Entropy Rate Maps of Complex Excitable Dynamics in Cardiac Monolayers

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.

[1]  L. Glass,et al.  Pacemaker interactions induce reentrant wave dynamics in engineered cardiac culture. , 2012, Chaos.

[2]  José Jalife,et al.  Rotors and the Dynamics of Cardiac Fibrillation , 2013, Circulation research.

[3]  Will Tribbey,et al.  Numerical Recipes: The Art of Scientific Computing (3rd Edition) is written by William H. Press, Saul A. Teukolsky, William T. Vetterling, and Brian P. Flannery, and published by Cambridge University Press, © 2007, hardback, ISBN 978-0-521-88068-8, 1235 pp. , 1987, SOEN.

[4]  Jung,et al.  Coherent structure analysis of spatiotemporal chaos , 2000, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[5]  Peter Grassberger,et al.  Entropy estimation of symbol sequences. , 1996, Chaos.

[6]  M. Gilli,et al.  Understanding Complex Systems , 1980 .

[7]  J. E. Glynn,et al.  Numerical Recipes: The Art of Scientific Computing , 1989 .

[8]  F. Fenton,et al.  Visualization of spiral and scroll waves in simulated and experimental cardiac tissue , 2008 .

[9]  R. Gray,et al.  Spatial and temporal organization during cardiac fibrillation , 1998, Nature.

[10]  S. Luther,et al.  Eliminating pinned spiral waves in cardiac monolayer by far field pacing , 2014, 2014 8th Conference of the European Study Group on Cardiovascular Oscillations (ESGCO).

[11]  Synchronization patterns in transient spiral wave dynamics. , 2011, Physical review. E, Statistical, nonlinear, and soft matter physics.

[12]  Annick Lesne,et al.  Estimating Kolmogorov Entropy from Recurrence Plots , 2015 .

[13]  Hannu Olkkonen,et al.  Computation of Hilbert Transform via Discrete Cosine Transform , 2010, J. Signal Inf. Process..

[14]  R. Gray,et al.  An Experimentalist's Approach to Accurate Localization of Phase Singularities during Reentry , 2004, Annals of Biomedical Engineering.

[15]  F. Fenton,et al.  Modeling wave propagation in realistic heart geometries using the phase-field method. , 2005, Chaos.

[16]  Dwight Barkley,et al.  Barkley model , 2008, Scholarpedia.

[17]  Jack M. Rogers,et al.  Combined phase singularity and wavefront analysis for optical maps of ventricular fibrillation , 2004, IEEE Transactions on Biomedical Engineering.

[18]  R. Aliev,et al.  A simple two-variable model of cardiac excitation , 1996 .

[19]  Alvin Shrier,et al.  Global organization of dynamics in oscillatory heterogeneous excitable media. , 2005, Physical review letters.

[20]  D. Barkley A model for fast computer simulation of waves in excitable media , 1991 .