Intermittent Self-Organization of Scroll Wave Turbulence in Three-Dimensional Excitable Media

Rotating spiral and scroll waves (vortices) are investigated in the FitzHugh–Nagumo model of excitable media. The focus is on a parameter region in which there exists bistability between alternative stable vortices with distinct periods. Response functions are used to predict the filament tension of the alternative scrolls and it is shown that the slow-period scroll has negative filament tension, while the filament tension of the fast-period scroll changes sign within a hysteresis loop. The predictions are confirmed by direct simulations. Further investigations show that the slow-period scrolls display features similar to delayed after-depolarization and tend to develop into turbulence similar to ventricular fibrillation (VF). Scrolls with positive filament tension collapse or stabilize, similar to monomorphic ventricular tachycardia (VT). Perturbations, such as boundary interaction or shock stimulus, can convert the vortex with negative filament tension into the vortex with positive filament tension. This may correspond to transition from VF to VT unrelated to pinning.

Wave propagation in the heart has a discrete nature, because it is mediated by discrete intercellular connections via gap junctions. Although effects of discreteness on wave propagation have been studied for planar traveling waves and vortexes (spiral waves) in two dimensions, its possible effects on vortexes (scroll waves) in three dimensions are not yet explored. In this article, we study the effect of discrete cell coupling on the filament dynamics in a generic model of an excitable medium. We find that reduced cell coupling decreases the line tension of scroll wave filaments and may induce negative filament tension instability in three-dimensional excitable lattices.

A rigorous thermodynamic formulation of the geometric model for heterogeneous nucleation including line tension effect is missing till date due to the associated mathematical hurdles. In this work, we develop a novel thermodynamic formulation based on Classical Nucleation Theory (CNT), which is supposed to illustrate a systematic and a more plausible analysis for the heterogeneous nucleation on a planar surface including the line tension effect. The appreciable range of the critical microscopic contact angle (θc), obtained from the generalized Young's equation and the stability analysis, is θ∞ < θc < θ' for positive line tension and is θM < θc < θ∞ for negative line tension. θ∞ is the macroscopic contact angle, θ' is the contact angle for which the Helmholtz free energy has the minimum value for the positive line tension, and θM is the local minima of the nondimensional line tension effect for the negative line tension. The shape factor f, which is basically the dimensionless critical free energy barrier, becomes higher for lower values of θ∞ and higher values of θc for positive line tension. The combined effect due to the presence of the triple line and the interfacial areas (f(L) + f(S)) in shape factor is always within (0, 3.2), resulting f in the range of (0, 1.7) for positive line tension. A formerly presumed appreciable range for θc(0 < θc < θ∞) is found not to be true when the effect of negative line tension is considered for CNT. Estimation based on the property values of some real fluids confirms the relevance of the present analysis.

Experiments and theoretical studies show that filament turbulence in bounded three-dimensional media can arise due to a number of different mechanisms or instabilities. In this paper, we show that in oscillatory media, as described by the complex Ginzburg-Landau equation, these different instabilities generate different turbulent filament behaviors that are reflected in the statistical properties on the surface of the medium. We find in particular that the specific filament dynamics in the regime of negative line tension and in the regime of amplitude turbulence can be unambiguously identified by the differing forms for the creation rates of filaments attached to the surface of the medium, as long as the system size is sufficiently large to ensure extensive turbulence. This implies that it is sufficient to study the dynamics on the surface, which allows one to make predictions even if the bulk dynamics is inaccessible. We also find that in the regime of amplitude turbulence the statistical properties of the turbulent dynamics on the surface of a three-dimensional medium are identical to that of a two-dimensional medium.

Spiral waves are a well-known and intensively studied dynamic phenomenon in excitable media of various types. Most studies have considered an excitable medium with a single stable resting state. However, spiral waves can be maintained in an excitable medium with bistability. Our calculations, performed using the widely used Barkley model, clearly show that spiral waves in the bistability region exhibit unique properties. For example, a spiral wave can either rotate around a core that is in an unexcited state, or the tip of the spiral wave describes a circular trajectory located inside an excited region. The boundaries of the parameter regions with positive and ‘negative’ cores have been defined numerically and analytically evaluated. It is also shown that the creation of a positive or ‘negative’ core may depend on the initial conditions, which leads to hysteresis of spiral waves. In addition, the influence of gradient flow on the dynamics of the spiral wave, which is related to the tension of the scroll wave filaments in a three-dimensional medium, is studied.

The elasticity of a contact line

Condensation of vapors on spherical nuclei and the line tension effect

A Statistical Mechanical Model of Heterogeneous Nucleation Including the Effects of Line Tension and Surface Diffusion

We present experimental and theoretical results on intrusion-extrusion cycles of water in hydrophobic mesoporous materials, characterized by independent cylindrical pores. The intrusion, which takes place above the bulk saturation pressure, can be well described using a macroscopic capillary model. Once the material is saturated with water, extrusion takes place upon reduction of the externally applied pressure. Our results for the extrusion pressure can only be understood by assuming that the limiting extrusion mechanism is the nucleation of a vapor bubble inside the pores. A comparison of calculated and experimental nucleation pressures shows that a proper inclusion of line tension effects is necessary to account for the observed values of nucleation barriers. Negative line tensions of order 10(-11) J m(-1) are found for our system, in reasonable agreement with other experimental estimates of this quantity.