Quantifying the effect of uncertainty in input parameters in a simplified bidomain model of partial thickness ischaemia

Abstract

Reduced blood flow in the coronary arteries can lead to damaged heart tissue (myocardial ischaemia). Although one method for detecting myocardial ischaemia involves changes in the ST segment of the electrocardiogram, the relationship between these changes and subendocardial ischaemia is not fully understood. In this study, we modelled ST-segment epicardial potentials in a slab model of cardiac ventricular tissue, with a central ischaemic region, using the bidomain model, which considers conduction longitudinal, transverse and normal to the cardiac fibres. We systematically quantified the effect of uncertainty on the input parameters, fibre rotation angle, ischaemic depth, blood conductivity and six bidomain conductivities, on outputs that characterise the epicardial potential distribution. We found that three typical types of epicardial potential distributions (one minimum over the central ischaemic region, a tripole of minima, and two minima flanking a central maximum) could all occur for a wide range of ischaemic depths. In addition, the positions of the minima were affected by both the fibre rotation angle and the ischaemic depth, but not by changes in the conductivity values. We also showed that the magnitude of ST depression is affected only by changes in the longitudinal and normal conductivities, but not by the transverse conductivities.

Keywords: Bidomain model; Conductivity values; Gaussian process emulators; Ischaemia; ST depression.

Fig. 1

The tissue-blood model used in the simulations, showing the epicardium at z = 0, the endocardium at z = 1 and the central region, which is ischaemic tissue that extends part way from the endocardium towards the epicardium. Blood extends from the endocardium (that is, for z > 1)

Fig. 2

Polynomial chaos mean epicardial potential distributions (in mV) for various values of ischaemia, produced with g _b = 6.5 mS/cm, fibre rotation = 100^∘ and varying the conductivities across the ranges given in Table 2. The solid line indicates the central ischaemic region and the dashed line is the zero of potential. The headings cminV, cmaxV and ominV give the values for the minimum (minV) and maximum (maxV) potentials (in mV) over either the central (c) ischaemic region or outside (o) this region

Fig. 3

Polynomial chaos mean epicardial potential distributions, produced with g _b = 6.5 mS/cm, fibre rotation = 100^∘, ischaemia = 30% and varying the conductivities across the ranges given in Table 2, showing a mean - std, b mean and c mean + std. Definitions are given in Fig. 2

Fig. 4

Polynomial chaos mean epicardial potential distributions, produced with g _b = 6.5 mS/cm and by varying the conductivities over the ranges in Table 2. From left to right across each row, fibre rotation is 60^∘, 100^∘ and 140^∘. The top row is 10% ischaemia, the middle row 30% and the bottom row 60% ischaemia. Definitions are given in Fig. 2

Fig. 5

Epicardial potential distributions, where each row uses the minimum, mean and maximum of a particular parameter’s values, for 30% ischaemia and mean values for all other variables. Definitions are given in Fig. 2. Distributions marked with asterisk exhibit ST depression (type 1) behaviour, those marked with number sign show ST elevation and the remainder demonstrate ST depression (type 2) behaviour

Fig. 6

Design data for the features centre minimum voltage (cminV), in mV, and ellipse angle, in degrees, of the epicardial potential distributions of ST depression (type 1). These are plotted against each of the eight input variables, with units of mS/cm for conductivities and degrees for fibre rotation

Fig. 7

Main effect plots for outputs of EPDs showing ST depression (type 1), a cminV, b ominV, c cmaxV and d ellipse angle. Plots are produced by allowing each input to vary over the normalised range [0,1], while all other inputs are fixed at a mean of 0.5 with a variance of 0.04

Fig. 8

Main effect plots for outputs of EPDs showing ST depression (type 2), a ominV, b cminV, c cmaxV and d angmin. Plots are produced by allowing each input to vary over the normalised range [0,1], while all other inputs are fixed at a mean of 0.5 with a variance of 0.04

Fig. 9

Main effect plots for outputs of EPDs showing ST elevation, a cmaxV, b ominV, c angmax and d angmin. Plots are produced by allowing each input to vary over the normalised range [0,1], while all other inputs are fixed at a mean of 0.5 with a variance of 0.04

Fig. 10

Design data for EPDs of type ST depression (type 2) and ST elevation showing the relationship between the angle of the minimum (angmin) and a fibre rotation angle and b depth of ischaemia