Next Article in Journal
Do Transitive Preferences Always Result in Indifferent Divisions?
Next Article in Special Issue
Entropy Measures in the Assessment of Heart Rate Variability in Patients with Cardiodepressive Vasovagal Syncope
Previous Article in Journal
Instantaneous 3D EEG Signal Analysis Based on Empirical Mode Decomposition and the Hilbert–Huang Transform Applied to Depth of Anaesthesia
Previous Article in Special Issue
Analyses of Heart Rate, Respiration and Cardiorespiratory Coupling in Patients with Schizophrenia
Article Menu

Export Article

Open AccessArticle
Entropy 2015, 17(3), 950-967;

Entropy Rate Maps of Complex Excitable Dynamics in Cardiac Monolayers

Max Planck Institute for Dynamics and Self-Organization, Am Faßberg 17, 37077 Göttingen, Germany
Institute for Nonlinear Dynamics, Georg-August-Universität Göttingen, Am Faßberg 17,37077 Göttingen, Germany
Author to whom correspondence should be addressed.
Academic Editor: Niels Wessel
Received: 16 December 2014 / Revised: 12 February 2015 / Accepted: 13 February 2015 / Published: 26 February 2015
(This article belongs to the Special Issue Entropy and Cardiac Physics)
Full-Text   |   PDF [2371 KB, uploaded 26 February 2015]


The characterization of spatiotemporal complexity remains a challenging task. This holds in particular for the analysis of data from fluorescence imaging (optical mapping), which allows for the measurement of membrane potential and intracellular calcium at high spatial and temporal resolutions and, therefore, allows for an investigation of cardiac dynamics. Dominant frequency maps and the analysis of phase singularities are frequently used for this type of excitable media. These methods address some important aspects of cardiac dynamics; however, they only consider very specific properties of excitable media. To extend the scope of the analysis, we present a measure based on entropy rates for determining spatiotemporal complexity patterns of excitable media. Simulated data generated by the Aliev–Panfilov model and the cubic Barkley model are used to validate this method. Then, we apply it to optical mapping data from monolayers of cardiac cells from chicken embryos and compare our findings with dominant frequency maps and the analysis of phase singularities. The studies indicate that entropy rate maps provide additional information about local complexity, the origins of wave breakup and the development of patterns governing unstable wave propagation. View Full-Text
Keywords: excitable media; fluorescence imaging; optical mapping; pattern formation; spatiotemporal cardiac dynamics excitable media; fluorescence imaging; optical mapping; pattern formation; spatiotemporal cardiac dynamics
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).

Share & Cite This Article

MDPI and ACS Style

Schlemmer, A.; Berg, S.; Shajahan, T.K.; Luther, S.; Parlitz, U. Entropy Rate Maps of Complex Excitable Dynamics in Cardiac Monolayers. Entropy 2015, 17, 950-967.

Show more citation formats Show less citations formats

Related Articles

Article Metrics

Article Access Statistics



[Return to top]
Entropy EISSN 1099-4300 Published by MDPI AG, Basel, Switzerland RSS E-Mail Table of Contents Alert
Back to Top