Abstract
Using detailed musculoskeletal models in computer simulations of human movement can provide insights into individual muscle and joint loading; however, these muscle models increase problem dimensionality and require difficult-to-fit parameters. Here, we provide a brief overview of a muscle model alternative, muscle torque generators (MTGs), and highlight how MTG functions have been used by researchers to generate accurate dynamic simulations of optimal sports performance. Multibody dynamic models of a golf drive, track cycling, and wheelchair propulsion were designed and actuated using MTGs. Each MTG was effectively a rotational, single muscle equivalent that contained joint angle/velocity scaling and passive elements to mimic Hill-type muscle model behaviour. Optimal control algorithms were used to predict how each model would execute their respective sports task; these results were compared against experimental data collected from elite athletes. Good agreement between simulated and experimental movement trajectories was observed, with relatively low computational times required for convergence of the MTG-driven multibody simulations.
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References
Alexander, R.M.: Optimum take-off techniques for high and long jumps. Philos. Trans. R. Soc. Lond. B, Biol. Sci. 329(1252), 3–10 (1990). https://doi.org/10.1098/rstb.1990.0144
Anderson, F.C., Pandy, M.G.: A dynamic optimization solution for vertical jumping in three dimensions. Comput. Methods Biomech. Biomed. Eng. 2(3), 201–231 (1999). https://doi.org/10.1080/10255849908907988
Anderson, D.E., Madigan, M.L., Nussbaum, M.A.: Maximum voluntary joint torque as a function of joint angle and angular velocity: model development and application to the lower limb. J. Biomech. 40(14), 3105–3113 (2007). https://doi.org/10.1016/j.jbiomech.2007.03.022
Arnold, E.M., Ward, S.R., Lieber, R.L., Delp, S.L.: A model of the lower limb for analysis of human movement. Ann. Biomed. Eng. 38(2), 269–279 (2010). https://doi.org/10.1007/s10439-009-9852-5
Balzerson, D., Banerjee, J., McPhee, J.: A three-dimensional forward dynamic model of the golf swing optimized for ball carry distance. Sports Eng. 19(4), 237–250 (2016). https://doi.org/10.1007/s12283-016-0197-7
Bastian, A.J., Zackowski, K.M., Thach, W.T.: Cerebellar ataxia: torque deficiency or torque mismatch between joints? J. Neurophysiol. 83(5), 3019–3030 (2000). https://doi.org/10.1152/jn.2000.83.5.3019
Bernstein, N.: The Co-ordination and Regulation of Movements. Pergamon Press, London (1967)
Brown, P., McPhee, J.: A continuous velocity-based friction model for dynamics and control with physically meaningful parameters. J. Comput. Nonlinear Dyn. 11(5), 054,502 (2016). https://doi.org/10.1115/1.4033658
Brown, C., McPhee, J.: Predictive forward dynamic simulation of manual wheelchair propulsion on a rolling dynamometer. ASME J. Biomech. Eng. 142(7), 071,008 (2020). https://doi.org/10.1115/1.4046298
Buffi, J.H., Werner, K., Kepple, T., Murray, W.M.: Computing muscle, ligament, and osseous contributions to the elbow varus moment during baseball pitching. Ann. Biomed. Eng. 43(2), 404–415 (2015). https://doi.org/10.1007/s10439-014-1144-z
Cleather, D.I., Bull, A.M.J.: Lower-extremity musculoskeletal geometry affects the calculation of patellofemoral forces in vertical jumping and weightlifting. Proc. Inst. Mech. Eng., H J. Eng. Med. 224(9), 1073–1083 (2010). https://doi.org/10.1243/09544119JEIM731
De Groote, F., Kinney, A.L., Rao, A.V., Fregly, B.J.: Evaluation of direct collocation optimal control problem formulations for solving the muscle redundancy problem. Ann. Biomed. Eng. 44(10), 2922–2936 (2016). https://doi.org/10.1007/s10439-016-1591-9
De Pieri, E., Lund, M.E., Gopalakrishnan, A., Rasmussen, K.P., Lunn, D.E., Ferguson, S.J.: Refining muscle geometry and wrapping in the TLEM 2 model for improved hip contact force prediction. PLoS ONE 13(9), e0204, 109 (2018). https://doi.org/10.1371/journal.pone.0204109
Domire, Z.J., Challis, J.H.: The influence of an elastic tendon on the force producing capabilities of a muscle during dynamic movements. Comput. Methods Biomech. Biomed. Eng. 10(5), 337–341 (2007). https://doi.org/10.1080/10255840701379562
Flash, T., Hogan, N.: The coordination of arm movements: an experimentally confirmed mathematical model. J. Neurosci. 5(7), 1688–1703 (1985)
Fukashiro, S., Hay, D.C., Nagano, A.: Biomechanical behavior of muscle-tendon complex during dynamic human movements. J. Appl. Biomech. 22(2), 131–147 (2006). https://doi.org/10.1123/jab.22.2.131
Fuss, F.K.: Influence of mass on the speed of wheelchair racing. Sports Eng. 12(1), 41–53 (2009). https://doi.org/10.1007/s12283-009-0027-2
Garner, B.A., Pandy, M.G.: Musculoskeletal model of the upper limb based on the visible human male dataset. Comput. Methods Biomech. Biomed. Eng. 4(2), 93–126 (2001). https://doi.org/10.1080/10255840008908000
Gidley, A.D.: The influence of musculoskeletal geometry on the metabolic cost of pedaling. PhD Thesis, University of Massachusetts Amherst (2016)
Gordon, A.M., Huxley, A.F., Julian, F.J.: The variation in isometric tension with sarcomere length in vertebrate muscle fibres. J. Physiol. 184(1), 170–192 (1966). https://doi.org/10.1113/jphysiol.1966.sp007909
Haering, D., Pontonnier, C., Bideau, N., Nicolas, G., Dumont, G.: Using torque-angle and torque-velocity models to characterize elbow mechanical function: modeling and applied aspects. J. Biomech. Eng. 141(8), 084,501 (2019). https://doi.org/10.1115/1.4043447
Heitmann, S., Ferns, N., Breakspear, M.: Muscle co-contraction modulates damping and joint stability in a three-link biomechanical limb. Front. Neurobot. 5, 5 (2011). https://doi.org/10.3389/fnbot.2011.00005
Hill, A.: The heat of shortening and the dynamic constants of muscle. Proc. R. Soc. Lond. B, Biol. Sci. 126(843), 136–195 (1938). https://doi.org/10.1098/rspb.1938.0050
Hoang, P.D., Gorman, R.B., Todd, G., Gandevia, S.C., Herbert, R.D.: A new method for measuring passive length-tension properties of human gastrocnemius muscle in vivo. J. Biomech. 38(6), 1333–1341 (2005). https://doi.org/10.1016/j.jbiomech.2004.05.046
Hume, P.A., Keogh, J., Reid, D.: The role of biomechanics in maximising distance and accuracy of golf shots. Sports Med. 35(5), 429–449 (2005). https://doi.org/10.2165/00007256-200535050-00005
Jansen, C., McPhee, J.: Predictive dynamic simulation of Olympic track cycling standing start using direct collocation optimal control. Multibody Syst. Dyn. 49(1), 53–70 (2020). https://doi.org/10.1007/s11044-020-09723-3
Jiang, Y., Van Wouwe, T., De Groote, F., Liu, C.K.: Synthesis of biologically realistic human motion using joint torque actuation. ACM Trans. Graph. 38(4), 1–12 (2019). https://doi.org/10.1145/3306346.3322966
Katz, B.: The relation between force and speed in muscular contraction. J. Physiol. 96(1), 45–64 (1939). https://doi.org/10.1113/jphysiol.1939.sp003756
Kelly, S.B., Brown, L.E., Hooker, S.P., Swan, P.D., Buman, M.P., Alvar, B.A., Black, L.E.: Comparison of concentric and eccentric bench press repetitions to failure. J. Strength Cond. Res. 29(4), 1027–1032 (2015). https://doi.org/10.1519/JSC.0000000000000713
Kentel, B.B., King, M.A., Mitchell, S.R.: Evaluation of a subject-specific, torque-driven computer simulation model of one-handed tennis backhand groundstrokes. J. Appl. Biomech. 27(4), 345–354 (2011). https://doi.org/10.1123/jab.27.4.345
King, M.A., Yeadon, M.R.: Determining subject-specific torque parameters for use in a torque-driven simulation model of dynamic jumping. J. Appl. Biomech. 18(3), 207–217 (2002). https://doi.org/10.1123/jab.18.3.207
King, M.A., Wilson, C., Yeadon, M.R.: Evaluation of a torque-driven model of jumping for height. J. Appl. Biomech. 22(4), 264–274 (2006)
Kordi, M., Goodall, S., Barratt, P., Rowley, N., Leeder, J., Howatson, G.: Relation between peak power output in sprint cycling and maximum voluntary isometric torque production. J. Electromyogr. Kinesiol. 35, 95–99 (2017). https://doi.org/10.1016/j.jelekin.2017.06.003
Lichtwark, G.A., Barclay, C.J.: The influence of tendon compliance on muscle power output and efficiency during cyclic contractions. J. Exp. Biol. 213(5), 707–714 (2010). https://doi.org/10.1242/jeb.038026
MacKenzie, S.J., Sprigings, E.J.: A three-dimensional forward dynamics model of the golf swing. Sports Eng. 11(4), 165–175 (2009). https://doi.org/10.1007/s12283-009-0020-9
McGill, S., Seguin, J., Bennett, G.: Passive stiffness of the lumbar torso in flexion, extension, lateral bending, and axial rotation. Effect of belt wearing and breath holding. Spine 19(6), 696–704 (1994). https://doi.org/10.1097/00007632-199403001-00009
McNally, W., McPhee, J.: Dynamic optimization of the golf swing using a six degree-of-freedom biomechanical model. Proceedings 2(6), 243 (2018). https://doi.org/10.3390/proceedings2060243
Millard, M., Uchida, T., Seth, A., Delp, S.L.: Flexing computational muscle: modeling and simulation of musculotendon dynamics. J. Biomech. Eng. 135(2), 021,005 (2013). https://doi.org/10.1115/1.4023390
Millard, M., Emonds, A.L., Harant, M., Mombaur, K.: A reduced muscle model and planar musculoskeletal model fit for the simulation of whole-body movements. J. Biomech. 89, 11–20 (2019). https://doi.org/10.1016/j.jbiomech.2019.04.004
Myers, J., Lephart, S., Tsai, Y.S., Sell, T., Smoliga, J., Jolly, J.: The role of upper torso and pelvis rotation in driving performance during the golf swing. J. Sports Sci. 26(2), 181–188 (2008). https://doi.org/10.1080/02640410701373543
Norman-Gerum, V.T.: Predictive dynamic simulation of healthy sit-to-stand movement. PhD Thesis, University of Waterloo, Waterloo, Canada (2019)
Pacejka, H.B.: Tyre and vehicle dynamics (2006). http://site.ebrary.com/id/10674718. OCLC: 845660293
Pandy, M.G., Anderson, F.C., Hull, D.G.: A parameter optimization approach for the optimal control of large-scale musculoskeletal systems. J. Biomech. Eng. 114(4), 450–460 (1992)
Patterson, M.A., Rao, A.V.: GPOPS-II: a MATLAB software for solving multiple-phase optimal control problems using hp-adaptive Gaussian quadrature collocation methods and sparse nonlinear programming. ACM Trans. Math. Softw. 41(1), 1–37 (2014). https://doi.org/10.1145/2558904
Porsa, S., Lin, Y.C., Pandy, M.G.: Direct methods for predicting movement biomechanics based upon optimal control theory with implementation in OpenSim. Ann. Biomed. Eng. 44(8), 2542–2557 (2016). https://doi.org/10.1007/s10439-015-1538-6
Quintavalla, S.: A generally applicable model for the aerodynamic behavior of golf balls. In: Science and Golf IV, 1st edn. Routledge, Abingdon-on-Thames (2003)
Riener, R., Edrich, T.: Identification of passive elastic joint moments in the lower extremities. J. Biomech. 32(5), 539–544 (1999)
Savelberg, H.H.C.M., Meijer, K.: Contribution of mono- and biarticular muscles to extending knee joint moments in runners and cyclists. J. Appl. Physiol. 94(6), 2241–2248 (2003). https://doi.org/10.1152/japplphysiol.01001.2002
Sawicki, G.S., Lewis, C.L., Ferris, D.P.: It pays to have a spring in your step. Exerc. Sport Sci. Rev. 37(3), 130–138 (2009). https://doi.org/10.1097/JES.0b013e31819c2df6
Sherman, M.A., Seth, A., Delp, S.L.: What is a moment arm? Calculating muscle effectiveness in biomechanical models using generalized coordinates. In: 9th International Conference on Multibody Systems, Nonlinear Dynamics, and Control, vol. 7B. American Society of Mechanical Engineers, Portland (2013). https://doi.org/10.1115/DETC2013-13633
Siebert, T., Rode, C., Herzog, W., Till, O., Blickhan, R.: Nonlinearities make a difference: comparison of two common Hill-type models with real muscle. Biol. Cybern. 98(2), 133–143 (2008). https://doi.org/10.1007/s00422-007-0197-6
Slowik, J.S., Neptune, R.R.: A theoretical analysis of the influence of wheelchair seat position on upper extremity demand. Clin. Biomech. 28(4), 378–385 (2013). https://doi.org/10.1016/j.clinbiomech.2013.03.004
Suzuki, Y., Nomura, T., Casadio, M., Morasso, P.: Intermittent control with ankle, hip, and mixed strategies during quiet standing: a theoretical proposal based on a double inverted pendulum model. J. Theor. Biol. 310, 55–79 (2012). https://doi.org/10.1016/j.jtbi.2012.06.019
Thelen, D.G.: Adjustment of muscle mechanics model parameters to simulate dynamic contractions in older adults. J. Biomech. Eng. 125(1), 70–77 (2003). https://doi.org/10.1115/1.1531112
van Ingen Schenau, G.J., Dorssers, W.M., Welter, T.G., Beelen, A., de Groot, G., Jacobs, R.: The control of mono-articular muscles in multijoint leg extensions in man. J. Physiol. 484(1), 247–254 (1995). https://doi.org/10.1113/jphysiol.1995.sp020662
van Soest, A.J., Bobbert, M.F.: The contribution of muscle properties in the control of explosive movements. Biol. Cybern. 69(3), 195–204 (1993). https://doi.org/10.1007/BF00198959
Wells, R.P.: Mechanical energy costs of human movement: an approach to evaluating the transfer possibilities of two-joint muscles. J. Biomech. 21(11), 955–964 (1988). https://doi.org/10.1016/0021-9290(88)90134-0
Westing, S.H., Cresswell, A.G., Thorstensson, A.: Muscle activation during maximal voluntary eccentric and concentric knee extension. Eur. J. Appl. Physiol. Occup. Physiol. 62(2), 104–108 (1991). https://doi.org/10.1007/bf00626764
Williams, C.A.: Maximum concentric, eccentric and isometric strength of trunk flexor and extensor muscles in athletes. University of Alberta Libraries (1992). https://doi.org/10.7939/R3VX0672H
Winter, D.A.: Biomechanics and Motor Control of Human Movement, 4th edn. Wiley, Hoboken (2009). OCLC: ocn318408191
Winters, J.M.: Hill-based muscle models: a systems engineering perspective. In: Winters, J.M., Woo, S.L.Y. (eds.) Multiple Muscle Systems, pp. 69–93. Springer New York, New York (1990)
Winters, J.M., Stark, L.: Analysis of fundamental human movement patterns through the use of in-depth antagonistic muscle models. IEEE Trans. Biomed. Eng. 32(10), 826–839 (1985). https://doi.org/10.1109/TBME.1985.325498
Winters, J.M., Stark, L.: Muscle models: what is gained and what is lost by varying model complexity. Biol. Cybern. 55(6), 403–420 (1987). https://doi.org/10.1007/BF00318375
Yamaguchi, G.T.: Dynamic Modeling of Musculoskeletal Motion: A Vectorized Approach for Biomechanical Analysis in Three Dimensions. Springer, Berlin (2006). OCLC: 150263239
Yeadon, M.R., King, M.A., Wilson, C.: Modelling the maximum voluntary joint torque/angular velocity relationship in human movement. J. Biomech. 39(3), 476–482 (2006). https://doi.org/10.1016/j.jbiomech.2004.12.012
Acknowledgements
This research was funded by McPhee’s Tier I Canada Research Chair in System Dynamics. Additional thanks for experimental participation and data collection by i) PING Inc., ii) Mike Patton and Will George of Cycling Canada, members of the Canadian track cycling team, and iii) Canadian Sports Institute Ontario.
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Inkol, K.A., Brown, C., McNally, W. et al. Muscle torque generators in multibody dynamic simulations of optimal sports performance. Multibody Syst Dyn 50, 435–452 (2020). https://doi.org/10.1007/s11044-020-09747-9
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DOI: https://doi.org/10.1007/s11044-020-09747-9