TY - THES
A1 - Sali, Adrian
T1 - Coupling of Monodomain and Eikonal Models for Cardiac Electrophysiology
N2 - The primary goal of this paper is to study the coupling of monodomain and eikonal
models for the numerical simulation of cardiac electrophysiology.
Eikonal models are nonlinear elliptic equations describing the excitation time of the
cardiac tissue. They are often used as very fast approximations for monodomain
or bidomain models - parabolic reaction-diffusion systems describing the excitation
wavefront in terms of ionic currents. The excitation front is a thin region with high
gradients, whereas excitation times vary over larger domains. Hence, eikonal equations
can be solved on much coarser grids than monodomain equations. Moreover,
as eikonal models are not time-dependent, no time integration is needed.
Eikonal models are derived from monodomain models making additional assumptions
and using certain approximations. While generally the approximation is rather
good, several specific situations are not well captured by eikonal models. We consider
coupling the two models, i.e. using the monodomain model in regions where more
accurate results or the shape of the wavefront are needed, and the eikonal model in
the remaining parts of the domain, where the excitation time is sufficient. Restricting
the monodomain simulation to a small subdomain reduces the computational
effort considerably.
Numerical methods for the simulation of the individual models are presented, with
the finite element method as the main ingredient. Coupling conditions as well as
algorithms for implementing the coupling are explained. The approximation quality
and efficiency of the coupled model is illustrated on simple geometries using an
Aliev-Panfilov membrane model.
Y1 - 2016
UR - https://opus4.kobv.de/opus4-zib/frontdoor/index/index/docId/6051
ER -