Probabilistic interpolation of uncertain local activation times on human atrial manifolds

Objective: Local activation time (LAT) mapping of the atria is important for targeted treatment of atrial arrhythmias, but current methods do not interpolate on the atrial manifold and neglect uncertainties associated with LAT observations. In this paper we describe novel methods to (i) quantify uncertainties in LAT arising from bipolar electrogram analysis and assignment of electrode recordings to the anatomical mesh, (ii) interpolate uncertain LAT measurements directly on left atrial manifolds to obtain complete probabilistic activation maps, and (iii) interpolate LAT jointly across both the manifold and different S1-S2 pacing protocols. Methods: A modified center of mass approach was used to process bipolar electrograms, yielding a LAT estimate and error distribution from the electrogram morphology. An error distribution for assigning measurements to the anatomical mesh was estimated. Probabilistic LAT maps were produced by interpolating on a left atrial manifold using Gaussian Markov random fields, taking into account observation errors and characterizing LAT predictions by their mean and standard deviation. This approach was extended to interpolate across S1-S2 pacing protocols. Results: We evaluated our approach using recordings from three patients undergoing atrial ablation. Cross-validation showed consistent and accurate prediction of LAT observations both at different locations on the left atrium and for different S1-S2 intervals. Significance: Interpolation of scalar and vector fields across anatomical structures from point measurements is a challenging problem in biomedical engineering, compounded by uncertainties in measurements and meshes. New methods and approaches are required, and in this paper we have demonstrated an effective method for probabilistic interpolation of uncertain LAT.