Integral representation of the linear Boltzmann operator for granular gas dynamics with applications

We investigate the properties of the collision operator associated to the linear Boltzmann equation for dissipative hard-spheres arising in granular gas dynamics. We establish that, as in the case of non-dissipative interactions, the gain collision operator is an integral operator whose kernel is made explicit. One deduces from this result a complete picture of the spectrum of the collision operator in an Hilbert space setting, generalizing results from T. Carleman to granular gases. In the same way, we obtain from this integral representation of the gain operator that the semigroup in L^1(\R \times \R,\d \x \otimes \d\v) associated to the linear Boltzmann equation for dissipative hard spheres is honest generalizing known results from the first author.Comment: 19 pages, to appear in Journal of Statistical Physic

Modelling and characterisation of a ultrasound-actuated needle for improved visibility in ultrasound-guided regional anaesthesia and tissue biopsy

AbstractClear needle visualisation is recognised as an unmet need for ultrasound guided percutaneous needle procedures including regional anaesthesia and tissue biopsy. With inadequate needle visibility, these procedures may result in serious complications or a failed operation. This paper reports analysis of the modal behaviour of a previously proposed ultrasound-actuated needle configuration, which may overcome this problem by improving needle visibility in colour Doppler imaging. It uses a piezoelectric transducer to actuate longitudinal resonant modes in needles (outer diameter 0.8–1.2mm, length>65mm). The factors that affect the needle’s vibration mode are identified, including the needle length, the transducer’s resonance frequency and the gripping position. Their effects are investigated using finite element modelling, with the conclusions validated experimentally. The actuated needle was inserted into porcine tissue up to 30mm depth and its visibility was observed under colour Doppler imaging. The piezoelectric transducer is able to generate longitudinal vibration with peak-to-peak amplitude up to 4μm at the needle tip with an actuating voltage of 20Vpp. Actuated in longitudinal vibration modes (distal mode at 27.6kHz and transducer mode at 42.2kHz) with a drive amplitude of 12–14Vpp, a 120mm needle is delineated as a coloured line in colour Doppler images, with both needle tip and shaft visualised. The improved needle visibility is maintained while the needle is advanced into the tissue, thus allowing tracking of the needle position in real time. Moreover, the needle tip is highlighted by strong coloured artefacts around the actuated needle generated by its flexural vibration. A limitation of the technique is that the transducer mode requires needles of specific lengths so that the needle’s resonance frequency matches the transducer. This may restrict the choice of needle lengths in clinical applications

Distinct choline metabolic profiles are associated with differences in gene expression for basal-like and luminal-like breast cancer xenograft models

<p>Abstract</p> <p>Background</p> <p>Increased concentrations of choline-containing compounds are frequently observed in breast carcinomas, and may serve as biomarkers for both diagnostic and treatment monitoring purposes. However, underlying mechanisms for the abnormal choline metabolism are poorly understood.</p> <p>Methods</p> <p>The concentrations of choline-derived metabolites were determined in xenografted primary human breast carcinomas, representing basal-like and luminal-like subtypes. Quantification of metabolites in fresh frozen tissue was performed using high-resolution magic angle spinning magnetic resonance spectroscopy (HR MAS MRS).</p> <p>The expression of genes involved in phosphatidylcholine (PtdCho) metabolism was retrieved from whole genome expression microarray analyses.</p> <p>The metabolite profiles from xenografts were compared with profiles from human breast cancer, sampled from patients with estrogen/progesterone receptor positive (ER+/PgR+) or triple negative (ER-/PgR-/HER2-) breast cancer.</p> <p>Results</p> <p>In basal-like xenografts, glycerophosphocholine (GPC) concentrations were higher than phosphocholine (PCho) concentrations, whereas this pattern was reversed in luminal-like xenografts. These differences may be explained by lower choline kinase (<it>CHKA</it>, <it>CHKB</it>) expression as well as higher PtdCho degradation mediated by higher expression of phospholipase A2 group 4A (<it>PLA2G4A</it>) and phospholipase B1 (<it>PLB1</it>) in the basal-like model. The glycine concentration was higher in the basal-like model. Although glycine could be derived from energy metabolism pathways, the gene expression data suggested a metabolic shift from PtdCho synthesis to glycine formation in basal-like xenografts. In agreement with results from the xenograft models, tissue samples from triple negative breast carcinomas had higher GPC/PCho ratio than samples from ER+/PgR+ carcinomas, suggesting that the choline metabolism in the experimental models is representative for luminal-like and basal-like human breast cancer.</p> <p>Conclusions</p> <p>The differences in choline metabolite concentrations corresponded well with differences in gene expression, demonstrating distinct metabolic profiles in the xenograft models representing basal-like and luminal-like breast cancer. The same characteristics of choline metabolite profiles were also observed in patient material from ER+/PgR+ and triple-negative breast cancer, suggesting that the xenografts are relevant model systems for studies of choline metabolism in luminal-like and basal-like breast cancer.</p

Integrative analyses identify modulators of response to neoadjuvant aromatase inhibitors in patients with early breast cancer

Introduction Aromatase inhibitors (AIs) are a vital component of estrogen receptor positive (ER+) breast cancer treatment. De novo and acquired resistance, however, is common. The aims of this study were to relate patterns of copy number aberrations to molecular and proliferative response to AIs, to study differences in the patterns of copy number aberrations between breast cancer samples pre- and post-AI neoadjuvant therapy, and to identify putative biomarkers for resistance to neoadjuvant AI therapy using an integrative analysis approach. Methods Samples from 84 patients derived from two neoadjuvant AI therapy trials were subjected to copy number profiling by microarray-based comparative genomic hybridisation (aCGH, n = 84), gene expression profiling (n = 47), matched pre- and post-AI aCGH (n = 19 pairs) and Ki67-based AI-response analysis (n = 39). Results Integrative analysis of these datasets identified a set of nine genes that, when amplified, were associated with a poor response to AIs, and were significantly overexpressed when amplified, including CHKA, LRP5 and SAPS3. Functional validation in vitro, using cell lines with and without amplification of these genes (SUM44, MDA-MB134-VI, T47D and MCF7) and a model of acquired AI-resistance (MCF7-LTED) identified CHKA as a gene that when amplified modulates estrogen receptor (ER)-driven proliferation, ER/estrogen response element (ERE) transactivation, expression of ER-regulated genes and phosphorylation of V-AKT murine thymoma viral oncogene homolog 1 (AKT1). Conclusions These data provide a rationale for investigation of the role of CHKA in further models of de novo and acquired resistance to AIs, and provide proof of concept that integrative genomic analyses can identify biologically relevant modulators of AI response

The Q2Q^2-dependence of the generalised Gerasimov-Drell-Hearn integral for the deuteron, proton and neutron

The Gerasimov-Drell-Hearn (GDH) sum rule connects the anomalous contribution to the magnetic moment of the target nucleus with an energy-weighted integral of the difference of the helicity-dependent photoabsorption cross sections. The data collected by HERMES with a deuterium target are presented together with a re-analysis of previous measurements on the proton. This provides a measurement of the generalised GDH integral covering simultaneously the nucleon-resonance and the deep inelastic scattering regions. The contribution of the nucleon-resonance region is seen to decrease rapidly with increasing $Q^2$. The DIS contribution is sizeable over the full measured range, even down to the lowest measured $Q^2$. As expected, at higher $Q^2$ the data are found to be in agreement with previous measurements of the first moment of $g_1$. From data on the deuteron and proton, the GDH integral for the neutron has been derived and the proton--neutron difference evaluated. This difference is found to satisfy the fundamental Bjorken sum rule at $Q^2 = 5$ GeV$^2$.Comment: 12 pages, 10 figure