Nonaxisymmetric mathematical model of the cardiac left ventricle anatomy

We describe a mathematical model of the shape and fibre direction field of the cardiac left ventricle. The ventricle is composed of surfaces which model myocardial sheets. On each surface, we construct a set of curves corresponding to myocardial fibres. Tangents to these curves form the myofibres direction field. The fibres are made as images of semicircle chords parallel to its diameter. To specify the left ventricle shape, we use a special coordinate system where the left ventricle boundaries are coordinate surfaces. We propose an analytic mapping from the semicircle to the special coordinate system. The model is correlated with Torrent-Guasp’s concept of the unique muscular band and with Pettigrew’s idea of nested surfaces. Subsequently, two models of concrete normal canine and human left ventricles are constructed based on experimental Diffusion Tensor Magnetic Resonance Imaging data. The input data for the models is only the left ventricle shape. In a local coordinate system connected with the left ventricle meridional section, we calculate two fibre inclination angles, i.e. true fibre angle and helix angle. We obtained the angles found from the Diffusion Tensor Magnetic Resonance Imaging data and compared them with the model angles. We give the angle plots and show that the model adequately reproduces the fibre architecture in the majority of the left ventricle wall. Based on the mathematical model proposed, one can construct a numerical mesh that makes it possible to solve electrophysiological and mechanical left ventricle activity problems in norm and pathology. In the special coordinate system mentioned, the numerical scheme is written in a rectangular area and the boundary conditions can simply be written. By changing the model parameters, one can set a general or regional ventricular wall thickening or the left ventricle shape change, which is typical for certain cardiac pathologies

The maximum depth of shower with E sub 0 larger than 10(17) eV on average characteristics of EAS different components

The extensive air shower (EAS) development model independent method of the determination of a maximum depth of shower (X sub m) is considered. X sub m values obtained on various EAS parameters are in a good agreement

Large-scale distribution of cosmic rays in right ascension as observed by the Yakutsk array at energies above 101810^{18} eV

We present the results of searches for anisotropy in the right ascension ($RA$) distribution of arrival directions of cosmic rays (CRs) detected with the Yakutsk array during the 1974--2008 observational period in the energy range above $10^{18}$ eV. Two methods of analysis are applied to two sub-samples of the data. Particularly, estimations of the first and second harmonic amplitudes are given, as well as the first harmonic phase in adjacent energy intervals. Analysis of variance demonstrates a significant contraction of the minimal width of the $RA$ distribution in the energy bin $(10^{19},1.78\times10^{19})$ eV with respect to the isotropic distribution, which may be attributed to a possible source of CRs within the interval $RA\in(15^0,45^0)$.Comment: 8 pages, 6 figures, 2 tables, accepted for publication in Astroparticle Physic

Drift of scroll wave filaments in an anisotropic model of the left ventricle of the human heart

Scroll waves are three-dimensional vortices which occur in excitable media. Their formation in the heart results in the onset of cardiac arrhythmias, and the dynamics of their filaments determine the arrhythmia type. Most studies of filament dynamics were performed in domains with simple geometries and generic description of the anisotropy of cardiac tissue. Recently, we developed an analytical model of fibre structure and anatomy of the left ventricle (LV) of the human heart. Here, we perform a systematic study of the dynamics of scroll wave filaments for the cases of positive and negative tension in this anatomical model. We study the various possible shapes of LV and different degree of anisotropy of cardiac tissue. We show that, for positive filament tension, the final position of scroll wave filament is mainly determined by the thickness of the myocardial wall but, however, anisotropy attracts the filament to the LV apex. For negative filament tension, the filament buckles, and for most cases, tends to the apex of the heart with no or slight dependency on the thickness of the LV. We discuss the mechanisms of the observed phenomena and their implications for cardiac arrhythmias

Enhancement of the Yakutsk array by atmospheric Cherenkov telescopes to study cosmic rays above 101510^{15} eV

The aim of the Yakutsk array enhancement project is to create an instrument to study the highest-energy galactic cosmic rays (CRs) -- their sources, energy spectrum, and mass composition. Additionally, there will be unique capabilities for investigations in the transition region between galactic and extragalactic components of CRs. Using the well-developed imaging atmospheric Cherenkov telescope technique adapted to the energy region $E>10^{15}$ eV, we plan to measure the longitudinal structure parameters of the shower, e.g., angular and temporal distributions of the Cherenkov signal related to $X_{max}$ and the mass composition of CRs. The main advantages of the Yakutsk array, such as its multi-component measurements of extensive air showers, and model-independent CR energy estimation based on Cherenkov light measurements, will be inherited by the instrument to be created.Comment: Proceedings of ECRS-2010, Turku; submitted to ASTRA (Astrophys. Space Sci. Trans

Constraints on the flux of primary cosmic-ray photons at energies E > 10^18 eV from Yakutsk muon data

Comparing the signals measured by the surface and underground scintillator detectors of the Yakutsk Extensive Air Shower Array, we place upper limits on the integral flux and the fraction of primary cosmic-ray photons with energies E > 10^18 eV, E > 2*10^18 eV and E > 4*10^18 eV. The large collected statistics of the showers measured by large-area muon detectors provides a sensitivity to photon fractions < 10^-2, thus achieving precision previously unreachable at ultra-high energies.Comment: journal version, including comparison to Auger results as requested by anonymous refere

Estimation of composition of cosmic rays with E sub zero approximately equals 10(17) - 10(18) eV

Fluctuations of the shower maximum depth obtained from analysis of electron and muon fluctuations and the extensive air showers (EAS) Cerenkov light on the Yakutsk array data and data of other arrays are considered. On the basis of these the estimation of composition of primaries with E sub 0 = 5.10 to the 17th power eV is received. Estimation of gamma-quanta flux with E sub 0 10 to the 17th power eV is given on the poor-muon showers