Metabolic cost calculations of gait using musculoskeletal energy models, a comparison study

Autoři: Anne D. Koelewijn aff001;  Dieter Heinrich aff003;  Antonie J. van den Bogert aff001
Působiště autorů: Parker Hannifin Laboratory for Human Motion and Control, Department of Mechanical Engineering, Cleveland State University, Cleveland, Ohio, United States of America aff001;  Biorobotics Laboratory, Institute of Bioengineering, École Polytechnique Fédérale de Lausanne, Lausanne, Switzerland aff002;  Department of Sport Science, University of Innsbruck, Innsbruck, Austria aff003
Vyšlo v časopise: PLoS ONE 14(9)
Kategorie: Research Article
doi: 10.1371/journal.pone.0222037


This paper compares predictions of metabolic energy expenditure in gait using seven metabolic energy expenditure models to assess their correlation with experimental data. Ground reaction forces, marker data, and pulmonary gas exchange data were recorded for six walking trials at combinations of two speeds, 0.8 m/s and 1.3 m/s, and three inclines, -8% (downhill), level, and 8% (uphill). The metabolic cost, calculated with the metabolic energy models was compared to the metabolic cost from the pulmonary gas exchange rates. A repeated measures correlation showed that all models correlated well with experimental data, with correlations of at least 0.9. The model by Bhargava et al. (J Biomech, 2004: 81-88) and the model by Lichtwark and Wilson (J Exp Biol, 2005: 2831-3843) had the highest correlation, 0.95. The model by Margaria (Int Z Angew Physiol Einschl Arbeitsphysiol, 1968: 339-351) predicted the increase in metabolic cost following a change in dynamics best in absolute terms.

Klíčová slova:

Biology and life sciences – Biochemistry – Bioenergetics – Metabolism – Energy metabolism – Anatomy – Musculoskeletal system – Skeletal joints – Body limbs – Legs – Ankles – Physiology – Physiological processes – Biological locomotion – Walking – Gait analysis – Muscle physiology – Muscle contraction – Biomechanics – Musculoskeletal mechanics – Medicine and health sciences


1. Ralston HJ. Energy-speed relation and optimal speed during level walking. Internationale Zeitschrift für Angewandte Physiologie Einschliesslich Arbeitsphysiologie. 1958;17(4):277–283.

2. Zarrugh M, Todd F, Ralston H. Optimization of energy expenditure during level walking. European Journal of Applied Physiology and Occupational Physiology. 1974;33(4):293–306. doi: 10.1007/bf00430237 4442409

3. Donelan J, Kram R, Kuo A. Mechanical and metabolic determinants of the preferred step width in human walking. Proceedings of the Royal Society of London B: Biological Sciences. 2001;268(1480):1985–1992. doi: 10.1098/rspb.2001.1761

4. Ortega JD, Farley CT. Minimizing center of mass vertical movement increases metabolic cost in walking. Journal of Applied Physiology. 2005;99(6):2099–2107. doi: 10.1152/japplphysiol.00103.2005 16051716

5. Gordon K, Ferris D, Kuo A. Metabolic and mechanical energy costs of reducing vertical center of mass movement during gait. Archives of Physical Medicine and Rehabilitation. 2009;90(1):136–144. doi: 10.1016/j.apmr.2008.07.014 19154840

6. Kenny GP, Notley SR, Gagnon D. Direct calorimetry: a brief historical review of its use in the study of human metabolism and thermoregulation. European journal of applied physiology. 2017;117(9):1765–1785. doi: 10.1007/s00421-017-3670-5 28689303

7. Bhargava LJ, Pandy MG, Anderson FC. A phenomenological model for estimating metabolic energy consumption in muscle contraction. Journal of Biomechanics. 2004;37(1):81–88. doi: 10.1016/s0021-9290(03)00239-2 14672571

8. Minetti A, Alexander RM. A theory of metabolic costs for bipedal gaits. Journal of Theoretical Biology. 1997;186(4):467–476. doi: 10.1006/jtbi.1997.0407 9278722

9. Umberger BR, Gerritsen KG, Martin PE. A model of human muscle energy expenditure. Computer methods in biomechanics and biomedical engineering. 2003;6(2):99–111. doi: 10.1080/1025584031000091678 12745424

10. Houdijk H, Bobbert M, De Haan A. Evaluation of a Hill based muscle model for the energy cost and efficiency of muscular contraction. Journal of Biomechanics. 2006;39(3):536–543. doi: 10.1016/j.jbiomech.2004.11.033 16389094

11. Zajac FE, Neptune RR, Kautz SA. Biomechanics and muscle coordination of human walking: part II: lessons from dynamical simulations and clinical implications. Gait & posture. 2003;17(1):1–17. doi: 10.1016/S0966-6362(02)00069-3

12. Koelewijn AD, Van den Bogert AJ. Joint contact forces can be reduced by improving joint moment symmetry in below-knee amputee gait simulations. Gait & Posture. 2016;49:219–225. doi: 10.1016/j.gaitpost.2016.07.007

13. Dembia CL, Silder A, Uchida TK, Hicks JL, Delp SL. Simulating ideal assistive devices to reduce the metabolic cost of walking with heavy loads. PloS one. 2017;12(7):e0180320. doi: 10.1371/journal.pone.0180320 28700630

14. Bregman D, Van der Krogt M, De Groot V, Harlaar J, Wisse M, Collins S. The effect of ankle foot orthosis stiffness on the energy cost of walking: a simulation study. Clinical Biomechanics. 2011;26(9):955–961. doi: 10.1016/j.clinbiomech.2011.05.007 21723012

15. Van den Bogert AJ, Hupperets M, Schlarb H, Krabbe B. Predictive musculoskeletal simulation using optimal control: effects of added limb mass on energy cost and kinematics of walking and running. Proceedings of the Institution of Mechanical Engineers, Part P: Journal of Sports Engineering and Technology. 2012; p. 1–11.

16. Dorn TW, Wang JM, Hicks JL, Delp SL. Predictive simulation generates human adaptations during loaded and inclined walking. PloS one. 2015;10(4):e0121407. doi: 10.1371/journal.pone.0121407 25830913

17. Miller R, Brandon S, Deluzio K. Predicting sagittal plane biomechanics that minimize the axial knee joint contact force during walking. Journal of Biomechanical Engineering. 2013;135(1):011007. doi: 10.1115/1.4023151 23363218

18. Huxley H. The double array of filaments in cross-striated muscle. The Journal of Biophysical and Biochemical Cytology. 1957;3(5):631–648. doi: 10.1083/jcb.3.5.631 13475381

19. Propp M. A model of muscle contraction based upon component studies. Lectures on Mathematics in the Life Sciences. 1986;16:61–119.

20. Winters J. Hill-based muscle models: a systems engineering perspective. In: Multiple Muscle Systems. Springer; 1990. p. 69–93.

21. Lichtwark GA, Wilson A. A modified Hill muscle model that predicts muscle power output and efficiency during sinusoidal length changes. Journal of Experimental Biology. 2005;208(15):2831–2843. doi: 10.1242/jeb.01709 16043588

22. Uchida TK, Hicks JL, Dembia CL, Delp SL. Stretching your energetic budget: how tendon compliance affects the metabolic cost of running. PloS one. 2016;11(3):e0150378. doi: 10.1371/journal.pone.0150378 26930416

23. Margaria R. Positive and negative work performances and their efficiencies in human locomotion. European journal of applied physiology and occupational physiology. 1968;25(4):339–351. doi: 10.1007/BF00699624

24. Kim J, Roberts D. A joint-space numerical model of metabolic energy expenditure for human multibody dynamic system. International Journal for Numerical Methods in Biomedical Engineering. 2015;31(9). doi: 10.1002/cnm.2721

25. Tsianos GA, Rustin C, Loeb GE. Mammalian muscle model for predicting force and energetics during physiological behaviors. IEEE Transactions on Neural Systems and Rehabilitation Engineering. 2012;20(2):117–133. doi: 10.1109/TNSRE.2011.2162851 21859633

26. Miller RH. A comparison of muscle energy models for simulating human walking in three dimensions. Journal of biomechanics. 2014;47(6):1373–1381. doi: 10.1016/j.jbiomech.2014.01.049 24581797

27. Lay AN, Hass CJ, Nichols TR, Gregor RJ. The effects of sloped surfaces on locomotion: an electromyographic analysis. Journal of biomechanics. 2007;40(6):1276–1285. doi: 10.1016/j.jbiomech.2006.05.023 16872616

28. Pickle NT, Grabowski AM, Auyang AG, Silverman AK. The functional roles of muscles during sloped walking. Journal of biomechanics. 2016;49(14):3244–3251. doi: 10.1016/j.jbiomech.2016.08.004 27553849

29. Margaria R. Biomechanics and Energetics of muscular exercise. Oxford University Press, USA; 1976.

30. Koelewijn AD, Heinrich D, van den Bogert AJ. Dataset for Metabolic Cost Calculations of Gait using Musculoskeletal Energy Models, a Comparison Study [Data set]; 2018. Available from:

31. Winter DA. Biomechanics and motor control of human movement. John Wiley & Sons; 2009.

32. de Groote F, Kinney AL, Rao AV, Fregly BJ. Evaluation of direct collocation optimal control problem formulations for solving the muscle redundancy problem. Annals of biomedical engineering. 2016;44(10):2922–2936. doi: 10.1007/s10439-016-1591-9 27001399

33. Wächter A, Biegler L. On the implementation of an interior-point filter line-search algorithm for large-scale nonlinear programming. Mathematical Programming. 2006;106(1):25–57. doi: 10.1007/s10107-004-0559-y

34. Winter D, Yack H. EMG profiles during normal human walking: stride-to-stride and inter-subject variability. Electroencephalography and clinical neurophysiology. 1987;67(5):402–411. doi: 10.1016/0013-4694(87)90003-4 2444408

35. Weir JdV. New methods for calculating metabolic rate with special reference to protein metabolism. The Journal of physiology. 1949;109(1-2):1–9. doi: 10.1113/jphysiol.1949.sp004363 15394301

36. Brockway J. Derivation of formulae used to calculate energy expenditure in man. Human nutrition Clinical nutrition. 1987;41(6):463–471. 3429265

37. Bakdash JZ, Marusich LR. Repeated measures correlation. Frontiers in Psychology. 2017;8. doi: 10.3389/fpsyg.2017.00456 28439244

38. Hicks JL, Uchida TK, Seth A, Rajagopal A, Delp SL. Is my model good enough? Best practices for verification and validation of musculoskeletal models and simulations of movement. Journal of biomechanical engineering. 2015;137(2):020905. doi: 10.1115/1.4029304 25474098

39. Koelewijn AD, Dorschky E, van den Bogert AJ. A metabolic energy expenditure model with a continuous first derivative and its application to predictive simulations of gait. Computer methods in biomechanics and biomedical engineering. 2018;21(8):521–531. doi: 10.1080/10255842.2018.1490954 30027769

40. Koelewijn AD. Predictive Simulations of Gait and Their Application in Prosthesis Design. Doctoral Dissertation, Cleveland State University; 2018.

41. Umberger BR. Stance and swing phase costs in human walking. Journal of the Royal Society Interface. 2010;7(50):1329–1340. doi: 10.1098/rsif.2010.0084

42. Kimel-Naor S, Gottlieb A, Plotnik M. The effect of uphill and downhill walking on gait parameters: A self-paced treadmill study. Journal of Biomechanics. 2017;60:142–149. doi: 10.1016/j.jbiomech.2017.06.030 28757238

43. Alexander N, Schwameder H. Effect of sloped walking on lower limb muscle forces. Gait & posture. 2016;47:62–67. doi: 10.1016/j.gaitpost.2016.03.022

44. Ellerby DJ, Henry HT, Carr JA, Buchanan CI, Marsh RL. Blood flow in guinea fowl Numida meleagris as an indicator of energy expenditure by individual muscles during walking and running. The Journal of physiology. 2005;564(2):631–648. doi: 10.1113/jphysiol.2005.082974 15731191

45. Crowninshield RD, Brand RA. A physiologically based criterion of muscle force prediction in locomotion. Journal of biomechanics. 1981;14(11):793–801. doi: 10.1016/0021-9290(81)90035-x 7334039

46. Delp S, Anderson F, Arnold A, Loan P, Habib A, John C, et al. OpenSim: open-source software to create and analyze dynamic simulations of movement. IEEE Transactions on Biomedical Engineering. 2007;54(11):1940–1950. doi: 10.1109/TBME.2007.901024 18018689

47. Kipp S, Byrnes WC, Kram R. Calculating metabolic energy expenditure across a wide range of exercise intensities: the equation matters. Applied Physiology, Nutrition, and Metabolism. 2018;43(6):639–642. doi: 10.1139/apnm-2017-0781 29401411

48. Peronnet F, Massicotte D. Table of nonprotein respiratory quotient: an update. Can J Sport Sci. 1991;16(1):23–29. 1645211

49. Silder A, Besier T, Delp SL. Predicting the metabolic cost of incline walking from muscle activity and walking mechanics. Journal of biomechanics. 2012;45(10):1842–1849. doi: 10.1016/j.jbiomech.2012.03.032 22578744

50. Visser M, Deurenberg P, van Staveren WA, Hautvast JG. Resting metabolic rate and diet-induced thermogenesis in young and elderly subjects: relationship with body composition, fat distribution, and physical activity level. The American journal of clinical nutrition. 1995;61(4):772–778. doi: 10.1093/ajcn/61.4.772 7702018

51. Compher C, Frankenfield D, Keim N, Roth-Yousey L, Evidence Analysis Working Group. Best practice methods to apply to measurement of resting metabolic rate in adults: a systematic review. Journal of the American Dietetic Association. 2006;106(6):881–903. doi: 10.1016/j.jada.2006.02.009 16720129

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