Nonlinear physics of electrical wave propagation in the heart: a review

The beating of the heart is a synchronized contraction of muscle cells (myocytes) that are triggered by a periodic sequence of electrical waves (action potentials) originating in the sino-atrial node and propagating over the atria and the ventricles. Cardiac arrhythmias like atrial and ventricular fibrillation (AF,VF) or ventricular tachycardia (VT) are caused by disruptions and instabilities of these electrical excitations, that lead to the emergence of rotating waves (VT) and turbulent wave patterns (AF,VF). Numerous simulation and experimental studies during the last 20 years have addressed these topics. In this review we focus on the nonlinear dynamics of wave propagation in the heart with an emphasis on the theory of pulses, spirals and scroll waves and their instabilities in excitable media and their application to cardiac modeling. After an introduction into electrophysiological models for action potential propagation, the modeling and analysis of spatiotemporal alternans, spiral and scroll meandering, spiral breakup and scroll wave instabilities like negative line tension and sproing are reviewed in depth and discussed with emphasis on their impact in cardiac arrhythmias.Peer ReviewedPreprin

Lagrangian study of surface transport in the Kuroshio Extension area based on simulation of propagation of Fukushima-derived radionuclides

Lagrangian approach is applied to study near-surface large-scale transport in the Kuroshio Extension area using a simulation with synthetic particles advected by AVISO altimetric velocity field. A material line technique is applied to find the origin of water masses in cold-core cyclonic rings pinched off from the jet in summer 2011. Tracking and Lagrangian maps provide the evidence of cross-jet transport. Fukushima derived caesium isotopes are used as Lagrangian tracers to study transport and mixing in the area a few months after the March of 2011 tsunami that caused a heavy damage of the Fukushima nuclear power plant (FNPP). Tracking maps are computed to trace the origin of water parcels with measured levels of Cs-134 and Cs-137 concentrations collected in two R/V cruises in June and July 2011 in the large area of the Northwest Pacific. It is shown that Lagrangian simulation is useful to finding the surface areas that are potentially dangerous due to the risk of radioactive contamination. The results of simulation are supported by tracks of the surface drifters which were deployed in the area

Competing mechanisms of stress-assisted diffusivity and stretch-activated currents in cardiac electromechanics

We numerically investigate the role of mechanical stress in modifying the conductivity properties of the cardiac tissue and its impact in computational models for cardiac electromechanics. We follow a theoretical framework recently proposed in [Cherubini, Filippi, Gizzi, Ruiz-Baier, JTB 2017], in the context of general reaction-diffusion-mechanics systems using multiphysics continuum mechanics and finite elasticity. In the present study, the adapted models are compared against preliminary experimental data of pig right ventricle fluorescence optical mapping. These data contribute to the characterization of the observed inhomogeneity and anisotropy properties that result from mechanical deformation. Our novel approach simultaneously incorporates two mechanisms for mechano-electric feedback (MEF): stretch-activated currents (SAC) and stress-assisted diffusion (SAD); and we also identify their influence into the nonlinear spatiotemporal dynamics. It is found that i) only specific combinations of the two MEF effects allow proper conduction velocity measurement; ii) expected heterogeneities and anisotropies are obtained via the novel stress-assisted diffusion mechanisms; iii) spiral wave meandering and drifting is highly mediated by the applied mechanical loading. We provide an analysis of the intrinsic structure of the nonlinear coupling using computational tests, conducted using a finite element method. In particular, we compare static and dynamic deformation regimes in the onset of cardiac arrhythmias and address other potential biomedical applications

Double step structure and meandering due to the many body interaction at GaN(0001) surface in N-rich conditions

Growth of gallium nitride on GaN(0001) surface is modeled by Monte Carlo method. Simulated growth is conducted in N-rich conditions, hence it is controlled by Ga atoms surface diffusion. It is shown that dominating four-body interactions of Ga atoms can cause step flow anisotropy. Kinetic Monte Carlo simulations show that parallel steps with periodic boundary conditions form double terrace structures, whereas initially V -shaped parallel step train initially bends and then every second step moves forward, building regular, stationary ordering as observed during MOVPE or HVPE growth of GaN layers. These two phenomena recover surface meandered pair step pattern observed, since 1953, on many semiconductor surfaces, such as SiC, Si or GaN. Change of terrace width or step orientation particle diffusion jump barriers leads either to step meandering or surface roughening. Additionally it is shown that step behavior changes with the Schwoebel barrier height. Furthermore, simulations under conditions corresponding to very high external particle flux result in triangular islands grown at the terraces. All structures, emerging in the simulations, have their corresponding cases in the experimental results.Comment: 25 pages, 8 figure

Spiral-wave dynamics in a mathematical model of human ventricular tissue with myocytes and Purkinje fibers

We present systematic numerical studies of the possible effects of the coupling of human endocardial and Purkinje cells at cellular and two-dimensional tissue levels. We find that the autorhythmic-activity frequency of the Purkinje cell in a composite decreases with an increase in the coupling strength; this can even eliminate the autorhythmicity. We observe a delay between the beginning of the action potentials of endocardial and Purkinje cells in a composite; such a delay increases as we decrease the diffusive coupling, and eventually a failure of transmission occurs. An increase in the diffusive coupling decreases the slope of the action-potential-duration-restitution curve of an endocardial cell in a composite. By using a minimal model for the Purkinje network, in which we have a two-dimensional, bilayer tissue, with a layer of Purkinje cells on top of a layer of endocardial cells, we can stabilize spiral-wave turbulence; however, for a sparse distribution of Purkinje-ventricular junctions, at which these two layers are coupled, we can also obtain additional focal activity and many complex transient regimes. We also present additional effects resulting from the coupling of Purkinje and endocardial layers and discuss the relation of our results to the studies performed in anatomically accurate models of the Purkinje network

Vernal Pool: A Participatory Art Project About Place + Precipitation

Produced by Karen Miranda Abel with Jessica Marion Barr, Vernal Pool is an immersive, elemental water installation created as a participatory, contemplative inquiry into our transitory interrelationships with water and landscape. From November 2013 to April 2014, 114 individuals across Canada and abroad gathered snow samples as a form of extrinsic artistic practice about place and precipitation. With the arrival of spring, the reservoir of melted snow was convened for four days at Toronto’s historic Gladstone Hotel to create Vernal Pool