Reconstruction of phase maps from the configuration of phase singularities in two-dimensional manifolds

Herlin, Antoine; Jacquemet, Vincent

doi:10.1103/physreve.85.051916

Cited by 4 publications

(2 citation statements)

References 8 publications

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“…A straight forward approach is therefore to look at the dynamics of spiral cores, which includes movement, pairwise appearance and annihilation [8]. Spiral core centers manifest as singularities in the phase map, and many efficient algorithms have been developed to identify and track them in their temporal evolution (e.g., [9,10]).…”

Section: Phase Singularity Analysismentioning

confidence: 99%

Entropy Rate Maps of Complex Excitable Dynamics in Cardiac Monolayers

Schlemmer

Berg

Shajahan

et al. 2015

Entropy

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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.

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Section: Phase Singularity Analysismentioning

confidence: 99%

Entropy Rate Maps of Complex Excitable Dynamics in Cardiac Monolayers

Schlemmer

Berg

Shajahan

et al. 2015

Entropy

View full text Add to dashboard Cite

show abstract

“…The analysis of phase singularities is a well-established method for the quantification of complexity in excitable media [44]. It is particularly useful for the analysis of cardiac dynamics [33,59,28,26,97,86,35].…”

Section: Analysis Of Phase Singularitiesmentioning

confidence: 99%

Intermittent Complexity Fluctuations during Ventricular Fibrillation

Alexander¹

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A statistical model of false negative and false positive detection of phase singularities

Jacquemet

2017

Chaos: An Interdisciplinary Journal of Nonlinear Science

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The complexity of cardiac fibrillation dynamics can be assessed by analyzing the distribution of phase singularities (PSs) observed using mapping systems. Interelectrode distance, however, limits the accuracy of PS detection. To investigate in a theoretical framework the PS false negative and false positive rates in relation to the characteristics of the mapping system and fibrillation dynamics, we propose a statistical model of phase maps with controllable number and locations of PSs. In this model, phase maps are generated from randomly distributed PSs with physiologically-plausible directions of rotation. Noise and distortion of the phase are added. PSs are detected using topological charge contour integrals on regular grids of varying resolutions. Over 100 × 106 realizations of the random field process are used to estimate average false negative and false positive rates using a Monte-Carlo approach. The false detection rates are shown to depend on the average distance between neighboring PSs expressed in units of interelectrode distance, following approximately a power law with exponents in the range of 1.14 to 2 for false negatives and around 2.8 for false positives. In the presence of noise or distortion of phase, false detection rates at high resolution tend to a non-zero noise-dependent lower bound. This model provides an easy-to-implement tool for benchmarking PS detection algorithms over a broad range of configurations with multiple PSs.

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Reconstruction of phase maps from the configuration of phase singularities in two-dimensional manifolds

Cited by 4 publications

References 8 publications

Entropy Rate Maps of Complex Excitable Dynamics in Cardiac Monolayers

Entropy Rate Maps of Complex Excitable Dynamics in Cardiac Monolayers

Intermittent Complexity Fluctuations during Ventricular Fibrillation

A statistical model of false negative and false positive detection of phase singularities

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