UC San Diego

Atrial fibrillation (AF) is the most common arrhythmia in the United States and is a risk factor for stroke and cardiac dysfunction. Pharmacological and surgical treatments of AF have limited efficacy, partly attributable to a limited understanding of its basic mechanisms. Patient-specific computational models have shown promise for planning personalized treatment strategies for AF, but progress is still nascent and computational studies do not currently solve in clinical timescales. In this dissertation, the author describes new finite element methods for modeling human AF, and then uses these methods in a patient-specific model to suggest mechanisms for AF maintenance and termination. A clinical description of AF and the basic mechanisms of AF are presented in Chapter 1. New methods for constructing cubic Hermite models of the atria from non-invasive imaging data are presented in Chapter 2, and these methods are extended to construct four-chamber models of the heart in Chapter 3. Heretofore, high-order finite element models have not been used on complicated shapes such as that of the atria and ventricular models with valve annuli, yet high-order models have attractive properties such as superior convergence compared to linear finite element models in electrophysiology and biomechanics problems, which can decrease the time required for simulations toward clinical timescales. Convergence properties of both cubic Hermite and cubic Hermite-style serendipity basis functions for the solution of the monodomain equation of cardiac electrophysiology are evaluated in Chapter 4. We find that cubic Hermite and cubic Hermite-style serendipity basis functions have superior convergence properties in the monodomain problem in comparison with linear finite elements for equal numbers of elements and integration points. In Chapter 5, we examine an experimental case study of AF with the aid of a patient-specific model. We find that meandering rotors are important focal sources of AF, and are made possible by remodeling of the action potential shape and a decrease in electrical anisotropy. Virtual radiofrequency ablation may terminate AF by creating a spatial excitable gap near the rotor and decreasing the fractionation exacerbated by rotor meander. We then speculate how patient-specific models of AF might be used in the future