Nonequilibrium arrhythmic states and transitions in a mathematical model for diffuse fibrosis in human cardiac tissue

We present a comprehensive numerical study of spiral-and scroll-wave dynamics in a state-of-the-art mathematical model for human ventricular tissue with fiber rotation, transmural heterogeneity, myocytes, and fibroblasts. Our mathematical model introduces fibroblasts randomly, to mimic diffuse fibrosis, in the ten Tusscher-Noble-Noble-Panfilov (TNNP) model for human ventricular tissue; the passive fibroblasts in our model do not exhibit an action potential in the absence of coupling with myocytes; and we allow for a coupling between nearby myocytes and fibroblasts. Our study of a single myocyte-fibroblast (MF) composite, with a single myocyte coupled to N-f fibroblasts via a gap-junctional conductance G(gap), reveals five qualitatively different responses for this composite. Our investigations of two-dimensional domains with a random distribution of fibroblasts in a myocyte background reveal that, as the percentage P-f of fibroblasts increases, the conduction velocity of a plane wave decreases until there is conduction failure. If we consider spiral-wave dynamics in such a medium we find, in two dimensions, a variety of nonequilibrium states, temporally periodic, quasiperiodic, chaotic, and quiescent, and an intricate sequence of transitions between them; we also study the analogous sequence of transitions for three-dimensional scroll waves in a three-dimensional version of our mathematical model that includes both fiber rotation and transmural heterogeneity. We thus elucidate random-fibrosis-induced nonequilibrium transitions, which lead to conduction block for spiral waves in two dimensions and scroll waves in three dimensions. We explore possible experimental implications of our mathematical and numerical studies for plane-, spiral-, and scroll-wave dynamics in cardiac tissue with fibrosis.

A Study of Early Afterdepolarizations in a Model for Human Ventricular Tissue

Sudden cardiac death is often caused by cardiac arrhythmias. Recently, special attention has been given to a certain arrhythmogenic condition, the long-QT syndrome, which occurs as a result of genetic mutations or drug toxicity. The underlying mechanisms of arrhythmias, caused by the long-QT syndrome, are not fully understood. However, arrhythmias are often connected to special excitations of cardiac cells, called early afterdepolarizations (EADs), which are depolarizations during the repolarizing phase of the action potential. So far, EADs have been studied mainly in isolated cardiac cells. However, the question on how EADs at the single-cell level can result in fibrillation at the tissue level, especially in human cell models, has not been widely studied yet. In this paper, we study wave patterns that result from single-cell EAD dynamics in a mathematical model for human ventricular cardiac tissue. We induce EADs by modeling experimental conditions which have been shown to evoke EADs at a single-cell level: by an increase of L-type Ca currents and a decrease of the delayed rectifier potassium currents. We show that, at the tissue level and depending on these parameters, three types of abnormal wave patterns emerge. We classify them into two types of spiral fibrillation and one type of oscillatory dynamics. Moreover, we find that the emergent wave patterns can be driven by calcium or sodium currents and we find phase waves in the oscillatory excitation regime. From our simulations we predict that arrhythmias caused by EADs can occur during normal wave propagation and do not require tissue heterogeneities. Experimental verification of our results is possible for experiments at the cell-culture level, where EADs can be induced by an increase of the L-type calcium conductance and by the application of I-Kr blockers, and the properties of the emergent patterns can be studied by optical mapping of the voltage and calcium.

Turbulent electrical activity at sharp-edged inexcitable obstacles in a model for human cardiac tissue

Wave propagation around various geometric expansions, structures, and obstacles in cardiac tissue may result in the formation of unidirectional block of wave propagation and the onset of reentrant arrhythmias in the heart. Therefore, we investigated the conditions under which reentrant spiral waves can be generated by high-frequency stimulation at sharp-edged obstacles in the ten Tusscher-Noble-Noble-Panfilov (TNNP) ionic model for human cardiac tissue. We show that, in a large range of parameters that account for the conductance of major inward and outward ionic currents of the model fast inward Na+ current (INa), L-type slow inward Ca2+ current (I-CaL), slow delayed-rectifier current (I-Ks), rapid delayed-rectifier current (I-Kr), inward rectifier K+ current (I-K1)], the critical period necessary for spiral formation is close to the period of a spiral wave rotating in the same tissue. We also show that there is a minimal size of the obstacle for which formation of spirals is possible; this size is similar to 2.5 cm and decreases with a decrease in the excitability of cardiac tissue. We show that other factors, such as the obstacle thickness and direction of wave propagation in relation to the obstacle, are of secondary importance and affect the conditions for spiral wave initiation only slightly. We also perform studies for obstacle shapes derived from experimental measurements of infarction scars and show that the formation of spiral waves there is facilitated by tissue remodeling around it. Overall, we demonstrate that the formation of reentrant sources around inexcitable obstacles is a potential mechanism for the onset of cardiac arrhythmias in the presence of a fast heart rate.

Spiral-wave dynamics in ionically realistic mathematical models for human ventricular tissue: the effects of periodic deformation

We carry out an extensive numerical study of the dynamics of spiral waves of electrical activation, in the presence of periodic deformation (PD) in two-dimensional simulation domains, in the biophysically realistic mathematical models of human ventricular tissue due to (a) ten-Tusscher and Panfilov (the TP06 model) and (b) ten-Tusscher, Noble, Noble, and Panfilov (the TNNPO4 model). We first consider simulations in cable-type domains, in which we calculate the conduction velocity theta and the wavelength lambda of a plane wave; we show that PD leads to a periodic, spatial modulation of theta and a temporally periodic modulation of lambda; both these modulations depend on the amplitude and frequency of the PD. We then examine three types of initial conditions for both TP06 and TNNPO4 models and show that the imposition of PD leads to a rich variety of spatiotemporal patterns in the transmembrane potential including states with a single rotating spiral (RS) wave, a spiral-turbulence (ST) state with a single meandering spiral, an ST state with multiple broken spirals, and a state SA in which all spirals are absorbed at the boundaries of our simulation domain. We find, for both TP06 and TNNPO4 models, that spiral-wave dynamics depends sensitively on the amplitude and frequency of PD and the initial condition. We examine how these different types of spiral-wave states can be eliminated in the presence of PD by the application of low-amplitude pulses by square- and rectangular-mesh suppression techniques. We suggest specific experiments that can test the results of our simulations.

Effect of dark matter halo on global spiral modes in galaxies

Low surface brightness (LSB) galaxies form a major class of galaxies, and are characterized by low disc surface density and low star formation rate. These are known to be dominated by dark matter halo from the innermost regions. Here, we study the role of the dark matter halo on the grand-design, m = 2, spiral modes in a galactic disc by carrying out a global mode analysis in the WKB approximation. The Bohr-Sommerfeld quantization rule is used to determine how many discrete global spiral modes are permitted. First, a typical superthin, LSB galaxy UGC 7321 is studied by taking only the galactic disc, modelled as a fluid; and then the disc embedded in a dark matter halo. We find that both cases permit the existence of global spiral modes. This is in contrast to earlier results where the inclusion of dark matter halo was shown to nearly fully suppress local, swing-amplified spiral features. Although technically global modes are permitted in the fluid model as shown here, we argue that due to lack of tidal interactions, these are not triggered in LSB galaxies. For comparison, we carried out a similar analysis for the Galaxy, for which the dark matter halo does not dominate in the inner regions. We show that here too the dark matter halo has little effect, hence the disc embedded in a halo is also able to support global modes. The derived pattern speed of the global mode agrees fairly well with the observed value for the Galaxy.

Topological constraints on scroll and spiral waves in excitable media

A conservation equation for topological charges of phase singularities (scroll and spiral waves) in excitable media is given. It provides some topological properties of scroll (spiral) waves: for example, the topological charge of the generated or annihilated spiral pair must be opposite. Additionally, we obtain another equation on scroll waves, which shows that singular filaments of scroll waves occur on a set of one-dimensional curves which may be either closed loops or infinite lines.

The study of banded spherulite patterns by coupled logistic map lattice model

Banded spherulite patterns are simulated in two dimensions by means of a coupled logistic map lattice model. Both target pattern and spiral pattern which have been proved to be existent experimentally in banded spherulite are obtained by choosing suitable parameters in the model. The simulation results also indicate that the band spacing is decreased with the increase of parameter mu in the logistic map and increased with the increase of the coupling parameter epsilon, which is quite similar to the results in some experiments. Moreover, the relationship between the parameters and the corresponding patterns is obtained, and the target patterns and spiral patterns are distinguished for a given group of initial values, which may guide the study of banded spherulite.

Simulation of Banded Spherulite Patterns by Coupled Logistic Map Lattice Model in Three Dimensions

Banded spherulite patterns are simulated in three dimensions by means of a Coupled Logistic map lattice model. The patterns obtained by numerical calculation are consistent with those in experiments. The simulation results also indicate that the hand spacing is decreased with the increase of parameter mu in the Logistic map and increased with the increase of the coupling parameter e for cube lattices, and increased with the increase of the thickness of the lattice for polymer film, which is quite similar to the results in some experiments. Spiral pattern in three dimensions is also shown in this paper, which helps us understand the form of banded spherulite in polymers.

Artificial surfaces of intertwined square spirals:A CPW model

Intertwining planar spirals arranged in doubly periodic arrays enables a substantially subwavelength response of the unit cell smaller than 1/40 of wavelength with large fractional bandwidths. These properties are important for application at low frequencies, conformal curved surfaces, or with compact radiators. It is shown that interleaving counter-wound spiral arms extended into adjacent unit cells dramatically increase the array equivalent capacitance while reducing the inductance. A coplanar waveguide (CPW) model has been developed to analytically estimate the equivalent capacitance and inductance of intertwined spiral array elements in terms of their geometrical parameters. The proposed CPW model is shown to provide an accurate prediction of the fundamental resonance frequency and can be instrumental in the design of the arrays for a specified frequency response. © 2012 IEEE.

Phenomenology of Resonance Reflectance by Intertwined Spiral Arrays

The physical mechanisms underlying the dramatic reduction of the unit cell electrical size along with broadening fractional bandwidths provided by intertwined spiral arrays are discussed. Based upon this insight, a multi-strip transmission line (MTL) model is developed to analytically estimate the equivalent capacitance and inductance of intertwined spiral array elements in terms of their geometrical parameters. The proposed MTL model enables an accurate prediction of the fundamental resonance characteristics and provides a valuable tool for design of the arrays with the specified frequency response.

Suprathermal electron evolution in a Parker spiral magnetic field

Suprathermal electrons (>70 eV) form a small fraction of the total solar wind electron density but serve as valuable tracers of heliospheric magnetic field topology. Their usefulness as tracers of magnetic loops with both feet rooted on the Sun, however, most likely fades as the loops expand beyond some distance owing to scattering. As a first step toward quantifying that distance, we construct an observationally constrained model for the evolution of the suprathermal electron pitch-angle distributions on open field lines. We begin with a near-Sun isotropic distribution moving antisunward along a Parker spiral magnetic field while conserving magnetic moment, resulting in a field-aligned strahl within a few solar radii. Past this point, the distribution undergoes little evolution with heliocentric distance. We then add constant (with heliocentric distance, energy, and pitch angle) ad-hoc pitch-angle scattering. Close to the Sun, pitch-angle focusing still dominates, again resulting in a narrow strahl. Farther from the Sun, however, pitch-angle scattering dominates because focusing is effectively weakened by the increasing angle between the magnetic field direction and intensity gradient, a result of the spiral field. We determine the amount of scattering required to match Ulysses observations of strahl width in the fast solar wind, providing an important tool for inferring the large-scale properties and topologies of field lines in the interplanetary medium. Although the pitch-angle scattering term is independent of energy, time-of-flight effects in the spiral geometry result in an energy dependence of the strahl width that is in the observed sense although weaker in magnitude.

Breaks in the radial oxygen abundance and corotation radius of three spiral galaxies

The correlation between the breaks in the metallicity distribution and the corotation radius of spiral galaxies has been already advocated in the past and is predicted by a chemodynamical model of our Galaxy that effectively introduces the role of spiral arms in the star formation rate. In this work, we present photometric and spectroscopic observations made with the Gemini Telescope for three of the best candidates of spiral galaxies to have the corotation inside the optical disc: IC 0167, NGC 1042 and NGC 6907. We observed the most intense and well-distributed H ii regions of these galaxies, deriving reliable galactocentric distances and oxygen abundances by applying different statistical methods. From these results, we confirm the presence of variations in the gradients of metallicity of these galaxies that are possibly correlated with the corotation resonance.

GALACTIC NONLINEAR DYNAMIC MODEL

We develop a model for spiral galaxies based on a nonlinear realization of the Newtonian dynamics starting from the momentum and mass conservations in the phase space. The radial solution exhibits a rotation curve in qualitative accordance with the observational data.

A model to explain spermatophore implantation in cephalopods (Mollusca: Cephalopoda) and a discussion on its evolutionary origins and significance

Male coleoid cephalopods produce spermatophores that can attach autonomously on the female's body during a complex process of evagination called the spermatophoric reaction, during which the ejaculatory apparatus and spiral filament of the spermatophore are everted and exposed to the external milieu. In some deepwater cephalopods, the reaction leads to the intradermal implantation of the spermatophore, a hitherto enigmatic phenomenon. The present study builds upon several lines of evidence to propose that spermatophore implantation is probably achieved through the combination of (1) an evaginating-tube mechanism performed by the everting ejaculatory apparatus and (2) the anchorage provided by the spiral filament's stellate particles. The proposed theoretical model assumes that, as it is exposed to the external milieu, each whorl of the spiral filament anchors to the surrounding tissue by means of its sharp stellate particles. As the ejaculatory apparatus tip continues evaginating, it grows in diameter and stretches lengthwise, enlarging the diameter of the whorl and propelling it, consequently tearing and pushing the anchored tissue outward and backward, and opening space for the next whorl to attach. After the ejaculatory apparatus has been everted and has perforated tissue, the cement body is extruded, possibly aiding in final attachment, and the sperm mass comes to lie inside the female tissue, encompassed by the everted ejaculatory apparatus tube. It is proposed that this unique, efficient spermatophore attachment mechanism possibly evolved in intimate relationship with the adoption of an active mode of life by coleoids. The possible roles of predation pressure and sperm competition in the evolution of this mechanism are also discussed. (c) 2012 The Linnean Society of London, Biological Journal of the Linnean Society, 2012, 105, 711726.

Newtonian acceleration scales in spiral galaxies

We revisit the issue of the constancy of the dark matter (DM) and baryonic Newtonian acceleration scales within the DM scale radius by considering a large sample of late-type galaxies. We rely on a Markov Chain Monte Carlo method to estimate the parameters of the halo model and the stellar mass-to-light ratio and then propagate the uncertainties from the rotation curve data to the estimate of the acceleration scales. This procedure allows us to compile a catalogue of 58 objects with estimated values of the B-band absolute magnitude M-B, the virial mass M-vir, and the DM and baryonic Newtonian accelerations (denoted as g(DM)(r(0)) and g(bar)(r(0)), respectively) within the scale radius r(0) which we use to investigate whether it is possible to define a universal acceleration scale. We find a weak but statistically meaningful correlation with M-vir thus making us argue against the universality of the acceleration scales. However, the results somewhat depend on the sample adopted so that a careful analysis of selection effects should be carried out before any definitive conclusion can be drawn.