Approaches for determining cardiac bidomain conductivity values: progress and challenges

Abstract

Modelling the electrical activity of the heart is an important tool for understanding electrical function in various diseases and conduction disorders. Clearly, for model results to be useful, it is necessary to have accurate inputs for the models, in particular the commonly used bidomain model. However, there are only three sets of experimentally determined four conductivity values for cardiac ventricular tissue and these are inconsistent, were measured around forty years ago, often produce different results in simulations, and do not fully represent the three dimensional anisotropic nature of cardiac tissue. Despite efforts in the intervening years, difficulties associated with making the measurements and also determining the conductivities from the experimental data have not yet been overcome. In this review, we summarise what is known about the conductivity values, as well as progress to date in meeting the challenges associated with both the mathematical modelling and the experimental techniques.

A space-fractional bidomain framework for cardiac electrophysiology: 1D alternans dynamics

“…In these settings, in fact, we observed that the asymmetry of the reference CV isoline in parametric space translates into different dynamical scenarios depending on the particular choice of the (σ i , σ e ) pair, with larger values of the conductivity parameter corresponding to the highest fractional exponent typically giving richer dynamics in terms of alternans and node formation. This adds to the challenges already existing for the classical Bidomain formulation in the proper estimation of suitable conductivities [59] and undoubtedly requires further investigation in higher spatial dimensions to better elucidate the effects of non-locality in either (or both) spatial domains. Finally, in line with well-established results for the standard case, for any particular parameter combination of the FBD we observe richer dynamical responses (allowing the formation of discordant alternans -if previously absent -and potentially increasing the number of nodes formed at a given BCL) when increasing the cable length or reducing the reference CV.…”

A modified approach to determine the six cardiac bidomain conductivities

“…A lack of understanding of cardiac tissue's electrical properties is one of the major challenges in being able to realistically simulate cardiac electrophysiological behaviour [1,2,3]. Such simulations can facilitate an understanding that often cannot be achieved through experimental means alone.…”

“…Studies in the past decade have proposed various techniques for retrieving all six bidomain conductivities, through either experimental and theoretical means [13,14], while several other studies were able to experimentally retrieve a subset of the conductivities [15,16,17]. However, no study has fully retrieved these values through purely experimental means [3].…”

“…More recent publications from Barr, Pollard and Waits [20,21,22] provide methods to separate the extracellular and intracellular contributions; however, they are limited by practical issues. Various other advances in this area and techniques to retrieve four of the six conductivities are detailed in [3].…”

Etiology-Specific Remodeling in Ventricular Tissue of Heart Failure Patients and Its Implications for Computational Modeling of Electrical Conduction

“…In addition to fibrosis and changes in interstitial space, the clefts that separate myocyte sheets modulates the conductivity of ES. The anisotropy of the ES conductivity is well-established and less pronounced than the anisotropy of the myocyte domain (Johnston and Johnston, 2020). Hence the bidomain model is more appropriate to describe features of fibrotic remodeling in cardiac tissues.…”