Numerical solution of the Dirichlet initial boundary value problem for the heat equation in exterior 3-dimensional domains using integral equations

A numerical method for the Dirichlet initial boundary value problem for the heat equation in the exterior and unbounded region of a smooth closed simply connected 3-dimensional domain is proposed and investigated. This method is based on a combination of a Laguerre transformation with respect to the time variable and an integral equation approach in the spatial variables. Using the Laguerre transformation in time reduces the parabolic problem to a sequence of stationary elliptic problems which are solved by a boundary layer approach giving a sequence of boundary integral equations of the first kind to solve. Under the assumption that the boundary surface of the solution domain has a one-to-one mapping onto the unit sphere, these integral equations are transformed and rewritten over this sphere. The numerical discretisation and solution are obtained by a discrete projection method involving spherical harmonic functions. Numerical results are included.

Numerical solution of a Cauchy problem for Laplace equation in 3-dimensional domains by integral equations

A numerical method based on integral equations is proposed and investigated for the Cauchy problem for the Laplace equation in 3-dimensional smooth bounded doubly connected domains. To numerically reconstruct a harmonic function from knowledge of the function and its normal derivative on the outer of two closed boundary surfaces, the harmonic function is represented as a single-layer potential. Matching this representation against the given data, a system of boundary integral equations is obtained to be solved for two unknown densities. This system is rewritten over the unit sphere under the assumption that each of the two boundary surfaces can be mapped smoothly and one-to-one to the unit sphere. For the discretization of this system, Weinert’s method (PhD, Göttingen, 1990) is employed, which generates a Galerkin type procedure for the numerical solution, and the densities in the system of integral equations are expressed in terms of spherical harmonics. Tikhonov regularization is incorporated, and numerical results are included showing the efficiency of the proposed procedure.

Enhanced 3-dimensional carbon nanotube based anodes for lithium-ion battery applications

A prototype 3-dimensional (3D) anode, based on multiwall carbon nanotubes (MWCNTs), for Li-ion batteries (LIBs), with potential use in Electric Vehicles (EVs) was investigated. The unique 3D design of the anode allowed much higher areal mass density of MWCNTs as active materials, resulting in more amount of Li+ ion intake, compared to that of a conventional 2D counterpart. Furthermore, 3D amorphous Si/MWCNTs hybrid structure offered enhancement in electrochemical response (specific capacity 549 mAhg–1 ). Also, an anode stack was fabricated to further increase the areal or volumetric mass density of MWCNTs. An areal mass density of the anode stack 34.9 mg/cm2 was attained, which is 1,342% higher than the value for a single layer 2.6 mg/cm2. Furthermore, the binder-assisted and hot-pressed anode stack yielded the average reversible, stable gravimetric and volumetric specific capacities of 213 mAhg–1 and 265 mAh/cm3, respectively (at 0.5C). Moreover, a large-scale patterned novel flexible 3D MWCNTs-graphene-polyethylene terephthalate (PET) anode structure was prepared. It generated a reversible specific capacity of 153 mAhg–1 at 0.17C and cycling stability of 130 mAhg –1 up to 50 cycles at 1.7C.

Easy preoperative planning of deeply located brain lesions using external skin reference and 3-Dimensional surface MRI

Open skull surgery of deeply located intracerebral lesions requires precise determination of the treatment area in 3-dimensional (3-D) space. 3-D MRI can give important additional information in presurgical determination of the surgical approach to the target, taking into account highly functional brain areas and important vascular structures. The day before surgery, a grid composed of 9 tubings intersecting at 90° at 1 cm intervals and filled with a Q1SO4 solution is firmly attached to the skin of the patient’s head in the presumed region of the craniotomy. A 3-D turbo-FLASH sequence is then performed in the sagittal plane after intravenous Gd-DOTA injection on a IT Magnetom. 3-D surface reconstruction of the cortical gyri and sulci is performed. Once the gyri are identified, the 3-D program is then implemented in order to perform a color display of the cortical veins and of the tumor boundaries. The surgical access is then chosen by the surgeon, taking into account highly functional areas. Finally, the boundaries of the tumor are projected on the cortex reconstruction and on the external reference placed on the skin. The entry place for surgery as well as the size of craniotomy are drawn on the skin and the tubed grid is removed. The accuracy of this method tested in 9 patients with deeply located brain tumors or arteriovenous malformations was very satisfactory. In daily practice, this method is a valuable technique providing important clinical information in determining the shortest and safest way through the brain tissue, decreasing possible functional deficit and reducing craniotomy size in cases of difficult to access deep brain areas. Our method does not require a stereotactic frame permanently fixed to the head of the patient during surgery. © 1994 S. Karger AG, Basel.

Reconstructability of 3-Dimensional Upper Ocean Circulation from SWOT Sea Surface Height Measurements

Utilizing the framework of effective surface quasi-geostrophic (eSQG) theory, we explored the potential of reconstructing the 3D upper ocean circulation structures, including the balanced vertical velocity (w) field, from high-resolution sea surface height (SSH) data of the planned SWOT satellite mission. Specifically, we utilized the 1/30°, submesoscale-resolving, OFES model output and subjected it through the SWOT simulator that generates the along-swath SSH data with expected measurement errors. Focusing on the Kuroshio Extension region in the North Pacific where regional Rossby numbers range from 0.22 to 0.32, we found that the eSQG dynamics constitutes an effective framework for reconstructing the 3D upper ocean circulation field. Using the modeled SSH data as input, the eSQG-reconstructed relative vorticity (ζ) and w fields are found to reach a correlation of 0.7–0.9 and 0.6–0.7, respectively, in the 1,000m upper ocean when compared to the original model output. Degradation due to the SWOT sampling and measurement errors in the input SSH data for the ζ and w reconstructions is found to be moderate, 5–25% for the 3D ζ field and 15-35% for the 3D w field. There exists a tendency for this degradation ratio to decrease in regions where the regional eddy variability (or Rossby number) increases.

A non-contrast self-navigated 3-dimensional MR technique for aortic root and vascular access route assessment in the context of transcatheter aortic valve replacement: proof of concept.

OBJECTIVES: Due to the high prevalence of renal failure in transcatheter aortic valve replacement (TAVR) candidates, a non-contrast MR technique is desirable for pre-procedural planning. We sought to evaluate the feasibility of a novel, non-contrast, free-breathing, self-navigated three-dimensional (SN3D) MR sequence for imaging the aorta from its root to the iliofemoral run-off in comparison to non-contrast two-dimensional-balanced steady-state free-precession (2D-bSSFP) imaging. METHODS: SN3D [field of view (FOV), 220-370 mm(3); slice thickness, 1.15 mm; repetition/echo time (TR/TE), 3.1/1.5 ms; and flip angle, 115°] and 2D-bSSFP acquisitions (FOV, 340 mm; slice thickness, 6 mm; TR/TE, 2.3/1.1 ms; flip angle, 77°) were performed in 10 healthy subjects (all male; mean age, 30.3 ± 4.3 yrs) using a 1.5-T MRI system. Aortic root measurements and qualitative image ratings (four-point Likert-scale) were compared. RESULTS: The mean effective aortic annulus diameter was similar for 2D-bSSFP and SN3D (26.7 ± 0.7 vs. 26.1 ± 0.9 mm, p = 0.23). The mean image quality of 2D-bSSFP (4; IQR 3-4) was rated slightly higher (p = 0.03) than SN3D (3; IQR 2-4). The mean total acquisition time for SN3D imaging was 12.8 ± 2.4 min. CONCLUSIONS: Our results suggest that a novel SN3D sequence allows rapid, free-breathing assessment of the aortic root and the aortoiliofemoral system without administration of contrast medium. KEY POINTS: • The prevalence of renal failure is high among TAVR candidates. • Non-contrast 3D MR angiography allows for TAVR procedure planning. • The self-navigated sequence provides a significantly reduced scanning time.

Enhanced 3-Dimensional Carbon Nanotube Based Anodes for Li-ion Battery Applications

A prototype 3-dimensional (3D) anode, based on multiwall carbon nanotubes (MWCNTs), for Li-ion batteries (LIBs), with potential use in Electric Vehicles (EVs) was investigated. The unique 3D design of the anode allowed much higher areal mass density of MWCNTs as active materials, resulting in more amount of Li+ ion intake, compared to that of a conventional 2D counterpart. Furthermore, 3D amorphous Si/MWCNTs hybrid structure offered enhancement in electrochemical response (specific capacity 549 mAhg-1). Also, an anode stack was fabricated to further increase the areal or volumetric mass density of MWCNTs. An areal mass density of the anode stack 34.9 mg/cm2 was attained, which is 1,342% higher than the value for a single layer 2.6 mg/cm2. Furthermore, the binder-assisted and hot-pressed anode stack yielded the average reversible, stable gravimetric and volumetric specific capacities of 213 mAhg-1 and 265 mAh/cm3, respectively (at 0.5C). Moreover, a large-scale patterned novel flexible 3D MWCNTs-graphene-polyethylene terephthalate (PET) anode structure was prepared. It generated a reversible specific capacity of 153 mAhg-1 at 0.17C and cycling stability of 130 mAhg-1 up to 50 cycles at 1.7C.

Numerical solution of an elliptic 3-dimensional Cauchy problem by the alternating method and boundary integral equations

We consider the Cauchy problem for the Laplace equation in 3-dimensional doubly-connected domains, that is the reconstruction of a harmonic function from knowledge of the function values and normal derivative on the outer of two closed boundary surfaces. We employ the alternating iterative method, which is a regularizing procedure for the stable determination of the solution. In each iteration step, mixed boundary value problems are solved. The solution to each mixed problem is represented as a sum of two single-layer potentials giving two unknown densities (one for each of the two boundary surfaces) to determine; matching the given boundary data gives a system of boundary integral equations to be solved for the densities. For the discretisation, Weinert's method [24] is employed, which generates a Galerkin-type procedure for the numerical solution via rewriting the boundary integrals over the unit sphere and expanding the densities in terms of spherical harmonics. Numerical results are included as well.

Complex networks analysis of manual and machine translations

Complex networks have been increasingly used in text analysis, including in connection with natural language processing tools, as important text features appear to be captured by the topology and dynamics of the networks. Following previous works that apply complex networks concepts to text quality measurement, summary evaluation, and author characterization, we now focus on machine translation (MT). In this paper we assess the possible representation of texts as complex networks to evaluate cross-linguistic issues inherent in manual and machine translation. We show that different quality translations generated by NIT tools can be distinguished from their manual counterparts by means of metrics such as in-(ID) and out-degrees (OD), clustering coefficient (CC), and shortest paths (SP). For instance, we demonstrate that the average OD in networks of automatic translations consistently exceeds the values obtained for manual ones, and that the CC values of source texts are not preserved for manual translations, but are for good automatic translations. This probably reflects the text rearrangements humans perform during manual translation. We envisage that such findings could lead to better NIT tools and automatic evaluation metrics.

Three-dimensional magnetic resonance observation of cartilage repair tissue (MOCART) score assessed with an isotropic three-dimensional true fast imaging with steady-state precession sequence at 3.0 Tesla

INTRODUCTION: Cartilage defects are common pathologies and surgical cartilage repair shows promising results. In its postoperative evaluation, the magnetic resonance observation of cartilage repair tissue (MOCART) score, using different variables to describe the constitution of the cartilage repair tissue and the surrounding structures, is widely used. High-field magnetic resonance imaging (MRI) and 3-dimensional (3D) isotropic sequences may combine ideal preconditions to enhance the diagnostic performance of cartilage imaging.Aim of this study was to introduce an improved 3D MOCART score using the possibilities of an isotropic 3D true fast imaging with steady-state precession (True-FISP) sequence in the postoperative evaluation of patients after matrix-associated autologous chondrocyte transplantation (MACT) as well as to compare the results to the conventional 2D MOCART score using standard MR sequences. MATERIAL AND METHODS: The study had approval by the local ethics commission. One hundred consecutive MR scans in 60 patients at standard follow-up intervals of 1, 3, 6, 12, 24, and 60 months after MACT of the knee joint were prospectively included. The mean follow-up interval of this cross-sectional evaluation was 21.4 +/- 20.6 months; the mean age of the patients was 35.8 +/- 9.4 years. MRI was performed at a 3.0 Tesla unit. All variables of the standard 2D MOCART score where part of the new 3D MOCART score. Furthermore, additional variables and options were included with the aims to use the capabilities of isotropic MRI, to include the results of recent studies, and to adapt to the needs of patients and physician in a clinical routine examination. A proton-density turbo spin-echo sequence, a T2-weighted dual fast spin-echo (dual-FSE) sequence, and a T1-weighted turbo inversion recovery magnitude (TIRM) sequence were used to assess the standard 2D MOCART score; an isotropic 3D-TrueFISP sequence was prepared to evaluate the new 3D MOCART score. All 9 variables of the 2D MOCART score were compared with the corresponding variables obtained by the 3D MOCART score using the Pearson correlation coefficient; additionally the subjective quality and possible artifacts of the MR sequences were analyzed. RESULTS: The correlation between the standard 2D MOCART score and the new 3D MOCART showed for the 8 variables "defect fill," "cartilage interface," "surface," "adhesions," "structure," "signal intensity," "subchondral lamina," and "effusion"-a highly significant (P < 0.001) correlation with a Pearson coefficient between 0.566 and 0.932. The variable "bone marrow edema" correlated significantly (P < 0.05; Pearson coefficient: 0.257). The subjective quality of the 3 standard MR sequences was comparable to the isotropic 3D-TrueFISP sequence. Artifacts were more frequently visible within the 3D-TrueFISP sequence. CONCLUSION: In the clinical routine follow-up after cartilage repair, the 3D MOCART score, assessed by only 1 high-resolution isotropic MR sequence, provides comparable information than the standard 2D MOCART score. Hence, the new 3D MOCART score has the potential to combine the information of the standard 2D MOCART score with the possible advantages of isotropic 3D MRI at high-field. A clear limitation of the 3D-TrueFISP sequence was the high number of artifacts. Future studies have to prove the clinical benefits of a 3D MOCART score.

Finite-element Analysis Of 3 Situations Of Trauma In The Human Edentulous Mandible.

Maxillofacial trauma resulting from falls in elderly patients is a major social and health care concern. Most of these traumatic events involve mandibular fractures. The aim of this study was to analyze stress distributions from traumatic loads applied on the symphyseal, parasymphyseal, and mandibular body regions in the elderly edentulous mandible using finite-element analysis (FEA). Computerized tomographic analysis of an edentulous macerated human mandible of a patient approximately 65 years old was performed. The bone structure was converted into a 3-dimensional stereolithographic model, which was used to construct the computer-aided design (CAD) geometry for FEA. The mechanical properties of cortical and cancellous bone were characterized as isotropic and elastic structures, respectively, in the CAD model. The condyles were constrained to prevent free movement in the x-, y-, and z-axes during simulation. This enabled the simulation to include the presence of masticatory muscles during trauma. Three different simulations were performed. Loads of 700 N were applied perpendicular to the surface of the cortical bone in the symphyseal, parasymphyseal, and mandibular body regions. The simulation results were evaluated according to equivalent von Mises stress distributions. Traumatic load at the symphyseal region generated low stress levels in the mental region and high stress levels in the mandibular neck. Traumatic load at the parasymphyseal region concentrated the resulting stress close to the mental foramen. Traumatic load in the mandibular body generated extensive stress in the mandibular body, angle, and ramus. FEA enabled precise mapping of the stress distribution in a human elderly edentulous mandible (neck and mandibular angle) in response to 3 different traumatic load conditions. This knowledge can help guide emergency responders as they evaluate patients after a traumatic event.