Mathematical Approaches to Understanding and Imaging Atrial Fibrillation

Abstract

Atrial fibrillation (AF) is the most common sustained arrhythmia in humans. The mechanisms that govern AF initiation and persistence are highly complex, of dynamic nature, and involve interactions across multiple temporal and spatial scales in the atria. This articles aims to review the mathematical modeling and computer simulation approaches to understanding AF mechanisms and aiding in its management. Various atrial modeling approaches are presented, with descriptions of the methodological basis and advancements in both lower-dimensional and realistic geometry models. A review of the most significant mechanistic insights made by atrial simulations is provided. The article showcases the contributions that atrial modeling and simulation have made not only to our understanding of the pathophysiology of atrial arrhythmias, but also to the development of AF management approaches. A summary of the future developments envisioned for the field of atrial simulation and modeling is also presented. The review contends that computational models of the atria assembled with data from clinical imaging modalities that incorporate electrophysiological and structural remodeling could become a first line of screening for new AF therapies and approaches, new diagnostic developments, and new methods for arrhythmia prevention.

Three‐dimensional Integrated Functional, Structural, and Computational Mapping to Define the Structural “Fingerprints” of Heart‐Specific Atrial Fibrillation Drivers in Human Heart Ex Vivo

“…Current ablation strategies for persistent/permanent AF or AF with concurrent cardiac diseases are disappointing, with a <30% long‐term success rate for single‐ablation procedures 1, 2, 3. This inadequate success rate may be because of the lack of basic understanding of the underlying atrial functional and structural substrates that sustain AF directly in human hearts4, 5, 6, 7 and emphasizes the need for quantitative tools to evaluate human atrial 3‐dimensional (3D) structural features in both clinical and experimental settings.…”

Atrial Fibrillation Compendium

“…6 Recognizing the importance of this area and the rapid pace of knowledge development, the Editorial Board of Circulation Research decided to develop a Compendium on Atrial Fibrillation. The compendium includes 6 state-of-the-art review articles on themes of clinical features and pathophysiology of AF, 1 molecular electrophysiology of AF initiation, maintenance, and progression, 7 autonomic nervous system control of AF, 8 genetic factors determining AF occurrence and risk, 9 the use of mathematical modeling to understand and manage AF better, 10 and the mechanisms governing present and future therapy of the arrhythmia. 11 The goal of the present article is to provide a context and unifying vision for the compendium, showing how each of the components relates to each other, to our overall understanding of AF, and to the future of the field.…”

The opportunities and challenges for biophysical modelling of beneficial and adverse drug actions on the heart

“…Modeling has therefore increasingly moved from understanding physiology and pathology to interpreting the effects of pharmacological agents 18,19 and medical interventions 17,20 . Here we discuss the recent advances that have led to models being used to interpret drug effects.…”