Abstract
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.
Highlights
The normal pumping of blood by mammalian hearts is initiated by electrical waves of excitation that propagate through cardiac tissue and induce cardiac contractions
The abnormal propagation of such waves can lead to cardiac arrhythmias, such as ventricular tachycardia (VT) and ventricular fibrillation (VF), which cause sudden cardiac death (SCD), which is among the leading causes of death in the industrialized world [1,2,3]
Our method of defibrillation using convolutional neural network (CNN) uses the image; the detection of spiral waves is crucial for the success of our defibrillation scheme
Summary
The normal pumping of blood by mammalian hearts is initiated by electrical waves of excitation that propagate through cardiac tissue and induce cardiac contractions. The principal cause of VT and VF are spiral or scroll waves of electrical activation in cardiac tissue; unbroken (broken) spiral or scroll waves are associated with VT (VF) [6,7,8] Such waves have been studied, e.g., in ex vivo [9,10,11] and in vivo [12,13,14] in mammalian hearts, in vitro [6,7,8,15] in cultures of cardiac myocytes, and in silico [16,17,18] in mathematical models for cardiac tissue. We demonstrate how to eliminate the broken or unbroken spiral waves by applying low-amplitude current stimuli at those positions at which the heatmap has high intensity; this is the mathematical analog of defibrillation [20]
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