Detecting spiral wave tips using deep learning

Henning Lilienkamp,Thomas Lilienkamp

doi:10.1038/s41598-021-99069-3

Abstract

The chaotic spatio-temporal electrical activity during life-threatening cardiac arrhythmias like ventricular fibrillation is governed by the dynamics of vortex-like spiral or scroll waves. The organizing centers of these waves are called wave tips (2D) or filaments (3D) and they play a key role in understanding and controlling the complex and chaotic electrical dynamics. Therefore, in many experimental and numerical setups it is required to detect the tips of the observed spiral waves. Most of the currently used methods significantly suffer from the influence of noise and are often adjusted to a specific situation (e.g. a specific numerical cardiac cell model). In this study, we use a specific type of deep neural networks (UNet), for detecting spiral wave tips and show that this approach is robust against the influence of intermediate noise levels. Furthermore, we demonstrate that if the UNet is trained with a pool of numerical cell models, spiral wave tips in unknown cell models can also be detected reliably, suggesting that the UNet can in some sense learn the concept of spiral wave tips in a general way, and thus could also be used in experimental situations in the future (ex-vivo, cell-culture or optogenetic experiments).

Highlights

The chaotic spatio-temporal electrical activity during life-threatening cardiac arrhythmias like ventricular fibrillation is governed by the dynamics of vortex-like spiral or scroll waves
In order to cover a broad range of cardiac cell models, we investigate in this study four different models, ranging from simplified ones to more complex ionic cell models, which describe the electrical action potential dynamics of cardiomyocytes: a three-variable minimal model[27] describing the porcine electrophysiology, the Bueno-Orovio–Cherry–Fenton m odel[28] with two different sets of parameters ( BOCFa and BOCFb, respectively), and the Luo-Rudy-I m odel[29] (LR-I)
After an exemplary demonstration of how the UNet predicts the location of spiral wave tips in the first subsection, we investigate in this study mainly two aspects: In the following subsection, we show what the influence of noise on the prediction accuracy is, which is measured in terms of the Fscore

Summary

Introduction

The chaotic spatio-temporal electrical activity during life-threatening cardiac arrhythmias like ventricular fibrillation is governed by the dynamics of vortex-like spiral or scroll waves. Spiral or scroll waves can be found and studied in 3D chemical reactions (scroll waves), like the Belousov–Zhabotinsky r eaction[14], in arrays of non-linear Chua’s circuits[15] or 2D lattices of van der Pol oscillators[16] For this purpose of tracking the positions of spiral wave tips over time, several different methods exist which are based on, for example, differentiating between different states of a grid c ell[17,18], finding intersections of contour lines[19], finding points of zero normal velocity of isopotential lines[20], investigating the curvature along isopotential lines[21], or using the pivot method[22].

Methods

Results

Conclusion