Skip to main content
SpringerLink
Log in

Nonlinear analysis of biological systems using short M-sequences and sparse-stimulation techniques

  • Research Articles
  • Published:
Annals of Biomedical Engineering Aims and scope Submit manuscript

Abstract

The m-sequence pseudorandom signal has been shown to be a more effective probing signal than traditional Gaussian white noise for studying nonlinear biological systems using cross-correlation techniques. The effectiveness is evidenced by the high signal-to-noise (S/N) ratio and speed of data acquisition. However, the “anomalies” that occur in the estimations of the cross-correlations represent an obstacle that prevents m-sequences from being more widely used for studying nonlinear systems. The sparse-stimulation method for measuring system kernels can help alleviate estimation errors caused by anomalies. In this paper, a “padded sparse-stimulation” method is evaluated, a modification of the “inserted sparse-stimulation” technique introduced by Sutter, along with a short m-sequence as a probing signal. Computer simulations show that both the “padded” and “inserted” methods can effectively eliminate the anomalies in the calculation of the second-order kernel, even when short m-sequences were used (length of 1023 for a binary m-sequence, and 728 for a ternary m-sequence). Preliminary experimental data from neuromagnetic studies of the human visual system are also presented, demonstrating that the system kernels can be measured with high signal-to-noise (S/N) ratios using short m-sequences.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Aine, C. J., S. Supek, and J. S. George. Temporal dynamics of visual-evoked neuromagnetic sources: Effects of stimulus parameters and selective attention.Int. J. Neurosci. 80:79–104, 1995.

    PubMed  CAS  Google Scholar 

  2. Aine, C. J., S. Supek, J. S. George, D. Ranken, J. Lewine, J. Sanders, E. Best, W. Tiee, E. R. Flynn, and C. C. Wood. Retinotopic organization of human visual cortex: Departures from the classical model.Cereb. Cortex 6:354–361, 1996.

    Article  PubMed  CAS  Google Scholar 

  3. Barker, H. A., and T. Pradisthayon. High-order autocorrelation functions of pseudorandom signals based on m sequences.Proc. IEEE. 117:1857–1863, 1970.

    Google Scholar 

  4. Barker, H. A., S. N. Obidegwu, and T. Pradisthayon. Performance of antisymmetric pseudorandom signals in the measurement of 2nd-order Volterra kernels by cross-correlation.Proc. IEE 119:353–362, 1972.

    Google Scholar 

  5. Baseler, H. A., E. E. Sutter, S. A. Klein, and T. Carney. The topography of visual invoked response properties across the visual field.EEG Clin. Neurophysiol. 90:65–81, 1994.

    Article  CAS  Google Scholar 

  6. Benardete, E. A., and J. D. Victor. An extension of the m-sequence technique for the analysis of multi-input non-linear systems. In: Advanced Methods of Physiological System Modeling, Vol. 3, edited by V. Z. Marmarelis. Plenum Press, New York, 1994, pp. 87–110.

    Google Scholar 

  7. Boyd, S., Y. S. Tang, and L. O. Chua. Measuring Volterra kernels.IEEE Trans. Circuits Syst. 30:571–577, 1983.

    Article  Google Scholar 

  8. Chen, H.-W., L. D. Jacobson, and J. P. Gaska. Structural classification of multi-input nonlinear systems.Biol. Cybern. 63:341–357, 1990.

    Article  PubMed  CAS  Google Scholar 

  9. Chen, H.-W., L. D. Jacobson, J. P. Gaska, and D. A. Pollen. Cross-correlation analyses of nonlinear systems with spatiotemporal inputs.IEEE Trans. Biomed. Eng. 40:1102–1113, 1993.

    Article  PubMed  CAS  Google Scholar 

  10. Chen, H.-W. Modeling and identification of parallel non-linear systems: Structural classification and parameter estimation methods.Proc. IEEE 83:39–66, 1995.

    Article  Google Scholar 

  11. Chua, L. O., and Y. Liao. Measuring Volterra kernels (II).Int. J. Circuit Theor. Appl. 17:151–190, 1989.

    Google Scholar 

  12. Chua, L. O., and Y. Liao. Measuring Volterra kernels III: How to estimate the highest significant order.Int. J. Circuit Theor. Appl. 19:189–209, 1991.

    Google Scholar 

  13. Citron, M. C., and V. Z. Marmarelis, Applications of minimum-order Wiener modeling to retinal ganglion cell spatiotemporal dynamics.Biol. Cybern. 57:241–247, 1987.

    Article  PubMed  CAS  Google Scholar 

  14. Davies, W. D. T. System Identification for Self-Adaptive Control. New York: Wiley-Interscience, 1970, 394 pp.

    Google Scholar 

  15. Emerson, R. C., J. R. Bergen, and E. H. Adelson. Directionally selective complex cells and the computation of motion energy in cat visual cortex.Vision Res. 32:203–218, 1992.

    Article  PubMed  CAS  Google Scholar 

  16. Gaska, J. P., L. D. Jacobson, H.-W. Chen, and D. A. Pollen. Space-time spectra of complex cell filters in the Macaque monkey: a comparison of results obtained with pseudo-white noise and grating stimuli.Vis. Neurosci. 11:805–821, 1994.

    Article  PubMed  CAS  Google Scholar 

  17. Jacobson, L. D., J. P. Gaska, H.-W. Chen, and D. A. Pollen. Structural testing of multi-input linear-nonlinear cascade models for cells in macaque striate cortex.Vision Res. 33:609–626, 1993.

    Article  PubMed  CAS  Google Scholar 

  18. Jones, J. P., and L. A. Palmer. The two-dimensional spatial structure of simple receptive fields in cat striate cortex.J. Neurophysiol. 58:1187–1211, 1987.

    PubMed  CAS  Google Scholar 

  19. Klein, S. Optimizing the estimation of nonlinear kernels, In: Nonlinear Vision, edited by R. B. Pinter and B. Nabet (eds.). Boca Raton: CRC Press, 1992, pp. 109–170.

    Google Scholar 

  20. Korenberg, M. J. Identification of biological cascades of linear and static nonlinear systems.Proc. Midwest Symp. Circuit Theor. 18:2:1–9, 1973.

    Google Scholar 

  21. Korenberg, M. J., S. B. Bruder, and P. J. McIlroy. Exact orthogonal kernel estimation from finite data records: Extending Wiener’s identification of nonlinear systems.Ann. Biomed. Eng. 16:201–214, 1988.

    Article  PubMed  CAS  Google Scholar 

  22. Korenberg, M. J. Parallel cascade identification and kernel estimation for nonlinear systems.Ann. Biomed. Eng. 19:429–455, 1991.

    Article  PubMed  CAS  Google Scholar 

  23. Lee, Y. W., and M. Schetzen. Measurement of the Wiener kernels of a nonlinear system by cross-correlation.Int. J. Control. 2:237–254, 1965.

    Google Scholar 

  24. Marmarelis, V. Z. Random versus pseudorandom test signals in nonlinear-system identification.Proc. IEE 125:425–428, 1978.

    Google Scholar 

  25. Marmarelis, P. Z., and V. Z. Marmarelis. Analysis of Physiological Systems: The White Noise Approach. New York: Plenum Press, 1978, 504 pp.

    Google Scholar 

  26. Marmarelis, V. Z. Practicable identification of nonstationary nonlinear systems.Proc IEE 128:211–214, 1981.

    Google Scholar 

  27. Marmarelis, V. Z. Identification of nonlinear biological systems using Laguerre expansions of kernels.Ann. Biomed. Eng. 21:573–589, 1993.

    Article  PubMed  CAS  Google Scholar 

  28. Marmarelis, V. Z., K. H. Chon, Y. M. Chen, D. J. Marsh, and H.-H. Holstein-Rathlou. Nonlinear analysis of renal autoregulation under broadband forcing conditions.Ann. Biomed. Eng. 21:591–603, 1993.

    Article  PubMed  CAS  Google Scholar 

  29. Naka, K.-I., H. M. Sakai, and N. Ishii. Generation and transformation of second-order nonlinearity in catfish retina.Ann. Biomed. Eng. 16:53–64, 1988.

    Article  PubMed  CAS  Google Scholar 

  30. Ogata, K. Modern Control Engineering, Englewood Cliffs, NJ: Prentice-Hall, 1970, 960 pp.

    Google Scholar 

  31. Ohzawa, I., R. D. Freeman, and G. C. DeAngelis. Stereoscopic depth discrimination in the visual cortex: Neurons ideally suited as disparity detectors.Science 249:1037–1041, 1990.

    Article  PubMed  CAS  Google Scholar 

  32. Oppenheim, A. V., A. S. Willsky, and I. T. Young. Signals and Systems. Englewood cliffs, NJ: Prentice-Hall, 1983.

    Google Scholar 

  33. Press, W. H., B. P. Flannery, S. A. teukolsky, and W. T. Vetterling. Numerical Recipes in C. Cambridge: Cambridge University, 1988, 1992, pp. 274–328, 347–608.

    Google Scholar 

  34. Ream, N. Nonlinear identification using inverse-repeat m-sequences.Proc. IEE 117:213–218, 1970.

    Google Scholar 

  35. Regan, D. Human Brain Electrophysiology—Evoked Potential and Evoked Magnetic Fields in Science and Medicine. New York: Elsevier Science Publishing Co., 1989, pp. 1–482.

    Google Scholar 

  36. Reid, R. C., and R. M. Shapley. Spatial structure of cone inputs to receptive fields in primate lateral geniculate nucleus.Nature 356:716–718, 1992.

    Article  PubMed  CAS  Google Scholar 

  37. Rugh, W. J. Nonlinear System Theory: The Volterra/Wiener Approach. Baltimore: Johns Hopkins University Press, 1981.

    Google Scholar 

  38. Sandberg, I. W. The mathematical foundations of associated expansions for mildy nonlinear systems.IEEE Trans. Circuits Syst. 30:441–445, 1983.

    Article  Google Scholar 

  39. Schetzen, M. The Volterra and Wiener Theories of Nonlinear Systems. New York: Wiley, 1980.

    Google Scholar 

  40. Srebro, R., and W. W. Wright. Pseudorandom sequences in the study of evoked potentials.Ann. N.Y. Acad. Sci. 388:98–112, 1982.

    Article  PubMed  CAS  Google Scholar 

  41. Srebro, R. An analysis of the VEP to luminance modulation and of its nonlinearity.Vision Res 32:1393–1404, 1992.

    Google Scholar 

  42. Sutter, E. A revised conception of visual receptive fields based upon pseudorandom spatiotemporal pattern stimuli. In: Proceedings of the First Symposium on Testing and Identification of Nonlinear Systems, edited by G. D. Mc-Cann and V. Z. Marmarelis. Pasadena: CIT, 1975, pp. 353–365.

    Google Scholar 

  43. Sutter, E. E. A practical nonstochastic approach to nonlinear time-domain analysis. In: Advanced Methods of Physiological System Modeling, edited by V. Z. marmarelis. Los Angeles, USC, 1987, pp. 303–315.

    Google Scholar 

  44. Sutter, E. A deterministic approach to nonlinear systems analysis. In: Nonlinear Vision, edited by R. B. Pinter and B. Nabet. Boca Raton: CRC Press, 1992, pp. 171–220.

    Google Scholar 

  45. Victor, J. D. Nonlinear systems analysis in vision: Overview of kernel methods. In: Nonlinear Vision, edited by R. B. Pinter and B. Nabet. Boca Raton: CRC Press, 1992, pp. 1–37.

    Google Scholar 

  46. Victor, J. D., and B. W. Knight. Nonlinear analysis with an arbitrary stimulus ensemble.Q. Appl. Math. 74:113–136, 1979.

    Google Scholar 

  47. Volterra, V. Theory of Functionals and of Integral and Integro-differential Equations. New York: Dover Publications, 1959.

    Google Scholar 

  48. Wiener, N. Nonlinear Problems in Random Theory. New York: The Technology Press of MIT and Wiley, 1958.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Biophysics Group, MS-D454, Los alamos National Laboratory, 87545, Los Alamos, NM, U.S.A.

    Hai-Wen Chen, Cheryl J. Aine, Elaine Best, Doug Ranken, Reid R. Harrison, Edward R. Flynn & C. C. Wood

Authors
  1. Hai-Wen Chen
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Cheryl J. Aine
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Elaine Best
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Doug Ranken
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Reid R. Harrison
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. Edward R. Flynn
    View author publications

    You can also search for this author in PubMed Google Scholar

  7. C. C. Wood
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Chen, HW., Aine, C.J., Best, E. et al. Nonlinear analysis of biological systems using short M-sequences and sparse-stimulation techniques. Ann Biomed Eng 24, 513–536 (1996). https://doi.org/10.1007/BF02648113

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02648113

Key words

Search

Navigation