Successive eigenvalue relaxation: a new method for the generalized eigenvalue problem and convergence estimates

We present a new subspace iteration method for the efficient computation of several smallest eigenvalues of the generalized eigenvalue problem Au = lambda Bu for symmetric positive definite operators A and B. We call this method successive eigenvalue relaxation, or the SER method (homoechon of the classical successive over-relaxation, or SOR method for linear systems). In particular, there are two significant features of SER which render it computationally attractive: (i) it can effectively deal with preconditioned large-scale eigenvalue problems, and (ii) its practical implementation does not require any information about the preconditioner used: it can routinely accommodate sophisticated preconditioners designed to meet more exacting requirements (e.g. three-dimensional elasticity problems with small thickness parameters). We endow SER with theoretical convergence estimates allowing for multiple and clusters of eigenvalues and illustrate their usefulness in a numerical example for a discretized partial differential equation exhibiting clusters of eigenvalues

Atheroprone flow activates inflammation via endothelial ATP-dependent P2X7-p38 signalling

Objective: Atherosclerosis is a focal disease occurring at arterial sites of disturbed blood flow that generates low oscillating shear stress. Endothelial inflammatory signalling is enhanced at sites of disturbed flow via mechanisms that are incompletely understood. The influence of disturbed flow on endothelial ATP receptors and downstream signalling was assessed. Methods and Results: Cultured human endothelial cells were exposed to atheroprotective (high uniform) or atheroprone (low oscillatory) shear stress for 72 hours prior to assessment of ATP responses. Imaging of cells loaded with a calcium-sensitive fluorescent dye revealed that atheroprone flow enhanced extracellular calcium influx in response to 300µM BzATP. Pretreatment with pharmacological inhibitors demonstrated that this process required P2X7 receptors. The mechanism involved altered expression of P2X7, which was induced by atheroprone flow conditions in cultured cells. Similarly, en face staining of the murine aorta revealed enriched P2X7 expression at an atheroprone site. Functional studies in cultured endothelial cells showed that atheroprone flow induced p38 phosphorylation and upregulation of E-selectin and IL-8 secretion via a P2X7-dependent mechanism. Moreover, genetic deletion of P2X7 significantly reduced E-selectin at atheroprone regions of the murine aorta. Conclusions: These findings reveal that P2X7 is regulated by shear forces leading to its accumulation at atheroprone sites that are exposed to disturbed patterns of blood flow. P2X7 promotes endothelial inflammation at atheroprone sites by transducing ATP signals into p38 activation. Thus P2X7 integrates vascular mechanical responses with purinergic signalling to promote endothelial dysfunction and may provide an attractive potential therapeutic target to prevent or reduce atherosclerosis

Endothelial repair in stented arteries is accelerated by inhibition of Rho-associated protein kinase.

AIMS: Stent deployment causes endothelial cell (EC) denudation, which promotes in-stent restenosis and thrombosis. Thus endothelial regrowth in stented arteries is an important therapeutic goal. Stent struts modify local hemodynamics, however the effects of flow pertubation on EC injury and repair are incompletely understood. By studying the effects of stent struts on flow and EC migration we identified an intervention that promotes endothelial repair in stented arteries. METHODS AND RESULTS: In vitro and in vivo models were developed to monitor endothelialization under flow and the influence of stent struts. A 2D parallel-plate flow chamber with 100 μm ridges arranged perpendicular to the flow was used. Live cell imaging coupled to computational fluid dynamic simulations revealed that EC migrate in the direction of flow upstream from the ridges but subsequently accumulate downstream from ridges at sites of bidirectional flow. The mechanism of EC trapping by bidirectional flow involved reduced migratory polarity associated with altered actin dynamics. Inhibition of Rho-associated protein kinase (ROCK) enhanced endothelialization of ridged surfaces by promoting migratory polarity under bidirectional flow (p<0.01). To more closely mimic the in vivo situation we cultured EC on the inner surface of polydimethylsiloxane tubing containing Coroflex Blue stents (65 μm struts) and monitored migration. ROCK inhibition significantly enhanced EC accumulation downstream from struts under flow (p<0.05). We investigated the effects of ROCK inhibition on re-endothelialization in vivo using a porcine model of EC denudation and stent placement. En face staining and confocal microscopy revealed that inhibition of ROCK using fasudil (30 mg/day via osmotic minipump) significantly increased re-endothelialization of stented carotid arteries (p<0.05). CONCLUSIONS: Stent struts delay endothelial repair by generating localised bidirectional flow which traps migrating EC. ROCK inhibitors accelerate endothelial repair of stented arteries by enhancing EC polarity and migration through regions of bidirectional flow

RAGE Expression in Human T Cells: A Link between Environmental Factors and Adaptive Immune Responses

The Receptor for Advanced Glycation Endproducts (RAGE) is a scavenger ligand that binds glycated endproducts as well as molecules released during cell death such as S100b and HMGB1. RAGE is expressed on antigen presenting cells where it may participate in activation of innate immune responses but its role in adaptive human immune responses has not been described. We have found that RAGE is expressed intracellularly in human T cells following TCR activation but constitutively on T cells from patients with diabetes. The levels of RAGE on T cells from patients with diabetes are not related to the level of glucose control. It co-localizes to the endosomes. Its expression increases in activated T cells from healthy control subjects but bystander cells also express RAGE after stimulation of the antigen specific T cells. RAGE ligands enhance RAGE expression. In patients with T1D, the level of RAGE expression decreases with T cell activation. RAGE+ T cells express higher levels of IL-17A, CD107a, and IL-5 than RAGE− cells from the same individual with T1D. Our studies have identified the expression of RAGE on adaptive immune cells and a role for this receptor and its ligands in modulating human immune responses

Towards accurate and precise T1 and extracellular volume mapping in the myocardium: a guide to current pitfalls and their solutions

Mapping of the longitudinal relaxation time (T1) and extracellular volume (ECV) offers a means of identifying pathological changes in myocardial tissue, including diffuse changes that may be invisible to existing T1-weighted methods. This technique has recently shown strong clinical utility for pathologies such as Anderson- Fabry disease and amyloidosis and has generated clinical interest as a possible means of detecting small changes in diffuse fibrosis; however, scatter in T1 and ECV estimates offers challenges for detecting these changes, and bias limits comparisons between sites and vendors. There are several technical and physiological pitfalls that influence the accuracy (bias) and precision (repeatability) of T1 and ECV mapping methods. The goal of this review is to describe the most significant of these, and detail current solutions, in order to aid scientists and clinicians to maximise the utility of T1 mapping in their clinical or research setting. A detailed summary of technical and physiological factors, issues relating to contrast agents, and specific disease-related issues is provided, along with some considerations on the future directions of the field. Towards accurate and precise T1 and extracellular volume mapping in the myocardium: a guide to current pitfalls and their solutions. Available from: https://www.researchgate.net/publication/317548806_Towards_accurate_and_precise_T1_and_extracellular_volume_mapping_in_the_myocardium_a_guide_to_current_pitfalls_and_their_solutions [accessed Jun 13, 2017]

'Les fleurs du mal' II: a dynamically adaptive wavelet method of arbitrary lines for nonlinear evolutionary problems-capturing steep moving fronts

C. Baudelaire's 'les fleurs du mal' is an allusion to various new developments ('les fleurs') of the method of arbitrary lines (mal) [L.S. Xanthis, C. Schwab, The method of arbitrary lines, C.R. Acad. Sci. Paris, Sér. I 312 (1991) 181–187]. Here we extend the wavelet-mal methodology (C.R. Mécanique 362, 2004) to the solution of nonlinear evolutionary partial differential equations (PDE) in arbitrary domains, exemplified by Burgers’ equation. We employ the 'arbitrary Lagrangian–Eulerian' (ALE) formulation and some attractive properties of the wavelet approximation theory to develop a dynamically adaptive, wavelet-mal solver that is capable of capturing the anisotropic, or multi-scale character of the steep (shock-like) moving fronts that arise in such problems. We show the efficacy and high accuracy of the wavelet-mal methodology by numerical examples involving the Burgers' equation in two spatial dimensions

'Les fleurs du mal': an adaptive wavelet method of arbitrary lines I: convection-diffusion problems

Baudelaire's ‘les fleurs du mal’ refers to various new developments ('les fleurs') of the method of arbitrary lines (mal), since it was first published (in C. R. Acad. Sci. Paris, Sér. I, in 1991). Here we revisit the basic mal (semi-discretization) methodology for stationary convection–diffusion problems and develop an adaptive, wavelet-based solver that is capable of capturing the thin layers that arise in such problems. We show the efficacy and high accuracy of the wavelet-mal solver by applying it to a challenging 2D problem involving both boundary and interior layers