Dimension Reduction for the Emulation of Cardiac Electrophysiology Models for Single Cells and Tissue

Widespread variability in the electrophysiological behaviour of individual cardiac cells, as well as between the hearts of different members of a population, presents a significant challenge to both the biological and mathematical understanding of cardiology. This variability underpins the differential responses to heterogeneities in pathologies of the heart, and to drug treatments, and so a thorough understanding is critical. A range of techniques exist for both uncertainty quantification and exploration of variability in mathematical models, but these require evaluation of the model at large numbers of points in a parameter space and the complexity of these models can make such analyses prohibitively computationally expensive. We demonstrate the use of dimension reduction to allow Gaussian processes to emulate the complex spatiotemporal outputs of heart models, thus making studies of variability feasible. Significant improvements in computational speed are achieved.