A posteriori error estimates for the monodomain model in cardiac electrophysiology

Abstract

We consider the monodomain model, a system of a parabolic semilinear reaction-diffusion equation coupled with a nonlinear ordinary differential equation, arising from the (simplified) mathematical description of the electrical activity of the heart. We derive a posteriori error estimators accounting for different sources of error (space/time discretization and linearization). We prove reliability and efficiency (this latter under a suitable assumption) of the error indicators. Finally, numerical experiments assess the validity of the theoretical results.

An integrative smoothed particle hydrodynamics framework for modeling cardiac function

“…In general, a good agreement is noted. It is observed that in accordance with the previous numerical estimation [35] and experimental observation [19],…”

“…Here, we consider the Aliev-Panfilow model with the constant parameters given in Table 1. Figure 7 reports the predicted evolution profile of the transmembrane potential at point (0.3, 0.7), and the comparison with those from Ratti and Verani [35]. In general, a good agreement is noted.…”

“…Following the work of Ratti and Verani [35], we consider a problem on the propagation of transmembrane potential. It is assumed that the transmembrane potential propagates in a two dimensional isotropic tissue in a square domain of (0, 1) 2 and the nondimensional time interval is set as (0, 16).…”

On the determination of ischemic regions in the monodomain model of cardiac electrophysiology from boundary measurements

“…Finally, the detection of arbitrarily large ischemic regions can be tackled, exploiting an analogous strategy as the one adopted in [6] (possibly reducing the computational effort by employing an adaptive solver of the monodomain system, as proposed in [32]).…”

“…This leads to solve a nonlinear problem at each timestep, which is performed via a Newton iterative algorithm. More details on the solver can be found in [32], where a thorough convergence analysis is performed.…”