  Atrial Fibrillation (AF) is characterized by disorganised electrical activity
in the atria and is known to be sustained by the presence of regions of
fibrosis (scars) or functional cellular remodeling, both of which may lead to
areas of slow conduction. Estimating the effective conductivity of the
myocardium and identifying regions of abnormal propagation is therefore crucial
for the effective treatment of AF. We hypothesise that the spatial distribution
of tissue conductivity can be directly inferred from an array of concurrently
acquired contact electrograms (EGMs). We generate a dataset of simulated
cardiac AP propagation using randomised scar distributions and a
phenomenological cardiac model and calculate contact EGMs at various positions
on the field. EGMs are enriched with noise extracted from biological data
acquired in the lab. A deep neural network, based on a modified U-net
architecture, is trained to estimate the location of the scar and quantify
conductivity of the tissue with a Jaccard index of 91%. We adapt a
wavelet-based surrogate testing analysis to confirm that the inferred
conductivity distribution is an accurate representation of the ground truth
input to the model. We find that the root mean square error (RMSE) between the
ground truth and our predictions is significantly smaller ($p_{val}<0.01$) than
the RMSE between the ground truth and surrogate samples.
