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Electrophysiology
Author(s) -
Griffith Boyce E.,
Peskin Charles S.
Publication year - 2013
Publication title -
communications on pure and applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 3.12
H-Index - 115
eISSN - 1097-0312
pISSN - 0010-3640
DOI - 10.1002/cpa.21484
Subject(s) - hodgkin–huxley model , cardiac electrophysiology , action (physics) , bidomain model , wavefront , electrophysiology , mathematics , cardiac action potential , neuroscience , physics , repolarization , biology , optics , quantum mechanics
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. © 2013 Wiley Periodicals, Inc.