Activation Dynamics in Anisotropic Cardiac Tissue via Decoupling

Abstract

Bidomain theory for cardiac tissue assumes two interpenetrating anisotropic media--intracellular (i) and extracellular (e)--connected everywhere via a cell membrane; four local parameters sigma(i,e)(l,t) specify conductivities in the longitudinal (l) and transverse (t) directions with respect to cardiac muscle fibers. The full bidomain model for the propagation of electrical activation consists of coupled elliptic-parabolic partial differential equations for the transmembrane potential upsilon(m) and extracellular potential phi(e), together with quasistatic equations for the flow of current in the extracardiac regions. In this work we develop a preliminary assessment of the consequences of neglecting the effect of the passive extracardiac tissue and intracardiac blood masses on wave propagation in isolated whole heart models and describe a decoupling procedure, which requires no assumptions on the anisotropic conductivities and which yields a single reaction-diffusion equation for simulating the propagation of activation. This reduction to a decoupled model is justified in terms of the dimensionless parameter epsilon = (sigma(i)(l)sigma(e)(t) - sigma(i)(t)sigma(e)(l))/(sigma(i)(l) + sigma(e)(l))(sigma(i)(t) + sigma(e)(t)). Numerical simulations are generated which compare propagation in a sheet H of cardiac tissue using the full bidomain model, an isolated bidomain model, and the decoupled model. Preliminary results suggest that the decoupled model may be adequate for studying general properties of cardiac dynamics in isolated whole heart models.

Mathematical Modeling of Electrocardiograms: A Numerical Study

“…Clements et al, 9 Potse et al 42 ). As a result, the intracardiac quantities (V m , u e ) can be obtained, independently of u T , by solving (2.7) with initial condition (2.8) and insulating conditions…”

“…Throughout this study, this system of equations will be termed RM (reference model), which is also known in the literature as full bidomain model (see e.g. Clements et al 9 ). The interested reader is referred to Boulakia et al 7 for a recent study on the mathematical well-posedness of this system, under appropriate assumptions on the structure of I ion and g.…”

“…Different conductivities values are available in the literature (see e.g. Clements et al, 9 Malmivuo and Plonsey, 35 Sundnes et al 51 ). The values used in our simulations, originally reported in Potse et al, 42 are given in Table 1.…”

An a posteriori error estimator for model adaptivity in electrocardiology

“…The Monodomain problem has been proposed as a simplification of the Bidomain one. It can be deduced in different ways (see [5,14,16] …”

Optimized Schwarz coupling of Bidomain and Monodomain models in electrocardiology

“…and, since the proportionality assumption D e = λD i entails D e D −1 − λ 1+λ I = 0, a formulation of the Monodomain model (see [6,17]) is then obtained from (2.9) as…”