Improving the accuracy of retrieved cardiac electrical conductivities

Accurate values for the six cardiac conductivities of the bidomain model are crucial for meaningful electrophysiological simulations of cardiac tissue and are yet to be achieved. A two-stage optimisation process is used to retrieve the cardiac conductivities from cardiac potentials measured on a multi-electrode array-the first stage simultaneously fits all six conductivities, and the second stage fits a subset of the conductivities (intracellular conductivities), while holding the remainder of the conductivities (extracellular conductivities) constant. Previous studies have shown that the intracellular conductivities are retrieved to a lesser degree of accuracy than extracellular conductivities. This study tests the proposition that there exists a relationship between the extracellular and intracellular conductivities during the second stage of the optimisation that affects the accuracy of the retrieved intracellular conductivities. A measure to quantify this relationship is developed using polynomial chaos. The results show that a significant relationship does exist, and thus any errors in the extracellular conductivities are magnified in the retrieved intracellular conductivities. Thus, it is suggested that future protocols for retrieving conductivities incorporate the uncertainty in the extracellular conductivities.