Construction of a Computer Model to Investigate Sawtooth Effects in the Purkinje System

Abstract

The sawtooth effect refers to how one end of a cardiac cell is depolarized, while the opposite end is hyperpolarized, upon exposure to an exogenous electric field. Although hypothesized, it has not been observed in tissue. The Purkinje system is a one-dimensional (1-D) cable-like system residing on the endocardial surface of the heart and is the most obvious candidate for the manifestation of this phenomenon. This paper describes a computer modeling study of the effect of electric fields on the Purkinje system. Starting with a three-dimensional geometrically realistic, finite element, ventricular description, a Purkinje system is constructed which adheres to general physiological principles. Electrical activity in the Purkinje is described by use of 1-D cubic Hermite finite elements. Such a formulation allows for accurate modeling of loading effects at the Purkinje-myocyte junctions, and for preserving the discrete nature of the system. The response of a strand of Purkinje cells to defibrillation strength shocks is computed under several conditions. Also, the response of the isolated Purkinje network is illustrated. Results indicate that the geometry of the Purkinje system is the greatest determinant for far field excitation of the system. Given parameters within the plausible physiological range, the 1-D nature of the Purkinje system may lead to sawtooth potentials which are large enough to affect excitation. Thus, the Purkinje system is capable of affecting the defibrillation process, and warrants further experimentation to elucidate its role.