Compensating for Fatigue-Induced Time-Varying Delayed Muscle Response in Neuromuscular Electrical Stimulation Control

Chapter
Part of the Advances in Delays and Dynamics book series (ADVSDD, volume 4)

Abstract

Neuromuscular electrical stimulation (NMES), often called functional electrical stimulation (FES),is a prescribed treatment for various neuromuscular disorders. When applied to articulate a person’s limb, the respective skeletal muscle groups are known to rapidly fatigue compared to muscles activated by the nervous system. Recent results have shown that muscles have a delayed response to electrical stimulation, and more recent results indicate that this delayed response increases as the muscle fatigues. A NMES control method is developed in this chapter as a means to compensate for the varying input delay for the uncertain nonlinear dynamics for the lower limb. Experimental results are provided to demonstrate the performance of the developed controller.

References

  1. 1.
    Abbas, J., Chizeck, H.: Feedback control of coronal plane hip angle in paraplegic subjects using functional neuromuscular stimulation. IEEE Trans. Biomed. Eng. 38(7), 687–698 (1991)CrossRefGoogle Scholar
  2. 2.
    Artstein, Z.: Linear systems with delayed controls: A reduction. IEEE Trans. Autom. Control 27(4), 869–879 (1982)MATHMathSciNetCrossRefGoogle Scholar
  3. 3.
    Bekiaris-Liberis, N., Krstic, M.: Compensation of time-varying input delay for nonlinear systems. In: Proceedings of the Mediterranean Conference on Control and Automation, pp. 1040–1045 (2011)Google Scholar
  4. 4.
    Bellman, M., Cheng, T.-H., Downey, R., Dixon, W.: Stationary cycling induced by switched functional electrical stimulation control. In: Proceedings of the American Control Conference, pp. 4802–4809 (2014)Google Scholar
  5. 5.
    Bickel, C., Gregory, C., Dean, J.: Motor unit recruitment during neuromuscular electrical stimulation: a critical appraisal. Eur. J. Appl. Physiol. 111(10), 2399–2407 (2011)CrossRefGoogle Scholar
  6. 6.
    Binder-Macleod, S., Lee, S., Baadte, S.: Reduction of the fatigue induced force decline in human skeletal muscle by optimized stimulation trains. Archives Phys. Med. Rehabil. 78(10), 1129–1137 (1997)CrossRefGoogle Scholar
  7. 7.
    Bresch-Pietri, D., Krstic, M.: Adaptive trajectory tracking despite unknown input delay and plant parameters. Automatica 45(9), 2074–2081 (2009)MATHMathSciNetCrossRefGoogle Scholar
  8. 8.
    Buford W. Jr., Ivey F. Jr., Malone, J., Patterson, R., Peare, G., Nguyen, D., Stewart, A.: Muscle balance at the knee—moment arms for the normal knee and the ACL—minus kne. IEEE Trans. Rehabitat. Eng. 5(4), 367–379 (1997)Google Scholar
  9. 9.
    Castillo-Toledo, B., Di Gennaro, S., Castro, G.: Stability analisys for a class of sampled nonlinear systems with time-delay. In: Proceedings of the IEEE Conference on Decision and Control, pp. 1575–1580 (2010)Google Scholar
  10. 10.
    Cavanagh, P., Komi, P.: Electromechanical delay in human skeletal muscle under concentric and eccentric contractions. Eur. J. Appl. Physiol. Occup. Physiol. 42(3), 159–163 (1979)CrossRefGoogle Scholar
  11. 11.
    Ce, E., Rampichini, S., Agnello, L., Veicsteinas, A., Esposito, F.: Effects of temperature and fatigue on the electromechanical delay components. Muscle Nerve 47(4), 566–576 (2013)CrossRefGoogle Scholar
  12. 12.
    Chang, G.-C., Lub, J.-J., Liao, G.-D., Lai, J.-S., Cheng, C.-K., Kuo, B.-L., Kuo, T.-S.: A neuro-control system for the knee joint position control with quadriceps stimulation. IEEE Trans. Rehabitat. Eng. 5(1), 2–11 (1997)CrossRefGoogle Scholar
  13. 13.
    Chen, B., Liu, X., Tong, S.: Robust fuzzy control of nonlinear systems with input delay. Chaos, Solitons, Fractals 37(3), 894–901 (2008)MATHMathSciNetCrossRefGoogle Scholar
  14. 14.
    Chiasson, J., Loiseau, J.: Applications of Time Delay Systems. Series Lecture Notes in Control and Information Sciences. Springer, New York (2007)MATHCrossRefGoogle Scholar
  15. 15.
    Doucet, B., Griffin, L.: Maximal versus submaximal intensity stimulation with variable patterns. Muscle Nerve 37(6), 770–777 (2008)CrossRefGoogle Scholar
  16. 16.
    Downey, R., Ambrosini, E., Ferrante, S., Pedrocchi, A., Dixon, W., Ferrigno, G.: Asynchronous stimulation with an electrode array reduces muscle fatigue during FES cycling. In: Proceedings of the International Functional Electrical Stimulation Society Conference, pp. 154–157 (2012)Google Scholar
  17. 17.
    Downey, R., Bellman, M., Sharma, N., Wang, Q., Gregory, C., Dixon, W.: A novel modulation strategy to increase stimulation duration in neuromuscular electrical stimulation. Muscle Nerve 44(3), 382–387 (2011)Google Scholar
  18. 18.
    Downey, R., Cheng, T.-H., Dixon, W.: Tracking control of a human limb during asynchronous neuromuscular electrical stimulation. In: Proceedings of the IEEE Conference on Decision and Control, pp. 139–144 (2013)Google Scholar
  19. 19.
    Duffell, L., Donaldson, N., Newham, D.: Power output during functional electrically stimulated cycling in trained spinal cord injured people. Neuromodulation: technology at the neural. Interface 13(1), 50–57 (2010)Google Scholar
  20. 20.
    Ebrahimpour, M., Erfanian, A.: Comments on sliding mode closed-loop control of FES: controlling the shank movement. IEEE Trans. Biomed. Eng. 55(12), 2842 (2008)CrossRefGoogle Scholar
  21. 21.
    Ferrante, S., Ambrosini, E., Ferrigno, G., Pedrocchi, A.: Biomimetic NMES controller for arm movements supported by a passive exoskeleton. In: Proceedings of the EMBC Annual International Conference, pp. 1888–1891 (2012)Google Scholar
  22. 22.
    Gollee, H., Hunt, K., Wood, D.: New results in feedback control of unsupported standing in paraplegia. IEEE Trans. Neural Syst. Rehabil. Eng. 12(1), 73–91 (2004)CrossRefGoogle Scholar
  23. 23.
    Gregory, C., Bickel, C.: Recruitment patterns in human skeletal muscle during electrical stimulation. Phys. Therapy 85(4), 358–364 (2005)Google Scholar
  24. 24.
    Gregory, C., Dixon, W., Bickel, C.: Impact of varying pulse frequency and duration on muscle torque production and fatigue. Muscle Nerve 35(4), 504–509 (2007)CrossRefGoogle Scholar
  25. 25.
    Gu, K., Kharitonov, V., Chen, J.: Stability of Time-Delay Systems. Birkhauser, Boston (2003)MATHCrossRefGoogle Scholar
  26. 26.
    Gu, K., Niculescu, S.-I.: Survey on recent results in the stability and control of time-delay systems. J. Dyn. Syst. Meas. Control 125(2), 158–165 (2003)CrossRefGoogle Scholar
  27. 27.
    Guo, L.: H infinity output feedback control for delay systems with nonlinear and parametric uncertainties. IEEE Proc. Control Theory Appl. 149(3), 226–236 (2002)CrossRefGoogle Scholar
  28. 28.
    Hausdorff, J., Durfee, W.: Open-loop position control of the knee joint using electrical stimulation of the quadriceps and hamstrings. Med. Biol. Eng. Comput. 29(3), 269–280 (1991)CrossRefGoogle Scholar
  29. 29.
    Hughes, A., Guo, L., De Weerth, S.: Interleaved multichannel epimysial stimulation for eliciting smooth contraction of muscle with reduced fatigue. In: Proceedings of the Annual International Conference of the IEEE Engineering in Medicine and Biology Society, pp. 6226–6229 (2010)Google Scholar
  30. 30.
    Hunt, K., Munih, M.: Feedback control of unsupported standing in paraplegia-part 1: optimal control approach. IEEE Trans. Rehabil. Eng. 5(4), 331–340 (1997)CrossRefGoogle Scholar
  31. 31.
    Jezernik, S., Wassink, R., Keller, T.: Sliding mode closed-loop control of FES: controlling the shank movement. IEEE Trans. Biomed. Eng. 51(2), 263–272 (2004)CrossRefGoogle Scholar
  32. 32.
    Karafyllis, I.: Finite-time global stabilization by means of time-varying distributed delay feedback. SIAM J. Control Optim. 45(1), 320–342 (2006)MATHMathSciNetCrossRefGoogle Scholar
  33. 33.
    Karafyllis, I., Malisoff, M., de Queiroz, M., Krstic, M., Yang, R.: Predictor-based tracking for neuromuscular electrical stimulation. Intern. J. Robust Nonlinear Control, to appear. doi:10.1002/rnc.3211
  34. 34.
    Karu, Z., Durfee, W., Barzilai, A.: Reducing muscle fatigue in FES applications by stimulating with N-let pulse trains. IEEE Trans. Biomed. Eng. 42(8), 809–817 (1995)CrossRefGoogle Scholar
  35. 35.
    Kawai, H., Bellman, M., Downey, R., Dixon, W.: Tracking control for FES-cycling based on force direction efficiency with antagonistic bi-articular muscles. In: Proceedings of the American Control Conference, pp. 5484–5489 (2014)Google Scholar
  36. 36.
    Kesar, T., Perumal, R., Reisman, D., Jancosko, A., Rudolph, K., Higginson, J., Binder-Macleod, S.: Functional electrical stimulation of ankle plantarflexor and dorsiflexor muscles: effects on poststroke gait. Stroke 40(12), 3821–3827 (2009)CrossRefGoogle Scholar
  37. 37.
    Khalil, H.: Nonlinear Systems, 3rd edn. Prentice-Hall, Englewood Cliffs, NJ (2002)MATHGoogle Scholar
  38. 38.
    Krevolin, J., Pandy, M., Pearce, J.: Moment arm of the patellar tendon in the human knee. J. Biomech. 37(5), 785–788 (2004)CrossRefGoogle Scholar
  39. 39.
    Krstic, M.: Delay Compensation for Nonlinear, Adaptive, and PDE Systems. Springer, New York (2009)MATHCrossRefGoogle Scholar
  40. 40.
    Krstic, M.: Input delay compensation for forward complete and strict-feedforward nonlinear systems. IEEE Trans. Autom. Control 55(2), 287–303 (2010)MathSciNetCrossRefGoogle Scholar
  41. 41.
    Krstic, M.: Lyapunov stability of linear predictor feedback for time-varying input delay. IEEE Trans. Autom. Control 55(2), 554–559 (2010)MathSciNetCrossRefGoogle Scholar
  42. 42.
    Krstic, M., Smyshlyaev, A.: Backstepping boundary control for first-order hyperbolic PDEs and application to systems with actuator and sensor delays. Syst. Control Lett. 57(9), 750–758 (2008)MATHMathSciNetCrossRefGoogle Scholar
  43. 43.
    Kurosawa, K., Futami, R., Watanabe, T., Hoshimiya, N.: Joint angle control by FES using a feedback error learning controller. IEEE Trans. Neural Syst. Rehabil. Eng. 13(3), 359–371 (2005)CrossRefGoogle Scholar
  44. 44.
    Li, W., Dong, Y., Wang, X.: Robust H\(^\infty \) control of uncertain nonlinear systems with state and input time-varying delays. In: Proceedings of the Chinese Control and Decision Conference, pp. 317–321 (2010)Google Scholar
  45. 45.
    Loiseau, J., Michiels, W., Niculescu, S.-I., Sipahi, R. (eds.): Topics in Time Delay Systems: Analysis, Algorithms, and Control. Springer, New York (2009)Google Scholar
  46. 46.
    Lozano, R., Castillo, P., Garcia, P., Dzul, A.: Robust prediction-based control for unstable delay systems: application to the yaw control of a mini-helicopter. Automatica 40(4), 603–612 (2004)MATHMathSciNetCrossRefGoogle Scholar
  47. 47.
    Mahmoud, M.: Robust Control and Filtering for Time-Delay Systems. Marcel Dekker, New York (2000)MATHGoogle Scholar
  48. 48.
    Malesevic, N., Popovic, L., Schwirtlich, L., Popovic, D.: Distributed low-frequency functional electrical stimulation delays muscle fatigue compared to conventional stimulation. Muscle Nerve 42(4), 556–562 (2010)CrossRefGoogle Scholar
  49. 49.
    Maneski, L., Malesevic, N., Savic, A., Keller, T., Popovic, D.: Surface-distributed low-frequency asynchronous stimulation delays fatigue of stimulated muscles. Muscle Nerve 48(6), 930–937 (2013)CrossRefGoogle Scholar
  50. 50.
    Manitius, A., Olbrot, A.: Finite spectrum assignment problem for systems with delays. IEEE Trans. Autom. Control 24(4), 541–552 (1979)MATHMathSciNetCrossRefGoogle Scholar
  51. 51.
    Mazenc, F., Bowong, S.: Tracking trajectories of the cart-pendulum system. Automatica 39(4), 677–684 (2003)MATHMathSciNetCrossRefGoogle Scholar
  52. 52.
    Mazenc, F., Mondie, S., Francisco, R.: Global asymptotic stabilization of feedforward systems with delay in the input. IEEE Trans. Autom. Control 49(5), 844–850 (2004)MathSciNetCrossRefGoogle Scholar
  53. 53.
    McDonnall, D., Clark, G., Normann, R.: Interleaved, multisite electrical stimulation of cat sciatic nerve produces fatigue-resistant, ripple-free motor responses. IEEE Trans. Neural Syst. Rehabil. Eng. 12(2), 208–215 (2004)CrossRefGoogle Scholar
  54. 54.
    Mizrahi, J., Levy, M., Ring, H., Isakov, E., Liberson, A.: EMG as an indicator of fatigue in isometrically FES-activated paralyzed muscles. IEEE Trans. Rehabitat. Eng. 2(2), 57–65 (1994)CrossRefGoogle Scholar
  55. 55.
    Nathan, R., Tavi, M.: The influence of stimulation pulse frequency on the generation of joint moments in the upper limb. IEEE Trans. Biomed. Eng. 37(3), 317–322 (1990)CrossRefGoogle Scholar
  56. 56.
    Nguyen, R., Masani, K., Micera, S., Morari, M., Popovic, M.: Spatially distributed sequential stimulation reduces fatigue in paralyzed triceps surae muscles: a case study. Artif. Organs 35(12), 1174–1180 (2011)CrossRefGoogle Scholar
  57. 57.
    Niculescu, S.-I., Gu, K.: Advances in Time-Delay Systems. Springer, New York (2004)MATHCrossRefGoogle Scholar
  58. 58.
    Paasuke, M., Ereline, J., Gapeveva, H.: Neuromuscular fatigue during repeated exhaustive submaximal static contractions of knee extensor muscles in endurance-trained, power-trained and untrained men. Acta Physiologica Scandinavica 166(4), 319–326 (1999)CrossRefGoogle Scholar
  59. 59.
    Popovic, L., Malesevic, N.: Muscle fatigue of quadriceps in paraplegics: Comparison between single vs. multi-pad electrode surface stimulation. In: Proceedings of the Annual International Conference of the IEEE Engineering in Medicine and Biology Society, pp. 6785–6788 (2009)Google Scholar
  60. 60.
    Previdi, F., Ferrarin, M., Savaresi, S., Bittanti, S.: Gain scheduling control of functional electrical stimulation for assisted standing up and sitting down in paraplegia: a simulation study. Intern. J. Adapt. Control Signal Process. 19(5), 327–338 (2005)MATHMathSciNetCrossRefGoogle Scholar
  61. 61.
    Prochazka, A., Gauthier, M., Wieler, M., Kenwell, Z.: The bionic glove: an electrical stimulator garment that provides controlled grasp and hand opening in quadriplegia. Archives Phys. Med. Rehabil. 78(6), 608–614 (1997)CrossRefGoogle Scholar
  62. 62.
    Richard, J.-P.: Time-delay systems: an overview of some recent advances and open problems. Automatica 39(10), 1667–1694 (2003)MATHMathSciNetCrossRefGoogle Scholar
  63. 63.
    Riener, R., Fuhr, T.: Patient-driven control of FES-supported standing up: a simulation study. IEEE Trans. Rehabitat. Eng. 6(2), 113–124 (1998)CrossRefGoogle Scholar
  64. 64.
    Sabut, S., Lenka, P., Kumar, R., Mahadevappa, M.: Effect of functional electrical stimulation on the effort and walking speed, surface electromyography activity, and metabolic responses in stroke subjects. J. Electromyogr. Kinesiol. 20(6), 1170–1177 (2010)CrossRefGoogle Scholar
  65. 65.
    Sabut, S., Sikdar, C., Mondal, R., Kumar, R., Mahadevappa, M.: Restoration of gait and motor recovery by functional electrical stimulation therapy in persons with stroke. Disabil. Rehabil. 32(19), 1594–1603 (2010)CrossRefGoogle Scholar
  66. 66.
    Schauer, T., Negard, N., Previdi, F., Hunt, K., Fraser, M., 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
  67. 67.
    Sharma, N., Bhasin, S., Wang, Q., Dixon, W.: Predictor-based control for an uncertain Euler-Lagrange system with input delay. Automatica 47(11), 2332–2342 (2011)MATHMathSciNetCrossRefGoogle Scholar
  68. 68.
    Sharma, M., Gregory, C., Dixon, W.: Predictor-based compensation for electromechanical delay during neuromuscular electrical stimulation. IEEE Trans. Neural Syst. Rehabil. Eng. 19(6), 601–611 (2011)CrossRefGoogle Scholar
  69. 69.
    Sharma, N., Gregory, C., Johnson, M., Dixon, W.: Closed-loop neural network-based NMES control for human limb tracking. IEEE Trans. Control Syst. Technol. 20(3), 712–725 (2012)CrossRefGoogle Scholar
  70. 70.
    Sharma, N., Stegath, K., Gregory, C., Dixon, W.: Nonlinear neuromuscular electrical stimulation tracking control of a human limb. IEEE Trans. Neural Syst. Rehabil. Eng. 17(6), 576–584 (2009)CrossRefGoogle Scholar
  71. 71.
    Sipahi, R., Niculescu, S.-I., Abdallah, C., Michiels, W., Gu, K.: Stability and stabilization of systems with time delay: limitations and opportunities. IEEE Control Syst. Mag. 31(1), 38–65 (2011)MathSciNetCrossRefGoogle Scholar
  72. 72.
    Smith, O.: A controller to overcome deadtime. ISA J. 6(2), 28–33 (1959)Google Scholar
  73. 73.
    Snyder-Mackler, L., Delitto, A., Stralka, S., Bailey, S.: Use of electrical stimulation to enhance recovery of quadriceps femoris muscle force production in patients following anterior cruciate ligament reconstruction. Phys. Ther. 74(10), 901–907 (1994)Google Scholar
  74. 74.
    Stackhouse, S., Binder-Macleod, S., Stackhouse, C., McCarthy, J., Prosser, L., Lee, S.: Neuromuscular electrical stimulation versus volitional isometric strength training in children with spastic diplegic cerebral palsy: A preliminary study. Neurorehabil. Neural Repair 21(6), 475–485 (2007)CrossRefGoogle Scholar
  75. 75.
    Thomsen, M., Veltink, P.: Influence of synchronous and sequential stimulation on muscle fatigue. Med. Biol. Eng. Comput. 35(3), 186–192 (1997)CrossRefGoogle Scholar
  76. 76.
    Wang, Z., Goldsmith, P., Tan, D.: Improvement on robust control of uncertain systems with time-varying input delays. IET Control Theory Appl. 1(1), 189–194 (2007)MathSciNetCrossRefGoogle Scholar
  77. 77.
    Watanabe, T., Futami, R., Hoshimiya, N., Handa, Y.: An approach to a muscle model with a stimulus frequency-force relationship for FES applications. IEEE Trans. Rehabil. Eng. 7(1), 12–17 (1999)CrossRefGoogle Scholar
  78. 78.
    Watanabe, K., Nobuyama, E., Kojima, A.: Recent advances in control of time delay systems-a tutorial review. In: Proceedings of the IEEE Conference on Decision and Control, pp. 2083–2089 (1996)Google Scholar
  79. 79.
    Wise, A., Morgan, D., Gregory, J., Proske, U.: Fatigue in mammalian skeletal muscle stimulated under computer control. J. Appl. Physiol. 90(1), 189–197 (2001)Google Scholar
  80. 80.
    Yan, T., Hui-Chan, C., Li, L.: Functional electrical stimulation improves motor recovery of the lower extremity and walking ability of subjects with first acute stroke: A randomized placebo-controlled trial. Stroke 36(1), 80–85 (2005)CrossRefGoogle Scholar
  81. 81.
    Yavuz, S., Sendemir-Urkmez, A., Turker, K.: Effect of gender, age, fatigue and contraction level on electromechanical delay. Clin. Neurophysiol. 121(10), 1700–1706 (2010)CrossRefGoogle Scholar
  82. 82.
    Yoshida, K., Horch, K.: Reduced fatigue in electrically stimulated muscle using dual channel intrafascicular electrodes with interleaved stimulation. Ann. Biomed. Eng. 21(6), 709–714 (1993)CrossRefGoogle Scholar
  83. 83.
    Yue, D., Han, Q.-L.: Delayed feedback control of uncertain systems with time-varying input delay. Automatica 41(2), 233–240 (2005)MATHMathSciNetCrossRefGoogle Scholar
  84. 84.
    Zhou, S., Lawson, D., Morrison, W., Fairweather, I.: Electromechanical delay in isometric muscle contractions evoked by voluntary, reflex and electrical stimulation. Eur. J. Appl. Physiol. Occup. Physiol. 70(2), 138–145 (1995)CrossRefGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  • R. Downey
    • 1
  • R. Kamalapurkar
    • 1
  • N. Fischer
    • 1
  • W. Dixon
    • 1
  1. 1.Department of Mechanical and Aerospace EngineeringGainesvilleUSA

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