  Unbroken and broken spiral waves, in partial-differential-equation (PDE)
models for cardiac tissue, are the mathematical analogs of life-threatening
cardiac arrhythmias, namely, ventricular tachycardia (VT) and
ventricular-fibrillation (VF). We develop a (a) deep-learning method for the
detection of unbroken and broken spiral waves and (b) the elimination of such
waves, e.g., by the application of low-amplitude control currents in the
cardiac-tissue context. Our method is based on a convolutional neural network
(CNN) that we train to distinguish between patterns with spiral waves S and
without spiral waves NS. We obtain these patterns by carrying out extensive
direct numerical simulations (DNS) of PDE models for cardiac tissue in which
the transmembrane potential V, when portrayed via pseudocolor plots, displays
patterns of electrical activation of types S and NS. We then utilize our
trained CNN to obtain, for a given pseudocolor image of V, a heat map that has
high intensity in the regions where this image shows the cores of spiral waves.
Given this heat map, we show how to apply low-amplitude Gaussian current pulses
to eliminate spiral waves efficiently. Our in silico results are of direct
relevance to the detection and elimination of these arrhythmias because our
elimination of unbroken or broken spiral waves is the mathematical analog of
low-amplitude defibrillation.
