CrossRefPubMedGoogle Scholar
  47. 47.
    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.CrossRefPubMedGoogle Scholar

Copyright information

© Biomedical Engineering Society 2018

Authors and Affiliations

  1. 1.Department of Mechanical EngineeringUniversity of MelbourneParkvilleAustralia
  2. 2.CED TechnologiesJacksonvilleUSA

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