Skip to main content

Abstract

Scientific efforts to understand the basic mechanisms of information processing and coding in the nervous system have produced a lot of remarkable work on the generation mechanism of action potentials (spikes), the properties of excitable membranes and the dynamic transformations of spike trains as they travel through the nervous system. Since the pivotal work of Hodgkin and Huxley (1952), who first proposed a quantitative dynamic model for the generation mechanism of action potentials in the squid axon, many competent investigators have explored mathematical aspects (for review see Cronin, 1987) and modifications of the original Hodgkin Huxley (H-H) model, motivated by a variety of reasons. Attempts to simplify the H-H model (i.e., reduce its complexity while maintaining its essential functional characteristics) have been motivated by the need to develop workable models of neuronal aggregates (networks) that incorporate the essential features of the spike generation mechanism while, at the same time, retain manageable computational complexity.

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

Access this chapter

eBook
USD 16.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 16.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  • Cronin, J., 1987, “Mathematical Aspects of Hodgkin-Huxley Neural Theory,”University Press, Cambridge.

    Book  MATH  Google Scholar 

  • Deutsch, S. and Micheli-Tzanakou, E., 1987, “Neuroelectric Systems,”New York University, New York.

    Google Scholar 

  • FitzHugh, R., 1969, Thresholds and plateaus in the Hodgkin-Huxley nerve equations, J. Gen. Physiol, 43:867–896.

    Google Scholar 

  • Guttman, R., Feldman, L., and Lecar, H., 1974, Squid axon membrane response to white noise stimulation, Biophys. J., 14:941–955.

    Article  Google Scholar 

  • Hodgkin, A.L., and Huxley, A.F., 1952, A quantitative description of membrane current and its application to conduction and excitation in nerve, J. Physiol., 117:500–544.

    Google Scholar 

  • Marmarelis, P.Z., and Marmarelis, V.Z., 1978, “Analysis of Physiological Systems: The White Noise Approach”,Plenum Press, New York.

    Google Scholar 

  • Marmarelis, V.Z., ed., 1987, “Advanced Methods of Physiological System Modeling: Volume I”,Biomedical Simulations Resource, University of Southern California, Los Angeles.

    Google Scholar 

  • Marmarelis, V.Z., 1988, Coherence and apparent transfer function measurements for nonlinear physiological systems, Ann. Biomed. Eng., 16:143–157.

    Article  Google Scholar 

  • Marmarelis, V.Z., 1989, Signal transformation and coding in neural systems, IEEE Trans. Biomed. Eng., 36:15–24.

    Article  Google Scholar 

  • Marmarelis, V.Z., Citron, M.C., and Vivo, C.P., 1986, Minimum-order Wiener modeling of spike-output systems, Biol. Cybern., 54:115–123.

    Article  MATH  Google Scholar 

  • Marmarelis, V.Z., and Herman, N., 1988, LYSIS: An interactive software system for nonlinear modeling and simulation, in “Modeling Sz Simulation on Microcomputers,”Society for Computer Simulation, San Diego, pp. 6–10.

    Google Scholar 

  • Sakai, H.M., and Naka, K-I, Signal transmission in the catfish retinal (IV), J. Neurophysiol., 58:1307–1328.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 1989 Plenum Press, New York

About this chapter

Cite this chapter

Courellis, S.H., Marmarelis, V.Z. (1989). Wiener Analysis of the Hodgkin-Huxley Equations. In: Marmarelis, V.Z. (eds) Advanced Methods of Physiological System Modeling. Springer, Boston, MA. https://doi.org/10.1007/978-1-4613-9789-2_16

Download citation

  • DOI: https://doi.org/10.1007/978-1-4613-9789-2_16

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-1-4613-9791-5

  • Online ISBN: 978-1-4613-9789-2

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics