APOE genotype influences triglyceride and C-reactive protein responses to altered dietary fat intake in UK adults

Background: The response of plasma lipids to dietary fat manipulation is highly heterogeneous, with some indications that APOE genotype may be important. Objective: The objective was to use a prospective recruitment approach to determine the effect of dietary fat quantity and composition on both lipid and nonlipid cardiovascular disease biomarkers according to APOE genotype. Design: Participants had a mean (±SD) age of 51 ± 9 y and a BMI (in kg/m2) of 26.0 ± 3.8 (n = 44 E3/E3, n = 44 E3/E4) and followed a sequential dietary intervention (the SATgenϵ study) in which they were assigned to a low-fat diet, a high-fat high-SFA (HSF) diet, and the HSF diet with 3.45 g DHA/d (HSF-DHA), each for 8 wk. Fasting blood samples were collected at the end of each intervention arm. Results: An overall diet effect was evident for all cholesterol fractions (P < 0.01), with no significant genotype × diet interactions observed. A genotype × diet interaction (P = 0.033) was evident for plasma triglycerides, with 17% and 30% decreases in APOE3/E3 and APOE3/E4 individuals after the HSF-DHA diet relative to the low-fat diet. A significant genotype × diet interaction (P = 0.009) was also observed for C-reactive protein (CRP), with only significant increases in concentrations after the HSF and HSF-DHA diets relative to the low-fat diet in the APOE3/E4 group (P < 0.015). Conclusions: Relative to the wild-type APOE3/E3 group, our results indicate a greater sensitivity of fasting triglycerides and CRP to dietary fat manipulation in those with an APOE3/E4 genotype (25% population), with no effect of this allelic profile on cholesterol concentrations. The SATgenϵ study was registered at clinicaltrials.gov as NCT01384032.

Substance P released by TRPV1-expressing neurons produces reactive oxygen species that mediate ethanol-induced gastric injury

Although neurokinin 1 receptor antagonists prevent ethanol (EtOH)-induced gastric lesions, the mechanisms by which EtOH releases substance P (SP) and SP damages the mucosa are unknown. We hypothesized that EtOH activates transient receptor potential vanilloid 1 (TRPV1) on sensory nerves to release SP, which stimulates epithelial neurokinin 1 receptors to generate damaging reactive oxygen species (ROS). SP release was assayed in the mouse stomach, ROS were detected using dichlorofluorescein diacetate, and neurokinin 1 receptors were localized by immunofluorescence. EtOH-induced SP release was prevented by TRPV1 antagonism. High dose EtOH caused lesions, and TRPV1 or neurokinin 1 receptor antagonism and neurokinin 1 receptor deletion inhibited lesion formation. Coadministration of low, innocuous doses of EtOH and SP caused lesions by a TRPV1-independent but neurokinin 1 receptor-dependent process. EtOH, capsaicin, and SP stimulated generation of ROS by superficial gastric epithelial cells expressing neurokinin 1 receptors by a neurokinin 1 receptor-dependent mechanism. ROS scavengers prevented lesions induced by a high EtOH dose or a low EtOH dose plus SP. Gastric lesions are caused by an initial detrimental effect of EtOH, which is damaging only if associated with TRPV1 activation, SP release from sensory nerves, stimulation of neurokinin 1 receptors on epithelial cells, and ROS generation.

Carbon monoxide inhibits L-type Ca2+ channels via redox modulation of key cysteine residues by mitochondrial reactive oxygen species

Conditions of stress, such as myocardial infarction, stimulate up-regulation of heme oxygenase (HO-1) to provide cardioprotection. Here, we show that CO, a product of heme catabolism by HO-1, directly inhibits native rat cardiomyocyte L-type Ca2+ currents and the recombinant alpha1C subunit of the human cardiac L-type Ca2+ channel. CO (applied via a recognized CO donor molecule or as the dissolved gas) caused reversible, voltage-independent channel inhibition, which was dependent on the presence of a spliced insert in the cytoplasmic C-terminal region of the channel. Sequential molecular dissection and point mutagenesis identified three key cysteine residues within the proximal 31 amino acids of the splice insert required for CO sensitivity. CO-mediated inhibition was independent of nitric oxide and protein kinase G but was prevented by antioxidants and the reducing agent, dithiothreitol. Inhibition of NADPH oxidase and xanthine oxidase did not affect the inhibitory actions of CO. Instead, inhibitors of complex III (but not complex I) of the mitochondrial electron transport chain and a mitochondrially targeted antioxidant (Mito Q) fully prevented the effects of CO. Our data indicate that the cardioprotective effects of HO-1 activity may be attributable to an inhibitory action of CO on cardiac L-type Ca2+ channels. Inhibition arises from the ability of CO to promote generation of reactive oxygen species from complex III of mitochondria. This in turn leads to redox modulation of any or all of three critical cysteine residues in the channel's cytoplasmic C-terminal tail, resulting in channel inhibition.

Trefftz discontinuous Galerkin methods for acoustic scattering on locally refined meshes

We extend the a priori error analysis of Trefftz-discontinuous Galerkin methods for time-harmonic wave propagation problems developed in previous papers to acoustic scattering problems and locally refined meshes. To this aim, we prove refined regularity and stability results with explicit dependence of the stability constant on the wave number for non convex domains with non connected boundaries. Moreover, we devise a new choice of numerical flux parameters for which we can prove L2-error estimates in the case of locally refined meshes near the scatterer. This is the setting needed to develop a complete hp-convergence analysis.

SANS/WANS time-resolving neutron scattering studies of polymer phase transitions using NIMROD

We use new neutron scattering instrumentation to follow in a single quantitative time-resolving experiment, the three key scales of structural development which accompany the crystallisation of synthetic polymers. These length scales span 3 orders of magnitude of the scattering vector. The study of polymer crystallisation dates back to the pioneering experiments of Keller and others who discovered the chain-folded nature of the thin lamellae crystals which are normally found in synthetic polymers. The inherent connectivity of polymers makes their crystallisation a multiscale transformation. Much understanding has developed over the intervening fifty years but the process has remained something of a mystery. There are three key length scales. The chain folded lamellar thickness is ~ 10nm, the crystal unit cell is ~ 1nm and the detail of the chain conformation is ~ 0.1nm. In previous work these length scales have been addressed using different instrumention or were coupled using compromised geometries. More recently researchers have attempted to exploit coupled time-resolved small-angle and wide-angle x-ray experiments. These turned out to be challenging experiments much related to the challenge of placing the scattering intensity on an absolute scale. However, they did stimulate the possibility of new phenomena in the very early stages of crystallisation. Although there is now considerable doubt on such experiments, they drew attention to the basic question as to the process of crystallisation in long chain molecules. We have used NIMROD on the second target station at ISIS to follow all three length scales in a time-resolving manner for poly(e-caprolactone). The technique can provide a single set of data from 0.01 to 100Å-1 on the same vertical scale. We present the results using a multiple scale model of the crystallisation process in polymers to analyse the results.

A fast two-grid and finite section method for a class of integral equations on the real line with application to an acoustic scattering problem in the half-plane

We consider the numerical treatment of second kind integral equations on the real line of the form ∅(s) = ∫_(-∞)^(+∞)▒〖κ(s-t)z(t)ϕ(t)dt,s=R〗 (abbreviated ϕ= ψ+K_z ϕ) in which K ϵ L_1 (R), z ϵ L_∞ (R) and ψ ϵ BC(R), the space of bounded continuous functions on R, are assumed known and ϕ ϵ BC(R) is to be determined. We first derive sharp error estimates for the finite section approximation (reducing the range of integration to [-A, A]) via bounds on (1-K_z )^(-1)as an operator on spaces of weighted continuous functions. Numerical solution by a simple discrete collocation method on a uniform grid on R is then analysed: in the case when z is compactly supported this leads to a coefficient matrix which allows a rapid matrix-vector multiply via the FFT. To utilise this possibility we propose a modified two-grid iteration, a feature of which is that the coarse grid matrix is approximated by a banded matrix, and analyse convergence and computational cost. In cases where z is not compactly supported a combined finite section and two-grid algorithm can be applied and we extend the analysis to this case. As an application we consider acoustic scattering in the half-plane with a Robin or impedance boundary condition which we formulate as a boundary integral equation of the class studied. Our final result is that if z (related to the boundary impedance in the application) takes values in an appropriate compact subset Q of the complex plane, then the difference between ϕ(s)and its finite section approximation computed numerically using the iterative scheme proposed is ≤C_1 [kh log⁡〖(1⁄kh)+(1-Θ)^((-1)⁄2) (kA)^((-1)⁄2) 〗 ] in the interval [-ΘA,ΘA](Θ<1) for kh sufficiently small, where k is the wavenumber and h the grid spacing. Moreover this numerical approximation can be computed in ≤C_2 N log⁡N operations, where N = 2A/h is the number of degrees of freedom. The values of the constants C1 and C2 depend only on the set Q and not on the wavenumber k or the support of z.

The domain derivative in rough-surface scattering and rigorous estimates for first-order perturbation theory

We investigate Fréchet differentiability of the scattered field with respect to variation in the boundary in the case of time–harmonic acoustic scattering by an unbounded, sound–soft, one–dimensional rough surface. We rigorously prove the differentiability of the scattered field and derive a characterization of the Fréchet derivative as the solution to a Dirichlet boundary value problem. As an application of these results we give rigorous error estimates for first–order perturbation theory, justifying small perturbation methods that have a long history in the engineering literature. As an application of our rigorous estimates we show that a plane acoustic wave incident on a sound–soft rough surface can produce an unbounded scattered field.

On the stability and convergence of the finite section method for integral equation formulations of rough surface scattering

We consider the Dirichlet and Robin boundary value problems for the Helmholtz equation in a non-locally perturbed half-plane, modelling time harmonic acoustic scattering of an incident field by, respectively, sound-soft and impedance infinite rough surfaces.Recently proposed novel boundary integral equation formulations of these problems are discussed. It is usual in practical computations to truncate the infinite rough surface, solving a boundary integral equation on a finite section of the boundary, of length 2A, say. In the case of surfaces of small amplitude and slope we prove the stability and convergence as A→∞ of this approximation procedure. For surfaces of arbitrarily large amplitude and/or surface slope we prove stability and convergence of a modified finite section procedure in which the truncated boundary is ‘flattened’ in finite neighbourhoods of its two endpoints. Copyright © 2001 John Wiley & Sons, Ltd.

A Nyström method for a class of integral equations on the real line with applications to scattering by diffraction gratings and rough surfaces

We propose a Nystr¨om/product integration method for a class of second kind integral equations on the real line which arise in problems of two-dimensional scalar and elastic wave scattering by unbounded surfaces. Stability and convergence of the method is established with convergence rates dependent on the smoothness of components of the kernel. The method is applied to the problem of acoustic scattering by a sound soft one-dimensional surface which is the graph of a function f, and superalgebraic convergence is established in the case when f is infinitely smooth. Numerical results are presented illustrating this behavior for the case when f is periodic (the diffraction grating case). The Nystr¨om method for this problem is stable and convergent uniformly with respect to the period of the grating, in contrast to standard integral equation methods for diffraction gratings which fail at a countable set of grating periods.

Scattering by infinite one-dimensional rough surfaces

We consider the Dirichlet boundary-value problem for the Helmholtz equation in a non-locally perturbed half-plane. This problem models time-harmonic electromagnetic scattering by a one-dimensional, infinite, rough, perfectly conducting surface; the same problem arises in acoustic scattering by a sound-soft surface. ChandlerWilde & Zhang have suggested a radiation condition for this problem, a generalization of the Rayleigh expansion condition for diffraction gratings, and uniqueness of solution has been established. Recently, an integral equation formulation of the problem has also been proposed and, in the special case when the whole boundary is both Lyapunov and a small perturbation of a flat boundary, the unique solvability of this integral equation has been shown by Chandler-Wilde & Ross by operator perturbation arguments. In this paper we study the general case, with no limit on surface amplitudes or slopes, and show that the same integral equation has exactly one solution in the space of bounded and continuous functions for all wavenumbers. As an important corollary we prove that, for a variety of incident fields including the incident plane wave, the Dirichlet boundary-value problem for the scattered field has a unique solution.

Scattering of electromagnetic waves by rough interfaces and inhomogeneous layers

We consider a two-dimensional problem of scattering of a time-harmonic electromagnetic plane wave by an infinite inhomogeneous conducting or dielectric layer at the interface between semi-infinite homogeneous dielectric half-spaces. The magnetic permeability is assumed to be a fixed positive constant. The material properties of the media are characterized completely by an index of refraction, which is a bounded measurable function in the layer and takes positive constant values above and below the layer, corresponding to the homogeneous dielectric media. In this paper, we examine only the transverse magnetic (TM) polarization case. A radiation condition appropriate for scattering by infinite rough surfaces is introduced, a generalization of the Rayleigh expansion condition for diffraction gratings. With the help of the radiation condition the problem is reformulated as an equivalent mixed system of boundary and domain integral equations, consisting of second-kind integral equations over the layer and interfaces within the layer. Assumptions on the variation of the index of refraction in the layer are then imposed which prove to be sufficient, together with the radiation condition, to prove uniqueness of solution and nonexistence of guided wave modes. Recent, general results on the solvability of systems of second kind integral equations on unbounded domains establish existence of solution and continuous dependence in a weighted norm of the solution on the given data. The results obtained apply to the case of scattering by a rough interface between two dielectric media and to many other practical configurations.

A uniqueness result for scattering by infinite rough surfaces

Consider the Dirichlet boundary value problem for the Helmholtz equation in a non-locally perturbed half-plane with an unbounded, piecewise Lyapunov boundary. This problem models time-harmonic electromagnetic scattering in transverse magnetic polarization by one-dimensional rough, perfectly conducting surfaces. A radiation condition is introduced for the problem, which is a generalization of the usual one used in the study of diffraction by gratings when the solution is quasi-periodic, and allows a variety of incident fields including an incident plane wave to be included in the results obtained. We show in this paper that the boundary value problem for the scattered field has at most one solution. For the case when the whole boundary is Lyapunov and is a small perturbation of a flat boundary we also prove existence of solution and show a limiting absorption principle.

Acoustic scattering by an inhomogeneous layer on a rigid plate

The problem of scattering of time-harmonic acoustic waves by an inhomogeneous fluid layer on a rigid plate in R2 is considered. The density is assumed to be unity in the media: within the layer the sound speed is assumed to be an arbitrary bounded measurable function. The problem is modelled by the reduced wave equation with variable wavenumber in the layer and a Neumann condition on the plate. To formulate the problem and prove uniqueness of solution a radiation condition appropriate for scattering by infinite rough surfaces is introduced, a generalization of the Rayleigh expansion condition for diffraction gratings. With the help of the radiation condition the problem is reformulated as a system of two second kind integral equations over the layer and the plate. Under additional assumptions on the wavenumber in the layer, uniqueness of solution is proved and the nonexistence of guided wave solutions of the homogeneous problem established. General results on the solvability of systems of integral equations on unbounded domains are used to establish existence and continuous dependence in a weighted norm of the solution on the given data.

Scattering by rough surfaces: the Dirichlet problem for the Helmholtz equation in a non-locally perturbed half-plane

We consider the Dirichlet boundary value problem for the Helmholtz equation in a non-locally perturbed half-plane, this problem arising in electromagnetic scattering by one-dimensional rough, perfectly conducting surfaces. We propose a new boundary integral equation formulation for this problem, utilizing the Green's function for an impedance half-plane in place of the standard fundamental solution. We show, at least for surfaces not differing too much from the flat boundary, that the integral equation is uniquely solvable in the space of bounded and continuous functions, and hence that, for a variety of incident fields including an incident plane wave, the boundary value problem for the scattered field has a unique solution satisfying the limiting absorption principle. Finally, a result of continuous dependence of the solution on the boundary shape is obtained.

Uniqueness results for direct and inverse scattering by infinite surfaces in a lossy medium

We consider the Dirichlet boundary-value problem for the Helmholtz equation, Au + x2u = 0, with Imx > 0. in an hrbitrary bounded or unbounded open set C c W. Assuming continuity of the solution up to the boundary and a bound on growth a infinity, that lu(x)l < Cexp (Slxl), for some C > 0 and S~< Imx, we prove that the homogeneous problem has only the trivial salution. With this resnlt we prove uniqueness results for direct and inverse problems of scattering by a bounded or infinite obstacle.