Rapid calibration of atrial electrophysiology models using Gaussian process emulators in the ensemble Kalman filter

Atrial fibrillation (AF) is a common cardiac arrhythmia characterised by disordered electrical activity in the atria. The standard treatment is catheter ablation, which is invasive and irreversible. Recent advances in computational electrophysiology offer the potential for patient-specific models that can be used to guide clinical decisions. To be of practical value, we must be able to rapidly calibrate physics-based models using routine clinical measurements. We pose this calibration task as a static inverse problem, where the goal is to infer spatially homogenous tissue-level electrophysiological parameters from the available observations. To make this tractable, we replace the expensive forward model with Gaussian process emulators (GPEs), and propose a novel adaptation of the ensemble Kalman filter (EnKF) for static non-linear inverse problems. The approach yields parameter samples that can be interpreted as coming from the best Gaussian approximation of the posterior distribution. We compare our results with those obtained using Markov chain Monte Carlo (MCMC) sampling and demonstrate the potential of the approach to enable near-real-time patient-specific calibration, a key step towards predicting outcomes of AF treatment within clinical timescales. The approach is readily applicable to a wide range of static inverse problems in science and engineering.