Singular Solutions of Protter’s Problem for a Class of 3-D Hyperbolic Equations

Недю Иванов Попиванов, Алексей Йорданов Николов - През 1952 г. М. Протър формулира нови гранични задачи за вълновото уравнение, които са тримерни аналози на задачите на Дарбу в равнината. Задачите са разгледани в тримерна област, ограничена от две характеристични конуса и равнина. Сега, след като са минали повече от 50 години, е добре известно, че за безброй гладки функции в дясната страна на уравнението тези задачи нямат класически решения, а обобщеното решение има силна степенна особеност във върха на характеристичния конус, която е изолирана и не се разпространява по конуса. Тук ние разглеждаме трета гранична задача за вълновото уравнение с младши членове и дясна страна във формата на тригонометричен полином. Дадена е по-нова от досега известната априорна оценка за максимално възможната особеност на решенията на тази задача. Оказва се, че при по-общото уравнение с младши членове възможната сингулярност е от същия ред като при чисто вълновото уравнение.

Fluorescence-enhanced optical imaging on three-dimensional phantoms using a hand-held probe based frequency-domain intensified charge coupled device (ICCD) optical imager

Fluorescence-enhanced optical imaging is an emerging non-invasive and non-ionizing modality towards breast cancer diagnosis. Various optical imaging systems are currently available, although most of them are limited by bulky instrumentation, or their inability to flexibly image different tissue volumes and shapes. Hand-held based optical imaging systems are a recent development for its improved portability, but are currently limited only to surface mapping. Herein, a novel optical imager, consisting primarily of a hand-held probe and a gain-modulated intensified charge coupled device (ICCD) detector, is developed towards both surface and tomographic breast imaging. The unique features of this hand-held probe based optical imager are its ability to; (i) image large tissue areas (5×10 sq. cm) in a single scan, (ii) reduce overall imaging time using a unique measurement geometry, and (iii) perform tomographic imaging for tumor three-dimensional (3-D) localization. Frequency-domain based experimental phantom studies have been performed on slab geometries (650 ml) under different target depths (1-2.5 cm), target volumes (0.45, 0.23 and 0.10 cc), fluorescence absorption contrast ratios (1:0, 1000:1 to 5:1), and number of targets (up to 3), using Indocyanine Green (ICG) as fluorescence contrast agents. An approximate extended Kalman filter based inverse algorithm has been adapted towards 3-D tomographic reconstructions. Single fluorescence target(s) was reconstructed when located: (i) up to 2.5 cm deep (at 1:0 contrast ratio) and 1.5 cm deep (up to 10:1 contrast ratio) for 0.45 cc-target; and (ii) 1.5 cm deep for target as small as 0.10 cc at 1:0 contrast ratio. In the case of multiple targets, two targets as close as 0.7 cm were tomographically resolved when located 1.5 cm deep. It was observed that performing multi-projection (here dual) based tomographic imaging using a priori target information from surface images, improved the target depth recovery over using single projection based imaging. From a total of 98 experimental phantom studies, the sensitivity and specificity of the imager was estimated as 81-86% and 43-50%, respectively. With 3-D tomographic imaging successfully demonstrated for the first time using a hand-held based optical imager, the clinical translation of this technology is promising upon further experimental validation from in-vitro and in-vivo studies.

A novel 3-D segmentation algorithm for anatomic liver and tumor volume calculations for liver cancer treatment planning

Three-Dimensional (3-D) imaging is vital in computer-assisted surgical planning including minimal invasive surgery, targeted drug delivery, and tumor resection. Selective Internal Radiation Therapy (SIRT) is a liver directed radiation therapy for the treatment of liver cancer. Accurate calculation of anatomical liver and tumor volumes are essential for the determination of the tumor to normal liver ratio and for the calculation of the dose of Y-90 microspheres that will result in high concentration of the radiation in the tumor region as compared to nearby healthy tissue. Present manual techniques for segmentation of the liver from Computed Tomography (CT) tend to be tedious and greatly dependent on the skill of the technician/doctor performing the task. ^ This dissertation presents the development and implementation of a fully integrated algorithm for 3-D liver and tumor segmentation from tri-phase CT that yield highly accurate estimations of the respective volumes of the liver and tumor(s). The algorithm as designed requires minimal human intervention without compromising the accuracy of the segmentation results. Embedded within this algorithm is an effective method for extracting blood vessels that feed the tumor(s) in order to plan effectively the appropriate treatment. ^ Segmentation of the liver led to an accuracy in excess of 95% in estimating liver volumes in 20 datasets in comparison to the manual gold standard volumes. In a similar comparison, tumor segmentation exhibited an accuracy of 86% in estimating tumor(s) volume(s). Qualitative results of the blood vessel segmentation algorithm demonstrated the effectiveness of the algorithm in extracting and rendering the vasculature structure of the liver. Results of the parallel computing process, using a single workstation, showed a 78% gain. Also, statistical analysis carried out to determine if the manual initialization has any impact on the accuracy showed user initialization independence in the results. ^ The dissertation thus provides a complete 3-D solution towards liver cancer treatment planning with the opportunity to extract, visualize and quantify the needed statistics for liver cancer treatment. Since SIRT requires highly accurate calculation of the liver and tumor volumes, this new method provides an effective and computationally efficient process required of such challenging clinical requirements.^

An automatic method of above-water iceberg 3-D profiling based on autonomous surface craft (ASC) using surface images and LIDAR

This thesis reports on a novel method to build a 3-D model of the above-water portion of icebergs using surface imaging. The goal is to work towards the automation of iceberg surveys, allowing an Autonomous Surface Craft (ASC) to acquire shape and size information. After collecting data and images, the core software algorithm is made up of three parts: occluding contour finding, volume intersection, and parameter estimation. A software module is designed that could be used on the ASC to perform automatic and fast processing of above-water surface image data to determine iceberg shape and size measurement and determination. The resolution of the method is calculated using data from the iceberg database of the Program of Energy Research and Development (PERD). The method was investigated using data from field trials conducted through the summer of 2014 by surveying 8 icebergs during 3 expeditions. The results were analyzed to determine iceberg characteristics. Limitations of this method are addressed including its accuracy. Surface imaging system and LIDAR system are developed to profile the above-water iceberg in 2015.

3-D reflection seismic imaging of the Hontomin structure in the Basque-Cantabrian Basin (Spain)

Peer reviewed

3-D reflection seismic imaging of the Hontomin structure in the Basque-Cantabrian Basin (Spain)

Peer reviewed

Prevention of bacterial translocation using β-(1-3)-D-glucan in small bowel ischemia and reperfusion in rats

To investigate the role of β-(1-3)-D-glucan on 99mTc labelled Escherichia coli translocation and cytokines secretion in rats submitted to small bowel ischemia/reperfusion injury. Methods: Five groups (n=10 each) of Wistar rats were subjected to control(C), sham(S), group IR subjected to 45 min of bowel ischemia/60 min of reperfusion(I/R), and group I/R+glucan subjected to 45 min of bowel ischemia/60 min of reperfusion(I/R) and injected with 2mg/Kg intramuscular. Translocation of labelled bacteria to mesenteric lymph nodes, liver, spleen, lung and serum was determined using radioactivity/count and colony forming units/g(CFU/g). Serum TNFα, IL-1β, IL-6, IL-10 were measured by ELISA. Results: CFU/g and radioactivity/count were higher in I/R than in I/R+glucan rats. In C, S and S+glucan groups, bacteria and radioactivity/count were rarely detected. The I/R+glucan rats had enhancement of IL-10 and suppressed production of serum TNFα, IL-1β and, IL-6, compared to I/R untreated animals. Conclusion: The β-(1-3)-D-glucan modulated the production of pro-inflammatory and anti-inflammatory cytokines during bowel ischemia/reperfusion, and attenuated translocation of labelled bacteria

Prevention of bacterial translocation using β-(1-3)-D-glucan in small bowel ischemia and reperfusion in rats

To investigate the role of β-(1-3)-D-glucan on 99mTc labelled Escherichia coli translocation and cytokines secretion in rats submitted to small bowel ischemia/reperfusion injury. Methods: Five groups (n=10 each) of Wistar rats were subjected to control(C), sham(S), group IR subjected to 45 min of bowel ischemia/60 min of reperfusion(I/R), and group I/R+glucan subjected to 45 min of bowel ischemia/60 min of reperfusion(I/R) and injected with 2mg/Kg intramuscular. Translocation of labelled bacteria to mesenteric lymph nodes, liver, spleen, lung and serum was determined using radioactivity/count and colony forming units/g(CFU/g). Serum TNFα, IL-1β, IL-6, IL-10 were measured by ELISA. Results: CFU/g and radioactivity/count were higher in I/R than in I/R+glucan rats. In C, S and S+glucan groups, bacteria and radioactivity/count were rarely detected. The I/R+glucan rats had enhancement of IL-10 and suppressed production of serum TNFα, IL-1β and, IL-6, compared to I/R untreated animals. Conclusion: The β-(1-3)-D-glucan modulated the production of pro-inflammatory and anti-inflammatory cytokines during bowel ischemia/reperfusion, and attenuated translocation of labelled bacteria

Improving the Accuracy of 3-D Reconstruction in Robotic Vision Applications

Thesis (Ph.D.)--University of Washington, 2016-08

Performance of case-based retrieval of 3-D shapes for the design of metal castings

Abstract not available

Parallelisation of a 3-D electromagnetic scattering code

A high-frequency time domain finite element scattering code using a combination of edge and piecewise constant elements on unstructured tetrahedral meshes is described. A comparison of computation with theory is given for scattering from a sphere. A parallel implementation making use of the bulk synchronous parallel (BSP) programming model is described in detail; a BSP performance model of the parallelized field calculation is derived and compared to timing measurements on up to 128 processors on a Cray T3D.

Prevention of bacterial translocation using β-(1-3)-D-glucan in small bowel ischemia and reperfusion in rats

To investigate the role of β-(1-3)-D-glucan on 99mTc labelled Escherichia coli translocation and cytokines secretion in rats submitted to small bowel ischemia/reperfusion injury. Methods: Five groups (n=10 each) of Wistar rats were subjected to control(C), sham(S), group IR subjected to 45 min of bowel ischemia/60 min of reperfusion(I/R), and group I/R+glucan subjected to 45 min of bowel ischemia/60 min of reperfusion(I/R) and injected with 2mg/Kg intramuscular. Translocation of labelled bacteria to mesenteric lymph nodes, liver, spleen, lung and serum was determined using radioactivity/count and colony forming units/g(CFU/g). Serum TNFα, IL-1β, IL-6, IL-10 were measured by ELISA. Results: CFU/g and radioactivity/count were higher in I/R than in I/R+glucan rats. In C, S and S+glucan groups, bacteria and radioactivity/count were rarely detected. The I/R+glucan rats had enhancement of IL-10 and suppressed production of serum TNFα, IL-1β and, IL-6, compared to I/R untreated animals. Conclusion: The β-(1-3)-D-glucan modulated the production of pro-inflammatory and anti-inflammatory cytokines during bowel ischemia/reperfusion, and attenuated translocation of labelled bacteria

Prevention of bacterial translocation using β-(1-3)-D-glucan in small bowel ischemia and reperfusion in rats

To investigate the role of β-(1-3)-D-glucan on 99mTc labelled Escherichia coli translocation and cytokines secretion in rats submitted to small bowel ischemia/reperfusion injury. Methods: Five groups (n=10 each) of Wistar rats were subjected to control(C), sham(S), group IR subjected to 45 min of bowel ischemia/60 min of reperfusion(I/R), and group I/R+glucan subjected to 45 min of bowel ischemia/60 min of reperfusion(I/R) and injected with 2mg/Kg intramuscular. Translocation of labelled bacteria to mesenteric lymph nodes, liver, spleen, lung and serum was determined using radioactivity/count and colony forming units/g(CFU/g). Serum TNFα, IL-1β, IL-6, IL-10 were measured by ELISA. Results: CFU/g and radioactivity/count were higher in I/R than in I/R+glucan rats. In C, S and S+glucan groups, bacteria and radioactivity/count were rarely detected. The I/R+glucan rats had enhancement of IL-10 and suppressed production of serum TNFα, IL-1β and, IL-6, compared to I/R untreated animals. Conclusion: The β-(1-3)-D-glucan modulated the production of pro-inflammatory and anti-inflammatory cytokines during bowel ischemia/reperfusion, and attenuated translocation of labelled bacteria

特大地震激发地球自由振荡的数值模拟研究

Large earthquakes, such as the Chile earthquake in 1960 and the Sumatra-Andaman earthquake on Dec 26, 2004 in Indonesia, have generated the Earth’s free oscillations. The eigenfrequencies of the Earth’s free oscillations are closely related to the Earth’s internal structures. The conventional methods, which mainly focus on calculating the eigenfrequecies by analytical ways, and the analysis on observations can not easily study the whole processes from earthquake occurrence to the Earth’s free oscillation inspired. Therefore, we try to use numerical method incorporated with large-scale parallel computing to study on the Earth’s free oscillations excited by giant earthquakes. We first give a review of researches and developments of the Earth’s free oscillation, and basical theories under spherical coordinate system. We then give a review of the numerical simulation of seismic wave propagation and basical theories of spectral element method to simulate global seismic wave propagation. As a first step to study the Earth’s free oscillations, we use a finite element method to simulate the propagation of elastic waves and the generation of oscillations of the chime bell of Marquis Yi of Zeng, by striking different parts of the bell, which possesses the oval crosssection. The bronze chime bells of Marquis Yi of Zeng are precious cultural relics of China. The bells have a two-tone acoustic characteristic, i.e., striking different parts of the bell generates different tones. By analysis of the vibration in the bell and the spectrum analysis, we further help the understanding of the mechanism of two-tone acoustic characteristics of the chime bell of Marquis Yi of Zeng. The preliminary calculations have clearly shown that two different modes of oscillation can be generated by striking different parts of the bell, and indicate that finite element numerical simulation of the processes of wave propagation and two-tone generation of the chime bell of Marquis Yi of Zeng is feasible. These analyses provide a new quantitative and visual way to explain the mystery of the two-tone acoustic characteristics. The method suggested by this study can be applied to simulate free oscillations excited by great earthquakes with complex Earth structure. Taking into account of such large-scale structure of the Earth, small-scale low-precision numerical simulation can not simply meet the requirement. The increasing capacity in high-performance parallel computing and progress on fully numerical solutions for seismic wave fields in realistic three-dimensional spherical models, Spectral element method and high-performance parallel computing were incorporated to simulate the seismic wave propagation processes in the Earth’s interior, without the effects of the Earth’s gravitational potential. The numerical simulation shows that, the results of the toroidal modes of our calculation agree well with the theoretical values, although the accuracy of our results is much limited, the calculated peaks are little distorted due to three-dimensional effects. There exist much great differences between our calculated values of spheroidal modes and theoretical values, because we don’t consider the effect the Earth’ gravitation in numerical model, which leads our values are smaller than the theoretical values. When , is much smaller, the effect of the Earth’s gravitation make the periods of spheroidal modes become shorter. However, we now can not consider effects of the Earth’s gravitational potential into the numerical model to simulate the spheroidal oscillations, but those results still demonstrate that, the numerical simulation of the Earth’s free oscillation is very feasible. We make the numerical simulation on processes of the Earth’s free oscillations under spherically symmetric Earth model using different special source mechanisms. The results quantitatively show that Earth’s free oscillations excited by different earthquakes are different, and oscillations at different locations are different for free oscillation excited by the same earthquake. We also explore how the Earth’s medium attenuation will take effects on the Earth’s free oscillations, and take comparisons with the observations. The medium attenuation can make influences on the Earth’s free oscillations, though the effects on lower-frequency fundamental oscillations are weak. At last, taking 2008 Wenchuan earthquake for example, we employ spectral element method incorporated with large-scale parallel computing technology to investigate the characteristics of seismic wave propagation excited by Wenchuan earthquake. We calculate synthetic seismograms with one-point source model and three-point source model respectively. Full 3-D visualization of the numerical results displays the profile of the seismic wave propagation with respect to time. The three-point source, which was proposed by the latest investigations through field observation and reverse estimation, can better demonstrate the spatial and temporal characteristics of the source rupture processes than one-point source. Primary results show that those synthetic signals calculated from three-point source agree well with the observations. This can further reveal that the source rupturing process of Wenchuan earthquake is a multi-rupture process, which is composed by at least three or more stages of rupture processes. In conclusion, the numerical simulation can not only solve some problems concluding the Earth’s ellipticity and anisotropy, which can be easily solved by conventional methods, but also finally solve the problems concluding topography model and lateral heterogeneity. We will try to find a way to fully implement self-gravitation in spectral element method in future, and do our best to continue researching the Earth’s free oscillations using the numerical simulations to see how the Earth’ lateral heterogeneous will affect the Earth’s free oscillations. These will make it possible to bring modal spectral data increasingly to bear on furthering our understanding of the Earth’s three-dimensional structure.

A new system for computer-aided preoperative planning and intraoperative navigation during corrective jaw surgery

A new system for computer-aided corrective surgery of the jaws has been developed and introduced clinically. It combines three-dimensional (3-D) surgical planning with conventional dental occlusion planning. The developed software allows simulating the surgical correction on virtual 3-D models of the facial skeleton generated from computed tomography (CT) scans. Surgery planning and simulation include dynamic cephalometry, semi-automatic mirroring, interactive cutting of bone and segment repositioning. By coupling the software with a tracking system and with the help of a special registration procedure, we are able to acquire dental occlusion plans from plaster model mounts. Upon completion of the surgical plan, the setup is used to manufacture positioning splints for intraoperative guidance. The system provides further intraoperative assistance with the help of a display showing jaw positions and 3-D positioning guides updated in real time during the surgical procedure. The proposed approach offers the advantages of 3-D visualization and tracking technology without sacrificing long-proven cast-based techniques for dental occlusion evaluation. The system has been applied on one patient. Throughout this procedure, we have experienced improved assessment of pathology, increased precision, and augmented control.