A new computational method was developed for modeling the effects of the geometric complexity, nonuniform muscle fiber orientation, and material inhomogeneity of the ventricular wall on cardiac impulse propagation. The method was used to solve a modification to the FitzHugh-Nagumo system of equations. The geometry, local muscle fiber orientation, and material parameters of the domain were defined using linear Lagrange or cubic Hermite finite element interpolation. Spatial variations of time-dependent excitation and recovery variables were approximated using cubic Hermite finite element interpolation, and the governing finite element equations were assembled using the collocation method. To overcome the deficiencies of conventional collocation methods on irregular domains, Galerkin equations for the no-flux boundary conditions were used instead of collocation equations for the boundary degrees-of-freedom. The resulting system was evolved using an adaptive Runge-Kutta method. Converged two-dimensional simulations of normal propagation showed that this method requires less CPU time than a traditional finite difference discretization. The model also reproduced several other physiologic phenomena known to be important in arrhythmogenesis including: Wenckebach periodicity, slowed propagation and unidirectional block due to wavefront curvature, reentry around a fixed obstacle, and spiral wave reentry. In a new result, we observed wavespeed variations and block due to nonuniform muscle fiber orientation. The findings suggest that the finite element method is suitable for studying normal and pathological cardiac activation and has significant advantages over existing techniques.

An automated method to estimate vector fields of propagation velocity from observed epicardial extracellular potentials is introduced. The method relies on fitting polynomial surfaces T(x, y) to the space-time (x, y, t) coordinates of activity. Both speed and direction of propagation are computed from the gradient of the local polynomial surface. The components of velocity, which are total derivatives, are expressed in terms of the partial derivatives which comprise the gradient of T. The method was validated on two-dimensional (2-D) simulations of propagation and then applied to cardiac mapping data. Conduction velocity was estimated at multiple epicardial locations during sinus rhythm, pacing, and ventricular fibrillation (VF) in pigs. Data were obtained via a 528-channel mapping system from 23 x 22 and 24 x 21 arrays of unipolar electrodes sutured to the right ventricular epicardium. Velocity estimates are displayed as vector fields and are used to characterize propagation qualitatively and quantitatively during both simple and complex rhythms.

Phase is a descriptor that tracks the progression of a defined region of myocardium through the action potential and has been demonstrated to be an effective parameter in analyzing spatiotemporal changes during fibrillation. In this review, the basic principles behind phase mapping are presented mainly in the context of ventricular fibrillation (VF), atrial fibrillation (AF), and fibrillation from experimental monolayer data. During fibrillation, the phase distribution changes over time, depending on activation patterns. Analyzing these phase patterns provides us insight into the fibrillatory dynamics and helps clarify the mechanisms of cardiac fibrillation and modulation by interventions. Winfree 1 introduced the phase analysis to study cardiac fibrillation in the late eighties. This time-encoding technique deals with a scenario where the activation periods are the same over the surface being mapped. To deal with the scenario of varying activation period over the mapped surface (common in animal and human fibrillation models), Gray et al 2,3 introduced the state-space encoding concept from nonlinear dynamics.In analyzing spatiotemporal phase maps constructed from electric or optical mapping of the surface of heart during VF, points around which the phase progresses through a complete cycle from Ϫ to ϩ are of great interest. At these points, the phase becomes indeterminate and the activation wave fronts hinge to these points and rotate around them in an organized fashion. These points in the phase map are called phase singularity (PS) points. Bray et al 4 developed a procedure to locate PS points in a phase map. Nash et al 5 used phase mapping to study the entire ventricular epicardium of human hearts with a sock containing 256 unipolar contact electrodes. The development of this phase mapping tool has led to better understanding of fibrillation dynamics as evidenced by the use of phase mapping in detecting PS and their role in demonstrating organization during VF. Some of these works and their findings are (1) PS colocalize with anatomic heterogeneities, and their spatial meandering is modulated by these heterogeneities, 6 (2) PS correlates with the locations of wave breaks, 7 (3) in myopathic human hearts, phase maps were used to show that the organization of electric activity were characterized by wave fronts emanating from a few rotors, 8 and (4) phase mapping technique has also been applied to investigate the mechanism of fibrillation. 7-9 Clinical electrophysiologists innovating therapies for both AF and VF are commonly not aware of phase mapping. This review addresses this shortcoming with the hope that by introducing the basic concepts of phase mapping to a greater audience, there will be an opportunity to devise therapies for these arrhythmias on a mechanistic basis.