Deconvolution and wavelet-based methods for membrane current estimation from simulated fractionated electrograms

In infarcted myocardium, extracellular recordings exhibit multiple deflections due to irregular pathway of the electric impulse. In this work the problem of distinguishing local from distant deflections is tackled. In order to evaluate the proposed methods in a controlled setting, simulated data are used, following both Beeler-Reuter and Luo-Rudy kinetics. The input is an array of electrograms positioned on grid-points of a rectangular grid and the output is an array of estimates of the membrane current. First, deconvolution techniques are used in the form of spatial filtering for membrane current estimation from the extracellular recordings. Second, the extracellular recordings undergo wavelet based transformation, followed by a spatial filter which enhances local activity deflections and suppresses distant activity deflections. It is shown that wavelet filtering of the extracellular recordings acts as an evaluator of the efficiency of the deconvolution techniques for the membrane current estimation. Subsequently, activation times based on the results from the two methods are used for the reconstruction of the propagation pattern in a zig-zag case in two-dimensional grids. It is shown that the wavelet-based method is more robust, and can work well even in cases where the grid interval in the y direction is four times larger than the single cell size.