The Sensitivity of the Passive Bidomain Equation to Variations in Six Conductivity Values

Abstract

Previous work has shown that variations in cardiac conductivity values have significant effects on the resulting epicardial potential distributions arising from subendocardial ischaemia. This work carries on from a previous study in this area by allowing for variation in (the more physiologically realistic) six, rather than four, conductivity values. This is achieved by relaxing the usual assumption that the cardiac conductivity values in both normal directions, one normal to the fibres within the sheet and the other normal to the sheet, are equal. An extended non-dimensional formulation is derived for the passive bidomain equation, leading to a normal direction dimensionless conductivity ratio, in addition to the previously found ratios in the transverse and longitudinal directions. Two six-conductivity datasets are used to set up a parameter space for the above ratios, from which epicardial potential distributions are derived and compared. Results from this study appear to support the conclusions of the previous four-conductivity study; that is, differences in epicardial potential distributions are best explained by variations in the ratio of the intracellular longitudinal conductivity to the intracellular transverse conductivity.