Spatio-Temporal Dynamics of Cardiac Physiopathology. Experiments, Theory and Simulations

The synergic union of hypothesis and techniques from physics, mathematics, mechanics, biomedical engineering, cardiology, medicine and computer science in general represent a standard approach in the current high level scientific research and clinical practice. The increasing role of computer models as a complement of experimental and clinical studies is helping noticeably to elucidate the basic mechanisms hidden into biological systems at different scales, starting from gene expression up to tissue remodeling. Nonlinear dynamical theories and massive computational efforts are being applied in order to discover the emerging behavior from such a complexity and new theoretical assumptions, corrected on experimental basis, permit scientists to gain the building of multiscale whole tissue models, able to route new trends both in experiments and theories. Models are, of course, approximations only of the actual physical system, and most of the scientists everyday using them, are well aware of this: if too simple, they fail to capture the salient behavior and have limited predictive ability; if too complex, they become computationally intractable. As in every engineering problem, the optimal choice of model structure and complexity depends on the questions to be addressed: nature of informations, time and space scales, computational demands, as an example. The heart is a complex nonlinear system. It interacts both mechanically and chemically with different scales and levels of organization: from subcellular ionic kinetics to cellular propagating phenomena, reaching the emergent tissue electro-mechanic behavior of the overall coupling. In heart dynamics, most cardiac propagation models have been developed to understand the factors contributing to conduction failure or rhythm instability. To capture their essence, two fundamentally linked key parts have been considered: the description of the membrane ion kinetics and the representation of the electrical properties of the tissue (both starting from the work of Hodgkin and Huxley in the '50s). When such a connection fails, the corresponding model can result in an inefficient or even wrong predictions for the clinical practice. This work was initiated into the growing awareness of significant importance and beauty of cardiac tissue as excitable medium and complex dynamical system. The understanding of spatio-temporal cardiac behaviors, their relation with arrhythmogenesis and their connection with mechanical and control problems, will represent the leitmotiv of the present dissertation. Studying the heart from different perspectives, i.e. experimental, theoretical and computational, has therefore lead us to several parallel insights into such a system. The main theme of this thesis is the study of cardiac spatio-temporal dynamics starting from experimental measurements, passing though the theoretical assessment of the data and ending with mathematical modeling formulations and numerical simulations. The purpose of this procedure is to act both as a basic science, trying to understand and unveil some of the physiological and pathological mechanisms underlying cardiac arrhythmias, and as an applied science, identifying synthetic indicators for a theoretical-based clinical practice.