The volume in focus: hardwareassisted focus and context effects for volume visualization

In many volume visualization applications there is some region of specific interest where we wish to see fine detail - yet we do not want to lose an impression of the overall picture. In this research we apply the notion of focus and context to texture-based volume rendering. A framework has been developed that enables users to achieve fast volumetric distortion and other effects of practical use. The framework has been implemented through direct programming of the graphics processor and integrated into a volume rendering system. Our driving application is the effective visualization of aneurysms, an important issue in neurosurgery. We have developed and evaluated an easy-to-use system that allows a neurosurgicalteam to explore the nature of cerebral aneurysms, visualizing the aneurysm itself in fine detail while still retaining a view of the surrounding vasculature

Targeted therapies to improve CFTR function in cystic fibrosis

Cystic fibrosis is the most common genetically determined, life-limiting disorder in populations of European ancestry. The genetic basis of cystic fibrosis is well established to be mutations in the cystic fibrosis transmembrane conductance regulator (CFTR) gene that codes for an apical membrane chloride channel principally expressed by epithelial cells. Conventional approaches to cystic fibrosis care involve a heavy daily burden of supportive treatments to combat lung infection, help clear airway secretions and maintain nutritional status. In 2012, a new era of precision medicine in cystic fibrosis therapeutics began with the licensing of a small molecule, ivacaftor, which successfully targets the underlying defect and improves CFTR function in a subgroup of patients in a genotype-specific manner. Here, we review the three main targeted approaches that have been adopted to improve CFTR function: potentiators, which recover the function of CFTR at the apical surface of epithelial cells that is disrupted in class III and IV genetic mutations; correctors, which improve intracellular processing of CFTR, increasing surface expression, in class II mutations; and production correctors or read-through agents, which promote transcription of CFTR in class I mutations. The further development of such approaches offers great promise for future therapeutic strategies in cystic fibrosis

On a conjecture of Bennewitz, and the behaviour of the Titchmarsh-Weyl matrix near a pole

For any real limit-$n$ $2n$th-order selfadjoint linear differential expression on $[0,\infty)$, Titchmarsh- Weyl matrices $M(\lambda)$ can be defined. Two matrices of particu lar interest are the matrices $M_D(\lambda)$ and $M_N(\lambda)$ assoc iated respectively with Dirichlet and Neumann boundary conditions at $x=0$. These satisfy $M_D(\lambda) = -M_{N}(\lambda)^{-1}$. It is known that when these matrices have poles (which can only lie on the real axis) the existence of valid HELP inequalities depends on their behaviour in the neighbourhood of these poles. We prove a conjecture of Bennewitz and use it, together with a new algorithm for computing the Laurent expansion of a Titchmarsh-Weyl matrix in the neighbourhood of a pole, to investigate the existence of HELP inequalities for a number of differential equations which have so far proved awkward to analys

Non-Linear Canonical Transformations in Classical and Quantum Mechanics

$p$-Mechanics is a consistent physical theory which describes both classical and quantum mechanics simultaneously through the representation theory of the Heisenberg group. In this paper we describe how non-linear canonical transformations affect $p$-mechanical observables and states. Using this we show how canonical transformations change a quantum mechanical system. We seek an operator on the set of $p$-mechanical observables which corresponds to the classical canonical transformation. In order to do this we derive a set of integral equations which when solved will give us the coherent state expansion of this operator. The motivation for these integral equations comes from the work of Moshinsky and a variety of collaborators. We consider a number of examples and discuss the use of these equations for non-bijective transformations.Comment: The paper has been improved in light of a referee's report. The paper will appear in the Journal of Mathematical Physics. 24 pages, no figure

Small oscillations and the Heisenberg Lie algebra

The Adler Kostant Symes [A-K-S] scheme is used to describe mechanical systems for quadratic Hamiltonians of $\mathbb R^{2n}$ on coadjoint orbits of the Heisenberg Lie group. The coadjoint orbits are realized in a solvable Lie algebra $\mathfrak g$ that admits an ad-invariant metric. Its quadratic induces the Hamiltonian on the orbits, whose Hamiltonian system is equivalent to that one on $\mathbb R^{2n}$. This system is a Lax pair equation whose solution can be computed with help of the Adjoint representation. For a certain class of functions, the Poisson commutativity on the coadjoint orbits in $\mathfrak g$ is related to the commutativity of a family of derivations of the 2n+1-dimensional Heisenberg Lie algebra $\mathfrak h_n$. Therefore the complete integrability is related to the existence of an n-dimensional abelian subalgebra of certain derivations in $\mathfrak h_n$. For instance, the motion of n-uncoupled harmonic oscillators near an equilibrium position can be described with this setting.Comment: 17 pages, it contains a theory about small oscillations in terms of the AKS schem

Elevated Paracellular Glucose Flux across Cystic Fibrosis Airway Epithelial Monolayers Is an Important Factor for Pseudomonas aeruginosa Growth.

People with cystic fibrosis (CF) who develop related diabetes (CFRD) have accelerated pulmonary decline, increased infection with antibiotic-resistant Pseudomonas aeruginosa and increased pulmonary exacerbations. We have previously shown that glucose concentrations are elevated in airway surface liquid (ASL) of people with CF, particularly in those with CFRD. We therefore explored the hypotheses that glucose homeostasis is altered in CF airway epithelia and that elevation of glucose flux into ASL drives increased bacterial growth, with an effect over and above other cystic fibrosis transmembrane conductance regulator (CFTR)-related ASL abnormalities. The aim of this study was to compare the mechanisms governing airway glucose homeostasis in CF and non-CF primary human bronchial epithelial (HBE) monolayers, under normal conditions and in the presence of Ps. aeruginosa filtrate. HBE-bacterial co-cultures were performed in the presence of 5 mM or 15 mM basolateral glucose to investigate how changes in blood glucose, such as those seen in CFRD, affects luminal Ps. aeruginosa growth. Calu-3 cell monolayers were used to evaluate the potential importance of glucose on Ps. aeruginosa growth, in comparison to other hallmarks of the CF ASL, namely mucus hyperviscosity and impaired CFTR-dependent fluid secretions. We show that elevation of basolateral glucose promotes the apical growth of Ps. aeruginosa on CF airway epithelial monolayers more than non-CF monolayers. Ps. aeruginosa secretions elicited more glucose flux across CF airway epithelial monolayers compared to non-CF monolayers which we propose increases glucose availability in ASL for bacterial growth. In addition, elevating basolateral glucose increased Ps. aeruginosa growth over and above any CFTR-dependent effects and the presence or absence of mucus in Calu-3 airway epithelia-bacteria co-cultures. Together these studies highlight the importance of glucose as an additional factor in promoting Ps. aeruginosa growth and respiratory infection in CF disease