Filament tension and phase-locked drift of meandering scroll waves

Rotating scroll waves are self-organising patterns which are found in many oscillating or excitable systems. Here we show that quasi-periodic (meandering) scroll waves, which include the rotors that organise cardiac arrhythmias, exhibit filament tension when averaged over the meander cycle. With strong filament curvature or medium thickness gradients, however, scroll wave dynamics are governed by phase-locked drift instead of filament tension. Our results are validated in computational models of cycloidal meander and a cardiac tissue model with linear core.Comment: accepted for publication in Physical Review Letters (December 2017

Noise Effects on the Complex Patterns of Abnormal Heartbeats

Patients at high risk for sudden death often exhibit complex heart rhythms in which abnormal heartbeats are interspersed with normal heartbeats. We analyze such a complex rhythm in a single patient over a 12-hour period and show that the rhythm can be described by a theoretical model consisting of two interacting oscillators with stochastic elements. By varying the magnitude of the noise, we show that for an intermediate level of noise, the model gives best agreement with key statistical features of the dynamics.Comment: 4 pages, 4 figures, RevTe

Mechanisms of Surviving Burial: Dune Grass Interspecific Differences Drive Resource Allocation After Sand Deposition

Sand dunes are important geomorphic formations of coastal ecosystems that are critical in protecting human populations that live in coastal areas. Dune formation is driven by ecomorphodynamic interactions between vegetation and sediment deposition. While there has been extensive research on responses of dune grasses to sand burial, there is a knowledge gap in understanding mechanisms of acclimation between similar, coexistent, dune-building grasses such as Ammophila breviligulata (C3), Spartina patens (C4), and Uniola paniculata (C4). Our goal was to determine how physiological mechanisms of acclimation to sand burial vary between species. We hypothesize that (1) in the presence of burial, resource allocation will be predicated on photosynthetic pathway and that we will be able to characterize the C3 species as a root allocator and the C4 species as leaf allocators. We also hypothesize that (2) despite similarities between these species in habitat, growth form, and life history, leaf, root, and whole plant traits will vary between species when burial is not present. Furthermore, when burial is present, the existing variability in physiological strategy will drive species-specific mechanisms of survival. In a greenhouse experiment, we exposed three dune grass species to different burial treatments: 0 cm (control) and a one-time 25-cm burial to mimic sediment deposition during a storm. At the conclusion of our study, we collected a suite of physiological and morphological functional traits. Results showed that Ammophila decreased allocation to aboveground biomass to maintain root biomass, preserving photosynthesis by allocating nitrogen (N) into light-exposed leaves. Conversely, Uniola and Spartina decreased allocation to belowground production to increase elongation and maintain aboveground biomass. Interestingly, we found that species were functionally distinct when burial was absent; however, all species became more similar when treated with burial. In the presence of burial, species utilized functional traits of rapid growth strategy, although mechanisms of change were interspecifically variable

Chain Restaurant Calorie Posting Laws, Obesity, and Consumer Welfare

The 2010 Patient Protection and Affordable Care Act (ACA) introduced a mandate requiring chain restaurants to post calorie counts on menus and menu boards. This paper investigates whether and why calorie posting laws work. To do so, we develop a model of calories consumed that highlights two potential channels through which mandates influence choice and outlines an empirical strategy to disentangle these alternatives. We test the predictions of our model using data from the Behavioral Risk Factor Surveillance System to compare changes in body mass index (BMI), obesity, and consumer well-being in locations that implemented calorie-posting laws between 2008 and 2011 to those in neighboring locations without such laws. We find that calorie mandates lead to a small but statistically significant reduction in average BMI of 0.2 kg/m2 (1.5 pounds) and reductions in self-reported measures of life satisfaction. Quantile regressions provide evidencethat reductions in BMI and life satisfaction are concentrated among those with healthy weight. Viewed in its totality, the pattern of results is consistent with an economic model in which calorie labels influence consumers both by providing information and by imposing a welfare-reducing moral cost on unhealthy eating

Complex Patterns in Reaction-Diffusion Systems: A Tale of Two Front Instabilities

Two front instabilities in a reaction-diffusion system are shown to lead to the formation of complex patterns. The first is an instability to transverse modulations that drives the formation of labyrinthine patterns. The second is a Nonequilibrium Ising-Bloch (NIB) bifurcation that renders a stationary planar front unstable and gives rise to a pair of counterpropagating fronts. Near the NIB bifurcation the relation of the front velocity to curvature is highly nonlinear and transitions between counterpropagating fronts become feasible. Nonuniformly curved fronts may undergo local front transitions that nucleate spiral-vortex pairs. These nucleation events provide the ingredient needed to initiate spot splitting and spiral turbulence. Similar spatio-temporal processes have been observed recently in the ferrocyanide-iodate-sulfite reaction.Comment: Text: 14 pages compressed Postscript (90kb) Figures: 9 pages compressed Postscript (368kb

Complex patterns of spontaneous initiations and terminations of reentrant circulation in a loop of cardiac tissue

A two-component model is developed that consists of a discrete loop of cardiac cells that circulates action potentials together with a cardiac pacing mechanism. Physiological properties of cells such as restitutions of refractoriness and of conduction velocity are given via experimentally measured functions. The dynamics of circulating pulses and their interactions with the pacer are regulated by two threshold relations. Patterns of spontaneous initiations and terminations of reentry (SITR) generated by this system are studied through numerical simulations and analytical observations. These patterns can be regular or irregular; causes of irregularities are identified as the threshold bistability of reentrant circulation (T-bistability) and in some cases, also phase-resetting interactions with the pacer.Comment: 27 pages, 10 figures, 61 references; A version of this paper (same results) is to appear in the Journal of Theoretical Biology; arXiv V2 adds helpful commments to facilitate reading and corrects minor errors in presentatio

Points, Walls and Loops in Resonant Oscillatory Media

In an experiment of oscillatory media, domains and walls are formed under the parametric resonance with a frequency double the natural one. In this bi-stable system, %phase jumps $\pi$ by crossing walls. a nonequilibrium transition from Ising wall to Bloch wall consistent with prediction is confirmed experimentally. The Bloch wall moves in the direction determined by its chirality with a constant speed. As a new type of moving structure in two-dimension, a traveling loop consisting of two walls and Neel points is observed.Comment: 9 pages (revtex format) and 6 figures (PostScript

From Labyrinthine Patterns to Spiral Turbulence

A new mechanism for spiral vortex nucleation in nongradient reaction diffusion systems is proposed. It involves two key ingredients: An Ising-Bloch type front bifurcation and an instability of a planar front to transverse perturbations. Vortex nucleation by this mechanism plays an important role in inducing a transition from labyrinthine patterns to spiral turbulence. PACS numbers: 05.45.+b, 82.20.MjComment: 4 pages uuencoded compressed postscrip

The Dynamics of Sustained Reentry in a Loop Model with Discrete Gap Junction Resistance

Dynamics of reentry are studied in a one dimensional loop of model cardiac cells with discrete intercellular gap junction resistance ($R$). Each cell is represented by a continuous cable with ionic current given by a modified Beeler-Reuter formulation. For $R$ below a limiting value, propagation is found to change from period-1 to quasi-periodic ($QP$) at a critical loop length ($L_{crit}$) that decreases with $R$. Quasi-periodic reentry exists from $L_{crit}$ to a minimum length ($L_{min}$) that is also shortening with $R$. The decrease of $L_{crit}(R)$ is not a simple scaling, but the bifurcation can still be predicted from the slope of the restitution curve giving the duration of the action potential as a function of the diastolic interval. However, the shape of the restitution curve changes with $R$.Comment: 6 pages, 7 figure

Instability and Spatiotemporal Dynamics of Alternans in Paced Cardiac Tissue

We derive an equation that governs the spatiotemporal dynamics of small amplitude alternans in paced cardiac tissue. We show that a pattern-forming linear instability leads to the spontaneous formation of stationary or traveling waves whose nodes divide the tissue into regions with opposite phase of oscillation of action potential duration. This instability is important because it creates dynamically an heterogeneous electrical substrate for inducing fibrillation if the tissue size exceeds a fraction of the pattern wavelength. We compute this wavelength analytically as a function of three basic length scales characterizing dispersion and inter-cellular electrical coupling.Comment: 4 pages, 3 figures, submitted to PR