Control of scroll wave turbulence using resonant perturbations

Turbulence of scroll waves is a sort of spatio-temporal chaos that exists in three-dimensional excitable media. Cardiac tissue and the Belousov-Zhabotinsky reaction are examples of such media. In cardiac tissue, chaotic behaviour is believed to underlie fibrillation which, without intervention, precedes cardiac death. In this study we investigate suppression of the turbulence using stimulation of two different types, "modulation of excitability" and "extra transmembrane current". With cardiac defibrillation in mind, we used a single pulse as well as repetitive extra current with both constant and feedback controlled frequency. We show that turbulence can be terminated using either a resonant modulation of excitability or a resonant extra current. The turbulence is terminated with much higher probability using a resonant frequency perturbation than a non-resonant one. Suppression of the turbulence using a resonant frequency is up to fifty times faster than using a non-resonant frequency, in both the modulation of excitability and the extra current modes. We also demonstrate that resonant perturbation requires strength one order of magnitude lower than that of a single pulse, which is currently used in clinical practice to terminate cardiac fibrillation. Our results provide a robust method of controlling complex chaotic spatio-temporal processes. Resonant drift of spiral waves has been studied extensively in two dimensions, however, these results show for the first time that it also works in three dimensions, despite the complex nature of the scroll wave turbulence.Comment: 13 pages, 12 figures, submitted to Phys Rev E 2008/06/13. Last version: 2008/09/18, after revie

Self-organization of conducting pathways explains electrical wave propagation in cardiac tissues with high fraction of nonconducting cells

Cardiac fibrosis occurs in many forms of heart disease and is considered to be one of the main arrhythmogenic factors. Regions with a high density of fibroblasts are likely to cause blocks of wave propagation that give rise to dangerous cardiac arrhythmias. Therefore, studies of the wave propagation through these regions are very important, yet the precise mechanisms leading to arrhythmia formation in fibrotic cardiac tissue remain poorly understood. Particularly, it is not clear how wave propagation is organized at the cellular level, as experiments show that the regions with a high percentage of fibroblasts (65-75%) are still conducting electrical signals, whereas geometric analysis of randomly distributed conducting and non-conducting cells predicts connectivity loss at 40% at the most (percolation threshold). To address this question, we used a joint in vitro-in silico approach, which combined experiments in neonatal rat cardiac monolayers with morphological and electrophysiological computer simulations. We have shown that the main reason for sustainable wave propagation in highly fibrotic samples is the formation of a branching network of cardiomyocytes. We have successfully reproduced the morphology of conductive pathways in computer modelling, assuming that cardiomyocytes align their cytoskeletons to fuse into cardiac syncytium. The electrophysiological properties of the monolayers, such as conduction velocity, conduction blocks and wave fractionation, were reproduced as well. In a virtual cardiac tissue, we have also examined the wave propagation at the subcellular level, detected wavebreaks formation and its relation to the structure of fibrosis and, thus, analysed the processes leading to the onset of arrhythmias. © 2019 Kudryashova et al

Controlling Excitable Waves in Cultured Cardio Myocyte(Poster session 1, New Frontiers in Colloidal Physics : A Bridge between Micro- and Macroscopic Concepts in Soft Matter)

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Maze solvers demystified and some other thoughts

There is a growing interest towards implementation of maze solving in spatially-extended physical, chemical and living systems. Several reports of prototypes attracted great publicity, e.g. maze solving with slime mould and epithelial cells, maze navigating droplets. We show that most prototypes utilise one of two phenomena: a shortest path in a maze is a path of the least resistance for fluid and current flow, and a shortest path is a path of the steepest gradient of chemoattractants. We discuss that substrates with so-called maze-solving capabilities simply trace flow currents or chemical diffusion gradients. We illustrate our thoughts with a model of flow and experiments with slime mould. The chapter ends with a discussion of experiments on maze solving with plant roots and leeches which show limitations of the chemical diffusion maze-solving approach.Comment: This is a preliminary version of the chapter to be published in Adamatzky A. (Ed.) Shortest path solvers. From software to wetware. Springer, 201

Quasiperiodic Patterns in Boundary-Modulated Excitable Waves

We investigate the impact of the domain shape on wave propagation in excitable media. Channelled domains with sinusoidal boundaries are considered. Trains of fronts generated periodically at an extreme of the channel are found to adopt a quasiperiodic spatial configuration stroboscopically frozen in time. The phenomenon is studied in a model for the photo-sensitive Belousov-Zabotinsky reaction, but we give a theoretical derivation of the spatial return maps prescribing the height and position of the successive fronts that is valid for arbitrary excitable reaction-diffusion systems.Comment: 4 pages (figures included

The study of the functionality of cardiomyocytes obtained from induced pluripotent stem cells for the modeling of cardiac arrhythmias based on long QT syndrome

There are risk factors that lead the normal conduction of excitation in the heart into a chaotic one. These factors include hereditary and acquired channelopathies. Many dangerous changes in the work of the heart can be identified using the patient’s electrocardiogram. Such relatively easily detectable changes include the long QT interval syndrome (LQTS). Despite a relatively high prevalence of hereditary LQTS, to which it is necessary to add both hereditary and induced LQTS as well as the ease of detection on the ECG, the mechanism of reentry formation in this syndrome is still un­known. What should be noted is a high variability of the hereditary syndrome and the fact of the connection between the increase in the heart rate and the risk of cardiac arrest. After an electrophysiological study on individual cardiac cells from patients with the LQT syndrome, it became apparent that the search for a mechanism for the transition of the normal heart rhythm to chaotic and fibrillation cannot be limited to recording ion currents in single cells. To solve this problem, we need a model of the behavior of cardiac tissue which reflects the relationship of various factors and the risk of reentry. In order to create an experimental model of LQTS in our work, the iPSC of a pati­ent-specific line from a healthy patient was differentiated into a monolayer of cardiac cells and the parameters of the excitation propagation were studied depending on the stage of differentiation. It was shown that a stable value of the propagation velocity and the response to periodic stimulation in the range of physiological values, are reached after the 30th day of dif­ferentiation

Theory of spiral wave dynamics in weakly excitable media: asymptotic reduction to a kinematic model and applications

In a weakly excitable medium, characterized by a large threshold stimulus, the free end of an isolated broken plane wave (wave tip) can either rotate (steadily or unsteadily) around a large excitable core, thereby producing a spiral pattern, or retract causing the wave to vanish at boundaries. An asymptotic analysis of spiral motion and retraction is carried out in this weakly excitable large core regime starting from the free-boundary limit of the reaction-diffusion models, valid when the excited region is delimited by a thin interface. The wave description is shown to naturally split between the tip region and a far region that are smoothly matched on an intermediate scale. This separation allows us to rigorously derive an equation of motion for the wave tip, with the large scale motion of the spiral wavefront slaved to the tip. This kinematic description provides both a physical picture and exact predictions for a wide range of wave behavior, including: (i) steady rotation (frequency and core radius), (ii) exact treatment of the meandering instability in the free-boundary limit with the prediction that the frequency of unstable motion is half the primary steady frequency (iii) drift under external actions (external field with application to axisymmetric scroll ring motion in three-dimensions, and spatial or/and time-dependent variation of excitability), and (iv) the dynamics of multi-armed spiral waves with the new prediction that steadily rotating waves with two or more arms are linearly unstable. Numerical simulations of FitzHug-Nagumo kinetics are used to test several aspects of our results. In addition, we discuss the semi-quantitative extension of this theory to finite cores and pinpoint mathematical subtleties related to the thin interface limit of singly diffusive reaction-diffusion models

Order Parameter Equations for Front Transitions: Planar and Circular Fronts

Near a parity breaking front bifurcation, small perturbations may reverse the propagation direction of fronts. Often this results in nonsteady asymptotic motion such as breathing and domain breakup. Exploiting the time scale differences of an activator-inhibitor model and the proximity to the front bifurcation, we derive equations of motion for planar and circular fronts. The equations involve a translational degree of freedom and an order parameter describing transitions between left and right propagating fronts. Perturbations, such as a space dependent advective field or uniform curvature (axisymmetric spots), couple these two degrees of freedom. In both cases this leads to a transition from stationary to oscillating fronts as the parity breaking bifurcation is approached. For axisymmetric spots, two additional dynamic behaviors are found: rebound and collapse.Comment: 9 pages. Aric Hagberg: http://t7.lanl.gov/People/Aric/; Ehud Meron: http://www.bgu.ac.il/BIDR/research/staff/meron.htm

Nuclear spin driven quantum relaxation in LiY_0.998Ho_0.002F_4

Staircase hysteresis loops of the magnetization of a LiY_0.998Ho_0.002F_4 single crystal are observed at subkelvin temperatures and low field sweep rates. This behavior results from quantum dynamics at avoided level crossings of the energy spectrum of single Ho^{3+} ions in the presence of hyperfine interactions. Enhanced quantum relaxation in constant transverse fields allows the study of the relative magnitude of tunnel splittings. At faster sweep rates, non-equilibrated spin-phonon and spin-spin transitions, mediated by weak dipolar interactions, lead to magnetization oscillations and additional steps.Comment: 5 pages, 5 eps figures, using RevTe

Reappraising foreground contamination in the COBE-DMR data

With the advent of all-sky H-Alpha surveys it is possible to determine a reliable free-free template of the diffuse interstellar medium (Dickinson, Davies & Davis 2003) which can be used in conjunction with the synchrotron and dust templates to correct CMB observations for diffuse Galactic foregrounds. We have used the COBE-DMR data at 31.5, 53 and 90 GHz and employed cross- correlation techniques to re-evaluate the foreground contributions, particularly that due to dust which is known to be correlated with H-Alpha (and free-free) emission.The DMR microwave maps are found to contain, as well as the expected synchrotron and free-free components, a component tightly correlated to the 140 micron dust maps of DIRBE. At 31.5, 53 and 90 GHz this emission is 6.3 +/- 0.6, 2.4 +/- 0.4 and 2.2 +/- 0.4 microK/(MJy/sr) at 140 microns respectively. When corrected for the contribution from thermal dust following model 7 of Finkbeiner, Davis & Schlegel (1999), a strong anomalous dust emission component remains, which is well-fitted by a frequency spectrum of the form $\nu^{-\beta}$ where beta ~ 2.5 in the DMR frequency range; this is the dominant foreground at 31.5 GHz. The result implies the presence of an emission component with a dust-like morphology but a synchrotron-like spectrum. We discuss the possible origins of this component and compare it with the recent WMAP interpretation. The better knowledge of the individual foregrounds provided by the present study enables a larger area of the sky (|b|>15) to be used to re-appraise the CMB quadrupole normalisation, Qrms-PS, and the scalar perturbations spectral index, n. We find Qrms-PS=15.2^{+2.8}_{-2.3} with a power-law spectral index of n=1.2 +/- 0.2. These values are consistent with previous COBE-DMR analyses and the WMAP 1-year analysis.Comment: 17 pages, 6 figures, replaced with version accepted for publication in MNRAS, contains new section comparing results to the WMAP foreground studie