Wavefront Dynamics Research Articles

Wavy fronts in a hyperbolic FitzHugh-Nagumo system and the effects of cross diffusion.

We study a hyperbolic version of the FitzHugh-Nagumo (also known as the Bonhoeffer-van der Pol) reaction-diffusion system. To be able to obtain analytical results, we employ a piecewise linear approximation of the nonlinear kinetic term. The hyperbolic version is compared with the standard parabolic FitzHugh-Nagumo system. We completely describe the dynamics of wavefronts and discuss the properties of the speed equation. The nonequilibrium Ising-Bloch bifurcation of traveling fronts is found to occur in the hyperbolic case as well as in the parabolic system. Waves in the hyperbolic case typically propagate with lower speeds, in absolute value, than waves in the parabolic one. We find the interesting feature that the hyperbolic and parabolic front trajectories coincide in the phase plane for the FitzHugh-Nagumo model with a diagonal diffusion matrix, which is the case of self-diffusion, and differ for the system with cross diffusion.

ChemInform Abstract: Reactive Multilayers Fabricated by Vapor Deposition: A Critical Review

AbstractReview: 252 refs.

Adaptation of Spike-Timing-Dependent Plasticity to Unsupervised Learning for Polychronous Wavefront Computing

Abstract Non-Von Neumann computational architectures have lately aroused significant interest as substrates for complex computation. One recent development in this domain is the Polychronous Wavefront Computing (PWC) computational model based on multiple wavefront dynamics. This model is an abstraction and simplification of the artificial neural network paradigm based on temporal and spatial patterns of activity in a pulse propagating media and their interaction with transponders. While this framework is capable of computing basic logical functions and exhibiting interesting dynamic behaviors, methods for unsupervised training of the framework have not been identified. The lack of input weights and the spatio-temporal nature of the PWC framework make direct application of weight adjusting learning methods (e.g., backpropagation) impractical. The paper will describe research into unsupervised learning for PWCs inspired by Spike-Timing-Dependent Plasticity (STDP) methods used with other types of polychronous models. The method is based on adding Leaky Integrate-and-Fire semantics to the PWC framework allowing analysis of activating wavefronts and determination of the optimal location for future stimulation. The transponder's location is then incrementally adjusted to improve its future response. The paper will discuss the learning approach and examine the results of applying the method over a series of stimulations to sample configurations.

Shock dynamics of phase diagrams

A thermodynamic phase transition denotes a drastic change of state of a physical system due to a continuous change of thermodynamic variables, as for instance pressure and temperature. The classical van der Waals equation of state is the simplest model that predicts the occurrence of a critical point associated with the gas–liquid phase transition. Nevertheless, below the critical temperature theoretical predictions of the van der Waals theory significantly depart from the observed physical behaviour. We develop a novel approach to classical thermodynamics based on the solution of Maxwell relations for a generalised family of nonlocal entropy functions. This theory provides an exact mathematical description of discontinuities of the order parameter within the phase transition region, it explains the universal form of the equations of state and the occurrence of triple points in terms of the dynamics of nonlinear shock wave fronts.

Modelo de propagación de ondas solitarias en el corazón

In cardiac electrical activity, different types of waves meander through the heart. We present a model of the electrical activity of the heart that proposes that the homogeneous wave fronts propagating through the heart are in fact solitons. We use a general set of reaction-diffusion equations known as the Barrio-Varea-Aragón-Maini (BVAM) model[1] that presents a wealth of non-linear bifurcations, and we are able to follow the route to chaos, using a mapping of the amplitude equations to the dynamics of the complex Ginzburg-Landau equation. We study the dynamics of wave fronts numerically in the BVAM model to describe the mechanisms leading to heart fibrillation and compare the findings with experimental data.

Microchannel-induced change of chemical wave propagation dynamics: importance of ratio between the inlet and the channel sizes

The ability to control chemical wave propagation dynamics could stimulate the science and technology of artificial and biological spatiotemporal oscillating phenomena. In contrast to the conventional chemical approaches to control the wave front dynamics, here we report a physical approach to tune the propagation dynamics under the same chemical conditions. By using well-designed microchannels with different channel widths and depths, the propagation velocity was successfully controlled based on two independent effects: (i) a transition in the proton diffusion mode and (ii) the formation of a slanted wave front. Numerical analysis yielded a simple relationship between the propagation velocity and the microchannel configuration, which offers a simple and general way of controlling chemical wave propagation.

Abstract 341: Estrogen Prevents Sudden Death and Spontaneous Ventricular Fibrillation Associated with Pulmonary Hypertension via Estrogen Receptor Beta Mediated Mechanism

Introduction: Previously we showed that right ventricular failure (RVF) secondary to pulmonary hypertension (PH) is associated with spontaneous ventricular fibrillation (VF) and sudden death in rats. We also discovered that estrogen (E2) therapy rescues severe PH and RVF. Estrogen receptor b (ERb) has been shown to play a protective role both in heart and lung. Here we hypothesize that E2 prevents sudden death and abolishes spontaneous VF associated with RVF through ERb. Methods: Male rats were treated with monocrotaline (MCT 60 mg/kg, s.c.) or PBS (CTRL, n=9). At day 21, MCT rats were left untreated to develop RVF by day 30 (n=9), or treated with E2 (42.5 ug/kg/day, s.c., n=9) with or without ERb antagonist PHTPP (850 ug/kg/day, s.c., n=8) from day 21 to day 30. RV ejection fraction (RVEF) was serially monitord with echocardiography. Direct RV catheterisation was performed terminally to record RV pressure (RVP). At ~day 30, hearts were studied in isolated-perfused Langendorff setting and microelectrode recordings were made. RV-epicardial activation pattern was optically mapped using fluorescent voltage-sensitive dye (RH-237). Trichrome staining was performed to assess cardiac fibrosis. Values are expressed as Mean±SEM. Results: By day 30, MCT rats developed severe PH (RVP=72±4 vs. 30±2 mmHg in CTRL, p<0.05) and RV failure (RVEF=33±3% vs. 65±1 in CTRL, p<0.05) with moderate RV fibrosis and ∼30% of RVF rats died suddenly. Early after depolarization (EADs) and spontaneous VF were observed in RVF group during normal Tyrode perfusion with wave front dynamics supported by both focal and multiple wavelet patterns. E2 therapy resulted in complete rescue of PH (RVP=38±3 mmHg, p<0.05 vs. RVF; RVEF=60±2%, p<0.05 vs. RVF; no signs of fibrosis) and none of the rats died in E2-groups. No VF was initiated in any of the control or E2 treated rat hearts. In the presence of ERb antagonist PHTPP, E2 could not rescue PH (RVP=60±4 vs. 38±3 in E2; RVEF=42±2 vs. 60±2 % in E2; p<0.05 vs. E2); moderate RV fibrosis was present and spontaneous EADs and VF were observed in all the hearts similar to RVF group. Conclusions: In conclusion, E2-therapy rescues PH-induced RVF and prevents VF by reversing PH-induced RV-dysfunction and fibrosis most likely through ERb-mediated mechanism.

ACOUSTIC WAVEFRONT TRACING IN INHOMOGENEOUS, MOVING MEDIA

We extend the Huygens wavefront tracing algorithm, which is a part of an open source Madagascar project, to sound propagation in inhomogeneous, moving media and apply it to a series of benchmark tasks. One set of tasks admits exact analytic solutions and serves the purpose of validation of the new algorithm. Another set of calculations demonstrates applicability of the algorithm to the studies of wavefront dynamics and stability in ocean and atmospheric acoustics. The method is based on a system of differential equations equivalent to the eikonal equation, but formulated in the ray coordinate system. In this paper, we present a first-order, two-dimensional discretization scheme that is interpreted very simply in terms of the Huygens' principle. The method has proved to be a convenient alternative to conventional ray tracing.

The role of fine‐scale anatomical structure in the dynamics of reentry in computational models of the rabbit ventricles

Fine-scale anatomical structures in the heart may play an important role in sustaining cardiac arrhythmias. However, the extent of this role and how it may differ between species are not fully understood. In this study we used computational modelling to assess the impact of anatomy upon arrhythmia maintenance in the rabbit ventricles. Specifically, we quantified the dynamics of excitation wavefronts during episodes of simulated tachyarrhythmias and fibrillatory arrhythmias, defined as being respectively characterised by relatively low and high spatio-temporal disorganisation. Two computational models were used: a highly anatomically detailed MR-derived rabbit ventricular model (representing vasculature, endocardial structures) and a simplified equivalent model, constructed from the same MR-data but lacking such fine-scale anatomical features. During tachyarrhythmias, anatomically complex and simplified models showed very similar dynamics; however, during fibrillatory arrhythmias, as activation wavelength decreased, the presence of fine-scale anatomical details appeared to marginally increase disorganisation of wavefronts during arrhythmias in the complex model. Although a small amount of clustering of reentrant rotor centres (filaments) around endocardial structures was witnessed in follow-up analysis (which slightly increased during fibrillation as rotor size decreased), this was significantly less than previously reported in large animals. Importantly, no anchoring of reentrant rotors was visibly identifiable in arrhythmia movies. These differences between tachy- and fibrillatory arrhythmias suggest that the relative size of reentrant rotors with respect to anatomical obstacles governs the influence of fine-scale anatomy in the maintenance of ventricular arrhythmias in the rabbit. In conclusion, our simulations suggest that fine-scale anatomical features play little apparent role in the maintenance of tachyarrhythmias in the rabbit ventricles and, contrary to experimental reports in larger animals, appear to play only a minor role in the maintenance of fibrillatory arrhythmias. These findings also have important implications in optimising the level of detail required in anatomical computational meshes frequently used in arrhythmia investigations.

Adaptive optics with pupil tracking for high resolution retinal imaging

Adaptive optics, when integrated into retinal imaging systems, compensates for rapidly changing ocular aberrations in real time and results in improved high resolution images that reveal the photoreceptor mosaic. Imaging the retina at high resolution has numerous potential medical applications, and yet for the development of commercial products that can be used in the clinic, the complexity and high cost of the present research systems have to be addressed. We present a new method to control the deformable mirror in real time based on pupil tracking measurements which uses the default camera for the alignment of the eye in the retinal imaging system and requires no extra cost or hardware. We also present the first experiments done with a compact adaptive optics flood illumination fundus camera where it was possible to compensate for the higher order aberrations of a moving model eye and in vivo in real time based on pupil tracking measurements, without the real time contribution of a wavefront sensor. As an outcome of this research, we showed that pupil tracking can be effectively used as a low cost and practical adaptive optics tool for high resolution retinal imaging because eye movements constitute an important part of the ocular wavefront dynamics.

Estrogen Therapy Abolishes Spontaneous Ventricular Arrhythmias in Right Ventricular Failure Induced by Pulmonary Hypertension

We previously have shown that pulmonary hypertension (PH)-induced right ventricular failure (RVF) is associated with increased incidence of sudden death caused by spontaneous ventricular fibrillation (VF). We also discovered that estrogen (E2) therapy rescues severe PH and RVF and results in 100% survival. Here we hypothesized that E2 abolishes spontaneous VF associated with RVF by restoring RVEF, reversing fibrosis and restoring PH-induced downregulation of repolarizing K-channel proteins Kv1.5 and KCNE-2 and SERCA-2a expression. Chronic PH-associated RVF was induced in male rats by s.c. monocrotaline (MCT, 60 mg/kg, n=10). Some MCT-rats were treated with E2 (42.5 ug/kg/day, s.c.) from day 21 (severe PH-stage) to day-30 (n=8). Saline treated rats served as control (n=8). At ∼day 30, hearts were studied in isolated-perfused Langendorff setting. RV-epicardial activation pattern was optically mapped using fluorescent voltage-sensitive dye (RH-237). By ∼day 30, 30% RVF rats died suddenly but none in the control or E2-groups. RVF hearts manifested EADs and spontaneous VF during normal Tyrode’s perfusion with wavefront dynamics supported by both focal and multiple wavelet patterns. No VF was initiated in any of the control or E2-treated hearts. SERCA-2a was reduced (∼15-fold) in RVF (0.06±0.01 vs. 1±0.26 control) that was reversed in E2-group (0.77±0.13, p<0.05 vs. RVF). Kv1.5 was reduced ∼8 fold in RVF (0.12±0.03 vs. 1±0.18 in control, p<0.05) and E2 partially restored Kv1.5 (0.46±0.06, p<0.05). KCNE2, an ancillary K-channel subunit, was reduced ∼3-fold in RVF (0.3±0.1 vs. 1±0.1, p<0.05) that was reversed by E2 (0.9±0.05, p<0.05). RVF was associated with moderate RV-fibrosis and severe reduction in RV-ejection fraction (RVEF) from 65±1 to 33±3%. E2- group did not show any fibrosis and RVEF was preserved (60±2%). In conclusion, E2-therapy rescues RVF and prevents VF by reversing PH-induced RV-fibrosis and reduced repolarization-reserve.

Cardiac excitation mechanisms, wavefront dynamics and strength–interval curves predicted by 3D orthotropic bidomain simulations

The assessment and understanding of cardiac excitation mechanisms is very important for the development and improvement of implantable cardiac devices, pacing protocols, and arrhythmia treatments. Previous bidomain simulation studies have investigated cathodal and anodal make/break mechanisms of cardiac excitation and strength–interval (S–I) curves in two-dimensional sheets or cylindrical domains, that by symmetry reduce to the two-dimensional case. In this work, cathodal and anodal S–I curves are studied by means of detailed bidomain simulations which include: (i) three-dimensional cardiac slabs; (ii) transmural fiber rotation; (iii) unequal orthotropic anisotropy of the conducting media; (iv) incorporation of funny and electroporation currents in the ventricular membrane model. The predicted shape of cathodal and anodal S–I curves exhibit the same features of the S–I curves observed experimentally and the break/make transition coincides with the final descending phase of the S–I curves. Away from the break/make transition, only the break or make excitation mechanism is observed independently of the stimulus strength, whereas within an interval at the break/make transition, new paradoxical excitation behaviors are observed that depend on the stimulus strength.

Speed of traveling fronts in a sigmoidal reaction-diffusion system

We study a sigmoidal version of the FitzHugh-Nagumo reaction-diffusion system based on an analytic description using piecewise linear approximations of the reaction kinetics. We completely describe the dynamics of wave fronts and discuss the properties of the speed equation. The speed diagrams show front bifurcations between branches with one, three, or five fronts that differ significantly from the classical FitzHugh-Nagumo model. We examine how the number of fronts and their speed vary with the model parameters. We also investigate numerically the stability of the front solutions in a case when five fronts exist.

Representing Cardiac Bidomain Bath-Loading Effects by an Augmented Monodomain Approach: Application to Complex Ventricular Models

Although the cardiac bidomain model has been widely used in the simulation of electrical activation, its relatively computationally expensive nature means that monodomain approaches are generally required for long-duration simulations (for example, investigations of arrhythmia mechanisms). However, the presence of a conducting bath surrounding the tissue is known to induce wavefront curvature (surface leading bulk), a phenomena absent in standard monodomain approaches. Here, we investigate the biophysical origin of the bidomain bath-loading induced wavefront curvature and present a novel augmented monodomain-equivalent bidomain approach faithfully replicating all aspects of bidomain wavefront morphology and conduction velocity, but with a fraction of the computational cost. Bath-loading effects are shown to be highly dependent upon specific conductivity parameters, but less dependent upon the thickness or conductivity of the surrounding bath, with even relatively thin surrounding fluid layers (~ 0.1 mm) producing significant wavefront curvature in bidomain simulations. We demonstrate that our augmented monodomain approach can be easily adapted for different conductivity sets and applied to anatomically complex models, thus facilitating fast and accurate simulation of cardiac wavefront dynamics during long-duration simulations, further aiding the faithful comparison of simulations with experiments.

Period-2 spiral waves supported by nonmonotonic wave dispersion

Rotating spiral waves appear ubiquitously in a wide range of nonlinear systems, and they play important roles in many biological phenomena. Recently, unusual spiral waves, which support period-2 dynamics, have been found in several different systems including cardiac tissues as well as nonlinear chemical reaction-diffusion systems. They are potentially significant as an intermediate dynamic state linking regularly rotating period-1 spiral waves to complex dynamic states such as cardiac fibrillations; for example, it is intrinsic of period-2 spiral waves to have "line defects" and their instability can lead to a spatiotemporal chaos. Previous mathematical models regarding period-2 spiral waves are mostly based on a coupled system of period-2 oscillators, but these are inappropriate for the description of a large class of systems that are composed of (nonoscillatory) excitable elements--a good example being the heart. In this paper we hypothesize that excitable media, which support a nonmonotonic conduction velocity dispersion relation, can sustain period-2 oscillatory spiral waves. We explicitly demonstrate that the new mechanism can create period-2 spirals by computer simulations on a simple mathematical model describing spiral wave front dynamics.

Dynamics of interface in three-dimensional anisotropic bistable reaction–diffusion system

This paper presents a theoretical investigation of dynamics of interface (wave front) in three-dimensional (3D) reaction–diffusion (RD) system for bistable media with anisotropy constructed by means of anisotropic surface tension. An equation of motion for the wave front is derived to carry out stability analysis of transverse perturbations, which discloses mechanism of pattern formation such as labyrinthine in 3D bistable media. Particularly, the effects of anisotropy on wave propagation are studied. It was found that, sufficiently strong anisotropy can induce dynamical instabilities and lead to breakup of the wave front. With the fast-inhibitor limit, the bistable system can further be described by a variational dynamics so that the boundary integral method is adopted to study the dynamics of wave fronts.

Generation of histo-anatomically representative models of the individual heart: tools and application.

This paper presents methods to build histo-anatomically detailed individualized cardiac models. The models are based on high-resolution three-dimensional anatomical and/or diffusion tensor magnetic resonance images, combined with serial histological sectioning data, and are used to investigate individualized cardiac function. The current state of the art is reviewed, and its limitations are discussed. We assess the challenges associated with the generation of histo-anatomically representative individualized in silico models of the heart. The entire processing pipeline including image acquisition, image processing, mesh generation, model set-up and execution of computer simulations, and the underlying methods are described. The multifaceted challenges associated with these goals are highlighted, suitable solutions are proposed, and an important application of developed high-resolution structure-function models in elucidating the effect of individual structural heterogeneity upon wavefront dynamics is demonstrated.

POLYCHRONOUS WAVEFRONT COMPUTATIONS

There is great interest in methods for computing that do not involve digital machines. Many computational paradigms were inspired by brain research, such as Boolean neuronal logic [McCulloch &amp; Pitts, 1943], the perceptron [Rosenblatt, 1958], attractor neural networks [Hopfield, 1982] and cellular neural nets [Chua &amp; Yang, 1988]. All these paradigms abstract biological circuits to artificial neural networks, i.e. interconnected units (neurons) that perform computations based on the connections between the units (synapses). Here we present a novel computational framework based on polychronous wavefront dynamics. It is entirely different from an artificial neural network paradigm, rather it is based on temporal and spatial patterns of activity in pulse-propagating media and their interaction with transponders, which create pulses in response to receiving appropriate inputs, e.g. two coincident input pulses. A pulse propagates as a circular wave from its source to other transponders. Computations result from interactions between transponders, and they are encoded by the exact physical locations of transponders and by precise timings of pulses. We illustrate temporal pattern recognition, reverberating memory, temporal signal analysis and basic logical operations using polychronous wavefront computations. This work reveals novel principles for designing nanoscale computational devices.

D,l-Sotalol at Therapeutic Concentrations Facilitates the Occurrence of Long-Lasting Non-Stationary Reentry During Ventricular Fibrillation in Isolated Rabbit Hearts

The effects of d,l-sotalol at therapeutic concentrations (<or=10 mg/L) on wavefront dynamics during ventricular fibrillation (VF) and electrophysiological heterogeneity remain unclear. By using an optical mapping system, epicardial activation patterns of VF were studied in 6 Langendorff-perfused rabbit hearts at baseline, during 10 mg/L d,l-sotalol infusion, and after washout. In an additional 4 hearts, action potential duration (APD), conduction velocity, and wavelength (WL) restitutions were determined. During d,l-sotalol infusion, VF was terminated in 3 of the 6 hearts. Only 1 heart developed transient ventricular tachycardia (VT). d,l-Sotalol reduced the number of phase singularities (ie, wavebreak) during VF (P<0.05), and it also increased the occurrence frequency (P<0.05) and lifespan (P<0.05) of epicardial reentry during VF. These reentries were non-stationary in nature and did not anchor on anatomical structures. Restitution data showed that d,l-sotalol flattened APD restitution. Furthermore, APD dispersion and spatial heterogeneity of restitutions were not enhanced by d,l-sotalol. d,l-Sotalol at therapeutic concentrations decreased wavebreak and facilitated the occurrence of long-lasting, non-stationary reentry during VF. However, VT rarely occurred. The related mechanisms include: (1) flattening of APD restitution without enhancement of spatial heterogeneity of electrophysiological properties, causing wavefront organization, and (2) WL prolongation, preventing steady anchoring of reentry.

Change in Conduction Velocity due to Fiber Curvature in Cultured Neonatal Rat Ventricular Myocytes

Computer modeling of cardiac propagation suggests that curvature of muscle fibers modulates conduction velocity (CV). The effect could be involved in arrhythmogenesis by altering the dynamics of reentrant wavefronts or by causing propagation block. To verify the existence of this effect experimentally, we measured CV in anisotropic neonatal rat ventricular myocyte monolayers. The orientation of the cells was directed by scratches machined into plastic coverslips. Each substrate contained a region in which scratch radius of curvature varied from 0.25 to 1.0 cm. The CV anisotropy ratio (longitudinal CV/transverse CV in straight fiber regions) was 2.3 +/- 0.3 (n = 38). We initiated wavefronts transverse to fibers with the fibers either curving toward or away from the wavefronts. Action potentials were recorded using a potentiometric dye and a video camera. Propagation was faster (p = 0.0003) when fibers curved toward wavefronts than when fibers curved in the opposite direction. The mean CV difference was 0.38 +/- 0.44 cm/s (n = 24), which is 3.5% of nominal straight fiber transverse CV (11.0 +/- 3.2 cm/s). The effect was also present (p = 0.07) when pacing was slowed from 350 to 500 ms (n = 6). In a control group (n = 8) with uncurved fibers, CV was the same in both directions (p = NS). We conclude that fiber curvature is a factor in modulating cardiac propagation.