A predictive method allowing the use of a single ionic model in numerical cardiac electrophysiology

Abstract

Abstract.One of the current debate about simulating the electrical activity in the heart is the following: Using a realistic anatomical setting, i.e. realistic geometries, fibres orientations, etc., is it enough to use a simplified 2-variable phenomenological model to reproduce the main characteristics of the cardiac action potential propagation, and in what sense is it sufficient? Using a combination of dimensional and asymptotic analysis, together with the well-known Mitchell−Schaeffer model, it is shown that it is possible to accurately control (at least locally) the solution while spatial propagation is involved. In particular, we reduce the set of parameters by writing the bidomain model in a new nondimensional form. The parameters of the bidomain model with Mitchell−Schaeffer ion kinetics are then set and shown to be in one-to-one relation with the main characteristics of the four phases of a propagated action potential. Explicit relations are derived using a combination of asymptotic methods and ansatz. These relations are tested against numerical results. We illustrate how these relations can be used to recover the time/space scales and speed of the action potential in various regions of the heart. Mathematics Subject Classification. 34C15, 35B40, 78A70, 92C50.

A two-variable model robust to pacemaker behaviour for the dynamics of the cardiac action potential

“…The sets of parameters that yield pacemaker cell behaviour do not delimit a closed region of the parameter space. This phenomenon has been observed and reported both in 0D and tissue models, [5], [22]. However, to the best of our knowledge there are no criteria for determining a priori which combination of parameters will produce pacemaker activity.…”

Mathematical analysis and 2-scale convergence of a heterogeneous microscopic bidomain model

“…In the literature, few works in that direction have been carried out, although we can cite [54] for a nondimensionalization analysis of the ionic term I ion and [43] for the analysis in the context of homogenization. We define L 0 as a characteristic length of the heart and T 0 as a characteristic time of a cardiac cycle.…”

Coupled lattice Boltzmann method for numerical simulations of fully coupled heart and torso bidomain system in electrocardiology

“…On the one hand, numerical results demonstrate the eectiveness and accuracy of our approach using general methods for bidomain type systems with full known data and chosen analytical solution. On the other one, we treat the model with realistic data to show good agreement with numerical results and potential behavior reported in the literature (see e.g., [7], [29]). The paper is structured as follows: rst, in Section 2 we introduce the full coupled heart and torso bidomain system and the MS ionic model.…”

“…(a) LBE according to time r by using (29) to computeρ e (x, r + ∆r; t + ∆t) (i.e., approximation of ρ e (x, t + ∆t)) . (b) If we don't reach the stopping criteria chosen to be:…”