Mathematical and numerical modeling of the cardiac electrophysiology: towards clinical application of cardiac simulations

The aim of this thesis is to present some tools aimed at fast and efficient, while still accurate, cardiac simulations, and to demonstrate their potential applicability in the clinical practice. First, we review the most used ionic models for human cardiomyocytes, and we present a highly efficient phenomenological model of human ventricular cells. Subsequently, we review the most used modeling strategies for cardiac tissue and the numerical methods employed to solve tissue-level cardiac models. In this context, we present a novel smoothed boundary approach to solve cardiac bidomain equations in anatomical models of the heart without the need for an unstructured mesh. Subsequently, we present a framework to build ready-to-use cardiac models from segmented anatomical images. The framework includes the assignment of fiber orientation and generation of the Purkinje system. Finally, we present some examples of applications of the methods and tools presented in this thesis. We report a computational study assessing arrhythmic factors associated with Brugada Syndrome. Then, we developed a reaction-diffusion 2D heart model for closed-loop evaluation of heart-pacemaker interaction, and we provided a hardware setup for the implementation of the closed-loop system. Finally, starting from late gadolinium-enhanced cardiac magnetic resonance images, we constructed patient-specific cardiac models of post-infarction patients, which allow for the investigation of the arrhythmic substrate and could identify the critical ablation targets.