Local Activation Time Annotation in Atrial Electrogram Arrays Using Deconvolution

An electrogram array can be modeled as a spatial convolution of transmembrane currents generated by each activated atrial cell, with an appropriate measurement function that depends on the cells' distance to the electrodes. Compared to electrograms, transmembrane currents suffer less from the superposition of far-field atrial activities as they are not affected by the spatial convolution. As a result, transmembrane currents represent more local information and estimation of the local activation time using the steepest deflection will be more accurate than when using fractionated electrograms. However, transmembrane current estimation from electrogram array recordings is an under-determined problem, having infinite solutions, among which the desired solution. To constrain the solution space, additional prior information can be used. As the temporal derivative of transmembrane currents are typically sparse, we use this as prior information. We use a Split Bregman method with a quick convergence rate to iteratively solve the problem. Our implementation of circulant operations in the formulation of the solution of each step, makes it possible to perform them very fast using FFTs. Using simulated electrograms, we show that the proposed approach outperforms the conventional approach of annotating the steepest deflection of electrograms as the activation time.