Improved image contrast with mangafodipir trisodium (MnDPDP) during MR-guided percutaneous cryosurgery of the liver

The present study was undertaken to measure the gain observed in the liver-to-tumor contrast of perioperative images when using mangafodipir trisodium, a liver-specific contrast agent, during percutaneous cryosurgery of the liver performed under the guidance of magnetic resonance images. Retrospective quantitative analyses of MR images were performed on eleven patients having a total of 30 liver tumors treated by MR-guided percutaneous cryosurgery. An initial group of four patients were treated with no contrast agent, and was compared with a second group of 7 patients who received an intravenous injection of 5 microM/kg of mangafodipir for their cryosurgery. The percutaneous cryosurgery was monitored under the near-real-time-imaging mode of a 0.5T open-configuration MRI system using a T(1)-weighted Gradient-recalled echo pulse sequence. A significant improvement in the liver-to-tumor contrast-to-noise ratio was observed with mangafodipir (p < 0.05, paired t test) in 0.5T preoperative images. Along with the stability of the mangafodipir contrast enhancement during the entire cryosurgical procedure, the resulting gain in contrast allowed for better visualizing the presence of residual untreated tumor margins at the periphery of the cryosurgery iceball directly from perioperative images acquired with patients under narcosis. Consequently, it not only became easier for the interventionalist to determine the need for an additional cryoprobe to increase the size of the iceball during the procedure, but also to decide on the appropriate end point of the cryosurgery.     

A Lindelöf space with no Lindelöf subspace of size

A consistent example of an uncountable Lindelöf (and hence normal) space with no Lindelöf subspace of size is constructed. It remains unsolved whether extra set-theoretic assumptions are necessary for the existence of such a space. However, our space has size and is a -space, i.e., 's are open, and for such spaces extra set-theoretic assumptions turn out to be necessary.

     

On productively Lindelöf spaces

The class of spaces such that their product with every Lindelöf space is Lindelöf is not well-understood. We prove a number of new results concerning such productively Lindelöf spaces with some extra property, mainly assuming the Continuum Hypothesis.     

CONSTRUCTION OF CONCEPTUAL KNOWLEDGE: THE CASE OF COMPUTER-AIDED EXPLORATION OF PERIOD DOUBLING

This research focuses on students using an experimental approach with computer software to give visual meaning to symbolic ideas and to provide a basis for further generalisation. They use computer software that draws orbits of x=f(x) iteration and are encouraged to investigate the iterations of f_λ(x)=λx(1-x) as λ increases. The iterations pass through successive acts of period-doubling as λ=λ₀, λ₁, λ₂, …,. students are invited to estimate the values of λ and to compare their experimental results with the theory of geometric convergence. The supervisor acts as a mentor, using various styles of questioning to provoke links between different ideas. A variety of data is collected to give evidence for the ways in which students develop conceptual links between symbolic theory and the visual and numeric aspects of computer experiment.     

Characterizingω 1 and the long line by their topological elementary reflections

Given a topological space 〈X, T〉 ∈M, an elementary submodel of set theory, we defineX _Mto beX ∩M with the topology generated by {U ∩M : U ∈T ∩M}. We prove that it is undecidable whetherX _Mhomeomorphic toω ₁ impliesX =X _M,yet it is true in ZFC that ifX _Mis homeomorphic to the long line, thenX =X _M.The former result generalizes to other cardinals of uncountable confinality while the latter generalizes to connected, locally compact, locally hereditarily LindelöfT ₂ spaces.     

Electroanalysis of some nitro-compounds using bulk bismuth electrode

Nitro compounds were usually determined electrochemically using the mercury drop with DPP technique. An alternate way to toxic mercury is the increasing use of the bismuth electrode as thin film electrodeposited on glassy carbon or copper for example, or as bulk bismuth disc. In the present paper several nitrocompounds were investigated: mononitrophenols, dinitrophenol, nitrobenzoic acid, nitrobenzaldehyde and a well known pesticide, parathion, which has a nitro group in para position on a phenyl cycle. Bulk bismuth electrode was a disc (cross section of a rod of 5 mm diameter embedded in Teflon®) polished with silicon carbide disc (P2400) and sonicated to remove any abrasive particle. The supporting electrolyte was the acetic buffer (pH 4.7), which was found suitable for all these compounds. Using cathodic sweep differential pulse voltammetry, it was noticed that according to the position of the nitro group on the cycle, the peak potentials might range between ?300 to ?750 mV vs. SCE. Limits of detection (LOD) and limits of quantification (LOQ) were determined for each compound whose response for increasing concentration was linear in the ～3–50 µmol L^?1 whatever the considered molecule. Adsorptive differential pulse voltammetry was found very efficient to determine parathion, because this molecule adsorbs on bismuth at ?0.2 V vs. SCE. Bulk bismuth electrode was compared to the hanging mercury drop electrode and led to an identical behaviour.     

Developing a theory of mathematical growth

In this paper I formulate a basic theoretical framework for the ways in which mathematical thinking grows as the child develops and matures into an adult. There is an essential need to focus on important phenomena, to name them and reflect on them to build rich concepts that are both powerful in use and yet simple to connect to other concepts. The child begins with human perception and action, linking them together in a coherent way. Symbols are introduced to denote mathematical processes (such as addition) that can be compressed as mathematical concepts (such as sum) to give symbols that operate flexibly as process and concept (procept). Knowledge becomes more sophisticated through building on experiences met before, focussing on relationships between properties, leading eventually to the advanced mathematics of concept definition and deduction. This gives a theoretical framework in which three modes of operation develop and grow in sophistication from conceptual-embodiment using thought experiments, to proceptual-symbolism using computation and symbol manipulation, then on to axiomatic-formalism based on concept definitions and formal proof.     

Productively Lindelöf and indestructibly Lindelöf spaces

There has recently been considerable interest in productively Lindelöf spaces, i.e. spaces such that their product with every Lindelöf space is Lindelöf. See e.g. , , , , ,  and , and work in progress by Brendle and Raghavan. Here we make several related remarks about such spaces. Indestructible Lindelöf spaces, i.e. spaces that remain Lindelöf in every countably closed forcing extension, were introduced in [28]. Their connection with topological games and selection principles was explored in [27]. We find further connections here.     

Quantitative sodium magnetic resonance imaging in food: Addressing sensitivity issues using single quantum chemical shift imaging at high field

According to various health organizations, the global consumption of salt is higher than recommended and needs to be reduced. Ideally, this would be achieved without losing the taste of the salt itself. In order to accomplish this goal, both at the industrial and domestic levels, we need to understand the mechanisms that govern the final distribution of salt in food. The in-silico solutions in use today greatly over-simplify the real food structure. Measuring the quantity of sodium at the local level is key to understanding sodium distribution. Sodium magnetic resonance imaging (MRI), a non-destructive approach, is the ideal choice for salt mapping along transformational process. However, the low sensitivity of the sodium nucleus and its short relaxation times make this imaging difficult. In this paper, we show how sodium MRI can be used to highlight salt heterogeneities in food products, provided that the temporal decay is modeled, thus correcting for differences in relaxation speeds. We then propose an abacus which shows the relationship between the signal-to-noise ratio of the sodium MRI, the salt concentration, the B0 field, and the spatial and temporal resolutions. This abacus simplifies making the right choices when implementing sodium MRI.