Design of a multi-electrode array to measure cardiac conductivities

Abstract

Accurate determination of cardiac tissue parameters is essential in bidomain models that simulate the electrical activity of the heart and thereby contribute to understanding cardiovascular disease. Recent experimental work indicated the need for six parameters, which measure electrical conductivity in two domains (extracellular and intracellular), along and across the cardiac fibres within a sheet and also between sheets. This is in contrast to the available experimentally determined conductivities, which are sets of four values, where it is assumed that conductivities across the fibres within a sheet and between the fibre sheets are equal. This study presents a mathematical model that incorporates six bidomain conductivities. It also discusses the design of a multi-electrode array and inversion method to retrieve these

Approaches for determining cardiac bidomain conductivity values: progress and challenges

“…In 2013, Johnston and Johnston presented [37,43,38] a new approach to find all six bidomain conductivities, along with the fibre rotation angle. The mathematical model and inversion technique were extensions of their previous work [51] (Section 5.1.6).…”

A modified approach to determine the six cardiac bidomain conductivities

“…The direct current being injected into the tissue ( 0 ) has a magnitude of 1 Amm −3 , similar in magnitude to values proposed and used in previous simulation studies of the myocardium [25,32]. Finally, and are fixed at 120°and 6.7 mS∕cm, respectively, as used in previous studies [25,24].…”

“…In the current study, the ventricular muscle is represented by a slab geometry to reduce the complexity of the solution techniques [24,25,23]. The model is constructed using a block of cardiac tissue, 2 cm in the and directions…”

“…The potentials are then used to simultaneously fit , , , , and using the solver. As in [24,23], initial values for the conductivities are taken to be 10 −3 S∕cm except for which is taken to be 10 −4 S∕cm. During the first pass, the Tikhonov functional ( 13), minimised by the solver is given by,…”

“…In previous work, multiplicative noise was introduced to the synthetic potential measurements at each electrode on the array [24,39,30] in order to mimic noise caused by uncorrelated sources. For example, geometric noise caused by the placement of the electrode array relative to the tissue, circuitry noise and inherent noise caused by equipment could all affect the potential measurements.…”