Electrophysiology

Boyce E. Griffith, Charles Peskin

Research output: Contribution to journalArticle

Abstract

Electrical signaling is a fast mode of communication for cells within an organism. We are concerned here with the formulation and analysis of mathematical models that are used to describe this important class of physiological processes. These models generally take the form of partial differential equations that are descendants of those introduced by Hodgkin and Huxley to describe the propagation of an action potential along the squid giant axon. We review that work here and then go on to describe more recent variations on the Hodgkin-Huxley theme, including the three-dimensional bidomain (and monodomain) equations for cardiac electrophysiology, multiscale models for the heart that take cellular structure into account near the action potential wavefront, and finally a more detailed reformulation of electrophysiology in terms of electrodiffusion.

Original languageEnglish (US)
Pages (from-to)1837-1913
Number of pages77
JournalCommunications on Pure and Applied Mathematics
Volume66
Issue number12
DOIs
StatePublished - Dec 2013

Fingerprint

Electrophysiology
Action Potential
Cardiac Electrophysiology
SQUID
Multiscale Model
Wavefronts
Reformulation
Wave Front
Partial differential equations
Partial differential equation
Mathematical Model
Propagation
Mathematical models
Three-dimensional
Formulation
Communication
Cell
Model
Review
Heart

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

Cite this

Electrophysiology. / Griffith, Boyce E.; Peskin, Charles.

In: Communications on Pure and Applied Mathematics, Vol. 66, No. 12, 12.2013, p. 1837-1913.

Research output: Contribution to journalArticle

Griffith, BE & Peskin, C 2013, 'Electrophysiology', Communications on Pure and Applied Mathematics, vol. 66, no. 12, pp. 1837-1913. https://doi.org/10.1002/cpa.21484
Griffith, Boyce E. ; Peskin, Charles. / Electrophysiology. In: Communications on Pure and Applied Mathematics. 2013 ; Vol. 66, No. 12. pp. 1837-1913.
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