A Comparison of Methods for Examining the Effect of Uncertainty in the Conductivities in a Model of Partial Thickness Ischaemia

Although models of cardiac ischaemia require values for electrical conductivities, no agreement yet exists on these values, nor how much effect uncertainty in the conductivities will have on simulation results. In this work, simulations of acute partial thickness (50% of the wall thickness) ischaemia are conducted in a half-ellipsoidal model of the left ventricle to produce epicardial potential distributions (EPDs), while simultaneously varying each of the six bidomain conductivity values. From these, emulators are produced using Gaussian Process emulators (GPE), Partial Least Squares (PLS), and generalised polynomial chaos expansion (PCE). All three approaches indicate that the EPDs are most sensitive to uncertainty in the longitudinal conductivities and the extracellular normal conductivity, and that variation in these conductivities has a significant effect on the EPDs. Varying the depth of the ischaemic region does not change the conductivities to which the main EPD features (a maximum and two flanking minima) are sensitive. For this work, the PCE approach has the advantage that it provides more information (that is, sensitivity over the ventricular surface, not just at the main features). However, GPE and PLS are able to supply information about the sensitivity of the position of the features that PCE is not. Finally, PLS and PCE can be performed using fewer points than for GPE.