针孔单光子发射计算机断层成像的空间分辨率研究

针孔单光子发射计算机断层(SPECT)成像的空间分辨率通常是根据Anger经验公式来进行估算,与实际测量存在较大偏差.本文通过对针孔成像的物理过程进行分析,提出了一个近似度更高的计算公式.利用精确的蒙特卡罗方法模拟针孔SPECT成像,采用OSEM(ordered subsets expectation maximization)算法对投影数据进行图像重建,并与模具实验进行比较,验证了理论公式的适用性.同时还讨论了体素尺寸、几何映射获取投影矩阵以及探测器尺寸与成像物体尺寸比值对断层图像空间分辨率的影响.实验结果显示,该理论公式所估算的空间分辨率比实验值平均偏小约10%,而Anger经验公式所估算的空间分辨率比实验值平均偏大约60%.因此,该理论公式能更好地估算针孔SPECT成像的空间分辨率,可为针孔SPECT系统的设计和使用提供有价值的参考.     

An improved automatic time-of-flight picker for medical ultrasound tomography

Objective and motivationTime-of-flight (TOF) tomography used by a clinical ultrasound tomography device can efficiently and reliably produce sound-speed images of the breast for cancer diagnosis. Accurate picking of TOFs of transmitted ultrasound signals is extremely important to ensure high-resolution and high-quality ultrasound sound-speed tomograms. Since manually picking is time-consuming for large datasets, we developed an improved automatic TOF picker based on the Akaike information criterion (AIC), as described in this paper.MethodsWe make use of an approach termed multi-model inference (model averaging), based on the calculated AIC values, to improve the accuracy of TOF picks. By using multi-model inference, our picking method incorporates all the information near the TOF of ultrasound signals. Median filtering and reciprocal pair comparison are also incorporated in our AIC picker to effectively remove outliers.ResultsWe validate our AIC picker using synthetic ultrasound waveforms, and demonstrate that our automatic TOF picker can accurately pick TOFs in the presence of random noise with absolute amplitudes up to 80% of the maximum absolute signal amplitude. We apply the new method to 1160 in vivo breast ultrasound waveforms, and compare the picked TOFs with manual picks and amplitude threshold picks. The mean value and standard deviation between our TOF picker and manual picking are 0.4 μs and 0.29 μs, while for amplitude threshold picker the values are 1.02 μs and 0.9 μs, respectively. Tomograms for in vivo breast data with high signal-to-noise ratio (SNR) (∼25 dB) and low SNR (∼18 dB) clearly demonstrate that our AIC picker is much less sensitive to the SNRs of the data, compared to the amplitude threshold picker.Discussion and conclusionsThe picking routine developed here is aimed at determining reliable quantitative values, necessary for adding diagnostic information to our clinical ultrasound tomography device - CURE. It has been successfully adopted into CURE, and allows us to generate such values reliably. We demonstrate that in vivo sound-speed tomograms with our TOF picks significantly improve the reconstruction accuracy and reduce image artifacts.     

三维电阻抗成像的体积元方法的数值模拟和分析

电阻抗成像是一类椭圆方程反问题,本文在三维区域上对其进行数值模拟和分析.对于椭圆方程Neumann边值正问题,本文提出了四面体单元上的一类对称体积元格式,并证明了格式的半正定性及解的存在性;引入单元形状矩阵的概念,简化了系数矩阵的计算;提出了对电阻率进行拼接逼近的方法来降低反问题求解规模,使之与正问题的求解规模相匹配;导出了误差泛函的Jacobi矩阵的计算公式,利用体积元格式的对称性和特殊的电流基向量,将每次迭代中需要求解的正问题的个数降到最低.一系列数值实验的结果验证了数学模型的可靠性和算法的可行性.本文所提出的这些方法,已成功应用于三维电阻抗成像的实际数值模拟.     

Numerical simulation and analysis of generalized difference method on triangular networks for electrical impedance tomography

Electrical impedance tomography is an inverse problem of elliptic differential equations. Numerical methods based on combining generalized difference method and Levenberg–Marquardt iteration on a planar domain are proposed. Positive semi-definiteness and existence of solution of the generalized difference scheme are proved. Element geometry matrix is introduced to shortcut calculation and standardize computer program. A series of numerical experiments verify the reliability of its mathematical model and the feasibility of the algorithm. A class of electrical current patterns is proposed to minimize the number of direct problems to be solved in each iteration. These methods have been applied successfully in practical simulation of electrical impedance tomography.     

Low rank matrix recovery from rank one measurements

We study the recovery of Hermitian low rank matrices $X\in {\mathbb{C}}^{n\times n}$ from undersampled measurements via nuclear norm minimization. We consider the particular scenario where the measurements are Frobenius inner products with random rank-one matrices of the form $a_j{a}_j^{?}$ for some measurement vectors $a_1,\dots ,a_m$, i.e., the measurements are given by $b_j=\mathrm{tr}(X{a}_j{a}_j^{?})$. The case where the matrix $X=x{x}^{?}$ to be recovered is of rank one reduces to the problem of phaseless estimation (from measurements $b_j=|〈x,a_j〉{|}^2$) via the PhaseLift approach, which has been introduced recently. We derive bounds for the number m of measurements that guarantee successful uniform recovery of Hermitian rank r matrices, either for the vectors $a_j$, $j=1,\dots ,m$, being chosen independently at random according to a standard Gaussian distribution, or $a_j$ being sampled independently from an (approximate) complex projective t-design with $t=4$. In the Gaussian case, we require $m\ge Crn$ measurements, while in the case of 4-designs we need $m\ge \mathit{Cr}n\log ?(n)$. Our results are uniform in the sense that one random choice of the measurement vectors $a_j$ guarantees recovery of all rank r-matrices simultaneously with high probability. Moreover, we prove robustness of recovery under perturbation of the measurements by noise. The result for approximate 4-designs generalizes and improves a recent bound on phase retrieval due to Gross, Krahmer and Kueng. In addition, it has applications in quantum state tomography. Our proofs employ the so-called bowling scheme which is based on recent ideas by Mendelson and Koltchinskii.     

An investigation of the accelerated thermal degradation of different epoxy resin composites using X-ray microcomputed tomography and optical coherence tomography

Epoxy resin composites reinforced with hollow glass microspheres, microlight microspheres, 3D parabeam glass, and E-Glass individually were subjected to accelerated thermal degradation conditions. X-ray microcomputed tomography (XμCT) was used to evaluate density changes, reinforcement filler damage, homogeneity, cracks and microcracks in the bulk of the different epoxy resin composites. XμCT 3D images, 2D reconstructed images and voids calculations revealed microspheres damage, filler distributions and showed cracks in all composites with different shapes and volume in response to the thermal degradation conditions. In addition, expansion of air bubbles/voids was observed and recorded in the microsphere and microlight epoxy composite samples. In a complementary way, optical coherence tomography (OCT) was used as a novel optical characterisation technique to study structural changes of the surface and near-surface regions of the composites, uncovering signs of surface shrinkage caused by the thermal treatment. Thus, combining XμCT and OCT proved useful in examining epoxy resin composites' structure, filler-resin interface and surface characteristics.     

Direct Insight into the Three‐Dimensional Internal Morphology of Solid–Liquid–Vapor Interfaces at Microscale

Solid–liquid–vapor interfaces dominated by the three‐phase contact line, usually performing as the active center in reactions, are important in biological and industrial processes. In this contribution, we provide direct three‐dimensional (3D) experimental evidence for the inside morphology of interfaces with either Cassie or Wenzel states at micron level using X‐ray micro‐computed tomography, which allows us to accurately “see inside” the morphological structures and quantitatively visualize their internal 3D fine structures and phases in intact samples. Furthermore, the in‐depth measurements revealed that the liquid randomly and partly located on the top of protrusions on the natural and artificial superhydrophobic surfaces in Cassie regime, resulting from thermodynamically optimal minimization of the surface energy. These new findings are useful for the optimization of classical wetting theories and models, which should promote the surface scientific and technological developments.     

Precision of Raman depolarization and optical attenuation measurements of sound tooth enamel

The demineralization of enamel that is associated with early caries formation affects the optical properties of the enamel. Polarized Raman spectroscopy and optical coherence tomography have been used to detect these changes and potentially offer a means to detect and monitor early caries development. The total optical attenuation coefficient as measured by optical coherence tomography and the polarization anisotropy of the Raman peak arising from the symmetric ν₁ vibration of at approximately 959 cm⁻¹ have been demonstrated as being sensitive markers of early caries. This ex vivo study on extracted human teeth demonstrates that these measurements can be made with reasonable precision with concomitantly good repeatability and reproducibility in sound enamel. Such reliability is crucial for these techniques to have a practical clinical value.     

Imaging the In Vivo Degradation of Tissue Engineering Implants by Use of Supramolecular Radiopaque Biomaterials

For in situ tissue engineering (TE) applications it is important that implant degradation proceeds in concord with neo‐tissue formation to avoid graft failure. It will therefore be valuable to have an imaging contrast agent (CA) available that can report on the degrading implant. For this purpose, a biodegradable radiopaque biomaterial is presented, modularly composed of a bisurea chain‐extended polycaprolactone (PCL2000‐U4U) elastomer and a novel iodinated bisurea‐modified CA additive (I‐U4U). Supramolecular hydrogen bonding interactions between the components ensure their intimate mixing. Porous implant TE‐grafts are prepared by simply electrospinning a solution containing PCL2000‐U4U and I‐U4U. Rats receive an aortic interposition graft, either composed of only PCL2000‐U4U (control) or of PCL2000‐U4U and I‐U4U (test). The grafts are explanted for analysis at three time points over a 1‐month period. Computed tomography imaging of the test group implants prior to explantation shows a decrease in iodide volume and density over time. Explant analysis also indicates scaffold degradation. (Immuno)histochemistry shows comparable cellular contents and a similar neo‐tissue formation process for test and control group, demonstrating that the CA does not have apparent adverse effects. A supramolecular approach to create solid radiopaque biomaterials can therefore be used to noninvasively monitor the biodegradation of synthetic implants.