Fractional diffusion models of cardiac electrical propagation: Role of structural heterogeneity in dispersion of repolarization

Impulse propagation in biological tissues is known to be modulated by structural heterogeneity. In cardiac muscle, improved understanding on how this heterogeneity influences electrical spread is key to advancing our interpretation of dispersion of repolarization. We propose fractional diffusion models as a novel mathematical description of structurally heterogeneous excitable media, as a means of representing the modulation of the total electric field by the secondary electrical sources associated with tissue inhomogeneities. Our results, analysed against in vivo human recordings and experimental data of different animal species, indicate that structural heterogeneity underlies relevant characteristics of cardiac electrical propagation at tissue level. These include conduction effects on action potential (AP) morphology, the shortening of AP duration along the activation pathway and the progressive modulation by premature beats of spatial patterns of dispersion of repolarization. The proposed approach may also have important implications in other research fields involving excitable complex media.

Topological properties and fractal analysis of a recurrence network constructed from fractional Brownian motions

Many studies have shown that we can gain additional information on time series by investigating their accompanying complex networks. In this work, we investigate the fundamental topological and fractal properties of recurrence networks constructed from fractional Brownian motions (FBMs). First, our results indicate that the constructed recurrence networks have exponential degree distributions; the average degree exponent 〈λ〉 increases first and then decreases with the increase of Hurst index H of the associated FBMs; the relationship between H and 〈λ〉 can be represented by a cubic polynomial function. We next focus on the motif rank distribution of recurrence networks, so that we can better understand networks at the local structure level. We find the interesting superfamily phenomenon, i.e., the recurrence networks with the same motif rank pattern being grouped into two superfamilies. Last, we numerically analyze the fractal and multifractal properties of recurrence networks. We find that the average fractal dimension 〈dB〉 of recurrence networks decreases with the Hurst index H of the associated FBMs, and their dependence approximately satisfies the linear formula 〈dB〉≈2-H, which means that the fractal dimension of the associated recurrence network is close to that of the graph of the FBM. Moreover, our numerical results of multifractal analysis show that the multifractality exists in these recurrence networks, and the multifractality of these networks becomes stronger at first and then weaker when the Hurst index of the associated time series becomes larger from 0.4 to 0.95. In particular, the recurrence network with the Hurst index H=0.5 possesses the strongest multifractality. In addition, the dependence relationships of the average information dimension 〈D(1)〉 and the average correlation dimension 〈D(2)〉 on the Hurst index H can also be fitted well with linear functions. Our results strongly suggest that the recurrence network inherits the basic characteristic and the fractal nature of the associated FBM series.

Numerical analysis of a new space-time variable fractional order advection-dispersion equation

Many physical processes appear to exhibit fractional order behavior that may vary with time and/or space. The continuum of order in the fractional calculus allows the order of the fractional operator to be considered as a variable. In this paper, we consider a new space–time variable fractional order advection–dispersion equation on a finite domain. The equation is obtained from the standard advection–dispersion equation by replacing the first-order time derivative by Coimbra’s variable fractional derivative of order α(x)∈(0,1]α(x)∈(0,1], and the first-order and second-order space derivatives by the Riemann–Liouville derivatives of order γ(x,t)∈(0,1]γ(x,t)∈(0,1] and β(x,t)∈(1,2]β(x,t)∈(1,2], respectively. We propose an implicit Euler approximation for the equation and investigate the stability and convergence of the approximation. Finally, numerical examples are provided to show that the implicit Euler approximation is computationally efficient.

Solution of a System of Generalized Abel Integral Equations Using Fractional Calculus

A method is presented for obtaining useful closed form solution of a system of generalized Abel integral equations by using the ideas of fractional integral operators and their applications. This system appears in solving certain mixed boundary value problems arising in the classical theory of elasticity.

Hydrogel-polymer electrolytes for electrochemical capacitors: an overview

Electrochemical capacitors are electrochemical devices with fast and highly reversible charge-storage and discharge capabilities. The devices are attractive for energy storage particularly in applications involving high-power requirements. Electrochemical capacitors employ two electrodes and an aqueous or a non-aqueous electrolyte, either in liquid or solid form; the latter provides the advantages of compactness, reliability, freedom from leakage of any liquid component and a large operating potential-window. One of the classes of solid electrolytes used in capacitors is polymer-based and they generally consist of dry solid-polymer electrolytes or gel-polymer electrolyte or composite-polymer electrolytes. Dry solid-polymer electrolytes suffer from poor ionic-conductivity values, between 10(-8) and 10(-7) S cm(-1) under ambient conditions, but are safer than gel-polymer electrolytes that exhibit high conductivity of ca. 10(-3) S cm(-1) under ambient conditions. The aforesaid polymer-based electrolytes have the advantages of a wide potential window of ca. 4 V and hence can provide high energy-density. Gel-polymer electrolytes are generally prepared using organic solvents that are environmentally malignant. Hence, replacement of organic solvents with water in gel-polymer electrolytes is desirable which also minimizes the device cost substantially. The water containing gel-polymer electrolytes, called hydrogel-polymer electrolytes, are, however, limited by a low operating potential-window of only about 1.23 V. This article reviews salient features of electrochemical capacitors employing hydrogel-polymer electrolytes.

Effect of Dietary Unsaturated Oils on the Biosynthesis of Cholesterol, and on Biliary and Fecal Excretion of Cholesterol and Bile Acids in Rats1

The aim of the present work was to investigate whether the hypocholesterolemic effect of polyunsaturated oils is due to inhibition of cholesterol synthesis or increased excretion of cholesterol and bile acids through the bile and feces of animals. Separate groups of rats were fed diets containing 10% safflower oil, coconut oil or hydrogenated vegetable oils for 30 days, after which the hepatic cholesterol and bile acid synthesis and their excretion through the bile and feces were studied. As compared to the rats in the other two groups, those given the diet containing 10% safflower oil showed markedly increased rates of bile flow and excreted through their bile and feces markedly higher amounts of cholesterol and bile acids. At the same time incorporation of [1-14C] acetate and [2-14C] mevalonate into the liver cholesterol and conversion of [4-14C] cholesterol into 14C-bile acids were also higher in the same rats. In the light of these observations it has been discussed that in the animals given polyunsaturated oils, biliary and fecal loss of cholesterol and bile acids far outweighs the activation of cholesterol synthesis and thereby effectively lowers the serum cholesterol levels.

A comparison of the excretion rate of endogenous purine derivatives in the urine of Bos indicus and Bos taurus steers

Estimates of microbial crude protein (MCP) production by ruminants, using a method based on the excretion of purine derivatives in urine, require an estimate of the excretion of endogenous purine derivatives (PD) by the animal. Current methods allocate a single value to all cattle. An experiment was carried out to compare the endogenous PD excretion in Bos taurus and high-content B. indicus (hereafter, B. indicus) cattle. Five Holstein–Friesian (B. taurus) and 5 Brahman (> 75% B. indicus) steers (mean liveweight 326 ± 3.0 kg) were used in a fasting study. Steers were fed a low-quality buffel grass (Cenchrus ciliaris; 59.4 g crude protein/kg dry matter) hay at estimated maintenance requirements for 19 days, after which hay intake was incrementally reduced for 2 days and the steers were fasted for 7 days. The excretion of PD in urine was measured daily for the last 6 days of the fasting period and the mean represented the daily endogenous PD excretion. Excretion of endogenous PD in the urine of B. indicus steers was less than half that of the B. taurus steers (190 µmol/kg W0.75.day v. 414 µmol/kg W0.75.day; combined s.e. 37.2 µmol/kg W0.75.day; P < 0.001). It was concluded that the use of a single value for endogenous PD excretion is inappropriate for use in MCP estimations and that subspecies-specific values would improve precision.

Thermodynamics of cobalt-manganese alloys using fluoride and oxide electrolytes

Abstract is not available.

Identification of dynamical systems with fractional derivative damping models using inverse sensitivity analysis

The problem of identifying parameters of time invariant linear dynamical systems with fractional derivative damping models, based on a spatially incomplete set of measured frequency response functions and experimentally determined eigensolutions, is considered. Methods based on inverse sensitivity analysis of damped eigensolutions and frequency response functions are developed. It is shown that the eigensensitivity method requires the development of derivatives of solutions of an asymmetric generalized eigenvalue problem. Both the first and second order inverse sensitivity analyses are considered. The study demonstrates the successful performance of the identification algorithms developed based on synthetic data on one, two and a 33 degrees of freedom vibrating systems with fractional dampers. Limited studies have also been conducted by combining finite element modeling with experimental data on accelerances measured in laboratory conditions on a system consisting of two steel beams rigidly joined together by a rubber hose. The method based on sensitivity of frequency response functions is shown to be more efficient than the eigensensitivity based method in identifying system parameters, especially for large scale systems.

On the order of the fractional Laplacian in determining the spatio-temporal evolution of a space-fractional model of cardiac electrophysiology

Space-fractional operators have been used with success in a variety of practical applications to describe transport processes in media characterised by spatial connectivity properties and high structural heterogeneity altering the classical laws of diffusion. This study provides a systematic investigation of the spatio-temporal effects of a space-fractional model in cardiac electrophysiology. We consider a simplified model of electrical pulse propagation through cardiac tissue, namely the monodomain formulation of the Beeler-Reuter cell model on insulated tissue fibres, and obtain a space-fractional modification of the model by using the spectral definition of the one-dimensional continuous fractional Laplacian. The spectral decomposition of the fractional operator allows us to develop an efficient numerical method for the space-fractional problem. Particular attention is paid to the role played by the fractional operator in determining the solution behaviour and to the identification of crucial differences between the non-fractional and the fractional cases. We find a positive linear dependence of the depolarization peak height and a power law decay of notch and dome peak amplitudes for decreasing orders of the fractional operator. Furthermore, we establish a quadratic relationship in conduction velocity, and quantify the increasingly wider action potential foot and more pronounced dispersion of action potential duration, as the fractional order is decreased. A discussion of the physiological interpretation of the presented findings is made.

Fractional power dependence of rate on activation energy for reactions with very low internal barriers

The dynamics of reactions with low internal barriers are studied both analytically and numerically for two different models. Exact expressions for the average rate,kI, are obtained by solving the associated first passage time problems. Both the average rate constant, kI, and the numerically calculated long-time rate constant, kL, show a fractional power law dependence on the barrier height for very low barriers. The crossover of the reaction dynamics from low to high barrier is investigated.

Characterization of a toxin from Parthenium hysterophorus and its mode of excretion in animals

Fractionation of methanolic extracts of air dried aerial parts ofParthenium resulted in the isolation of a toxic constituent which was identified as parthenin, the major sesquiterpene lactone from the weed. The LD50 (minimal lethal dose required to cause 50% mortality) for parthenin in rats was 42 mg/kg body weight. When [3H]-parthenin was given orally or by intravenous administration, radioactivity appeared in the milk of lactating laboratory and dairy animals. Tissue distribution of radioactivity revealed that maximum label was detectable in kidneys.

Mordenite-incorporated PVA-PSSA membranes as electrolytes for DMFCs

Composite membranes with mordenite (MOR) incorporated in poly vinyl alcohol (PVA)–polystyrene sulfonic acid (PSSA) blend tailored with varying degree of sulfonation are reported. Such a membrane comprises a dispersed phase of mordenite and a continuous phase of the polymer that help tuning the flow of methanol and water across it. The membranes on prolonged testing in a direct methanol fuel cell (DMFC) exhibit mitigated methanol cross-over from anode to the cathode. The membranes have been tested for their sorption behaviour, ion-exchange capacity, electrochemical selectivity and mechanical strength as also characterized by Fourier transform infrared spectroscopy and thermogravimetric analysis. Water release kinetics has been measured by magnetic resonance imaging (NMR imaging) and is found to be in agreement with the sorption data. Similarly, methanol release kinetics studied by volume-localized NMR spectroscopy (point resolved spectroscopy, PRESS) clearly demonstrates that the dispersion of mordenite in PVA–PSSA retards the methanol release kinetics considerably. A peak power-density of 74 mW/cm2 is achieved for the DMFC using a PVA–PSSA membrane electrolyte with 50% degree of sulfonation and 10 wt.% dispersed mordenite phase. A methanol cross-over current as low as 7.5 mA/cm2 with 2 M methanol feed at the DMFC anode is observed while using the optimized composite membrane as electrolyte in the DMFC, which is about 60% and 46% lower than Nafion-117 and PVA–PSSA membranes, respectively, when tested under identical conditions.

Urinary excretion of antioxidants in healthy humans following queen garnet plum juice ingestion: a new plum variety rich in antioxidant compounds

In recent years, there has been intense interest in the potential health benefits of dietary derived plant polyphenols and antioxidants. A new variety of Prunus salicina, Queen Garnet plum (QGP), was developed as a high anthocyanin, high antioxidant plum, in a Queensland Government breeding program. Following consumption of 400 mL QGP juice (QGPJ; 1,117 mg anthocyanins) by two healthy male subjects, QGP anthocyanins (cyanidin-3-glucoside and cyanidin-3-rutinoside) were excreted mainly as methylated and glucuronidated metabolites in urine (0.5% of the ingested dose within 24 h). Furthermore, QGPJ intake resulted in a threefold increase in hippuric acid excretion (potential biomarker for total polyphenols intake and metabolite), an increased urinary antioxidant capacity and a decreased malondialdehyde excretion (biomarker for oxidative stress) within 24 h as compared with the polyphenol-/antioxidant-free control. Results from this pilot study suggest that metabolites, and not the native QGP anthocyanins/polyphenols, are most likely the bioactive compounds in vivo.