A FINITE-VOLUME MODEL OF CARDIAC PROPAGATION

This paper describes a two-dimensional cardiac propagation model based on the finite volume method (FVM). This technique, originally derived and applied within the field of computational fluid dynamics, is well suited to the investigation of conduction in cardiac electrophysiolog y. Specifically, the FVM permits the consideration of propagation in a realistic structure, subject to arbitrary fiber orientations and regi onally defined properties. In this application of the FVM, an arbitrar ily shaped domain is decomposed into a set of constitutive quadrilater als. Calculations are performed in a computational space, in which the quadrilaterals are all represented simply as squares. Results are rel ated to their physical-space equivalents by means of a transformation matrix. The method is applied to a number of cases. First, large-scale propagation is considered, in which a magnetic resonance-imaged cardi ac cross-section serves as the governing geometry. Next, conduction is examined in the presence of an isthmus formed by the microvasculature in a slice of papillary muscle tissue. Under ischemic conditions, the safety factor for propagation is seen to be related to orientation of the fibers within the isthmus. Finally, conduction is studied in the presence of an inexcitable obstacle and a curved fiber field. This exa mple illustrates the dramatic influence of the complex orientation of the fibers on the resulting activation pattern. The FVM provides a mea ns of accurately modeling the cardiac structure and can help bridge th e gap between computation and experiment in cardiac electrophysiology.