Quenched chiral logarithms in lattice QCD with overlap Dirac quarks

We examine quenched chiral logarithms in lattice QCD with overlap Dirac quarks. From our data of m_pi^2, we determine the coefficient of quenched chiral logarithm delta = 0.203(14), 0.176(17), 0.193(17) and 0.200(13) for lattices of sizes 8^3 times 24, 10^3 times 24, 12^3 times 24 and 16^3 times 32 respectively. Also, for the first three lattice sizes, we measure the index susceptibility of the overlap Dirac operator, and use the exact relation between the index susceptibility and the eta' mass in quenched chiral perturbation theory to obtain an independent determination of delta = 0.198(27), 0.173(24), 0.169(22), which are in good agreement with those determined from m_pi^2.Comment: Lattice2002(chiral), 3 pages, 2 figure

Light quark masses in quenched QCD with exact chiral symmetry

The parameters in the pseudoscalar meson mass formula in quenched chiral perturbation theory to one-loop order are determined by quenched lattice QCD with overlap Dirac operator, and from which the light quark masses are determined with the experimental inputs of pion and kaon masses, and the pion decay constant. Our results are $m_{u,d} = 5.3 \pm 0.3$ MeV, and $m_s = 115\pm 8$ MeV, in the $\bar{MS}$ scheme at scale $\mu = 2$ GeV.Comment: 5 pages, LaTeX, in v2: the missing numerical factor in (13) is restored, and the physical quark masses (16)-(17) are in good agreement with the current lattice world averag

Quenched chiral logarithms in lattice QCD with exact chiral symmetry

We examine quenched chiral logarithms in lattice QCD with overlap Dirac quark. For 100 gauge configurations generated with the Wilson gauge action at $\beta = 5.8$ on the $8^3 \times 24$ lattice, we compute quenched quark propagators for 12 bare quark masses. The pion decay constant is extracted from the pion propagator, and from which the lattice spacing is determined to be 0.147 fm. The presence of quenched chiral logarithm in the pion mass is confirmed, and its coefficient is determined to be $\delta = 0.203 \pm 0.014$, in agreement with the theoretical estimate in quenched chiral perturbation theory. Further, we obtain the topological susceptibility of these 100 gauge configurations by measuring the index of the overlap Dirac operator. Using a formula due to exact chiral symmetry, we obtain the $\eta'$ mass in quenched chiral perturbation theory, $m_{\eta'} = (901 \pm 64)$ Mev, and an estimate of $\delta = 0.197 \pm 0.027$, which is in good agreement with that determined from the pion mass.Comment: 24 pages, 6 EPS figures; v2: some clarifications added, to appear in Physical Review

A New Segmentation Algorithm for Prostate Boundary Detection in 2D Ultrasound Images

Prostate segmentation is a required step in determining the volume of a prostate, which is very important in the diagnosis and the treatment of prostate cancer. In the past, radiologists manually segment the two-dimensional cross-sectional ultrasound images. Typically, it is necessary for them to outline at least a hundred of cross-sectional images in order to get an accurate estimate of the prostate's volume. This approach is very time-consuming. To be more efficient in accomplishing this task, an automated procedure has to be developed. However, because of the quality of the ultrasound image, it is very difficult to develop a computerized method for defining boundary of an object in an ultrasound image. The goal of this thesis is to find an automated segmentation algorithm for detecting the boundary of the prostate in ultrasound images. As the first step in this endeavour, a semi-automatic segmentation method is designed. This method is only semi-automatic because it requires the user to enter four initialization points, which are the data required in defining the initial contour. The discrete dynamic contour (DDC) algorithm is then used to automatically update the contour. The DDC model is made up of a set of connected vertices. When provided with an energy field that describes the features of the ultrasound image, the model automatically adjusts the vertices of the contour to attain a maximum energy. In the proposed algorithm, Mallat's dyadic wavelet transform is used to determine the energy field. Using the dyadic wavelet transform, approximate coefficients and detailed coefficients at different scales can be generated. In particular, the two sets of detailed coefficients represent the gradient of the smoothed ultrasound image. Since the gradient modulus is high at the locations where edge features appear, it is assigned to be the energy field used to drive the DDC model. The ultimate goal of this work is to develop a fully-automatic segmentation algorithm. Since only the initialization stage requires human supervision in the proposed semi-automatic initialization algorithm, the task of developing a fully-automatic segmentation algorithm is reduced to designing a fully-automatic initialization process. Such a process is introduced in this thesis. In this work, the contours defined by the semi-automatic and the fully-automatic segmentation algorithm are compared with the boundary outlined by an expert observer. Tested using 8 sample images, the mean absolute difference between the semi-automatically defined and the manually outlined boundary is less than 2. 5 pixels, and that between the fully-automatically defined and the manually outlined boundary is less than 4 pixels. Automated segmentation tools that achieve this level of accuracy would be very useful in assisting radiologists to accomplish the task of segmenting prostate boundary much more efficiently

Area-preserving mapping of 3D ultrasound carotid artery images using density-equalizing reference map

Carotid atherosclerosis is a focal disease at the bifurcations of the carotid artery. To quantitatively monitor the local changes in the vessel-wall-plus-plaque thickness (VWT) and compare the VWT distributions for different patients or for the same patients at different ultrasound scanning sessions, a mapping technique is required to adjust for the geometric variability of different carotid artery models. In this work, we propose a novel method called density-equalizing reference map (DERM) for mapping 3D carotid surfaces to a standardized 2D carotid template, with an emphasis on preserving the local geometry of the carotid surface by minimizing the local area distortion. The initial map was generated by a previously described arc-length scaling (ALS) mapping method, which projects a 3D carotid surface onto a 2D non-convex L-shaped domain. A smooth and area-preserving flattened map was subsequently constructed by deforming the ALS map using the proposed algorithm that combines the density-equalizing map and the reference map techniques. This combination allows, for the first time, one-to-one mapping from a 3D surface to a standardized non-convex planar domain in an area-preserving manner. Evaluations using 20 carotid surface models show that the proposed method reduced the area distortion of the flattening maps by over 80% as compared to the ALS mapping method

Analysis of carotid lumen surface morphology using three-dimensional ultrasound imaging

Carotid plaque surface irregularity and ulcerations play an important role in the risk of ischemic stroke. Ulcerated or fissured plaque, characterized by irregular surface morphology, exposes thrombogenic materials to the bloodstream, possibly leading to life- or brain-threatening thrombosis and embolization. Therefore, the quantification of plaque surface irregularity is important to identify high-risk plaques that would likely lead to vascular events. Although a number of studies have characterized plaque surface irregularity using subjective classification schemes with two or more categories, only a few have quantified surface irregularity using an objective and continuous quantity, such as Gaussian or mean curvature. In this work, our goal was to use both Gaussian and mean curvatures for identifying ulcers from 3D carotid ultrasound (US) images of human subjects. Before performing experiments using patient data, we verified the numerical accuracy of the surface curvature computation method using discrete spheres and tori with different sampling intervals. We also showed that three ulcers of the vascular phantom with 2 mm, 3 mm and 4 mm diameters were associated with high Gaussian and mean curvatures, and thus, were easily detected. Finally, we demonstrated the application of the proposed method for detecting ulcers on luminal surfaces, which were segmented from the 3D US images acquired for two human subjects

Quantification of carotid vessel wall and plaque thickness change using 3D ultrasound images

Quantitative measurements of carotid plaque burden progression or regression are important in monitoring patients and in evaluation of new treatment options. 3D ultrasound (US) has been used to monitor the progression or regression of carotid artery plaques. This paper reports on the development and application of a method used to analyze changes in carotid plaque morphology from 3D US. The technique used is evaluated using manual segmentations of the arterial wall and lumen from 3D US images acquired in two imaging sessions. To reduce the effect of segmentation variability, segmentation was performed five times each for the wall and lumen. The mean wall and lumen surfaces, computed from this set of five segmentations, were matched on a point-by-point basis, and the distance between each pair of corresponding points served as an estimate of the combined thickness of the plaque, intima, and media (vessel-wall-plus-plaque thickness or VWT). The VWT maps associated with the first and the second US images were compared and the differences of VWT were obtained at each vertex. The 3D VWT and VWT-Change maps may provide important information for evaluating the location of plaque progression in relation to the localized disturbances of flow pattern, such as oscillatory shear, and regression in response to medical treatments

On topological properties of vacuum defects in lattice Yang-Mills theories

We study correlations between low-lying modes of the overlap Dirac operator and vacuum defects, center vortices and three-dimensional volumes, in lattice SU(2) gluodynamics. The low-lying modes are apparently sensitive to topological properties of the underlying gluon field configurations while the vacuum defects are crucial for the confinement. We find distinct positive correlation in both cases. In case of vortices the correlation is stronger