Wavefront propagation in an activation model of the anisotropic cardiac tissue: asymptotic analysis and numerical simulations

Abstract

In this paper we present a macroscopic model of the excitation process in the myocardium. The composite and anisotropic structure of the cardiac tissue is represented by a bidomain, i.e. a set of two coupled anisotropic media. The model is characterized by a non linear system of two partial differential equations of parabolic and elliptic type. A singular perturbation analysis is carried out to investigate the cardiac potential field and the structure of the moving excitation wavefront. As a consequence the cardiac current sources are approximated by an oblique dipole layer structure and the motion of the wavefront is described by eikonal equations. Finally numerical simulations are carried out in order to analyze some complex phenomena related to the spreading of the wavefront, like the front-front or front-wall collision. The results yielded by the excitation model and the eikonal equations are compared.

Efficient probabilistic model personalization integrating uncertainty on data and parameters: Application to Eikonal-Diffusion models in cardiac electrophysiology

“…Among the different models describing the electrical activity in the cardiac tissue, Fink et al (2011);Clayton et al (2011), here we chose to focus on the Eikonal-Diffusion (ED) model Colli Franzone et al (1990), as it allows a compact formulation while still including important nonlinearities. Moreover, by using the anisotropic Fast-Marching Method, Konukoglu et al (2007), Eikonal models can be solved rapidly which makes them suitable for clinical applications, Chinchapatnam et al (2008), and treatment simulations, Pernod et al (2011).…”

Toward Patient-Specific Myocardial Models of the Heart

“…Biophysical: semilinear evolution PDE with ionic models (up to 50 equations for ions and channels) [33][34][35][36][37] Phenomenologic: semilinear evolution PDE with mathematical simplifications of biophysical models (bidomain, monodomain) [38][39][40] Eikonal: one static nonlinear PDE for the depolarization time derived from the previous models (Eikonal-curvature, Eikonaldiffusion) [41,42].…”

A Fast-Marching Approach to Cardiac Electrophysiology Simulation for XMR Interventional Imaging

“…2 [3]: c √ kD ∇T − Dκ(T ) = ∂ t T , and an evolution term and finite elements to the Eq. 3 [4]: ∂ t T + c √ kD ∇T − D∆T = 1. A time dependant PDE like these needs up to thousands of iterations, each of which might be a linear (or non-linear) system to solve.…”