Progress and Open Questions in the Identification of Electrically Stimulated Human Muscle for Stroke Rehabilitation

  • Fengmin Le
  • Chris T. Freeman
  • Ivan Markovsky
  • Eric Rogers


Recent work involving the use of robots in stroke rehabilitation has developed model-based algorithms to control the application of functional electrical stimulation to the upper limb of stroke patients with incomplete paralysis to assist in reaching tasks. This, in turn, requires the identification of the response of a human muscle to electrical stimulation. In this chapter an overview of the progress reported in the literature is given together with some currently open research questions.


Linear Parameter Recursive Little Square Stroke Rehabilitation Iterative Learn Control Muscle Model 


  1. 1.
    Parker, V.M., Wade, D.T., Langton-Hewer, R.: Loss of arm function after stroke: measurement, frequency and recovery. Int. Rehabil. Med. 8(4), 69–73 (1986) Google Scholar
  2. 2.
    Broeks, J.G., Lankhorst, G.J., Rumping, K., Previo, A.J.: The long-term outcome of arm function after stroke: results of a follow-up study. Disabil. Rehabil. 21, 357–364 (1999) CrossRefGoogle Scholar
  3. 3.
    de Kroon, J.R., van der Lee, J.H., Ijzerman, M.J., Lankhorst, G.J.: Therapeutic electrical stimulation to improve motor control and functional abilities of the upper extremity after stroke: a systematic review. Clin. Rehabil. 16(4), 350–360 (2002) CrossRefGoogle Scholar
  4. 4.
    De Kroon, J.R., Ijzerman, M.J., Chae, J.J., Lankhorst, G.J., Zilvold, G.: Relation between stimulation characteristics and clinical outcome in studies using electrical stimulation to improve motor control of the upper extremety in stroke. J. Rehabil. Med. 37(2), 65–74 (2005) CrossRefGoogle Scholar
  5. 5.
    Pomeroy, V.M., King, L., Pollack, A., Baily-Hallon, A., Longhorne, P.: Electrostimulation for promoting recovery of movement or functional ability after stroke. The Cochrane Database of Systematic Reviews, Issue 2 (2006) Google Scholar
  6. 6.
    Burridge, J.H., Ladouceur, M.: Clinical and therapeutic applications of neuromuscular stimulation: a review of current use and speculation into future developments. Neuromodulation 4(4), 147–154 (2001) CrossRefGoogle Scholar
  7. 7.
    Rushton, D.N.: Functional electrical stimulation and rehabilitation—an hypothesis. Med. Eng. Phys. 25(1), 75–78 (2003) CrossRefGoogle Scholar
  8. 8.
    Le, F., Markovsky, I., Freeman, C.T., Rogers, E.: Identification of electrically stimulated muscle models of stroke patients. Control Eng. Pract. 18(4), 396–407 (2010) CrossRefGoogle Scholar
  9. 9.
    Thorsen, R., Spadone, R., Ferrarin, M.: A pilot study of myoelectrically controlled FES of upper extremity. IEEE Trans. Neural Syst. Rehabil. Eng. 9(2), 161–168 (2001) CrossRefGoogle Scholar
  10. 10.
    Baker, L.L., McNeal, D.R., Benton, L.A., Bowman, B.R., Waters, R.L.: NeuroMuscular Electrical Stimulation: A Practical Guide, 3rd edn. (1993) Google Scholar
  11. 11.
    Freeman, C.T., Hughes, A.-M., Burridge, J.H., Chappell, P.H., Lewin, P.L., Rogers, E.: Iterative learning control of FES applied to the upper extremity for rehabilitation. Control Eng. Pract. 17(3), 368–381 (2009) CrossRefGoogle Scholar
  12. 12.
    Freeman, C.T., Hughes, A.-M., Burridge, J.H., Chappell, P.H., Lewin, P.L., Rogers, E.: A robotic workstation for stroke rehabilitation of the upper extremity using FES. Med. Eng. Phys. 31(3), 364–373 (2009) CrossRefGoogle Scholar
  13. 13.
    Freeman, C.T., Hughes, A.-M., Burridge, J.H., Chappell, P.H., Lewin, P.L., Rogers, E.: A model of the upper extremity using surface FES for stroke rehabilitation. J. Biomed. Eng. 131(1), 031011 (2009) Google Scholar
  14. 14.
    Hughes, A.-M., Freeman, C.T., Burridge, J.H., Chappell, P.H., Lewin, P.L., Rogers, E.: Feasibility of iterative learning control mediated by functional electrical stimulation for reaching after stroke. Neurorehabil. Neural Repair 23(6), 559–568 (2009) CrossRefGoogle Scholar
  15. 15.
    Arimoto, S., Kawamura, S., Miyazaki, F.: Bettering operations of robots by learning. J. Robot. Syst. 1, 123–140 (1984) CrossRefGoogle Scholar
  16. 16.
    Bristow, D.A., Tharayil, M., Alleyne, A.G.: A survey of iterative learning control. IEEE Control Syst. Mag. 26(3), 96–114 (2006) CrossRefGoogle Scholar
  17. 17.
    Ahn, H.-S., Chen, Y., Moore, K.L.: Iterative learning control: brief survey and categorization. IEEE Trans. Syst. Man Cybern. 37(6), 1109–1121 (2007) Google Scholar
  18. 18.
    Popovic, D., Popovic, M.: Tuning of a nonanalytical hierarchical control system for reaching with FES. IEEE Trans. Biomed. Eng. 45(2), 203–212 (1998) CrossRefGoogle Scholar
  19. 19.
    Crago, P.E., Nakai, R.J., Chizeck, H.J.: Feedback regulation of hand grasp opening and contact force during stimulation of paralysed muscle. IEEE Trans. Biomed. Eng. 38(1), 17–28 (1991) CrossRefGoogle Scholar
  20. 20.
    Chizeck, H.J., Lan, N., Palmieri, L.S., Crago, P.L.: Feedback control of electrically stimulated muscle using simultaneous pulse width and stimulus period modulation. IEEE Trans. Biomed. Eng. 38(12), 1224–1234 (1991) CrossRefGoogle Scholar
  21. 21.
    Watanabe, T., Iibuchi, K., Kurosawa, K., Hoshimiya, N.: A method of multichannel PID control of two-degree-of-freedom wrist joint movements by functional electrical stimulation. Syst. Comput. Jpn. 34(5), 319–328 (2003) CrossRefGoogle Scholar
  22. 22.
    Hatwell, M.S., Oderkerk, B.J., Sacher, C.A., Inbar, G.F.: Patient-driven control of FES-supported standing up: a simulation study. IEEE Trans. Rehabil. Eng. 36(6), 683–691 (1991) MathSciNetGoogle Scholar
  23. 23.
    Previdi, F., Schauer, T., Savaresi, S.M., Hunt, K.J.: Data-driven control design for neuroprotheses: a virtual reference feedback tuning (VRFT) approach. IEEE Trans. Control Syst. Technol. 12(1), 176–182 (2004) CrossRefGoogle Scholar
  24. 24.
    Hill, A.V.: Then heat of shortening and the dynamic constants of a muscle. Proc. R. Soc. Lond. B, Biol. Sci. 126, 136–195 (1938) CrossRefGoogle Scholar
  25. 25.
    Lan, N.: Stability analysis for postural control in a two-joint limb system. IEEE Trans. Neural Syst. Rehabil. Eng. 10(4), 249–259 (2002) MathSciNetCrossRefGoogle Scholar
  26. 26.
    Riener, R., Fuhr, T.: Patient-driven control of FES-supported standing up: a simulation study. IEEE Trans. Rehabil. Eng. 6(2), 113–124 (1998) CrossRefGoogle Scholar
  27. 27.
    Jezernik, S., Wassink, R.G.V., Keller, T.: Sliding mode closed-loop control of FES: controlling the shank movement. IEEE Trans. Rehabil. Eng. 51(2), 263–272 (2004) Google Scholar
  28. 28.
    Schauer, T., Negard, N.O., Previdi, F., Hunt, K.J., Fraser, M.H., Ferchland, E., Raisch, J.: Online identification and nonlinear control of the electrically stimulated quadriceps muscle. Control Eng. Pract. 13(9), 1207–1219 (2005) CrossRefGoogle Scholar
  29. 29.
    Ferrarin, M., Palazzo, F., Riener, R., Quintern, J.: Model-based control of FES induced single joint movements. IEEE Trans. Neural Syst. Rehabil. Eng. 9(3), 245–257 (2001) CrossRefGoogle Scholar
  30. 30.
    Hunt, K.J., Munih, M., Donaldson, N.N., Barr, F.M.D.: Investigation of the Hammerstein hypothesis in the modeling of electrically stimulated muscle. IEEE Trans. Rehabil. Eng. 45(8), 998–1009 (1998) Google Scholar
  31. 31.
    Reiner, R., Quintern, J.: A physiologically based model of muscle activation verified by electrical stimulation. Bioelectrochem. Bioenerg. 43, 257–264 (1997) CrossRefGoogle Scholar
  32. 32.
    Previdi, F., Carpanzano, E.: Design of a gain scheduling controller for knee-joint angle control by using functional electrical stimulation. IEEE Trans. Control Syst. Technol. 11(3), 310–324 (2003) CrossRefGoogle Scholar
  33. 33.
    Happee, R., Van der Helm, F.C.T.V.: The control of shoulder muscles during goal directed movements, an inverse dynamic analysis. J. Biomed. Eng. 28(10), 1179–1191 (1995) Google Scholar
  34. 34.
    Durfee, W.K., MacLean, K.E.: Methods for estimating isometric recruitment curves of electrically stimulated muscle. IEEE Trans. Biomed. Eng. 36(7), 654–667 (1989) CrossRefGoogle Scholar
  35. 35.
    Baratta, R., Solomonow, M.: The dynamic response model of nine different skeletal muscles. IEEE Trans. Biomed. Eng. 37(3), 243–251 (1990) CrossRefGoogle Scholar
  36. 36.
    Veltink, P.H., Chizeck, H.J., Crago, P.E., El-Bialy, A.: Nonlinear joint angle control for artificially stimulate muscle. IEEE Trans. Biomed. Eng. 39(4), 368–380 (1992) CrossRefGoogle Scholar
  37. 37.
    Chizeck, H.J., Crago, P.E., Kofman, L.S.: Robust closed-Loop control of isometric muscle force using pulsewidth modulation. IEEE Trans. Biomed. Eng. 35(7), 510–517 (1988) CrossRefGoogle Scholar
  38. 38.
    Bernotas, L., Crago, P.E., Chizeck, H.J.: A discrete-time model of electrically stimulated muscle. IEEE Trans. Biomed. Eng. 33(9), 829–838 (1986) CrossRefGoogle Scholar
  39. 39.
    Durfee, W.K., Palmer, K.L.: Estimation of force-activation, force-length, and force-velocity properties in isolated, electrically stimulated muscle. IEEE Trans. Biomed. Eng. 41(3), 205–216 (1994) CrossRefGoogle Scholar
  40. 40.
    Crago, P.E., Peckham, P.H., Thorpe, G.B.: Modulation of muscle force by recruitment during intramuscular stimulation. IEEE Trans. Biomed. Eng. 27(12), 679–684 (1980) CrossRefGoogle Scholar
  41. 41.
    Ding, J., Wexler, A.S., Binder-MacLeod, S.A.: A mathematical model that predicts the force-frequency relationship of human skeletal muscle. Muscle Nerve 26(2), 477–485 (2002) CrossRefGoogle Scholar
  42. 42.
    Carroll, S.G., Triolo, R.J., Chizeck, H.J., Kobetic, R., Marsolias, E.B.: Tetanic responses of electrically stimulated paralyzed muscle at varying interpulse intervals. IEEE Trans. Biomed. Eng. 36(7), 644–653 (1989) CrossRefGoogle Scholar
  43. 43.
    Dempsey, E.J., Westwick, D.T.: Identification of Hammerstein models with cubic spline nonlinearities. IEEE Trans. Biomed. Eng. 51(2), 237–245 (2004) CrossRefGoogle Scholar
  44. 44.
    Marquardt, D.: An algorithm for least-squares estimation from linear parameters. SIAM J. Appl. Math. 11, 431–441 (1963) MathSciNetMATHCrossRefGoogle Scholar
  45. 45.
    Zhu, Y.: Identification of Hammerstein models for control using ASYM. Int. J. Control 73(18), 1692–1702 (2000) MATHCrossRefGoogle Scholar
  46. 46.
    Graham, G.M., Thrasher, T.A., Popovic, M.R.: The effect of random modulation of functional electrical stimulation parameters on muscle fatigue. IEEE Trans. Neural Syst. Rehabil. Eng. 14(1), 38–45 (2006) CrossRefGoogle Scholar
  47. 47.
    Le, F., Markovsky, I., Freeman, C.T., Rogers, E.: Identification of electrically stimulated muscle after stroke. In: Proc. European Control Conference, pp. 3208–3213 (2009) Google Scholar
  48. 48.
    Bako, L., Mercere, G., Lecoeuche, S., Lovera, M.: Recursive subspace identification of Hammerstein models based on least squares support vector machines. IET Proc. D 3(9), 1209–1216 (2009) MathSciNetGoogle Scholar
  49. 49.
    Greblicki, W.: Stochastic approximation in nonparametric identification of Hammerstein systems. IEEE Trans. Autom. Control 47(11), 1800–1810 (2002) MathSciNetCrossRefGoogle Scholar
  50. 50.
    Chen, H.F.: Pathwise convergence of recursive identification algorithms for Hammerstein systems. IEEE Trans. Autom. Control 49(4), 1641–1649 (2004) CrossRefGoogle Scholar
  51. 51.
    Bai, E.W.: An optimal two-stage identification algorithm for Hammerstein-Wiener nonlinear systems. Automatica 34(3), 333–338 (1998) MathSciNetMATHCrossRefGoogle Scholar
  52. 52.
    Chang, F.H.I., Luus, R.: A non-iterative method for identification using Hammerstein model. IEEE Trans. Autom. Control 16(5), 464–468 (1971) CrossRefGoogle Scholar
  53. 53.
    Zhao, W.X., Chen, H.F.: Adaptive tracking and recursive identification for Hammerstein systems. Automatica, 45(12), 2773–2783 (2009) MathSciNetMATHCrossRefGoogle Scholar
  54. 54.
    Chia, T.L., Chow, P.C., Chizeck, H.J.: Recursive parameter identification of constrained systems: an application to electrically stimulated muscle. IEEE Trans. Biomed. Eng. 38(5), 429–442 (1991) CrossRefGoogle Scholar
  55. 55.
    Ponikvar, M., Munih, M.: Setup and procedure for online identification of electrically stimulated muscle With Matlab Simulink. IEEE Trans. Neural Syst. Rehabil. Eng. 9(3), 295–301 (2001) CrossRefGoogle Scholar

Copyright information

© Springer-Verlag London Limited 2012

Authors and Affiliations

  • Fengmin Le
    • 1
  • Chris T. Freeman
    • 1
  • Ivan Markovsky
    • 1
  • Eric Rogers
    • 1
  1. 1.School of Electronics and Computer ScienceUniversity of SouthamptonSouthamptonUK

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