A mathematical model of atrioventricular conduction block using the excitability recovery curve of the myocardial cell

Abstract

A simple mathematical model of AV conduction block was constructed on the basis of single-cell electrophysiological experiments concerning the rate-dependent property of excitability of the AV nodal cells (the excitability recovery curve, ERC). This ERC was analogous to the phase response curve (PRC) of cardiac pacemaker cells, which the authors had previously used to construct a model of modulated parasystole. Computer simulation was used to reproduce the ERC. The single-cell ERC was then extended to the entire AV node, and this curve was used to formulate a mathematical model of AV conduction block as a nonlinear, first-order difference equation of the successive PR intervals of the ECG. This model predicted a variety of ECG patterns of AV conduction block: normal rhythm, first-degree block, and several second-degree blocks of complex Wenckebach periodicity in relation to the sinus rate and the shape of the ERC. By assuming this model it was possible to identify the underlying ERC of actual ECGs with complex Wenckebach periodicity.