Fiber architecture in remodeled myocardium revealed with a quantitative diffusion CMR tractography framework and histological validation

Background: The study of myofiber reorganization in the remote zone after myocardial infarction has been performed in 2D. Microstructural reorganization in remodeled hearts, however, can only be fully appreciated by considering myofibers as continuous 3D entities. The aim of this study was therefore to develop a technique for quantitative 3D diffusion CMR tractography of the heart, and to apply this method to quantify fiber architecture in the remote zone of remodeled hearts. Methods: Diffusion Tensor CMR of normal human, sheep, and rat hearts, as well as infarcted sheep hearts was performed ex vivo. Fiber tracts were generated with a fourth-order Runge-Kutta integration technique and classified statistically by the median, mean, maximum, or minimum helix angle (HA) along the tract. An index of tract coherence was derived from the relationship between these HA statistics. Histological validation was performed using phase-contrast microscopy. Results: In normal hearts, the subendocardial and subepicardial myofibers had a positive and negative HA, respectively, forming a symmetric distribution around the midmyocardium. However, in the remote zone of the infarcted hearts, a significant positive shift in HA was observed. The ratio between negative and positive HA variance was reduced from 0.96 +/- 0.16 in normal hearts to 0.22 +/- 0.08 in the remote zone of the remodeled hearts (p<0.05). This was confirmed histologically by the reduction of HA in the subepicardium from -52.03 degrees +/- 2.94 degrees in normal hearts to -37.48 degrees +/- 4.05 degrees in the remote zone of the remodeled hearts (p < 0.05). Conclusions: A significant reorganization of the 3D fiber continuum is observed in the remote zone of remodeled hearts. The positive (rightward) shift in HA in the remote zone is greatest in the subepicardium, but involves all layers of the myocardium. Tractography-based quantification, performed here for the first time in remodeled hearts, may provide a framework for assessing regional changes in the left ventricle following infarction.

Influence of Goertler vortices spanwise wavelength on heat transfer rates

The boundary layer over concave surfaces can be unstable due to centrifugal forces, giving rise to Goertler vortices. These vortices create two regions in the spanwise direction—the upwash and downwash regions. The downwash region is responsible for compressing the boundary layer toward the wall, increasing the heat transfer rate. The upwash region does the opposite. In the nonlinear development of the Goertler vortices, it can be observed that the upwash region becomes narrow and the spanwise–average heat transfer rate is higher than that for a Blasius boundary layer. This paper analyzes the influence of the spanwise wavelength of the Goertler the heat transfer. The equation is written in vorticity-velocity formulation. The time integration is done via a classical fourth-order Runge-Kutta method. The spatial derivatives are calculated using high-order compact finite difference and spectral methods. Three different wavelengths are analyzed. The results show that steady Goertler flow can increase the heat transfer rates to values close to the values of turbulence, without the existence of a secondary instability. The geometry (and computation domain) are presented

Mechanical Alterations in airway smooth muscle after interaction with indoor pollutant – A mathematical model.

The viscoelasticity of mammalian lung is determined by the mechanical properties and structural regulation of the airway smooth muscle (ASM). The exposure to polluted air may deteriorate these properties with harmful consequences to individual health. Formaldehyde (FA) is an important indoor pollutant found among volatile organic compounds. This pollutant permeates through the smooth muscle tissue forming covalent bonds between proteins in the extracellular matrix and intracellular protein structure changing mechanical properties of ASM and inducing asthma symptoms, such as airway hyperresponsiveness, even at low concentrations. In the experimental scenario, the mechanical effect of FA is the stiffening of the tissue, but the mechanism behind this effect is not fully understood. Thus, the aim of this study is to reproduce the mechanical behavior of the ASM, such as contraction and stretching, under FA action or not. For this, it was created a two-dimensional viscoelastic network model based on Voronoi tessellation solved using Runge-Kutta method of fourth order. The equilibrium configuration was reached when the forces in different parts of the network were equal. This model simulates the mechanical behavior of ASM through of a network of dashpots and springs. This dashpot-spring mechanical coupling mimics the composition of the actomyosin machinery of ASM through the contraction of springs to a minimum length. We hypothesized that formation of covalent bonds, due to the FA action, can be represented in the model by a simple change in the elastic constant of the springs, while the action of methacholine (MCh) reduce the equilibrium length of the spring. A sigmoid curve of tension as a function of MCh doses was obtained, showing increased tension when the muscle strip was exposed to FA. Our simulations suggest that FA, at a concentration of 0.1 ppm, can affect the elastic properties of the smooth muscle ¯bers by a factor of 120%. We also analyze the dynamic mechanical properties, observing the viscous and elastic behavior of the network. Finally, the proposed model, although simple, incorporates the phenomenology of both MCh and FA and reproduces experimental results observed with in vitro exposure of smooth muscle to FA. Thus, this new mechanical approach incorporates several well know features of the contractile system of the cells in a tissue level model. The model can also be used in different biological scales.

Mechanical alterations in airway smooth muscle after interaction with indoor pollutant - A mathematical model

The viscoelasticity of mammalian lung is determined by the mechanical properties and structural regulation of the airway smooth muscle (ASM). The exposure to polluted air may deteriorate these properties with harmful consequences to individual health. Formaldehyde (FA) is an important indoor pollutant found among volatile organic compounds. This pollutant permeates through the smooth muscle tissue forming covalent bonds between proteins in the extracellular matrix and intracellular protein structure changing mechanical properties of ASM and inducing asthma symptoms, such as airway hyperresponsiveness, even at low concentrations. In the experimental scenario, the mechanical effect of FA is the stiffening of the tissue, but the mechanism behind this effect is not fully w1derstood. Thus, the aim of this study is to reproduce the mechanical behavior of the ASM, such as contraction and stretching, under FA action or not. For this, it was created a two-dimensional viscoelastic network model based on Voronoi tessellation solved using Runge-Kutta method of fourth order. The equilibrium configuration was reached when the forces in different parts of the network were equal. This model simulates the mechanical behavior of ASM through of a network of dashpots and springs. This dashpot-spring mechanical coupling mimics the composition of the actomyosin machinery of ASM through the contraction of springs to a minimum length. We hypothesized that formation of covalent bonds, due to the FA action, can be represented in the model by a simple change in the elastic constant of the springs, while the action of methacholinc (MCh) reduce the equilibrium length of the spring. A sigmoid curve of tension as a function of MCh doses was obtained, showing increased tension when the muscle strip was exposed to FA. Our simulations suggest that FA, at a concentration of 0.1 ppm, can affect the elastic properties of the smooth muscle fibers by a factor of 120%. We also analyze the dynamic mechanical properties, observing the viscous and elastic behavior of the network. Finally, the proposed model, although simple, ir1corporates the phenomenology of both MCh and FA and reproduces experirnental results observed with ir1 vitro exposure of smooth muscle to .FA. Thus, this new mechanical approach incorporates several well know features of the contractile system of the cells ir1 a tissue level model. The model can also be used in different biological scales.

Predicted preoperative maximal static respiratory pressures in adult cardiac surgeries: evaluation of two formulas

Objectives: Cardiac surgery (CC) determines systemic and pulmonary changes that require special care. What motivated several studies conducted in healthy subjects to assess muscle strength were the awareness of the importance of respiratory muscle dysfunction in the development of respiratory failure. These studies used maximal inspiratory pressure (MIP) and maximal expiratory pressure (MEP) values. This study examined the concordance between the values predicted by the equations proposed by Black & Hyatt and Neder, and the measured values in cardiac surgery (CS) patients. Methods: Data were collected from preoperative evaluation forms. The Lin coefficient and Bland-Altman plots were used for statistical concordance analysis. The multiple linear regression and analysis of variance (ANOVA) were used to produce new formulas. Results: There were weak correlations of 0.22 and 0.19 in the MIP analysis and of 0.10 and 0.32 in the MEP analysis, for the formulas of Black & Hyatt and Neder, respectively. The ANOVA for both MIP and MEP were significant (P <0.0001), and the following formulas were developed: MIP = 88.82 - (0.51 x age) + (19.86 x gender), and MEP = 91.36 -(030 x age) + (29.92 x gender). Conclusions: The Black and Hyatt and Neder formulas predict highly discrepant values of MIP and MEP and should not be used to identify muscle weakness in CS patients.

Differential calculus and integration of generalized functions over membranes

In this paper we continue the development of the differential calculus started in Aragona et al. (Monatsh. Math. 144: 13-29, 2005). Guided by the so-called sharp topology and the interpretation of Colombeau generalized functions as point functions on generalized point sets, we introduce the notion of membranes and extend the definition of integrals, given in Aragona et al. (Monatsh. Math. 144: 13-29, 2005), to integrals defined on membranes. We use this to prove a generalized version of the Cauchy formula and to obtain the Goursat Theorem for generalized holomorphic functions. A number of results from classical differential and integral calculus, like the inverse and implicit function theorems and Green's theorem, are transferred to the generalized setting. Further, we indicate that solution formulas for transport and wave equations with generalized initial data can be obtained as well.

A new long-term lifetime distribution induced by a latent complementary risk framework

In this paper, we proposed a new three-parameter long-term lifetime distribution induced by a latent complementary risk framework with decreasing, increasing and unimodal hazard function, the long-term complementary exponential geometric distribution. The new distribution arises from latent competing risk scenarios, where the lifetime associated scenario, with a particular risk, is not observable, rather we observe only the maximum lifetime value among all risks, and the presence of long-term survival. The properties of the proposed distribution are discussed, including its probability density function and explicit algebraic formulas for its reliability, hazard and quantile functions and order statistics. The parameter estimation is based on the usual maximum-likelihood approach. A simulation study assesses the performance of the estimation procedure. We compare the new distribution with its particular cases, as well as with the long-term Weibull distribution on three real data sets, observing its potential and competitiveness in comparison with some usual long-term lifetime distributions.

Asymptotic integral kernel for ensembles of random normal matrices with radial potentials

The method of steepest descent is used to study the integral kernel of a family of normal random matrix ensembles with eigenvalue distribution P-N (z(1), ... , z(N)) = Z(N)(-1)e(-N)Sigma(N)(i=1) V-alpha(z(i)) Pi(1 <= i<j <= N) vertical bar z(i) - z(j)vertical bar(2), where V-alpha(z) = vertical bar z vertical bar(alpha), z epsilon C and alpha epsilon inverted left perpendicular0, infinity inverted right perpendicular. Asymptotic formulas with error estimate on sectors are obtained. A corollary of these expansions is a scaling limit for the n-point function in terms of the integral kernel for the classical Segal-Bargmann space. (C) 2012 American Institute of Physics. [http://dx.doi.org/10.1063/1.3688293]

Modelling Mathematical Reasoning in Physics Education

Many findings from research as well as reports from teachers describe students' problem solving strategies as manipulation of formulas by rote. The resulting dissatisfaction with quantitative physical textbook problems seems to influence the attitude towards the role of mathematics in physics education in general. Mathematics is often seen as a tool for calculation which hinders a conceptual understanding of physical principles. However, the role of mathematics cannot be reduced to this technical aspect. Hence, instead of putting mathematics away we delve into the nature of physical science to reveal the strong conceptual relationship between mathematics and physics. Moreover, we suggest that, for both prospective teaching and further research, a focus on deeply exploring such interdependency can significantly improve the understanding of physics. To provide a suitable basis, we develop a new model which can be used for analysing different levels of mathematical reasoning within physics. It is also a guideline for shifting the attention from technical to structural mathematical skills while teaching physics. We demonstrate its applicability for analysing physical-mathematical reasoning processes with an example.

Variance Effective Population Size for Dioecious Species

The concept of effective population size (N(e)) is an important measure of representativeness in many areas. In this research, we consider the statistical properties of the number of contributed gametes under practical situations by adapting Crow and Denninston's (1988) N(e) formulas for dioecious species. Three sampling procedures were considered. In all circumstances, results show that as the offspring sex ratio (r) deviates from 0.5, N(e) values become smaller, and the efficiency of gametic control for increasing N(e) is reduced. For finite populations, where all individuals are potentially functional parents, the reduction in N(e) due to an unequal sex ratio can be compensated for through female gametic control when 0.28 <= r <= 0.72. This outcome is important when r is unknown. When only a fraction of the individuals in a population is taken for reproduction, N(e) is meaningful only if the size of the reference population is clearly defined. Gametic control is a compensating factor in accession regeneration when the viability of the accession is around 70 or 75%. For germ-plasm collection, when parents are a very small fraction of the population, maximum N(e) will be approximately 47 and 57% of the total number of offspring sampled, with female gametic control, r varying between 0.3 and 0.5, and being constant over generations.

Bioelectrical impedance with different equations versus deuterium oxide dilution method for the inference of body composition in healthy older persons

There is no consensus regarding the accuracy of bioimpedance for the determination of body composition in older persons. This study aimed to compare the assessment of lean body mass of healthy older volunteers obtained by the deuterium dilution method (reference) with those obtained by two frequently used bioelectrical impedance formulas and one formula specifically developed for a Latin-American population. A cross-sectional study. Twenty one volunteers were studied, 12 women, with mean age 72 +/- 6.7 years. Urban community, Ribeiro Preto, Brazil. Fat free mass was determined, simultaneously, by the deuterium dilution method and bioelectrical impedance; results were compared. In bioelectrical impedance, body composition was calculated by the formulas of Deuremberg, Lukaski and Bolonchuck and Valencia et al. Lean body mass of the studied volunteers, as determined by bioelectrical impedance was 37.8 +/- 9.2 kg by the application of the Lukaski e Bolonchuk formula, 37.4 +/- 9.3 kg (Deuremberg) and 43.2 +/- 8.9 kg (Valencia et. al.). The results were significantly correlated to those obtained by the deuterium dilution method (41.6 +/- 9.3 Kg), with r=0.963, 0.932 and 0.971, respectively. Lean body mass obtained by the Valencia formula was the most accurate. In this study, lean body mass of older persons obtained by the bioelectrical impedance method showed good correlation with the values obtained by the deuterium dilution method. The formula of Valencia et al., developed for a Latin-American population, showed the best accuracy.

CP asymmetries in the supersymmetric trilepton signal at the LHC

In the CP-violating Minimal Supersymmetric Standard Model, we study the production of a neutralino-chargino pair at the LHC. For their decays into three leptons, we analyze CP asymmetries which are sensitive to the CP phases of the neutralino and chargino sector. We present analytical formulas for the entire production and decay process, and identify the CP-violating contributions in the spin correlation terms. This allows us to define the optimal CP asymmetries. We present a detailed numerical analysis of the cross sections, branching ratios, and the CP observables. For light neutralinos, charginos, and squarks, the asymmetries can reach several 10%. We estimate the discovery potential for the LHC to observe CP violation in the trilepton channel.

Nondetection Index of Anti-Islanding Passive Protection of Synchronous Distributed Generators

Synchronous distributed generators are prone to operate islanded after contingencies, which is usually not allowed due to safety and power-quality issues. Thus, there are several anti-islanding techniques; however, most of them present technical limitations so that they are likely to fail in certain situations. Therefore, it is important to quantify and determine whether the scheme under study is adequate or not. In this context, this paper proposes an index to evaluate the effectiveness of anti-islanding frequency-based relays commonly used to protect synchronous distributed generators. The method is based on the calculation of a numerical index that indicates the time period that the system is unprotected against islanding considering the global period of analysis. Although this index can precisely be calculated based on several electromagnetic transient simulations, a practical method is also proposed to calculate it directly from simple analytical formulas or lookup tables. The results have shown that the proposed approach can assist distribution engineers to assess and set anti-islanding protection schemes.

GEDI: a user-friendly toolbox for analysis of large-scale gene expression data

Abstract Background Several mathematical and statistical methods have been proposed in the last few years to analyze microarray data. Most of those methods involve complicated formulas, and software implementations that require advanced computer programming skills. Researchers from other areas may experience difficulties when they attempting to use those methods in their research. Here we present an user-friendly toolbox which allows large-scale gene expression analysis to be carried out by biomedical researchers with limited programming skills. Results Here, we introduce an user-friendly toolbox called GEDI (Gene Expression Data Interpreter), an extensible, open-source, and freely-available tool that we believe will be useful to a wide range of laboratories, and to researchers with no background in Mathematics and Computer Science, allowing them to analyze their own data by applying both classical and advanced approaches developed and recently published by Fujita et al. Conclusion GEDI is an integrated user-friendly viewer that combines the state of the art SVR, DVAR and SVAR algorithms, previously developed by us. It facilitates the application of SVR, DVAR and SVAR, further than the mathematical formulas present in the corresponding publications, and allows one to better understand the results by means of available visualizations. Both running the statistical methods and visualizing the results are carried out within the graphical user interface, rendering these algorithms accessible to the broad community of researchers in Molecular Biology.

Sharp estimates for eigenvalues of integral operators generated by dot product kernels on the sphere

We obtain explicit formulas for the eigenvalues of integral operators generated by continuous dot product kernels defined on the sphere via the usual gamma function. Using them, we present both, a procedure to describe sharp bounds for the eigenvalues and their asymptotic behavior near 0. We illustrate our results with examples, among them the integral operator generated by a Gaussian kernel. Finally, we sketch complex versions of our results to cover the cases when the sphere sits in a Hermitian space.