Sensitivity analysis of kernel estimates: Implications in nonlinear physiological system identification

Annals of Biomedical Engineering

Volumn 26, Issue 3, 1998, Pages 488-501

  Westwick, David T ^a   Suki, Bêla ^a   Lutchen, Kenneth R ^a  

^a Boston University   (United States)

Author keywords

Analysis of variance; Laguerre expansion; Least squares regression; Orthogonal algorithm; Peripheral auditory system model

Indexed keywords

ALGORITHM; ARTICLE; BIOLOGICAL MODEL; HEARING; MONTE CARLO METHOD; NONLINEAR SYSTEM; PHYSIOLOGY; REGRESSION ANALYSIS;

ALGORITHMS; AUDITORY PERCEPTION; LEAST-SQUARES ANALYSIS; MODELS, BIOLOGICAL; MONTE CARLO METHOD; NONLINEAR DYNAMICS;

EID: 0032067588     PISSN: 00906964     EISSN: None     Source Type: Journal    
DOI: 10.1114/1.40     Document Type: Article

References (28)

1. Amorocho, J., and A. Brandstetter. Determination of nonlinear functional response functions in rainfall runoff processes. Water Resour. Res. 7:1087-1101, 1971.
2. Beck, J. V., and K. J. Arnold. Parameter Estimation in Engineering and Science. New York: Wiley, 1977, pp. 213-333.
3. Billings, S. A., and W. S. F. Voon. Correlation based model validity tests for non-linear models. Int. J. Control 44:235-244, 1986.
4. Boyd, S., and L. O. Chua. Fading memory and the problem of approximating nonlinear operators with Volterra series. IEEE Trans. Circuits Syst. CAS-32:1150-1161, 1985.
5. Chon, K. H., Y. M. Chen, V. Z. Marmarelis, D. J. Marsh, and N. H. Holstein-Rathlou. Detection of interactions between myogenic and TGF mechanisms using nonlinear analysis. Am. J. Physiol. 267:F160-F173, 1994.
6. Chon, K. H., N.-H. Holstein-Rathlou, D. J. Marsh, and V. Z. Marmarelis. Parametric and nonparametric nonlinear modeling of renal autoregulation dynamics. In: Advanced Methods of Physiological System Modeling, Vol. 3, edited by V. Z. Marmarelis. New York: Plenum, 1994, pp. 195-210.
7. Efron, B. The Jackknife, the Bootstrap and Other Resampling Plans. Philadelphia: Society for Industrial and Applied Mathematics, 1982, pp. 29-35.
8. Emerson, R. C., M. J. Korenberg, and M. C. Citron. Identification of complex-cell intensive nonlinearities in a cascade model of cat visual cortex. Biol. Cybern. 66:291-300, 1992.
9. French, A. S., and M. J. Korenberg. Disection of a nonlinear cascade model for sensory encoding. Ann. Biomed. Eng. 19:473-484, 1991.
10. French, A. S., A. E. C. Pece, and M. J. Korenberg. Nonlinear models of transduction and adaptation in Locust photoreceptors. In: Advanced Methods of Physiological System Modeling, Vol. 2, edited by V. Z. Marmarelis. New York: Plenum, 1989, pp. 81-95.
11. Hunter, I. W., and M. J. Korenberg. The identification of nonlinear biological systems: Wiener and Hammerstein cascade models. Biol. Cybern. 55:135-144, 1986.
12. Korenberg, M. J. Functional expansions, parallel cascades, and nonlinear difference equations. In: Advanced Methods of Physiological System Modeling, Vol. 1, edited by V. Z. Marmarelis. New York: Plenum, 1987, pp. 221-240.
13. Korenberg, M. J. Identifying nonlinear difference equation and functional expansion representations: The fast orthogonal algorithm. Ann. Biomed. Eng. 16:123-142, 1988.
14. Korenberg, M. J. Parallel cascade identification and kernel estimation for nonlinear systems. Ann. Biomed. Eng. 19:429-455, 1991.
15. Korenberg, M. J., and I. W. Hunter. The identification of nonlinear biological systems: LNL cascade models. Biol. Cybern. 55:125-134, 1986.
16. Korenberg, M. J., and I. W. Hunter. The identification of nonlinear biological systems: Wiener kernel approaches. Ann. Biomed. Eng. 18:629-654, 1990.
17. Korenberg, M. J., and I. W. Hunter. The identification of nonlinear biological systems: Volterra kernel approaches. Ann. Biomed. Eng. 24:250-268, 1996.
18. Korenberg, M. J., H. M. Sakai, and K.-I. Naka. Dissection of the neuron network in the catfish inner retina. III interpretation of spike kernels. J. Neurophysiol. 61:1110-1120, 1989.
19. Lee Y. W., and M. Schetzen. Measurement of the Wiener kernels of a non-linear system by cross-correlation. Int. J. Control 2:237-254, 1965.
20. Ljung, L. System Identification: Theory for the User. Englewood Cliffs: Prentice-Hall, 1987, pp. 434-456.
21. Marmarelis, V. Z. Identification of nonlinear biological systems using Laguerre expansions of kernels. Ann. Biomed. Eng. 21:573-589, 1993.
22. Marmarelis, V. Z., K. H. Chon, Y. M. Chen, D. J. Marsh, and N. H. Holstein-Rathlou. Nonlinear analysis of renal autoregulation under broadband forcing conditions. Ann. Biomed. Eng. 21:591-603, 1993.
23. Marmarelis, P. Z., and V. Z. Marmarelis. Analysis of Physiological Systems. New York: Plenum, 1978, pp. 1-487.
24. Pfeiffer, R. R. A model for two-tone inhibition of single cochlear nerve fibres. J. Acoust. Soc. Am. 48:1373-1378, 1970.
25. Sakuranaga, M., S. Sato, E. Hida, and K-I. Naka. Nonlinear analysis: mathematical theory and biological applications. CRC Crit. Rev. Biomed. Eng. 14:127-184, 1986.
26. Swerup, C. On the choice of noise for the analysis of the peripheral auditory system. Biol. Cybern. 29:97-104, 1978.
27. Watanabe, A., and L. Stark. Kernel method for nonlinear analysis: identification of a biological control system. Math. Biosci. 27:99-108, 1975.
28. Zhang, Q., B. Suki, D. T. Westwick, and K. R. Lutchen. Factors affecting Volterra kernel estimation: Emphasis on lung tissue viscoelasticity. Ann. Biomed. Eng. 26:103-116.