System Identification and Neuromuscular Modeling
Chapter
Abstract
“System identification” is a term that describes mathematical techniques used to infer the properties of an unknown system from measurements of the system inputs and outputs. Typically, the inputs to the system are controlled by the experimenter, although the only real requirements are that all the inputs and outputs are known and measurable and that the inputs sufficiently excite the system. System identification techniques have been applied to a wide range of problems, this chapter focuses on applications related to the neuromuscular system (i.e., muscle, joint, and limb mechanics) as well as the neural signals that control posture and movement.
Keywords
Joint Stiffness Neuromuscular System Volterra Kernel Functional Expansion Wiener Kernel
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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References
- Acosta, A.M. and Kirsch, R.F. (1996a). Endpoint stiffness estimation for assessing arm stability. 1st Ann. Conf. Int. Funct. Elec. Stim. Soc., 1:60.Google Scholar
- Acosta, A.M. and Kirsch, R.F. (1996b). A planar manipulator for the study of multi-joint human arm posture and movement control. 9th Eng. Found. Conf. Biomech. Neur. Cont. Mov., 9:1–2.Google Scholar
- Agarwal, G.C. and Gottlieb, G.L. (1977). Compliance of the human ankle joint. Trans. ASME, 99:166–170.Google Scholar
- Akaike, H. (1994). A new look at the statistical model identification. IEEE Trans. Auto. Cont., 19:716–23.CrossRefGoogle Scholar
- An, C.H., Atkeson, C.G., and Hollerbach, J.M. (1988). Model-Based Control of a Robot Manipulator. The MIT Press, Cambridge, Massachusetts.Google Scholar
- Barden, J.A. (1981). Estimate of rate constants of muscle crossbridge turnover based on dynamic mechanical measurements. Physiol. Chem. and Phys., 13:211–219.Google Scholar
- Bendat, J.S. and Piersol, A.G. (1986). Random Data: Analysis and Measurement Procedures (Second edition). Wiley-Interscience, New York.Google Scholar
- Bennett, D.J. (1993). Torques generated at the human elbow joint in response to constant position errors imposed during voluntary movements. Exp. Brain Res., 95:488–498.PubMedGoogle Scholar
- Bennett, D.J., Hollerbach, J.M., Xu, Y., and Hunter, I.W. (1992). Time-varying stiffness of human elbow joint during cyclic voluntary movement. Exp. Brain Res., 88:433–442.PubMedCrossRefGoogle Scholar
- Bizzi, E., Polit, A., and Morasso, P. (1976). Mechanisms underlying achievement of final head position. J. Neurophysiol., 39:435–444.PubMedGoogle Scholar
- Boyd, S. and Chua, L.O. (1985). Fading memory and the problem of approximating nonlinear operators with Volterra series. IEEE Trans. Cir. Sys., CAS-32:1150–1161.CrossRefGoogle Scholar
- Calancie, B. and Stein, R.B. (1987). Measurement of rate constants for the contractile cycle of intact mammalian muscle fibers. Biophys. J., 51:149–159.PubMedCrossRefGoogle Scholar
- Chen, S. and Billings, S.A. (1989). Representation of non-linear systems: the NARMAX model. Int. J. Cont., 49:1013–1032.Google Scholar
- Chizeck, H.J., Lan, N., Streeter-Palmieri, L., and Crago, P.E. (1991). Feedback control of electrically stimulated muscle using simultaneous pulse width and stimulus period modulation. IEEE Trans. Biomed. Eng., 38:1224–1234.PubMedCrossRefGoogle Scholar
- Cooker, H.S., Larson, C.R., and Luschei, E.S. (1980). Evidence that the human jaw stretch reflex increases the resistance of the mandible to small displacements. J. Physiol., 308:61–78.PubMedGoogle Scholar
- Crago, P., Lemay, M., and Liu, L. (1990). External control of limb movements involving environmental interactions. In Multiple Muscle Systems: Biomechanics and Movement Organization. Winters, J. and Woo, S.-Y. (eds.), pp. 343–359. Springer-Verlag, New York.Google Scholar
- Evans, C.M., Fellows, S.J., Rack, P.M.H., Ross, H.F., and Walters, D.K.W. (1983). Response of the normal human ankle joint to imposed sinusoidal movements. J. Physiol., 344:483–502PubMedGoogle Scholar
- Gomi, H. and Kawato, M. (1996). Equilibrium-point control hypothesis examined by measured arm stiffness during multi-joint movement. Science, 272:117–120.PubMedCrossRefGoogle Scholar
- Hunter, I.W. (1986). Experimental comparison of Wiener and Hammerstein cascade models of frog muscle fiber mechanics. Biophys. J., 49:81a.Google Scholar
- Hunter, I.W. and Kearney, R.E. (1982a). Dynamics of human ankle stiffness: variation with mean ankle torque. J. Biomech., 15:747–752.PubMedCrossRefGoogle Scholar
- Hunter, I.W. and Kearney, R.E. (1982b). Two-sided linear filter identification. Med. Biol. Eng. Comput., 21:203–209.CrossRefGoogle Scholar
- Hunter, I.W. and Kearney, R.E. (1983). Invariance of ankle dynamic stiffness during fatiguing muscle contractions. J. Biomech., 16:985–991.PubMedCrossRefGoogle Scholar
- Huxley, A.F. (1957). Muscle structure and theories of contraction. Prog. Biophys. Biophys. Chem., 7:255–318.PubMedGoogle Scholar
- Joyce, G.C., Rack, P.M.H., and Ross, H.F. (1974). The forces generated at the human elbow joint in response to imposed sinusoidal movements of the forearm. J. Physiol., 240:351–374.PubMedGoogle Scholar
- Kawai, M. and Schachat, F. H. (1984). Differences in the transient response of fast and slow skeletal muscle fibers. Biophys. J., 45:1145–1151.PubMedCrossRefGoogle Scholar
- Kearney, R.E. and Hunter, I.W. (1982). Dynamics of human ankle stiffness: variation with displacement amplitude. J. Biomech., 15:753–756.PubMedCrossRefGoogle Scholar
- Kearney, R.E. and Hunter, I.W. (1983). System identification of human triceps surae stretch reflex dynamics. Exp. Brain Res., 51:117–127.PubMedCrossRefGoogle Scholar
- Kearney, R.E. and Hunter, I.W. (1984). System identification of human stretch reflex dynamics: tibialis anterior. Exp. Brain Res., 56:117–127.CrossRefGoogle Scholar
- Kearney, R.E. and Hunter, I.W. (1988). Nonlinear identification of stretch reflex dynamics. Ann. Biomed. Eng., 16:79–94.PubMedCrossRefGoogle Scholar
- Kearney, R.E. and Hunter, I.W. (1990). System identification of human joint dynamics. Crit. Rev. Biomed. Eng., 18:55–87.PubMedGoogle Scholar
- Kearney, R.E., Stein, R.B., and Parameswaran, L. (1996). Identification of intrinsic and reflex contributions to human ankle stiffness dynamics. IEEE Trans. Biomed. Eng., (in Press).Google Scholar
- Kirsch, R. and Kearney, R. (1993). Identification of time-varying dynamics of the human triceps surae stretch reflex: II. Rapid imposed movement. Exp. Brain Res., 97:128–138.PubMedCrossRefGoogle Scholar
- Kirsch, R. and Rymer, W. (1992). Neural compensation for fatigue induced changes in muscle stiffness during perturbations of elbow angle in man. J. Neurophysiol., 68:449–470.PubMedGoogle Scholar
- Kirsch, R., Boskov, D., and Rymer, W. (1994). Muscle stiffness during transient and continuous movements of cat muscle: perturbation characteristics and physiological relevance. IEEE Trans. Biomed. Eng., 41:700–758.CrossRefGoogle Scholar
- Kirsch, R., Kearney, R., and MacNeil, J. (1993). Identification of time-varying dynamics of the human triceps surae stretch reflex: I. Rapid isometric contraction. Exp. Brain Res., 97:115–127.PubMedCrossRefGoogle Scholar
- Kirsch, R.F., Perreault, E.J., and Acosta, A.M. (1996) Identification of multi-input dynamic systems: limb stiffness dynamics. 9th Eng. Found. Conf. Biomech. Neur. Cont. Mov., 9:46–47.Google Scholar
- Kirsch, R.E. and Kearney, R.E. (1996). Identification of time-varying stiffness dynamics of the human ankle during an imposed movement. Exp. Brain Res., (in Press).Google Scholar
- Korenberg, M. and Hunter, I. (1990). The identification of nonlinear biological systems: Wiener kernel approaches. Ann. Biomed. Eng., 18:629–54.PubMedCrossRefGoogle Scholar
- Korenberg, M.J. (1991). Parallel cascade identification and kernel estimation for nonlinear systems. Ann. Biomed. Eng., 19:429–455.PubMedCrossRefGoogle Scholar
- Korenberg, M.J. and Hunter, I.W. (1986). The identification of nonlinear biological systems: LNL cascade models. Biol. Cybern., 55:125–134.PubMedGoogle Scholar
- Kröller, J., Grüsser, O.-J., and Weiss, L.-R. (1985). The response of primary muscle spindle endings to random muscle stretch: a quantitative analysis. Exp. Brain Res., 61:1–10.PubMedCrossRefGoogle Scholar
- Kukreja, S.L., Kearney, R.E., and L., G.H. (1996). Estimation of continuous-time models from sampled data via the bilinear transform. Proc. 18th Annu. Int. Conf. IEEE Eng. Med. Biol. Soc., Amsterdam, The Netherlands.Google Scholar
- Lacquaniti, F., Borghese, N.A., and Carrozzo, M. (1991) Transient reversal of the stretch reflex in human arm muscles. J. Neurophysiol., 66:939–954.PubMedGoogle Scholar
- Lacquaniti, F., Carrozzo, M., and Borghese, N.A. (1993). Time-varying mechanical behavior of multi-jointed arm in man. J. Neurophysiol., 69:1443–1464.PubMedGoogle Scholar
- Lakie, M., Walsh, E.G., and Wright, G.W. (1984). Resonance at the wrist demonstrated by the use of a torque motor an instrumental analysis of muscle tone in man. J. Physiol., 353:265–285.PubMedGoogle Scholar
- Ljung, L. (1987). System Identification for the User. Englewood Cliffs. Prentice-Hall, New Jersey.Google Scholar
- MacNeil, J.B., Kearney, R.E., and Hunter, I.W. (1992). Identification of time-varying biological systems from ensemble data. IEEE Trans. Biomed. Eng., 39:1213–1225.PubMedCrossRefGoogle Scholar
- Marmarelis, P.Z. and Marmarelis, V.A. (1978). Analysis of Physiological Systems: The White Noise Approach. Plenum Press, New York.Google Scholar
- Marmarelis, V.Z. (1989a). Signal transformation and coding in neural systems. IEEE Trans. Biomed. Eng., 36:15–24.PubMedCrossRefGoogle Scholar
- Marmarelis, V.Z. (1989b). Volterra-Wiener analysis of a class of nonlinear feedback systems and application to sensory biosystems. In Advanced Methods of Physiological Systems Modeling. Marmarelis, V.Z. (ed.), pp. 302, Plenum Press, New York.Google Scholar
- Marmarelis, V.Z. (1993). Identification of nonlinear biological systems using laguerre expansions of kernels. Ann. Biomed. Eng., 21:573–589.PubMedCrossRefGoogle Scholar
- McIntyre, J., Mussa-Ivaldi, F., and Bizzi, E. (1996). The control of stable arm postures in the multi-joint arm. Exp. Brain Res., 110:248–264.PubMedCrossRefGoogle Scholar
- Mussa-Ivaldi, F.A., Hogan, N., and Bizzi, E. (1985). Neural, mechanical and geometric factors subserving arm position in humans. J. Neurosci., 5:2732–2743.PubMedGoogle Scholar
- Palm, G. (1979). On representation and approximation of nonlinear systems. Biol. Cybern., 34:49–52CrossRefGoogle Scholar
- Peckham, P.H. and Keith, W. (1992). Motor prostheses for restoration of upper extremity function. In Neural Prostheses: Replacing Motor Function After Disease or Injury. Stein, R.B., Peckham, P.H., and Popovic, D.P. (eds.), Oxford University Press, New York.Google Scholar
- Poppele, R.E. (1981). An analysis of muscle spindle behavior using randomly applied stretches. Neuroscience, 6:1157–1165.PubMedCrossRefGoogle Scholar
- Rissanen, J. (1978). Modelling by shortest data description. Automatica, 14:465–471.CrossRefGoogle Scholar
- Robinson, C.J., Flaherty, B., Fehr, L., Agarwal, G.C., Harris, G.F., and Gottlieb, G.L. (1994). Biomechanical and reflex responses to joint perturbations during electrical stimulation of muscle: instrumentation and measurement techniques. Med. Biol. Eng. Comput., 32:261–272.PubMedCrossRefGoogle Scholar
- Sakai, H.M. (1992). White-noise analysis in neurophysiology. Physiol. Rev., 72:491–505.PubMedGoogle Scholar
- Shue, G., Crago, P.E., and Chizeck, H.J. (1995). Muscle-joint models incorporating activation dynamics, moment-angle, and moment-velocity properties. IEEE Trans. Biomed. Eng., 42:212–223.PubMedCrossRefGoogle Scholar
- Soechting, J., Dufresne, J., and Lacquaniti, F. (1981). Time-varying properties of myotatic response in man during some simple motor tasks. J. Neurophysiol., 46:1226–1243.PubMedGoogle Scholar
- Stein, R.B., Rolf, R., and Calancie, B. (1986). Improved methods for studying the mechanical properties of biological systems with random length changes. Med. Biol. Eng. Comput., 24:292–300.PubMedCrossRefGoogle Scholar
- Tai, C. and Robinson, C.J. (1995). Variation of human knee stiffness with angular perturbation intensity. Proc. 17th Annu. Int. Conf. IEEE Eng. Med. Biol. Soc., Montreal, Canada.Google Scholar
- Tsuji, T., Morasso, P., Goto, K., and Ito, K. (1995). Hand impedance characteristics during maintained posture. Biol. Cybern., 2:475–485.CrossRefGoogle Scholar
- Verhaegen, M. and DeWilde, P. (1992). Subspace model identification part 1. The output-error state-space model identification class of algorithms. Int. J. Cont., 56:1187–1210.CrossRefGoogle Scholar
- Viviani, P. and Berthoz, A. (1975). Dynamics of the head-neck system in response to small perturbations: analysis and modeling in the frequency domain. Biol. Cybern., 19:19–37.PubMedCrossRefGoogle Scholar
- Volterra, V. (1959). Theory of functionals and of integral and integro-differential equations. Dover, New York.Google Scholar
- Weiss, P.L., Hunter, I.W., and Kearney, R. (1988). Human ankle joint stiffness over the full range of muscle activation levels. J. Biomech., 21:539–544.PubMedCrossRefGoogle Scholar
- Weiss, P.L., Kearney, R.E., and Hunter, I.W. (1986a). Position dependence of ankle joint dynamics: passive mechanics. J. Biomech., 19:727–735.PubMedCrossRefGoogle Scholar
- Weiss, P.L., Kearney, R.E., and Hunter, I.W. (1986b). Position dependence of ankle joint dynamics: active mechanics. J. Biomech., 19:737–751.PubMedCrossRefGoogle Scholar
- Westwick, D.T. (1996). Methods for the identification of multiple-input nonlinear systems. Ph.D. Thesis. Depart. Elec. Eng. Biomed. Eng., McGill University, Montreal.Google Scholar
- Westwick, D.T. and Kearney, R.E. (1996a). Identification of physiological systems: a robust method for non-parametric impulse response estimation. Med. Biol. Eng. Comput., (in press).Google Scholar
- Westwick, D.T. and Kearney, R. E. (1996b). Robust Nonlinear System Identification Using Band-Limited Inputs. Ann. Biomed. Eng. (in press).Google Scholar
- Wiener, N. (1958). Nonlinear Problems in Random Theory. John Wiley & Sons, New York.Google Scholar
- Zahalak, G.I. (1981). A distribution-moment approximation for kinetic theories of muscular contraction. Math. Biosci., 55:89–114.CrossRefGoogle Scholar
- Zahalak, G.I. and Heyman, S.J. (1979). A quantitative evaluation of the frequency-response characteristics of active human skeletal muscle in vivo. Trans. ASME, 101:28–37.Google Scholar
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