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An efficient bidomain model of electrical activity in cardiac specialized conduction system fibers is developed and applied to a geometric model of the specialized conduction system and the ventricles. The bidomain model allows the impact of externally applied electric fields on the specialized conduction system to be studied. To model this system, the three-dimensional bidomain equations for a fiber are reduced to one-dimensional equations governing electrical propagation by averaging over the fiber cross section. The one-dimensional equations are coupled to the surrounding three-dimensional extracellular electrical field to allow their use in defibrillation studies. A finite element method, with semi-implicit time stepping, is developed to numerically solve the equations. Current flow through fiber branch points is governed by Kirchhoff's law and imposed directly in a weak formulation of the equations for use with the finite element method. Coupling between intracellular potential in distal system Purkinje fibers and the myocardium at discrete Purkinjeventricular junctions is modelled using a resistor model. Simulations of electrical activation through a geometric model of the specialized conduction system are presented. The simulations demonstrate physiologically realistic activation sequences under sinus rhythm and the impact of a large externally applied extracellular field on the specialized conduction system. © 2012 Society for Industrial and Applied Mathematics.

Original publication

DOI

10.1137/11082796X

Type

Journal article

Journal

SIAM Journal on Applied Mathematics

Publication Date

06/11/2012

Volume

72

Pages

1618 - 1643