Citation

Green HS, Triffet T. Math. Model. 1980; 1(1): 41-61.

Copyright

(Copyright © 1980, Elsevier Publishing)

DOI

10.1016/0270-0255(80)90006-8

PMID

unavailable

Abstract

An electrochemical theory of the action potential is described, which takes into account the electric field produced by the ions themselves in the Debye layer. It is shown that under suitable conditions oscillations can arise, involving relatively large fluctuations of the concentrations of sodium and calcium at the internal surface of the neural membrane. It is possible in this way to account quantitatively for the general character, amplitude and frequency of the action potential, without postulating large variations in the ionic conductances of the membrane. Formulas for the available energy and information associated with a neuron are derived by a variational method. Problems which arise in the modelling of extended nervous systems are discussed, and methods are applied to model the experimental behavior of a ganglion of the leech.