Mathematical simulation of propagated electrical excitation in the human ventricular myocardium.

摘要

Mathematical models for simulating the electrical propagation phenomena in the heart can provide valuable insight into the normal and pathological process of cardiac depolarization and repolarization. Using a model based on anisotropic bidomain theory and a physiologically accurate transmembrane ionic current term, we investigated action-potential propagation in one-, two-, and three-dimensional domains representing the ventricular myocardium. The model of the current flow in cardiac tissue consisted of two coupled partial differential equations for the bidomain case, or a single partial differential equation for the reduced monodomain case. Additionally coupled to this was a system of nonlinear ordinary differential equations that determine the time-varying ionic current at each point in the domain. The total ionic current was described by a realistic membrane model that employs Hodgkin-Huxley formalism to reconstruct the cardiac action potential. A novel approach for the numerical solution of these equations was developed based on the method of lines: the partial differential equations were discretized in space and the resultant differential-algebraic equations were then solved using the robust numerical software package DASPK.; In a three-dimensional bidomain block of human ventricular myocardium, we investigated the propagation of excitation under assumption of equal and unequal anisotropy ratio---to answer the question of whether the former adequately describes physiological characteristics of ventricular myocardium. The simulations demonstrated the sensitivity of the spread of activation and potential time courses and distributions to the underlying electrical properties of cardiac tissue.; We explored the basis for electrocardiographic waveforms using a bidomain model incorporating transmural electrical heterogeneity. The simulations demonstrated that a T wave with the same polarity as the QRS complex can be generated by a model of cardiac tissue that includes the three cell types: endocardial, M cell, and epicardial. Of key importance in generating a "correct" T wave was the presence of a transmural dispersion of repolarization. Furthermore, it was observed that a J wave is produced by the heterogeneous distribution of the transient outward current, Ito, across the ventricular wall.; The model has been shown to be a useful representation of human ventricular myocardium for experimental data of activation under normal conditions. A uniqueness of this model is its ability to simulate---by virtue of having physiologically accurate description of transmembrane ionic currents---the effect of therapeutic drugs.