Prediction of crank torque and pedal angle profiles during pedaling movements by biomechanical optimization

Abstract

This paper introduces the inverse-inverse dynamics method for prediction of human movement and applies it to prediction of cycling motions. Inverse-inverse dynamics optimizes a performance criterion by variation of a parameterized movement. First, a musculoskeletal model of cycling is built in the AnyBody Modeling System (AMS). The movement is then parameterized by means of time functions controlling selected degrees-of-freedom (DOF) of the model. Subsequently, the parameters of these functions are optimized to produce an optimum posture or movement according to a user-defined cost function and constraints. The cost function and the constraints typically express performance, comfort, injury risk, fatigue, muscle load, joint forces and other physiological properties derived from the detailed musculoskeletal analysis. A physiology-based cost function that expresses the integral effort over a cycle to predict the motion pattern and crank torque was used. An experiment was conducted on a group of eight highly trained male cyclists to compare experimental observations to the simulation results. The proposed performance criterion predicts realistic crank torque profiles and ankle movement patterns.

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References

  1. Abdel-Malek K, Mi Z, Yang J, Nebel K (2006) Optimization-based trajectory planning of the human upper body. Robotica 24:683–696

    Article  Google Scholar 

  2. Abdel-Malek K, Arora JS (2013) Human Motion Simulation: Predictive Dynamics. Elsevier, USA

    Google Scholar 

  3. Anderson FC, Pandy MG (1999) A dynamic optimization solution for vertical jumping in three dimensions. Comput Methods Biomech Biomed Engin 2:201–231

    Article  Google Scholar 

  4. Anderson FC, Pandy MG (2001a) Dynamic optimization of human walking. J Biomech Eng 123:381–390

    Article  Google Scholar 

  5. Anderson FC, Pandy MG (2001b) Static and dynamic optimization solutions for gait are practically equivalent. J Biomech 34:153–161

    Article  Google Scholar 

  6. Annegarn J, Rasmussen J, Savelberg HHCM, Verdijk LB, Meijer K (2006) Scaling strength in human simulation models. Vlaams Tijdschrift voor Sportgeneeskund & -Wetenschappen 108:46

    Google Scholar 

  7. Bertucci W, Duc S, Villerius V, Grappe F (2005a) Validity and reliability of the Axiom PowerTrain cycle ergometer when compared with an SRM powermeter. Int J Sports Med 26:59–65

    Article  Google Scholar 

  8. Bertucci W, Grappe F, Groslambert A (2007) Laboratory versus outdoor cycling conditions: differences in pedaling biomechanics. J Appl Biomech 23:87–92

    Google Scholar 

  9. Bertucci W, Grappe F, Girard A, Betik A, Rouillon JD (2005b) Effects on the crank torque profile when changing pedalling cadence in level ground and uphill road cycling. J Biomech 38:1003–1010

    Article  Google Scholar 

  10. Box M (1965) A new method of constrained optimization and a comparison with other methods. Comput J 8:42–52

    Article  MATH  MathSciNet  Google Scholar 

  11. Carpes FP, Rossato M, Faria I, Bolli Mota C (2007) Bilateral pedaling asymmetry during a simulated 40-km cycling time-trial. J Sports Med Phys Fitness 47:51–57

    Google Scholar 

  12. Chaffin DB (2002) On simulating human reach motions for ergonomics analyses. Hum Factor Ergon Man 12:235–247

    Article  Google Scholar 

  13. Chaffin DB, Andersson GBJ, Martin BJ (2006) Occupational Biomechanics. John Wiley & Sons, New York

    Google Scholar 

  14. Chapman AR, Vicenzino B, Blanch P, Knox JJ, Dowlan S, Hodges PW (2008) The influence of body position on leg kinematics and muscle recruitment during cycling. J Sci Med Sport 11:519–526

    Article  Google Scholar 

  15. Crowninshield RD, Brand RA (1981) A physiologically based criterion of muscle force prediction in locomotion. J Biomech 14:793–801

    Article  Google Scholar 

  16. Damsgaard M, Rasmussen J, Christensen ST, Surma E, de Zee M (2006) Analysis of musculoskeletal systems in the AnyBody Modeling System. Simul Model Pract Theor 14:1100–1111

    Article  Google Scholar 

  17. Davis RR, Hull ML (1981) Measurement of pedal loading in bicycling: 2nd Analysis and results. J Biomech 14:857–872

    Article  Google Scholar 

  18. Delp SL (1990) Surgery Simulation: A Computer Graphics System to Analyze and Design Musculoskeletal Reconstructions of the Lower Limb. Ph.D. thesis, Department of Mechanical Engineering, Stanford University, Stanford, CA

  19. Delp SL, Loan JP, Hoy MG, Zajac FE, Topp EL, Rosen JM (1990) An interactive graphics-based model of the lower extremity to study orthopaedic surgical procedures. IEEE Trans Biomed Eng 37:757–767

    Article  Google Scholar 

  20. Erdemir A, McLean S, Herzog W, Van den Bogert AJ (2007) Model-based estimation of muscle forces exerted during movements. Clin Biomech 22:131–154

    Article  Google Scholar 

  21. Faraway JJ, Zhang X, Chaffin DB (1999) Rectifying postures reconstructed from joint angles to meet constraints. J Biomech 32:733–736

    Article  Google Scholar 

  22. Fregly BJ, Zajac FE, Dairaghi CA (1996) Crank inertial load has little effect on steady-state pedaling coordination. J Biomech 29:1559–1567

    Article  Google Scholar 

  23. Geers TL (1984) An objective error measure for the comparison of calculated and measured transient response histories. Shock Vib Bull 54:99–107

    Google Scholar 

  24. Glitsch U, Baumann W (1997) The three-dimensional determination of internal loads in the lower extremity. J Biomech 30:1123–1131

    Article  Google Scholar 

  25. Howard B, Cloutier A, Yang J (2012) Physics-based seated posture prediction for pregnant women and validation considering ground and seat pan contacts. J Biomech Eng 134:071004–1-10

    Article  Google Scholar 

  26. Howard B, Yang J, Ozsoy B (2014) Optimal posture and supporting hand force prediction for common automobile assembly one-hand tasks. J Mech Robotics 6:021009–1-10

    Article  Google Scholar 

  27. Kim HJ, Abdel-Malek K, yang J, Marler RT (2006) prediction and analysis of human motion dynamics performing various tasks. Int J Hum Factor Model Simul 1:69–94

    Article  Google Scholar 

  28. Koopman B, Grootenboer HJ, De Jongh HJ (1995) An inverse dynamics model for the analysis, reconstruction and prediction of bipedal walking. J Biomech 28:1369–1376

    Article  Google Scholar 

  29. Marler RT, Arora JS, Yang J, Kim HJ, Abdel-Malek K (2009) Use of multi-objective optimization for digital human posture prediction. Eng Optim 41:925–943

    Article  Google Scholar 

  30. Neptune RR, Hull ML (1998) Evaluation of performance criteria for simulation of submaximal steady-state cycling using a forward dynamic model. J Biomech Eng 120:334–341

    Article  Google Scholar 

  31. Neptune RR, Hull ML (1999) A theoretical analysis of preferred pedaling rate selection in endurance cycling. J Biomech 32:409–415

    Article  Google Scholar 

  32. Newmiller J, Hull ML, Zajac FE (1988) A mechanically decoupled two force component bicycle pedal dynamometer. J Biomech 21:375–386

    Article  Google Scholar 

  33. Pandy MG, Zajac FE, Sim E, Levine WS (1990) An optimal control model for maximum-height human jumping. J Biomech 23:1185–1198

    Article  Google Scholar 

  34. Prilutsky BI, Gregor RJ (2000) Analysis of muscle coordination strategies in cycling. IEEE Trans Rehabil Eng 8:362–370

    Article  Google Scholar 

  35. Raasch CC, Zajac FE (1999) Locomotor strategy for pedaling: muscle groups and biomechanical functions. J Neurophysiol 82:515–525

    Google Scholar 

  36. Rasmussen J, Damsgaard M, Christensenm ST (2000) Inverse-inverse dynamics simulation of musculo-skeletal systems. In: Proceedings of the 12th Conference of the European Society of Biomechanics, Royal Academy of Medicine in Ireland, ISBN 0-9538809-0-7

  37. Rasmussen J, Damsgaard M, Voigt M (2001) Muscle recruitment by the min/max criterion — a comparative numerical study. J Biomech 34:409–415

    Article  Google Scholar 

  38. Rasmussen J, de Zee M, Damsgaard M, Christensen ST, Marek C, Siebertz K (2005) A general method for scaling musculo-skeletal models, international symposium on computer simulation in biomechanics,United States

  39. Rasmussen J, Christensen ST, Siebertz K, Rausch J (2006) Posture and movement prediction by means of musculoskeletal optimization. SAE Technical Paper. doi:10.4271/2006-01-2342

  40. Redfield R, Hull M (1986a) Prediction of pedal forces in bicycling using optimization methods. J Biomech 19:523–540

    Article  Google Scholar 

  41. Redfield R, Hull ML (1986b) On the relation between joint moments and pedalling rates at constant power in bicycling. J Biomech 19:317–329

    Article  Google Scholar 

  42. Sprague MA, Geers TL (2003) Spectral elements and field separation for an acoustic fluid subject to cavitation. J Comput Phys 184:149–162

    Article  MATH  Google Scholar 

  43. Wang XG, Verriest JP (1998) A geometric algorithm to predict the arm reach posture for computer-aided ergonomic evaluation. J Visual Comput Animat 9:33–47

    Article  Google Scholar 

  44. Wang XG (1999) A behavior-based inverse kinematics algorithm to predict arm prehension postures for computer-aided ergonomic evaluation. J Biomech 32:453–460

    Article  Google Scholar 

  45. Xiang Y, Arora JS, Abdel-Malek K (2010a) Physics-based modeling and simulation of human walking: A review of optimization-based and other approaches. Struct Multidiscip Optim 42:1–23

    Article  MATH  MathSciNet  Google Scholar 

  46. Xiang Y, Arora JS, Rahmatalla S, Marler T, Bhatt R, Abdel-Malek K (2010b) Human lifting simulation using a multi-objective optimization approach. Multibody Syst Dyn 23:1–21

    Article  MATH  MathSciNet  Google Scholar 

  47. Xiang Y, Arora JS, Abdel-Malek K (2011) Optimization-based prediction of asymmetric human gait. J Biomech 44:683–693

    Article  Google Scholar 

  48. Yang J, Marler RT, Kim H, Arora J, Abdel-Malek K (2004) Multi-objective optimization for upper body posture prediction. In: 10th AIAA/ISSMO multidisciplinary analysis and optimization conference, Albany, New York, USA

  49. Yang J, Marler T, Rahmatalla S (2011) Multi-objective optimization-based method for kinematic posture prediction: development and validation. Robotica 29:245–253

    Article  Google Scholar 

  50. Zajac FE (1993) Muscle coordination of movement: A perspective. J Biomech 26:Supplement 1:109–124

    Article  Google Scholar 

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Acknowledgments

This work was supported by the Danish Advanced Technology Foundation.

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Correspondence to Saeed Davoudabadi Farahani.

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Farahani, S.D., Bertucci, W., Andersen, M.S. et al. Prediction of crank torque and pedal angle profiles during pedaling movements by biomechanical optimization. Struct Multidisc Optim 51, 251–266 (2015). https://doi.org/10.1007/s00158-014-1135-6

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Keywords

  • Musculoskeletal models
  • Optimization-based movement prediction
  • Inverse-inverse dynamics
  • Performance criterion