A bidomain model for anisotropic cardiac muscle

Abstract

Cardiac muscle is considered to consist of an intracellular domain and an extracellular or interstitial domain. Current passes from one domain to the other through the cell membrane. Electric potentials in interstitial space are shown to be associated with current sources proportional to the spatial gradient of the cellular transmembrane action potential, phi m. Hence, given the distribution of phi m throughout the myocardium, one can calculate the surface electrocardiogram and extracorporeal magnetocardiogram. The problem is considerably complicated when anisotropy is considered. If interstitial space is approximately isotropic, however, the sources are still proportional to delta phi m. It is shown that the effects of intracellular anisotropy on the surface electrocardiogram may be relatively small. The inverse problem is discussed briefly, with consideration of the relationship of the magnetocardiogram to the electrocardiogram. Finally, it is shown that if the heart can be considered to be bounded by a closed surface, then the value of phi m on this surface is uniquely related to the surface electrocardiogram to within a constant, provided there are no internal discontinuities. Such discontinuities, however, would be expected to occur in cases of ischemia and necrosis.

Remodeling of cardiac passive electrical properties and susceptibility to ventricular and atrial arrhythmias

“…This is also reflected in the use of bi-domain or multi-domain models for the simulation of cardiac impulse propagation, taking extracellular conductivity and fibroblasts into account (Jack et al, 1975;Peskoff, 1979;Geselowitz and Miller, 1983;Roberts et al, 2008;Sachse et al, 2009). The group of Veeraraghavan et al (2012) suggested that the effect of gap junction conductance on impulse propagation is modulated by the fraction of extracellular space.…”

Estimating Local Apparent Conductivity with a 2-D Electrophysiological Model of the Heart

“…Very accurate models such as bidomain models ( [6]) or LuoRudy models ( [9]) provide excellent insight into the physiological phenomena provoking the electrical activity of the heart but are probably too sophisticated for our inverse problem. Indeed, these models are designed to capture very subtle modifications in the shape of the action potential whereas we only measure here the depolarization times.…”

Online Noninvasive Localization of Accessory Pathways in the EP Lab

“…The coupling of these two modalities in time and space permits the imaging of electrical function when applying bioelectromagnetical field theory and solving an ill-posed inverse problem [4,5,6,7]. The primary electrical source in the cardiac muscle is the spatio-temporal distribution of the transmembrane potential (TMP) ϕ m [4,5,8,9]. The potential on the chest surface and the potential on all other conductivity interfaces are related to ϕ m by a Fredholm integral equation of second kind.…”