Anomalous thresholds and edge singularities in Electrical Impedance Tomography

Studies of models of current flow behaviour in Electrical Impedance Tomography (EIT) have shown that the current density distribution varies extremely rapidly near the edge of the electrodes used in the technique. This behaviour imposes severe restrictions on the numerical techniques used in image reconstruction algorithms. In this paper we have considered a simple two dimensional case and we have shown how the theory of end point/pinch singularities which was developed for studying the anomalous thresholds encountered in elementary particle physics can be used to give a complete description of the analytic structure of the current density near to the edge of the electrodes. As a byproduct of this study it was possible to give a complete description of the Riemann sheet manifold of the eigenfunctions of the logarithmic kernel. These methods can be readily extended to other weakly singular kernels.Comment: Correction of a misprint which occurred in the unnumbered formula preceding Eq. (14), LaTeX file as an uuencoded file, 40 pages with 12 figures, uses epsf.st

Surface dosimetry for breast radiotherapy in the presence of immobilization cast material

Curative breast radiotherapy typically leaves patients with varying degrees of cosmetic damage. One problem interfering with cosmetically acceptable breast radiotherapy is the external contour for large pendulous breasts which often results in high doses to skin folds. Thermoplastic casts are often employed to secure the breasts to maintain setup reproducibility and limit the presence of skin folds. This paper aims to determine changes in surface dose that can be attributed to the use of thermoplastic immobilization casts. Skin dose for a clinical hybrid conformal/IMRT breast plan was measured using radiochromic film and MOSFET detectors at a range ofwater equivalent depths representative of the different skin layers. The radiochromic film was used as an integrating dosimeter, while the MOSFETs were used for real-time dosimetry to isolate the contribution of skin dose from individual IMRT segments. Strips of film were placed at various locations on the breast and the MOSFETs were used to measure skin dose at 16 positions spaced along the film strips for comparison of data. The results showed an increase in skin dose in the presence of the immobilization cast of up to 45.7% and 62.3% of the skin dose without the immobilization cast present as measured with Gafchromic EBT film and MOSFETs, respectively. The increase in skin dose due to the immobilization cast varied with the angle of beam incidence and was greatest when the beam was normally incident on the phantom. The increase in surface dose with the immobilization cast was greater under entrance dose conditions compared to exit dose conditions

New Structural and Functional Contexts of the Dx[DN]xDG Linear Motif: Insights into Evolution of Calcium-Binding Proteins

Binding of calcium ions (Ca2+) to proteins can have profound effects on their structure and function. Common roles of calcium binding include structure stabilization and regulation of activity. It is known that diverse families – EF-hands being one of at least twelve – use a Dx[DN]xDG linear motif to bind calcium in near-identical fashion. Here, four novel structural contexts for the motif are described. Existing experimental data for one of them, a thermophilic archaeal subtilisin, demonstrate for the first time a role for Dx[DN]xDG-bound calcium in protein folding. An integrin-like embedding of the motif in the blade of a β-propeller fold – here named the calcium blade – is discovered in structures of bacterial and fungal proteins. Furthermore, sensitive database searches suggest a common origin for the calcium blade in β-propeller structures of different sizes and a pan-kingdom distribution of these proteins. Factors favouring the multiple convergent evolution of the motif appear to include its general Asp-richness, the regular spacing of the Asp residues and the fact that change of Asp into Gly and vice versa can occur though a single nucleotide change. Among the known structural contexts for the Dx[DN]xDG motif, only the calcium blade and the EF-hand are currently found intracellularly in large numbers, perhaps because the higher extracellular concentration of Ca2+ allows for easier fixing of newly evolved motifs that have acquired useful functions. The analysis presented here will inform ongoing efforts toward prediction of similar calcium-binding motifs from sequence information alone

Kryptoracemates

Racemic crystals normally crystallise in centrosymmetric spacegroups containing equal numbers of enantiomers. More rarely, racemates may crystallise in non-centrosymmetric space-groups having glide symmetry or, even more rarely, in space-groups devoid of a centre of inversion, having no rotary-inversion axes nor glide plane. The latter class of crystals form the subject of the present bibliographic review – a survey of kryptoracemic behaviour. The term kryptoracemic alludes to the presence of a hidden or non-crystallographic centre of inversion between two molecules that might otherwise be expected to crystallise in an achiral space-group, often about a centre of inversion. Herein, examples of molecules with stereogenic centres crystallising in one of the 65 Sohncke space-groups are described. Genuine kryptoracemates, i.e. crystals comprising only enantiomorphous pairs are described followed by an overview of non-genuine kryptoracemates whereby the crystal also contains other species such as solvent and/or counterions. A full range, i.e. one to six, stereogenic centres are noted in genuine kryptoracemates. Examples will also be described whereby there are more that one enantiomeric pair of molecules in the crystallographic asymmetric unit. A more diverse range of examples are available for non-genuine kryptoracemates. There are unbalanced species where in addition to the enantiomeric pair of molecules, there is another enantiomeric molecule present. There are examples of genuine co-crystals, solvated species and of salts. Finally, special examples will be highlighted where the counterions are chiral and where they are disparate, both circumstances promoting kryptoracemic behaviour

POMPUS: an optimized EIT reconstruction algorithm

Electrical impedance tomography (EIT) is a non-invasive imaging technique which aims to image the impedance of material within a test volume from electrical measurements made on the surface. The reconstruction of impedance images is an ill-posed problem which is both extremely sensitive to noise and highly computationally intensive. This paper defines an experimental measurement in EIT and calculates optimal experiments which maximize the distinguishability between the region to be imaged and a best estimate conductivity distribution. These optimal experiments can be derived from measurements made on the boundary. We describe a reconstruction algorithm, known as POMPUS, which is based on the use of optimal experiments. We have shown that, given some mild constraints, if POMPUS converges, it converges to a stationary point of our objective function. It is demonstrated to be many times faster than standard, Newton based, reconstruction algorithms. Results using synthetic data indicate that the images produced by POMPUS are comparable to those produced by these standard algorithms