Skip to main content
SpringerLink
Log in

A note on mathematical models for the interaction of neural elements

  • Published:
The bulletin of mathematical biophysics Aims and scope Submit manuscript

Abstract

By introducing a plausible model for the initiation of axonal impulses the output is obtained as a function of the input incoming impulses. If the temporal aspects of the excitatory process resulting from the afferent impulses are sufficiently rapid one obtains the discontinuous or microscopic model of McCulloch-Pitts. If these are sufficiently slow a continuous model, such as Rashevsky’s one or two factor theory, is a natural model. But the linear relation between the strength of excitation of one axon and excitatory factor of the next will not in general hold. However, under conditions which are not too restrictive the linear relation with threshold can be considered as satisfactory approximation over a fairly wide range of values.

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

Literature

  • Grundfest, H. 1957. “Electrical Inexcitability of Synapses and Some Consequences in the Central Nervous System.”Physiol. Rev. 37, 337–361.

    Google Scholar 

  • Kamiya, S. 1958. “On the Biophysics of Vision.”Bull. Math. Biophysics,20, 343–73.

    Google Scholar 

  • Landahl, H. D. 1938. “The Relation between the Intensity of Excitation and the Number of Neurons Traversed.”Psychometrika,3, 291–295.

    Article  MATH  Google Scholar 

  • Landahl, H. D. 1945. “A Note on the Mathematical Biophysics of Central Excitation and Inhibition.”Bull. Math. Biophysics,7, 219–21.

    Google Scholar 

  • —. 1959. “Biological Periodicities: Mathematical Biology and Aging.” In Birren, J.Handbook on Aging and the Individual. Chicago: University of Chicago Press. 81–115.

    Google Scholar 

  • Landahl, H. D., McCulloch, W. S. and Pitts, W. 1943. “A Statistical Consequence of the Logical Calculus of Nervous Nets.”Bull. Math. Biophysics 5, 135–39.

    MATH  MathSciNet  Google Scholar 

  • McCulloch, W. S. and Pitts, W. 1943. “A Logical Calculus for Ideas Immanent in Nervous Activity.”Bull. Math. Biophysics,5, 115–33.

    MATH  MathSciNet  Google Scholar 

  • Rashevsky, N. 1945. “A Suggestion for Another Statistical Interpretation of the Fundamental Equations of the Mathematical Biophysics of the Central Nervous System.”Bull. Math. Biophysics,7, 223–26.

    Google Scholar 

  • —. 1948.Mathematical Biophysics. Chicago: University of Chicago Press.

    MATH  Google Scholar 

  • Tobias, J. 1959. “Biophysical Aspects of Conduction and Transmission in the Nervous System.”Ann. Rev. Physiol,21, 299–324.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Committee on Mathematical Biology, The University of Chicago, Chicago, USA

    H. D. Landahl

Authors
  1. H. D. Landahl
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

This research was supported in whole or in part by the U. S. Air Force under Contract AF 49(638)-414 monitored by the Air Force Office of Scientific Research.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Landahl, H.D. A note on mathematical models for the interaction of neural elements. Bulletin of Mathematical Biophysics 23, 91–97 (1961). https://doi.org/10.1007/BF02476576

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02476576

Keywords

Search

Navigation