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