Propagation Of Excitation Waves Research Articles

Nucleation of reaction-diffusion waves on curved surfaces

We study reaction-diffusion waves on curved two-dimensional surfaces, and determine the influence of curvature upon the nucleation and propagation of spatially localized waves in an excitable medium modelled by the generic FitzHugh–Nagumo model. We show that the stability of propagating wave segments depends crucially on the curvature of the surface. As they propagate, they may shrink to the uniform steady state, or expand, depending on whether they are smaller or larger, respectively, than a critical nucleus. This critical nucleus for wave propagation is modified by the curvature acting like an effective space-dependent local spatial coupling, similar to diffuson, thus extending the regime of propagating excitation waves beyond the excitation threshold of flat surfaces. In particular, a negative gradient of Gaussian curvature , as on the outside of a torus surface (positive ), when the wave segment symmetrically extends into the inside (negative ), allows for stable propagation of localized wave segments remaining unchanged in size and shape, or oscillating periodically in size.

Influence of Acidity on Spiral Waves in a Bubble-Free Belousov-Zhabotinsky Reaction with Pyrogallol

Spiral waves are ubiquitously observed in a variety of physical and biological systems, including superconductors, superfluids, CO-oxidation on platinum surfaces, cell aggregation of slime mold and arrhythmia in cardiac tissues. Such spiral waves are uniquely explained by a reaction-diffusion mechanism. Due to easy preparation and convenient detection, the excitable chemical Belousov-Zhabotinsky (BZ) reaction is employed to study spiral waves in experiments. We studied the influence of initial concentration of H 2 SO 4 ((H 2 SO 4 )) on the dynamics of spiral waves in a thin layer of the BZ reaction with pyrogallol. This reaction has an advantage over the classical BZ reaction with malonic acid, as it is bubble-free. We found that the spiral tip, i.e., the organizing center, moved along so-called meandering trajectories with three or four outward petals. In addition, the area occupied by the spiral tip decreased when (H 2 SO 4 ) was increased. We further investigated the dynamics far from the organizing center by measuring properties of propagating fronts. An increase of (H 2 SO 4 ) resulted in a simultaneous decrease of the wavelength and wave period. In contrast, the wave speed grew with (H 2 SO 4 ). Since disturbances by the byproduct CO 2 bubbles are avoided and the wave velocity is sufficiently low, the results present a suitable guideline for further investigations on propagating excitation waves in two- and three-dimensional excitable media, especially observations of wave instabilities in three-dimensional systems using optical tomography.

Finite-element simulation of myocardial electrical excitation

Based on a single-domain model of myocardial conduction, isotropic and anisotropic finite element models of the myocardium are developed allowing excitation wave propagation to be studied. The Aliev-Panfilov phenomenological equations were used as the relations between the transmembrane current and the transmembrane potential. Interaction of an additional source of initial excitation with an excitation wave that passed and the spread of the excitation wave are studied using heart tomograms. A numerical solution is obtained using a splitting algorithm that allows the nonlinear boundary-value problem to be reduced to a sequence of simpler problems: ordinary differential equations and linear boundary-value problems in partial derivatives.

Finite element modeling of impulsive excitation and shear wave propagation in an incompressible, transversely isotropic medium

Elastic properties of materials can be measured by observing shear wave propagation following localized, impulsive excitations and relating the propagation velocity to a model of the material. However, characterization of anisotropic materials is difficult because of the number of elasticity constants in the material model and the complex dependence of propagation velocity relative to the excitation axis, material symmetries, and propagation directions. In this study, we develop a model of wave propagation following impulsive excitation in an incompressible, transversely isotropic (TI) material such as muscle. Wave motion is described in terms of three propagation modes identified by their polarization relative to the material symmetry axis and propagation direction. Phase velocities for these propagation modes are expressed in terms of five elasticity constants needed to describe a general TI material, and also in terms of three constants after the application of two constraints that hold in the limit of an incompressible material. Group propagation velocities are derived from the phase velocities to describe the propagation of wave packets away from the excitation region following localized excitation. The theoretical model is compared to the results of finite element (FE) simulations performed using a nearly incompressible material model with the five elasticity constants chosen to preserve the essential properties of the material in the incompressible limit. Propagation velocities calculated from the FE displacement data show complex structure that agrees quantitatively with the theoretical model and demonstrates the possibility of measuring all three elasticity constants needed to characterize an incompressible, TI material.

Construction of 3D MR image-based computer models of pathologic hearts, augmented with histology and optical fluorescence imaging to characterize action potential propagation

Cardiac computer models can help us understand and predict the propagation of excitation waves (i.e., action potential, AP) in healthy and pathologic hearts. Our broad aim is to develop accurate 3D MR image-based computer models of electrophysiology in large hearts (translatable to clinical applications) and to validate them experimentally. The specific goals of this paper were to match models with maps of the propagation of optical AP on the epicardial surface using large porcine hearts with scars, estimating several parameters relevant to macroscopic reaction-diffusion electrophysiological models. We used voltage-sensitive dyes to image AP in large porcine hearts with scars (three specimens had chronic myocardial infarct, and three had radiofrequency RF acute scars). We first analyzed the main AP waves' characteristics: duration (APD) and propagation under controlled pacing locations and frequencies as recorded from 2D optical images. We further built 3D MR image-based computer models that have information derived from the optical measures, as well as morphologic MRI data (i.e., myocardial anatomy, fiber directions and scar definition). The scar morphology from MR images was validated against corresponding whole-mount histology. We also compared the measured 3D isochronal maps of depolarization to simulated isochrones (the latter replicating precisely the experimental conditions), performing model customization and 3D volumetric adjustments of the local conductivity. Our results demonstrated that mean APD in the border zone (BZ) of the infarct scars was reduced by ~13% (compared to ~318 ms measured in normal zone, NZ), but APD did not change significantly in the thin BZ of the ablation scars. A generic value for velocity ratio (1:2.7) in healthy myocardial tissue was derived from measured values of transverse and longitudinal conduction velocities relative to fibers direction (22 cm/s and 60 cm/s, respectively). The model customization and 3D volumetric adjustment reduced the differences between measurements and simulations; for example, from one pacing location, the adjustment reduced the absolute error in local depolarization times by a factor of 5 (i.e., from 58 ms to 11 ms) in the infarcted heart, and by a factor of 6 (i.e., from 60 ms to 9 ms) in the heart with the RF scar. Moreover, the sensitivity of adjusted conductivity maps to different pacing locations was tested, and the errors in activation times were found to be of approximately 10-12 ms independent of pacing location used to adjust model parameters, suggesting that any location can be used for model predictions.

Photo-Control of Excitation Waves in Cardiomyocyte Tissue Culture

Azobenzene photoswitches were recently reported to control the activity of neural cells and heart beat in leeches. Here, we report photocontrol of excitation of cultured cardiomyocytes that have been made light sensitive by using the addition of azobenzene trimethylammonium bromide (AzoTAB). The trans-isomer of AzoTAB reversibly suppresses spontaneous activity and propagation of excitation waves, whereas the cis-isomer has no detectable effect on the electrical properties of cardiomyocytes. Photoisomerization of AzoTAB was achieved by switching the illumination wavelength, λ, from ~440 nm (trans-isomer) to ~350 nm (cis-isomer). Simultaneous irradiation at two wavelengths with properly chosen intensities allowed for dynamic control of the cis-isomer/trans-isomer ratio and the level of excitability from normal to fully unexcitable. Experiments were conducted by using AzoTAB-treated confluent monolayers of neonatal rat cardiomyocytes. Excitation waves were monitored by using the Ca2+-sensitive fluorescent dye Fluo-4. By projecting two-wavelength illumination patterns onto otherwise uniform cell layers, we were able to create excitable networks with the desired topology, dimensions, and functional properties. The present article discusses potential applications of this technique for the analysis of complex patterns of electrical excitation and cardiac arrhythmias.

Critical scale of propagation influences dynamics of waves in a model of excitable medium

BackgroundDuration and speed of propagation of the pulse are essential factors for stability of excitation waves. We explore the propagation of excitation waves resulting from periodic stimulation of an excitable cable to determine the minimal stable pulse duration in a rate-dependent modification of a Chernyak-Starobin-Cohen reaction-diffusion model.ResultsVarious pacing rate dependent features of wave propagation were studied computationally and analytically. We demonstrated that the complexity of responses to stimulation and evolution of these responses from stable propagation to propagation block and alternans was determined by the proximity between the minimal level of the recovery variable and the critical excitation threshold for a stable solitary pulse.ConclusionThese results suggest that critical propagation of excitation waves determines conditions for transition to unstable rhythms in a way similar to unstable cardiac rhythms. Established conditions were suitably accurate regardless of rate dependent features and the magnitude of the slopes of restitution curves.

Wave–particle duality of single surface plasmon polaritons

When light interacts with metal surfaces, it excites electrons, which can form propagating excitation waves called surface plasmon polaritons. These collective electronic excitations can produce strong electric fields localized to subwavelength distance scales 1 , which makes surface plasmon polaritons interesting for several applications. Many of these potential uses, and in particular those related to quantum networks 2 , r equire a deep understanding of the fundamental quantum properties of surface plasmon polaritons. Remarkably, these collective electron states preserve many key quantum mechanical properties of the photons used to excite them, including entanglement 3,4 and sub-Poissonian statistics 5 . Here, we show that a single-photon source coupled to a silver nanowire excites single surface plasmon polaritons that exhibit both wave and particle properties, similar to those of single photons. Furthermore, the detailed analysis of the spectral interference pattern provides a new method to characterize the dimensions of metallic waveguides with nanometre accuracy.

On Propagation of Excitation Waves in Moving Media: The FitzHugh-Nagumo Model

BackgroundExistence of flows and convection is an essential and integral feature of many excitable media with wave propagation modes, such as blood coagulation or bioreactors.Methods/ResultsHere, propagation of two-dimensional waves is studied in parabolic channel flow of excitable medium of the FitzHugh-Nagumo type. Even if the stream velocity is hundreds of times higher that the wave velocity in motionless medium (), steady propagation of an excitation wave is eventually established. At high stream velocities, the wave does not span the channel from wall to wall, forming isolated excited regions, which we called “restrictons”. They are especially easy to observe when the model parameters are close to critical ones, at which waves disappear in still medium. In the subcritical region of parameters, a sufficiently fast stream can result in the survival of excitation moving, as a rule, in the form of “restrictons”. For downstream excitation waves, the axial portion of the channel is the most important one in determining their behavior. For upstream waves, the most important region of the channel is the near-wall boundary layers. The roles of transversal diffusion, and of approximate similarity with respect to stream velocity are discussed.ConclusionsThese findings clarify mechanisms of wave propagation and survival in flow.

Repolarization of the rabbit cardiac ventricles after an increase of potassium concentration in the plasma

The sequence of ventricular epicardium repolarization in rabbits with hypokalemia is directed from the apex of the heart to its base in accordance with distribution of local repolarization intervals. Under conditions of hyperkalemia, the propagation of excitation wave is inhibited without changes in its sequence; while the duration of repolarization decrease mainly in zones where it was initially long (the base of the right ventricle), as a result of which the distribution of local repolarization intervals becomes more uniform and a relationship between the repolarization and activation sequences is formed.

Streamless aggregation of Dictyostelium in the presence of isopropylidenadenosin

Starving cells of Dictyostelium discoideum undergo a developmental cycle were cAMP is autocatalytically produced and relayed from cell to cell, resulting in the propagation of excitation waves over a spatially extended population. Later on the homogeneous cell layer transforms into a pattern of cell streams directed perpendicular to the cAMP waves. Here we chemically influence aggregation competent cells by isopropylidenadenosin (IPA), an adenosine derivative. It can be assumed, that IPA acts via specific adenosine binding sites localized in the cellular membrane. We find, however, that pattern formation and cellular aggregation under the influence of IPA differ considerably compared to experiments with adenosine. In particular, our observations point towards an inhibitory effect on adenylate cyclase (ACA), the key enzyme in the autocatalytic production process of cAMP inside the cell. Our results suggest the existence of a direct coupling (via intracellular affection) or indirect coupling (via inhibition of cAMP binding) of the specific adenosine receptors to the regulatory circuit that controls cyclic intra- and extracellular cAMP concentration.

Anomalous absorption of radiowaves by small-scale cylindrical irregularities stretched along the magnetic field

Results are presented from calculations of the anomalous absorption of an ordinary radiowave in the ionospheric plasma by a system of small-scale cylindrical density irregularities such that δN < 0. Account is taken of the effect of density perturbations on the propagation of excited cold waves and their conversion into plasma waves. It is shown that this effect attenuates the anomalous absorption of the radiowave. However, for sufficiently large density perturbations (about 6% or more), the absorption is substantial even for irregularities having comparatively large transverse sizes (about 5 m). The fluxes of cold and plasma waves excited by a radiowave in the anomalous absorption process are determined.

Compensation of curvature effects by illumination

Front deformation of initially planar excitation waves can be observed in nonplanar media or in spatially heterogeneously illuminated systems. The deformation of propagating reaction–diffusion waves in either of these systems has been investigated earlier separately. Here we present a combination of both heterogeneous systems, which can lead to a compensation of wave deformations. Our theoretical analysis of the evolution of propagating excitation waves, based on the framework of a kinematical theory, shows that the curvature effect can be compensated by illumination. Supporting experiments were performed with the light-sensitive Belousov–Zhabotinsky system.

Microgravity dependence of excitable biological and physicochemical media

Neuronal tissue and especially the central nervous system (CNS) is an excitable medium. Self-organisation, pattern formation, and propagating excitation waves as typical characteristics in excitable media consequently have been found in neuronal tissue. The properties of such phenomena in excitable media do critically depend on the parameters (i.e., electromagnetic fields, temperature, chemical drugs) of the system and on small external forces to which gravity belongs. The spreading depression, a propagating excitation depression wave of neuronal activity, is one of the best described of the those wave phenomena in the CNS. Especially in the retina as a true part of the CNS it can be easily observed with optical techniques due to the high intrinsic optical signal of this tissue. Another of such waves in neuronal tissue is the propagating action potential in nerve fibres. In this paper, data from our laboratories concerning the influence of gravity on the velocity of propagating waves in excitable media are summarized mainly in terms of the retinal spreading depression and propagating action potentials. Additionally, we have used waves in gels of the Belousov-Zhabotinsky reaction as the physicochemical model system of biological activity as the properties of these waves follow the same theories as the spreading depression and action potentials and they have some striking similarities in wave behavior. Thus propagating Belousov-Zhabotinsky waves are described by their gravity dependence.

Spatiotemporal Networks in Addressable Excitable Media

Spatiotemporal networks are studied in a photosensitive Belousov-Zhabotinsky medium that allows both local and nonlocal transmission of excitation. Local transmission occurs via propagating excitation waves, while nonlocal transmission takes place by nondiffusive jumps to destination sites linked to excited sites in the medium. Static, dynamic, and domain link networks are experimentally and computationally characterized. Transitions to synchronized behavior are exhibited with increasing link density, and power-law relations are observed for first-coverage time as a function of link probability.

Increase of the Transparency for Cosmic Radio Waves due to the Decrease of Density of the Ionosphere Caused by Acoustic Waves

Ultra low frequency (ULF) acoustic waves, propagating in the ionosphere, may produce a decrease of the ionospheric density of the F-layer. In turn, decreasing the density of the ionospheric plasma results in the increase of the transparency of the ionosphere for cosmic radio waves. In this paper, simulations of nonlinear frequency down-conversion of extremely low frequency (ELF) acoustic waves into ULF acoustic waves are presented. The propagation of excited ULF waves within the non-isothermal ionosphere is simulated, and the increase of the transparency of the ionospheric F-layer for cosmic radio waves due to plasma density modulation is also considered. We argue that this phenomenon takes place jointly with an increase of the transparency caused by the periodic structure of extremely low frequency (ELF) acoustic waves in the E-layer of the ionosphere. Both phenomena have previously been confirmed experimentally.

Control of spiral waves in excitable media

The propagation of spiral-shaped excitation waves is a prominent example of self-organization in nonequilibrium systems. The properties of these waves are studied in a chemical model system––the Belousov–Zhabotinsky (BZ) reaction––and in various biological excitable media such as heart or neuronal tissue. An important aspect lies in finding tools for external control of these waves. A light-sensitive variant of the BZ reaction has proven to be a suitable system for investigating local and global control by means of a time-dependent uniform illumination. A local feedback control, in which short light pulses are applied at instants corresponding to the passage of a wave front through a measuring point, results in a drift of the spiral center along a discrete set of stable circular orbits. In a confined-domain control, where the illumination intensity is taken to be proportional to the average wave activity observed in a circular domain of the reaction layer, the stabilization and destabilization of spiral wave trajectories are demonstrated. The presented methods could be useful for the control of biological excitation waves.

MODELING EXCITATION AND PROPAGATION OF ACTION POTENTIALS ACROSS INHOMOGENEOUS VENTRICULAR TISSUE

Heterogeneity in the electrical activity across the ventricular wall might result from transmural differences in myocardial membrane ionic current densities. Computational models of endo- and epi-cardial action potentials of guinea-pig myocytes were developed, assuming transmural differences in the ionic current densities and kinetics of i Kr and i Ks . The cell models were able to reproduce the characteristics of action potentials of endo and epi cells. One- and two-dimensional models of ventricular tissue were also developed to study the effects of transmural heterogeneity on the propagation of excitation waves across the ventricle wall. It was shown that intercellular coupling reduces the transmural heterogeneity across the ventricle wall.

Standing excitation waves in the heart induced by strong alternating electric fields.

We studied the effect of sinusoidal electric fields on cardiac tissue both experimentally and numerically. We found that periodic forcing at 5-20 Hz using voltage applied in the bathing solution could stop the propagation of excitation waves by producing standing waves of membrane depolarization. These patterns were independent of the driving frequency in contrast to classical standing waves. The stimulus strength required for pattern formation was large compared to the excitation threshold. A novel tridomain representation of cardiac tissue was required to reproduce this behavior numerically.

Excitation Wave Propagation as a Possible Mechanism for Signal Transmission in Pancreatic Islets of Langerhans

In response to glucose application, β-cells forming pancreatic islets of Langerhans start bursting oscillations of the membrane potential and intracellular calcium concentration, inducing insulin secretion by the cells. Until recently, it has been assumed that the bursting activity of β-cells in a single islet of Langerhans is synchronized across the whole islet due to coupling between the cells. However, time delays of several seconds in the activity of distant cells are usually observed in the islets of Langerhans, indicating that electrical/calcium wave propagation through the islets can occur. This work presents both experimental and theoretical evidence for wave propagation in the islets of Langerhans. Experiments with Fura-2 fluorescence monitoring of spatiotemporal calcium dynamics in the islets have clearly shown such wave propagation. Furthermore, numerical simulations of the model describing a cluster of electrically coupled β-cells have supported our view that the experimentally observed calcium waves are due to electric pulses propagating through the cluster. This point of view is also supported by independent experimental results. Based on the model equations, an approximate analytical expression for the wave velocity is introduced, indicating which parameters can alter the velocity. We point to the possible role of the observed waves as signals controlling the insulin secretion inside the islets of Langerhans, in particular, in the regions that cannot be reached by any external stimuli such as high glucose concentration outside the islets.