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Using generalised polynomial chaos to examine various parameters in a half-ellipsoidal ventricular model of partial thickness ischaemia

Elevation and depression in the ST segment of the electrocardiogram is commonly used as part of a diagnosis of myocardial ischaemia, although there is not yet a clear correlation between these observations and partial thickness ischaemia. In this work, we use a half-ellipsoid bidomain model of subendocardial ischaemia in a ventricle to study the effect of changes in model parameters on ST segment epicardial potential distributions (EPDs). We use generalised polynomial chaos techniques to produce mean EPDs, where the six bidomain conductivity values are varied, as well as blood conductivity and fibre rotation, for a number of different representations of the ischaemic region. We find that, as the thickness of the ischaemic region (i.e. the ischaemic depth) increases, the character of the mean EPD first changes from a single minimum approximately above the ischaemic region, to a maximum over the ischaemic region, with the minimum moving to a border of the ischaemic region. Next a second minimum develops, in addition to the previous maximum and minimum. In contrast, the strength of the maximum and the minima is only affected in a minor way by changes in the width of the ischaemic border and the position of the ischaemic region, provided it is not near the apex or base of the ventricle. When the size of the ischaemic region is increased, the magnitudes of both the maximum and the minima increase, but their character does not change. In summary, the qualitative progression of the mean EPD with increasing ischaemic depth, from single minimum through to a maximum surrounded by two minima, is the same, regardless of the size and position of the ischaemic region.