A novel phantom and method for comprehensive 3-dimensional measurement and correction of geometric distortion in magnetic resonance imaging

A phantom that can be used for mapping geometric distortion in magnetic resonance imaging (MRI) is described. This phantom provides an array of densely distributed control points in three-dimensional (3D) space. These points form the basis of a comprehensive measurement method to correct for geometric distortion in MR images arising principally from gradient field non-linearity and magnet field inhomogeneity. The phantom was designed based on the concept that a point in space can be defined using three orthogonal planes. This novel design approach allows for as many control points as desired. Employing this novel design, a highly accurate method has been developed that enables the positions of the control points to be measured to sub-voxel accuracy. The phantom described in this paper was constructed to fit into a body coil of a MRI scanner, (external dimensions of the phantom were: 310 mm x 310 mm x 310 mm), and it contained 10,830 control points. With this phantom, the mean errors in the measured coordinates of the control points were on the order of 0.1 mm or less, which were less than one tenth of the voxel's dimensions of the phantom image. The calculated three-dimensional distortion map, i.e., the differences between the image positions and true positions of the control points, can then be used to compensate for geometric distortion for a full image restoration. It is anticipated that this novel method will have an impact on the applicability of MRI in both clinical and research settings. especially in areas where geometric accuracy is highly required, such as in MR neuro-imaging. (C) 2004 Elsevier Inc. All rights reserved.

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.

Expression of the proto-oncogene c-fos in three-dimensional fetal brain cell cultures and the lack of correlation with maturation-inducing stimuli.

Previous work has shown that aggregating fetal brain cell cultures are able to attain a highly differentiated state, and that their development is greatly enhanced by growth and/or differentiation factors such as epidermal growth factor (EGF), basic fibroblast growth factor (bFGF), and the protein kinase C-activating tumor promoter mezerein. The present study shows that in these 3-dimensional cultures the peptide growth factors EGF and bFGF as well as mezerein are able to induce the expression of the proto-oncogene c-fos. This induction was rapid and transient, in good agreement with observations reported from a wide variety of cell types in vitro. The maximal levels of c-fos mRNA found after stimulation were low in immature cultures and increased greatly as maturation progressed. Of the three factors tested, mezerein was the most potent inducer of c-fos. In contrast to the peptide growth factors EGF and bFGF which were found to induce c-fos only in glial cells, mezerein was stimulatory in glial cells as well as in neurons. A similar cell type specificity has been observed previously for the maturation-enhancing response in immature aggregate cultures. However, in the present study no correlation was found between the degree of c-fos induction and the extent of the maturation-enhancing stimulation. Immature cultures known to be most sensitive and responsive to these maturation-enhancing agents required relatively high doses of peptide growth factors for the induction of c-fos, and the maximal levels of c-fos mRNA elicited were much lower than those in differentiated cultures which did not show any long-term response to these stimuli.(ABSTRACT TRUNCATED AT 250 WORDS)