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

Existence of a rotating wave pattern in a disk for a wave front interaction model

[[abstract]]We study the rotating wave patterns in an excitable medium in a disk. This wave pattern is rotating along the given disk boundary with a constant angular speed. To study this pattern we use the wave front interaction model proposed by Zykov in 2007. This model is derived from the FitzHugh-Nagumo equation and it can be described by two systems of ordinary differential equations for wave front and wave back respectively. Using a delicate shooting argument with the help of the comparison principle, we derive the existence and uniqueness of rotating wave patterns for any admissible angular speed with convex front in a given disk.[[incitationindex]]SCI[[booktype]]紙本[[booktype]]電子

Genetic Aspects of Pathogenesis of Congenital Spastic Cerebral Paralysis

Congenital spastic cerebral palsy (СР) is a large group of non-progressive disorders of the nervous system. The basis of the pathogenesis of these conditions is considered the impact of many factors. The clinical diversity of the disease and the syndromic principle of classification determine the existing uncertainties in the diagnosis of these diseases. The multifactorial nature of the underlying brain lesions is obvious and beyond doubt. The volume of information accumulated to date does not allow one to exclude the role and significance of the direct effect of acute asphyxiation in childbirth on a fetus normally formed during pregnancy, the role of infectious brain lesions, and disorders of neuronal migration. It is impossible to ignore the dependence of the clinical picture of the disease on what stage of ontogenesis the impact of the damaging agent occurs. As one of the pathogenetic factors, the genetic determinism of the phenotype of the clinical picture of a disease is fairly considered. This review focuses on the genetic aspects of the pathogenesis of this pathology. The information on monogenic mechanisms of inheritance is analyzed in detail. Such genetically determined mechanisms of pathogenesis as the inheritance of prerequisites for brain trauma in the perinatal period are considered separately. The new clinically significant variants of chromosomal mutations found in patients with CР are reviewed in detail,  the evidence of the influence of genetic factors on the development of cerebral palsy in the absence of a pronounced monogenic cause of the disease, obtained through twin studies, is reviewed.  Lit search of polymorphisms markers of predisposition to the development of cerebral palsy genes of the folate cycle, genes of glutamate receptors, the gene of apolipoprotein and of the gene for the transcription factor of oligodendrocytes (OLIG2) in Detail the role of epigenetic effects on the activity of genes coding for mitochondrial proteins

Dynamics of lattice spins as a model of arrhythmia

We consider evolution of initial disturbances in spatially extended systems with autonomous rhythmic activity, such as the heart. We consider the case when the activity is stable with respect to very smooth (changing little across the medium) disturbances and construct lattice models for description of not-so-smooth disturbances, in particular, topological defects; these models are modifications of the diffusive XY model. We find that when the activity on each lattice site is very rigid in maintaining its form, the topological defects - vortices or spirals - nucleate a transition to a disordered, turbulent state.Comment: 17 pages, revtex, 3 figure

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

The study of TIM polymer composite materials thermal conductivity

A recent trend in electronic technology deals with a sharp performance increase within decrease dimensions and mass of devices. High-performance thermal interface materials (TIM) primarily thermal pastes are indispensable to application. A number of filler materials: ceramics (aluminum nitride, silicon carbide, alumina) metals (aluminum, copper) and graphite were considered to apply. The data containing average particles size, specific surface area, and maximal volume and mass fraction for various materials was obtained. The thermal conductivity of samples with aluminum and graphite dramatically exceed values obtained within mathematical models' calculation. The highest thermal conductivity values were obtained for SiC (1.37 W/(m·K)), AlN (1.09 W/(m·K)), C (2.85 W/(m·K)) and Al (1.20 W/(m·K)), that mad the mentioned above materials the most promising for high-performance thermal pastes. © 2019 Author(s)

The study of TIM polymer composite materials thermal conductivity

Support by the Ministry of Education and Science of the Russian Federation is gratefully acknowledged: calculation results (chapter 3.1) were obtained under research project # 3.6064.2017/8.9 and experimental results (chapter 3.2) - under project # 3.10704.2018/11.12

Theory of Spike Spiral Waves in a Reaction-Diffusion System

We discovered a new type of spiral wave solutions in reaction-diffusion systems --- spike spiral wave, which significantly differs from spiral waves observed in FitzHugh-Nagumo-type models. We present an asymptotic theory of these waves in Gray-Scott model. We derive the kinematic relations describing the shape of this spiral and find the dependence of its main parameters on the control parameters. The theory does not rely on the specific features of Gray-Scott model and thus is expected to be applicable to a broad range of reaction-diffusion systems.Comment: 4 pages (REVTeX), 2 figures (postscript), submitted to Phys. Rev. Let

Controlling domain patterns far from equilibrium

A high degree of control over the structure and dynamics of domain patterns in nonequilibrium systems can be achieved by applying nonuniform external fields near parity breaking front bifurcations. An external field with a linear spatial profile stabilizes a propagating front at a fixed position or induces oscillations with frequency that scales like the square root of the field gradient. Nonmonotonic profiles produce a variety of patterns with controllable wavelengths, domain sizes, and frequencies and phases of oscillations.Comment: Published version, 4 pages, RevTeX. More at http://t7.lanl.gov/People/Aric