Fields Notes 18.1 - Page 15

Workshop on Mathematical Methods in Cardiac Electrophysiology November 4-6, 2017 • Fields Institute Organizers: Yves Bourgault (University of Ottawa), Yves Coudière (Inria), Edward Vigmond (Liryc­, L'Institut de RYthmologie et modélisation Cardiaque à Bordeaux) This workshop was jointly sponsored by the Institut national de recherche en informatique et en automatique (Inria), the Centre national de la recherche scientifique (CNRS), the Fields Institute, and the University of Ottawa. The talks focused on the development of new ideas for mathematical modelling, current computational methods for numerical solutions, the use of control and dynamical system theory, data assimilation, and uncertainty quantification in the analysis of cardiac electrophysiology (EP) models. These talks reflected the fact that mathematical modelling and numerical methods are increasingly important tools for understanding and treating cardiac EP pathologies. This is recognized well beyond the immediate modelling community. For instance, atrial fibrillation is the subject of much current research and was broadly covered during the talks. The analysis of the dynamics of re-entrant waves underlying atrial fibrillation is challenging and requires new ideas. The impact of the cardiac tissue microstructure on wave conduction is still not well understood. New models and methods to adjust conductivities in partial differential equations were presented to account for tissue heterogeneities. These methods constitute a subset of all the model personalization strategies that were also well addressed during the workshop together with the required link with the latest medical imaging techniques used in cardiology. Another difficulty of the current EP research is the plethora of mathematical models available Nattle / shutterstock.com to represent the ionic activity in cardiomyocytes. Some talks introduced statistical methods to study uncertainty and variability in those ionic models. The numerical solution of the bidomain and monodomain models, upon which most cardiac EP simulations rely, is still very challenging. Aside from the development of adaptive and high‑order numerical methods, the most impressive results presented