State space representation of nerve excitation

Abstract

SummaryWhile the Hodgkin-Huxley model may be useful for some gross large-scale phenomena of nerve excitation, a critical analysis using more recently available system theoretic analysis reveals major inconsistencies and inadequacies with several fundamental assumptions of Hodgkin and Huxley. We have stated that the original cable equations are not applicable in the submicroscopic domain of a molecular or ionic nature. This leads to a mapping error, in that real three-dimensional vector space features of a cylindrical cable are mapped onto a scalar one-dimensional space in the classic cable equation. Furthermore only symmetrical voltage clamp experiments have been done, in which the physical arrangement ignores any real space or time phasic features. The Hodgkin-Huxley approach to modeling the nerve impulse ignores the vector nature of current densities and potentials, as well as the phase problems inherent in any three-dimensional wave problem. Only when these vector and phase properties are recognized, could we hope to begin to relate the macroscopic neuro-physiologic observations with the submicroscopic quantum properties of lipid and lipid protein membranes in ionic aqueous environments. The Hodgkin-Huxley model of ionic events will remain an important one in the efforts to understand excitation phenomena. It might be considered in analogy to the Bohr atom model, which while incorrect in many details gave the right answer for certain (largely spectroscopic) data for extremely simple situations. Nevertheless the Bohr model of the atom directed scientists down the right avenues to the eventual development of modern quantum theory. One can hope that critical evaluation of both data and experiments will lead to additional experiments and eventually a more acceptable theory of nerve excitation.