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Front. Phys. | doi: 10.3389/fphy.2018.00039

Spatiotemporal Permutation Entropy as a Measure for Complexity of Cardiac Arrhythmia

 Alexander Schlemmer1, 2*,  Sebastian Berg1, 2, Thomas Lilienkamp1, 2,  Stefan Luther1, 2, 3, 4, 5 and  Ulrich Parlitz1, 2, 3
  • 1Max-Planck-Institut für Dynamik und Selbstorganisation, Germany
  • 2Institute for Nonlinear Dynamics, Fakultät für Physik, Georg-August-Universität Göttingen, Germany
  • 3Partner site Goettingen, Deutsches Zentrum für Herz-Kreislaufforschung (DZHK), Germany
  • 4Institute of Pharmacology and Toxicology, Universitätsmedizin Göttingen, Germany
  • 5Department of Physics and Department of Bioengineering, Northeastern University, United States

Permutation entropy (PE) is a robust quantity for measuring the complexity of time series. In the cardiac community it is predominantly used in the context of electrocardiogram (ECG) signal analysis for diagnoses and predictions with a major application found in heart rate variability parameters. In this article we are combining spatial and temporal PE to form a spatiotemporal PE that captures both, complexity of spatial structures and temporal complexity at the same time. We demonstrate that the spatiotemporal PE (STPE) quantifies complexity using two datasets from simulated cardiac arrhythmia and compare it to phase singularity analysis and spatial PE (SPE).
These datasets simulate ventricular fibrillation (VF) on a two-dimensional and a three-dimensional medium using the Fenton-Karma model.
We show that SPE and STPE are robust against noise and demonstrate its usefulness for extracting complexity features at different spatial scales.

Keywords: permutation entropy, cardiac arrhythmia, Fenton-Karma simulation, Complexity, excitable media, Phase singularities

Received: 15 Jan 2018; Accepted: 13 Apr 2018.

Edited by:

Alain J. Pumir, École Normale Supérieure de Lyon, France

Reviewed by:

Tommaso Gili, Enrico Fermi Center
Jacobo Cal-Gonzalez, Medizinische Universität Wien, Austria
Sergio Alonso, Universitat Politecnica de Catalunya, Spain  

Copyright: © 2018 Schlemmer, Berg, Lilienkamp, Luther and Parlitz. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) and the copyright owner are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.

* Correspondence: Mr. Alexander Schlemmer, Max-Planck-Institut für Dynamik und Selbstorganisation, Göttingen, Germany,