Reappraisal of the effective elastic thickness for the sub-Andes using 3-D finite element flexural modelling, gravity and geological constraints

P>Estimates of effective elastic thickness (T(e)) for the western portion of the South American Plate using, independently, forward flexural modelling and coherence analysis, suggest different thermomechanical properties for the same continental lithosphere. We present a review of these T(e) estimates and carry out a critical reappraisal using a common methodology of 3-D finite element method to solve a differential equation for the bending of a thin elastic plate. The finite element flexural model incorporates lateral variations of T(e) and the Andes topography as the load. Three T(e) maps for the entire Andes were analysed: Stewart & Watts (1997), Tassara et al. (2007) and Perez-Gussinye et al. (2007). The predicted flexural deformation obtained for each T(e) map was compared with the depth to the base of the foreland basin sequence. Likewise, the gravity effect of flexurally induced crust-mantle deformation was compared with the observed Bouguer gravity. T(e) estimates using forward flexural modelling by Stewart & Watts (1997) better predict the geological and gravity data for most of the Andean system, particularly in the Central Andes, where T(e) ranges from greater than 70 km in the sub-Andes to less than 15 km under the Andes Cordillera. The misfit between the calculated and observed foreland basin subsidence and the gravity anomaly for the Maranon basin in Peru and the Bermejo basin in Argentina, regardless of the assumed T(e) map, may be due to a dynamic topography component associated with the shallow subduction of the Nazca Plate beneath the Andes at these latitudes.

Gamma Knife(A (R)) 3-D Dose Distribution Mapping by Magnetic Resonance Imaging

In medical processes where ionizing radiation is used, dose planning and dose delivery are the key elements to patient safety and treatment success, particularly, when the delivered dose in a single session of treatment can be an order of magnitude higher than the regular doses of radiotherapy. Therefore, the radiation dose should be well defined and precisely delivered to the target while minimizing radiation exposure to surrounding normal tissues [1]. Several methods have been proposed to obtain three-dimensional (3-D) dose distribution [2, 3]. In this paper, we propose an alternative method, which can be easily implemented in any stereotactic radiosurgery center with a magnetic resonance imaging (MRI) facility. A phantom with or without scattering centers filled with Fricke gel solution is irradiated with Gamma Knife(A (R)) system at a chosen spot. The phantom can be a replica of a human organ such as head, breast or any other organ. It can even be constructed from a real 3-D MR image of an organ of a patient using a computer-aided construction and irradiated at a specific region corresponding to the tumor position determined by MRI. The spin-lattice relaxation time T (1) of different parts of the irradiated phantom is determined by localized spectroscopy. The T (1)-weighted phantom images are used to correlate the image pixels intensity to the absorbed dose and consequently a 3-D dose distribution with a high resolution is obtained.

3-D volume rendering maxillofacial analysis of angular measurements by multislice CT

Objective. This study was designed to determine the precision and accuracy of angular measurements using three-dimensional computed tomography (3D-CT) volume rendering by computer systems. Study design. The study population consisted of 28 dried skulls that were scanned with a 64-row multislice CT, and 3D-CT images were generated. Angular measurements, (n = 6) based upon conventional craniometric anatomical landmarks (n = 9), were identified independently in 3D-CT images by 2 radiologists, twice each, and were then performed by 3D-CT imaging. Subsequently, physical measurements were made by a third examiner using a Beyond Crysta-C9168 series 900 device. Results. The results demonstrated no statistically significant difference between interexaminer and intraexaminer analysis. The mean difference between the physical and 3-D-based angular measurements was -1.18% and -0.89%, respectively, for both examiners, demonstrating high accuracy. Conclusion. Maxillofacial analysis of angular measurements using 3D-CT volume rendering by 64-row multislice CT is established and can be used for orthodontic and dentofacial orthopedic applications.

Programs to compute magnetization to density ratio and the magnetization inclination from 3-D gravity and magnetic anomalies

Vector field formulation based on the Poisson theorem allows an automatic determination of rock physical properties (magnetization to density ratio-MDR-and the magnetization inclination-MI) from combined processing of gravity and magnetic geophysical data. The basic assumptions (i.e., Poisson conditions) are: that gravity and magnetic fields share common sources, and that these sources have a uniform magnetization direction and MDR. In addition, the previously existing formulation was restricted to profile data, and assumed sufficiently elongated (2-D) sources. For sources that violate Poisson conditions or have a 3-D geometry, the apparent values of MDR and MI that are generated in this way have an unclear relationship to the actual properties in the subsurface. We present Fortran programs that estimate MDR and MI values for 3-D sources through processing of gridded gravity and magnetic data. Tests with simple geophysical models indicate that magnetization polarity can be successfully recovered by MDR-MI processing, even in cases where juxtaposed bodies cannot be clearly distinguished on the basis of anomaly data. These results may be useful in crustal studies, especially in mapping magnetization polarity from marine-based gravity and magnetic data. (c) 2007 Elsevier Ltd. All rights reserved.

An improved finite element space for discontinuous pressures

We consider incompressible Stokes flow with an internal interface at which the pressure is discontinuous, as happens for example in problems involving surface tension. We assume that the mesh does not follow the interface, which makes classical interpolation spaces to yield suboptimal convergence rates (typically, the interpolation error in the L(2)(Omega)-norm is of order h(1/2)). We propose a modification of the P(1)-conforming space that accommodates discontinuities at the interface without introducing additional degrees of freedom or modifying the sparsity pattern of the linear system. The unknowns are the pressure values at the vertices of the mesh and the basis functions are computed locally at each element, so that the implementation of the proposed space into existing codes is straightforward. With this modification, numerical tests show that the interpolation order improves to O(h(3/2)). The new pressure space is implemented for the stable P(1)(+)/P(1) mini-element discretization, and for the stabilized equal-order P(1)/P(1) discretization. Assessment is carried out for Poiseuille flow with a forcing surface and for a static bubble. In all cases the proposed pressure space leads to improved convergence orders and to more accurate results than the standard P(1) space. In addition, two Navier-Stokes simulations with moving interfaces (Rayleigh-Taylor instability and merging bubbles) are reported to show that the proposed space is robust enough to carry out realistic simulations. (c) 2009 Elsevier B.V. All rights reserved.

Determination of Very Slow Diffusion of Paramagnetic Ions by NMR Spectroscopy

In this paper, we propose a new method of measuring the very slow paramagnetic ion diffusion coefficient using a commercial high-resolution spectrometer. If there are distinct paramagnetic ions influencing the hydrogen nuclear magnetic relaxation time differently, their diffusion coefficients can be measured separately. A cylindrical phantom filled with Fricke xylenol gel solution and irradiated with gamma rays was used to validate the method. The Fricke xylenol gel solution was prepared with 270 Bloom porcine gelatin, the phantom was irradiated with gamma rays originated from a (60)Co source and a high-resolution 200 MHz nuclear magnetic resonance (NMR) spectrometer was used to obtain the phantom (1)H profile in the presence of a linear magnetic field gradient. By observing the temporal evolution of the phantom NMR profile, an apparent ferric ion diffusion coefficient of 0.50 mu m(2)/ms due to ferric ions diffusion was obtained. In any medical process where the ionizing radiation is used, the dose planning and the dose delivery are the key elements for the patient safety and success of treatment. These points become even more important in modern conformal radio therapy techniques, such as stereotactic radiosurgery, where the delivered dose in a single session of treatment can be an order of magnitude higher than the regular doses of radiotherapy. Several methods have been proposed to obtain the three-dimensional (3-D) dose distribution. Recently, we proposed an alternative method for the 3-D radiation dose mapping, where the ionizing radiation modifies the local relative concentration of Fe(2+)/Fe(3+) in a phantom containing Fricke gel and this variation is associated to the MR image intensity. The smearing of the intensity gradient is proportional to the diffusion coefficient of the Fe(3+) and Fe(2+) in the phantom. There are several methods for measurement of the ionic diffusion using NMR, however, they are applicable when the diffusion is not very slow.