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.

Emission features of microstructures fabricated by two-photon polymerization containing three organic dyes

Fabrication of microstructures containing active compounds, such as fluorescent dyes and nanoparticles have been exploited in the last few years, aiming at applications from photonics to biology. Here we fabricate, using two-photon polymerization, microstructures containing the fluorescent dyes Stilbene 420, Disodium Fluorescein and Rhodamine B. The produced microstructures, containing dyes at specific sites, present good structural integrity and a broad fluorescence spectrum, from about 350 nm until 700 nm. Such spectrum can be tuned by using different excitation wavelengths and selecting the excitation position in the microstructure. These results are interesting for designing multi-doped structures, presenting tunable and broad fluorescence spectrum. (C)2012 Optical Society of America

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.

Ex vivo investigation of novel wound healing therapies and development of a 3-D human skin equivalent wound model

It has previously been found that complexes comprised of vitronectin and growth factors (VN:GF) enhance keratinocyte protein synthesis and migration. More specifically, these complexes have been shown to significantly enhance the migration of dermal keratinocytes derived from human skin. In view of this, it was thought that these complexes may hold potential as a novel therapy for healing chronic wounds. However, there was no evidence indicating that the VN:GF complexes would retain their effect on keratinocytes in the presence of chronic wound fluid. The studies in this thesis demonstrate for the first time that the VN:GF complexes not only stimulate proliferation and migration of keratinocytes, but also these effects are maintained in the presence of chronic wound fluid in a 2-dimensional (2-D) cell culture model. Whilst the 2-D culture system provided insights into how the cells might respond to the VN:GF complexes, this investigative approach is not ideal as skin is a 3-dimensional (3-D) tissue. In view of this, a 3-D human skin equivalent (HSE) model, which reflects more closely the in vivo environment, was used to test the VN:GF complexes on epidermopoiesis. These studies revealed that the VN:GF complexes enable keratinocytes to migrate, proliferate and differentiate on a de-epidermalised dermis (DED), ultimately forming a fully stratified epidermis. In addition, fibroblasts were seeded on DED and shown to migrate into the DED in the presence of the VN:GF complexes and hyaluronic acid, another important biological factor in the wound healing cascade. This HSE model was then further developed to enable studies examining the potential of the VN:GF complexes in epidermal wound healing. Specifically, a reproducible partial-thickness HSE wound model was created in fully-defined media and monitored as it healed. In this situation, the VN:GF complexes were shown to significantly enhance keratinocyte migration and proliferation, as well as differentiation. This model was also subsequently utilized to assess the wound healing potential of a synthetic fibrin-like gel that had previously been demonstrated to bind growth factors. Of note, keratinocyte re-epitheliasation was shown to be markedly improved in the presence of this 3-D matrix, highlighting its future potential for use as a delivery vehicle for the VN:GF complexes. Furthermore, this synthetic fibrin-like gel was injected into a 4 mm diameter full-thickness wound created in the HSE, both keratinocytes and fibroblasts were shown to migrate into this gel, as revealed by immunofluorescence. Interestingly, keratinocyte migration into this matrix was found to be dependent upon the presence of the fibroblasts. Taken together, these data indicate that reproducible wounds, as created in the HSEs, provide a relevant ex vivo tool to assess potential wound healing therapies. Moreover, the models will decrease our reliance on animals for scientific experimentation. Additionally, it is clear that these models will significantly assist in the development of novel treatments, such as the VN:GF complexes and the synthetic fibrin-like gel described herein, ultimately facilitating their clinical trial in the treatment of chronic wounds.

Magnetic resonance imaging: An accurate, radiation-free, alternative to computed tomography for the primary imaging and three-dimensional reconstruction of the bony orbit

Purpose: To determine the extent to which the accuracy of magnetic resonance imaging (MRI) based virtual 3-dimensional (3D) models of the intact orbit can approach that of the gold standard, computed tomography (CT) based models. The goal was to determine whether MRI is a viable alternative to CT scans in patients with isolated orbital fractures and penetrating eye injuries, pediatric patients, and patients requiring multiple scans in whom radiation exposure is ideally limited. Materials and Methods: Patients who presented with unilateral orbital fractures to the Royal Brisbane and Women’s Hospital from March 2011 to March 2012 were recruited to participate in this cross-sectional study. The primary predictor variable was the imaging technique (MRI vs CT). The outcome measurements were orbital volume (primary outcome) and geometric intraorbital surface deviations (secondary outcome)between the MRI- and CT-based 3D models. Results: Eleven subjects (9 male) were enrolled. The patients’ mean age was 30 years. On average, the MRI models underestimated the orbital volume of the CT models by 0.50 0.19 cm3 . The average intraorbital surface deviation between the MRI and CT models was 0.34 0.32 mm, with 78 2.7% of the surface within a tolerance of 0.5 mm. Conclusions: The volumetric differences of the MRI models are comparable to reported results from CT models. The intraorbital MRI surface deviations are smaller than the accepted tolerance for orbital surgical reconstructions. Therefore, the authors believe that MRI is an accurate radiation-free alternative to CT for the primary imaging and 3D reconstruction of the bony orbit. �

Compressible second-order boundary layers for three-dimensional stagnation point flows with mass transfer

All the second-order boundary-layer effects have been studied for the steady laminar compressible 3-dimensional stagnation-point flows with variable properties and mass transfer for both saddle and nodal point regions. The governing equations have been solved numerically using an implicit finite-difference scheme. Results for the heat transfer and skin friction have been obtained for several values of the mass-transfer rate, wall temperature, and also for several values of parameters characterizing the nature of stagnation point and variable gas properties. The second-order effects on the heat transfer and skin friction at the wall are found to be significant and at large injection rates, they dominate over the results of the first-order boundary layer, but the effect of large suction is just the opposite. In general, the second-order effects are more pronounced in the saddle-point region than in the nodal-point region. The overall heat-transfer rate for the 3-dimensional flows is found to be more than that of the 2-dimensional flows.