Tomographic reconstruction of shock layer flows

The tomographic reconstruction of supersonic flows faces two challenges. Firstly, techniques used in the past, such as the direct Fourier method (DFM) (Gottlieb and Gustafsson in On the direct Fourier method for computer tomography, 1998; Morton in Tomographic imaging of supersonic flows, 1995) or various backprojection (Kak and Slaney in Principles of computerized tomographic imaging, vol. 33 in Classics in Applied Mathematics, 2001) techniques, have only been able to reconstruct areas of the flow which are upstream of any opaque objects, such as a model. Secondly, shock waves create sharp discontinuities in flow properties, which can be difficult to reconstruct both in position and in magnitude with limited data. This paper will present a reconstruction method, matrix inversion using ray-tracing and least squares conjugate gradient (MI-RLS), which uses geometric ray-tracing and a sparse matrix iterative solver (Paige and Saunders in ACM Trans. Math. Softw. 8(1):43–71, 1982) to overcome both of these challenges. It will be shown, through testing with a phantom object described in tomographic literature, that the results compare favourably to those produced by the DFM technique. Finally, the method will be used to reconstruct three-dimensional density fields from interferometric shock layer images, with good resolution (Faletič in Tomographic reconstruction of shock layer flows, 2005). This paper was based on work that was presented at the 3rd International Symposium on Interdisciplinary Shock Wave Research, Canberra, Australia, March 1–3, 2006.     

On-chip pre-concentration and complexation of [¹⁸F]fluoride ions via regenerable anion exchange particles for radiochemical synthesis of Positron Emission Tomography tracers

Microfluidic approaches have demonstrated a relevant impact on radiochemical reactions involving Positron Emission Tomography (PET) nuclides, due to shorter reaction times and smaller precursor quantities. However, little attention has been given to the integration of the initial pre-concentration and drying of radioactive [(18)F]fluoride ions, required for the labeling of radiotracer compounds. In this work we report the design, fabrication and implementation of a glass microfluidic device filled with recyclable anion exchange particles for the repeated recovery of [(18)F] and [(19)F]fluoride ions. The device was first tested with non radioactive [(19)F]fluoride ions and it was shown to repeatedly trap and elute >95% fluoride over 40 successive experimental runs with no decrease in efficiency. The same device was then tested for the trapping and release of [(18)F]fluoride ions over 20 experiments with no measurable decrease in performance. Finally, the [(18)F]fluoride ions were eluted as a K(18)F/K2.2.2 complex, dried by repeated dissolution in acetonitrile and evaporation of residual water, and reacted with ethyl ditosylate (EtDT) leading to the desired product ([(18)F]fluoroethyltosylate) with 96 ± 3% yield (RCY). The overall time needed for conditioning, trapping, elution and regeneration was less than 6 min. This approach will be of great benefit towards an integrated platform able to perform faster and safer radiochemical synthesis on the micro-scale.     

Covering shadows with a smaller volume

For n?2 a construction is given for convex bodies K and L in Rn such that the orthogonal projection Lu onto the subspace u^⊥ contains a translate of Ku for every direction u, while the volumes of K and L satisfy Vn(K)>Vn(L).A more general construction is then given for n-dimensional convex bodies K and L such that each orthogonal projection Lξ onto a k-dimensional subspace ξ contains a translate of Kξ, while the mth intrinsic volumes of K and L satisfy Vm(K)>Vm(L) for all m>k.For each k=1,…,n, we then define the collection Cn,k to be the closure (under the Hausdorff topology) of all Blaschke combinations of suitably defined cylinder sets (prisms).It is subsequently shown that, if L∈Cn,k, and if the orthogonal projection Lξ contains a translate of Kξ for every k-dimensional subspace ξ of Rn, then Vn(K)?Vn(L).The families Cn,k, called k-cylinder bodies of Rn, form a strictly increasing chain

Cn,1⊂Cn,2⊂?⊂Cn,n−1⊂Cn,n,     

CT在腺瘤性结节性甲状腺肿和乳头状甲状腺癌鉴别诊断中的价值

目的探讨CT在腺瘤性结节性甲状腺肿（ANG）和乳头状甲状腺癌（PTC）鉴别诊断中的价值。方法搜集经病理证实的105例112枚ANG和181例196枚PTC的CT资料,对性别、年龄、瘤体的形态、甲状腺边缘中断征、钙化、强化程度、增强后边界、淋巴结转移进行分析,统计强化程度高于周围甲状腺对ANG的诊断和甲状腺边缘中断征对PTC的诊断敏感度、特异度、阳性预测值、准确度。结果 ANG和PTC在瘤体形态、甲状腺边缘中断征、细钙化、粗钙化、强化程度、增强后瘤体边缘等方面均有统计学意义（均P＜0.05）,而在是否多发、环状钙化方面均无统计学差异（均P＞0.05）。181例PTC中,淋巴结转移75例。强化程度高于周围甲状腺对ANG诊断的敏感度、特异度、阳性预测值、准确度分别为67.9%、100%、100%、87.6%。甲状腺边缘中断征对PTC诊断的敏感度、特异度、阳性预测值、准确度分别为87.0%、91.1%、93.6%、88.6%。结论瘤体形态规则、强化程度高于周围甲状腺有助于ANG的诊断,而瘤体形态不规则、甲状腺边缘中断征、细钙化、粗钙化、淋巴结转移等有助于PTC的诊断;是否多发和环状钙化对ANG和PTC的鉴别诊断无意义。     

Power limitations in fiber-optic frequency-division multiplexed systems

Abstract

Launch power is limited to the milliwatt level by stimulated Brillouin scattering (SBS) in a single-channel, coherent fiber-optic network. Increasing the number of frequency-division multiplexed channels causes the power limit to decrease quickly to submilliwatt levels due to three-wave intermodulation to keep the signal-to-noise ratio from deteriorating significantly. As the number of channels increases, stimulated Raman scattering (SRS) begins to dominate. If a maximum of 0.5–dB depletion in the highest-frequency channel is allowed, SRS dominates when the number of multiplexed channels reaches about 300. Generally, the launch-power-limiting phenomenon is dependent on the number of channels being multiplexed.     

Discrete tomography: Determination of finite sets by X-rays

We study the determination of finite subsets of the integer lattice , , by X-rays. In this context, an X-ray of a set in a direction gives the number of points in the set on each line parallel to . For practical reasons, only X-rays in lattice directions, that is, directions parallel to a nonzero vector in the lattice, are permitted. By combining methods from algebraic number theory and convexity, we prove that there are four prescribed lattice directions such that convex subsets of (i.e., finite subsets with ) are determined, among all such sets, by their X-rays in these directions. We also show that three X-rays do not suffice for this purpose. This answers a question of Larry Shepp, and yields a stability result related to Hammer's X-ray problem. We further show that any set of seven prescribed mutually nonparallel lattice directions in have the property that convex subsets of are determined, among all such sets, by their X-rays in these directions. We also consider the use of orthogonal projections in the interactive technique of successive determination, in which the information from previous projections can be used in deciding the direction for the next projection. We obtain results for finite subsets of the integer lattice and also for arbitrary finite subsets of Euclidean space which are the best possible with respect to the numbers of projections used.

     

CycloSiFA: The Next Generation of Silicon-Based Fluoride Acceptors for Positron Emission Tomography (PET)

The ring-opening Si-fluorination of a variety of azasilole derivatives cyclo-1-(iPr₂Si)−4-X−C₆H₃−2-CH₂NR ( 4 : R=2,6-iPr₂C₆H₃, X=H; 4 a : R=2,4,6-Me₃C₆H₂, X=H; 9 : R=2,6-iPr₂C₆H₃, X=tBuMe₂SiO; 10 : R=2,6-iPr₂C₆H₃, X=OH; 13 : R=2,6-iPr₂C₆H₃, X=HCCCH₂O; 22 : R=2,6-iPr₂C₆H₃, X=tBuMe₂SiCH₂O) with different ¹⁹F-fluoride sources was studied, optimized and the experience gained was used in a translational approach to create a straightforward ¹⁸F-labelling protocol for the azasilole derivatives [¹⁸F] 6 and [¹⁸F] 14 . The latter constitutes a potential clickable CycloSiFA prosthetic group which might be used in PET tracer development using Cu-catalysed triazole formation. Based on our findings, CycloSiFA has the potential to become a new entry into non-canonical labelling methodologies for radioactive PET tracer development.     

基于蛇形光路的PET探测器作用深度提取方法

为实现正电子发射断层成像(Positron Emission Tomography,PET)探测器的作用深度(Depth Of Interaction,DOI)信息获取,本文提出一种基于分光技术的探测器设计方案.探测器采用晶体单元与硅光电倍增管(Silicon Photomultiplier,SiPM)一对一耦合、蛇形光路的设计和单端Anger加权读出方法进行DOI解码.基于GATE软件进行蒙特卡罗模拟,建立8×1的LSO晶体阵列(单根晶体尺寸3.1×3.1×20mm3);模拟泛场照射获取位置查找表;并进行不同深度的模拟,获得各晶体在各深度的空间分辨率.结果显示所模拟的探测器模块DOI分辨率在1.0~6.7mm之间,平均值为3.2mm.本文提出的基于蛇形光路的PET探测器方案能在维持系统成本和复杂度的前提下实现DOI解码,提升PET系统的成像性能.     

THREE-DIMENSIONAL NUMERICAL LOCALIZATION OF IMPERFECTIONS BASED ON A LIMIT MODEL IN ELECTRIC FIELD AND A LIMIT PERTURBATION MODEL

From a limit model in electric field obtained by letting the frequency vanish in the time-harmonic Maxwell equations, we consider a limit perturbation model in the tangential boundary trace of the curl of the electric field for localizing numerically certain small electromagnetic inhomogeneities, in a three-dimensional bounded domain. We introduce here two localization procedures resulting from the combination of this limit perturbation model with each of the following inversion processes： the Current Projection method and an Inverse Fourier method. Each localization procedure uses, as data, a finite number of boundary measurements, and is employed in the single inhomogeneity case; only the one based on an Inverse Fourier method is required in the multiple inhomogeneities case. Our localization approach is numerically suitable for the context of inhomogeneities that are not purely electric. We compare the numerical results obtained from the two localization procedures in the single inhomogeneity configuration, and describe, in various settings of multiple inhomogeneities, the results provided by the procedure based on an Inverse Fourier method.