Abstract
The aim of this study is to estimate the stiffness of the muscle-tendon unit, of human lower limb, during the execution of a normal gait cycle. Unlike the analytical techniques already widely validated in literature and discussed below, a probabilistic approach based on the Gaussian Mixture Model (GMM) has been adopted here for the computation of the muscle-tendon unit stiffness. The obtained results for the major muscle groups are shown. The effectiveness of the proposed approach has been evaluated by computing the Root Mean Square (RMS) error between the stiffness calculated analytically and those calculated using the GMM, for each subject.
Keywords
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsNotes
- 1.
- 2.
- 3.
The musculoskeletal setting files are provided free of charge with the OpenSim software: https://simtk.org/home/opensim.
- 4.
A detailed description of the adopted knee model is available at: http://simtk-confluence.stanford.edu:8080/display/OpenSim/Gait+2392+and+2354+Models.
References
Mussa-Ivaldi, F.A., Hogan, N., Bizzi, E. (1985). Neural, mechanical, and geometric factors subserving arm posture in humans. J. of Neurosci 5, 2732–2743.
Piovesan, D., Morasso, P., Giannoni, P., Casadio, M. (2013a). Arm Stiffness During Assisted Movement After Stroke: The Influence of Visual Feedback and Training. Neural Systems and Rehabilitation Engineering, IEEE Trans. on 21, 454–465.
Piovesan, D., Pierobon, A., Dizio, P., Lackner, J.R. (2013b). Experimental measure of arm stiffness during single reaching movements with a time-frequency analysis. Journal of Neurophysiology 110, 2484–2496.
Arnold, M., Hamner, S.R., Seth, A., Millard, M. (2013). How muscle fiber lengths and velocities affect muscle force generation as humans walk and run at different speeds. The Journal of Experimental Biology, 216, pp 2150–2160, March 2013.
Miller, R.H. (2014). A comparison of muscle energy models for simulating human walking in three dimensions. Journal of Biomechanics, 2014.
Shamaei, K., Sawicki, G.S., Dollar, A.M. (2013a). Estimation of Quasi-Stiffness of the Human Knee in the Stance Phase of Walking. PLoS ONE 8(3):e59993.
Shamaei, K. Sawicki, G.S., Dollar, A.M. (2013b). Estimation of Quasi-Stiffness and Propulsive Work of the Human Ankle in the Stance Phase of Walking. PLoS ONE 8(3): e59935.
Rouse, E.J., Gregg, R.D., Hargrove, L.J., Sensinger, J.W. (2013). The Difference Between Stiffness and Quasi-Stiffness in the Context of Biomechanical Modeling. IEEE Trans. On Biomedical Engineering, vol. 60, N.2, February 2013.
Calinon, S., Sardellitti, I., Caldwell, D. (2010). Learning-based control strategy for safe human-robot interaction exploiting task and robot redundancies. Int. Conf. on Intelligent Robots and Systems, 249–254.
Michieletto, S., Chessa, N., Menegatti, E. (2013). Learning how to approach industrial robot tasks from natural demonstrations. 2013 IEEE Workshop on Advanced Robotics and its Social Impacts (ARSO), Tokyo, 2013.
Rozo, L., Calinon, S., Caldwell, D.G., Jimenez, P., Torras, C. (2013). Learning collaborative impedance-based robot behaviors. Proc. of the AAAI Conf. on Artificial Intelligence.
Liu, M.Q., Anderson, F.C., Schwartz, M.H., Delp, S.L. (2008). Muscle contributions to support and progression over a range of walking speeds. Journal of Biomechanics, Nov. 2008, 41(15):3243–3252.
Delp, S.L., Anderson, F.C., Arnold, S.A., Loan, P. Habib, A., John, C.T., Guendelman, E., Thelen, D.G. (2007). OpenSim: Open-Source Software to Create and Analyze Dynamic Simulations of Movement. IEEE Trans. on Biomedical Engineering, Vol. 54, No. 11, Nov. 2007.
Delp., S.L., Loan, J.P., Hoy, M.G., Zajac, F.E., Topp, E.L., and Rosen, J.M. (1990). An interactive graphics-based model of the lower extremity to study orthopaedic surgical procedures. IEEE Trans. on Biomedical Engineering, 37, 757–767.
Anderson, F.C., and Pandy, M.G. (1999). A Dynamic Optimization Solution for Vertical Jumping in Three Dimensions. Comput Methods Biomech Biomed Engin 2, 201–231.
Yamaguchi, G.T., and Zajac, F.E. (1989). A planar model of the knee joint to characterize the knee extensor mechanism. J. Biomech 22, 1–10.
Nisell, R., Nemeth, G., and Ohlsen, H. (1986). Joint forces in extension of the knee. Analysis of a mechanical model. Acta Orthop Scand 57, 41–46.
Thelen, D.G., and Anderson, F.C. (2006). Using computed muscle control to generate dynamic contractions in older adults. J. Biomech Eng 125, 70–77.
Hu, X., Murray, W.M., Perreault, E.J. (2011). Muscle short-range stiffness can be used to estimate the endpoint stiffness of the human arm. Journal of Neurophysiology 205:1633–1641, 2011.
Pfeifer, S., Hardegger, M., Vallery, H., List, R., Foresti, M., Riener, R., Perreault, E.J. (2011). Model-Based Estimation of Active Knee Stiffness. 2011 IEEE Int. Conf. on Rehabilitation Robotics, Rehab Week Zurich, ETH Zurich Science City, Switzerland, June 29–July 1, 2011.
Pfeifer, S., Vallery, H., Hardegger, M., Riener, R., Perrault, E.J. (2012). Model-Based Estimation of Knee Stiffness. IEEE Trans. on Biomedical Engineering, Vol. 59, No. 9, Sept. 2012.
Dempster, A.P., Laird, N.M., Rubin, D.B. (1977). Maximum likelihood from incomplete data via the em algorithm. Journal of the Royal Statistical Society. Series B (Methodological), pp. 1–38, 1977.
DeGroot, M. (1970). Optimal Statistical Decisions. McGraw-Hill, 1970.
Schwartz, G. (1978). Estimating the dimension of a model. The annals of statistics, 6(2):461–464, 1978.
Michieletto, S., Rizzi, A., & Menegatti, E. Robot learning by observing humans activities and modeling failures. In IROS workshops: Cognitive Robotics Systems (CRS2013), IEEE (Nov 2013).
Acknowledgments
This research has been supported by “Consorzio Ethics” through a grant for research activity on the project “Rehabilitation Robotics”, and by the Faculty research grant at Gannon University.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2016 Springer International Publishing Switzerland
About this paper
Cite this paper
Bortoletto, R., Michieletto, S., Pagello, E., Piovesan, D. (2016). Human Muscle-Tendon Stiffness Estimation During Normal Gait Cycle Based on Gaussian Mixture Model. In: Menegatti, E., Michael, N., Berns, K., Yamaguchi, H. (eds) Intelligent Autonomous Systems 13. Advances in Intelligent Systems and Computing, vol 302. Springer, Cham. https://doi.org/10.1007/978-3-319-08338-4_86
Download citation
DOI: https://doi.org/10.1007/978-3-319-08338-4_86
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-08337-7
Online ISBN: 978-3-319-08338-4
eBook Packages: EngineeringEngineering (R0)