Electromagnetic fields inside a lossy, multilayered spherical head phantom excited by MRI coils: models and methods

The precise evaluation of electromagnetic field (EMF) distributions inside biological samples is becoming an increasingly important design requirement for high field MRI systems. In evaluating the induced fields caused by magnetic field gradients and RF transmitter coils, a multilayered dielectric spherical head model is proposed to provide a better understanding of electromagnetic interactions when compared to a traditional homogeneous head phantom. This paper presents Debye potential (DP) and Dyadic Green's function (DGF)-based solutions of the EMFs inside a head-sized, stratified sphere with similar radial conductivity and permittivity profiles as a human head. The DP approach is formulated for the symmetric case in which the source is a circular loop carrying a harmonic-formed current over a wide frequency range. The DGF method is developed for generic cases in which the source may be any kind of RF coil whose current distribution can be evaluated using the method of moments. The calculated EMFs can then be used to deduce MRI imaging parameters. The proposed methods, while not representing the full complexity of a head model, offer advantages in rapid prototyping as the computation times are much lower than a full finite difference time domain calculation using a complex head model. Test examples demonstrate the capability of the proposed models/methods. It is anticipated that this model will be of particular value for high field MRI applications, especially the rapid evaluation of RF resonator (surface and volume coils) and high performance gradient set designs.

Comparative adsorption of spherical argon and flexible n-butane in carbon slit pores - a GCMC computer simulation study

In this paper we investigate the difference between the adsorption of spherical molecule argon (at 87.3 K) and the flexible normal butane (at an equivalent temperature of 150 K) in carbon slit pores. These temperatures are equivalent in the sense that they have the same relative distances between their respective triple points and critical points. Higher equivalent temperatures are also studied (122.67 K for argon and 303 K for n-butane) to investigate the effects of temperature on the 2D-transition in adsorbed density. The Grand Canonical Monte Carlo simulation is used to study the adsorption of these two model adsorbates. Beside the longer computation times involved in the computation of n-butane adsorption, n-butane exhibits many interesting behaviors such as: (i) the onset of adsorption occurs sooner (in terms of relative pressure), (ii) the hysteresis for 2D- and 3D-transitions is larger, (iii) liquid-solid transition is not possible, (iv) 2D-transition occurs for n-butane at 150 K while it does not happen for argon except for pores that accommodate two layers of molecules, (v) the maximum pore density is about four times less than that of argon and (vi) the sieving pore width is slightly larger than that for argon. Finally another feature obtained from the Grand Canonical Monte Carlo (GCMC) simulation is the configurational arrangement of molecules in pores. For spherical argon, the arrangement is rather well structured, while for n-butane the arrangement depends very much on the pore size. (C) 2004 Elsevier B.V. All rights reserved.

The displacement and strain field of three-dimensional rheologic model of earthquake preparation

Based on the three-dimensional elastic inclusion model proposed by Dobrovolskii, we developed a rheological inclusion model to study earthquake preparation processes. By using the Corresponding Principle in the theory of rheologic mechanics, we derived the analytic expressions of viscoelastic displacement U(r, t) , V(r, t) and W(r, t), normal strains epsilon(xx) (r, t), epsilon(yy) (r, t) and epsilon(zz) (r, t) and the bulk strain theta (r, t) at an arbitrary point (x, y, z) in three directions of X axis, Y axis and Z axis produced by a three-dimensional inclusion in the semi-infinite rheologic medium defined by the standard linear rheologic model. Subsequent to the spatial-temporal variation of bulk strain being computed on the ground produced by such a spherical rheologic inclusion, interesting results are obtained, suggesting that the bulk strain produced by a hard inclusion change with time according to three stages (alpha, beta, gamma) with different characteristics, similar to that of geodetic deformation observations, but different with the results of a soft inclusion. These theoretical results can be used to explain the characteristics of spatial-temporal evolution, patterns, quadrant-distribution of earthquake precursors, the changeability, spontaneity and complexity of short-term and imminent-term precursors. It offers a theoretical base to build physical models for earthquake precursors and to predict the earthquakes.

Operator-induced errors in Hartmann-Shack wavefront sensing:model eye study

Purpose: To evaluate the effects of instrument realignment and angular misalignment during the clinical determination of wavefront aberrations by simulation in model eyes. Setting: Aston Academy of Life Sciences, Aston University, Birmingham, United Kingdom. Methods: Six model eyes were examined with wavefront-aberration-supported cornea ablation (WASCA) (Carl Zeiss Meditec) in 4 sessions of 10 measurements each: sessions 1 and 2, consecutive repeated measures without realignment; session 3, realignment of the instrument between readings; session 4, measurements without realignment but with the model eye shifted 6 degrees angularly. Intersession repeatability and the effects of realignment and misalignment were obtained by comparing the measurements in the various sessions for coma, spherical aberration, and higher-order aberrations (HOAs). Results: The mean differences between the 2 sessions without realignment of the instrument were 0.020 μm ± 0.076 (SD) for Z3 - 1(P = .551), 0.009 ± 0.139 μm for Z3 1(P = .877), 0.004 ± 0.037 μm for Z4 0 (P = .820), and 0.005 ± 0.01 μm for HO root mean square (RMS) (P = .301). Differences between the nonrealigned and realigned instruments were -0.017 ± 0.026 μm for Z3 - 1(P = .159), 0.009 ± 0.028 μm for Z3 1 (P = .475), 0.007 ± 0.014 μm for Z4 0(P = .296), and 0.002 ± 0.007 μm for HO RMS (P = 0.529; differences between centered and misaligned instruments were -0.355 ± 0.149 μm for Z3 - 1 (P = .002), 0.007 ± 0.034 μm for Z3 1(P = .620), -0.005 ± 0.081 μm for Z4 0(P = .885), and 0.012 ± 0.020 μm for HO RMS (P = .195). Realignment increased the standard deviation by a factor of 3 compared with the first session without realignment. Conclusions: Repeatability of the WASCA was excellent in all situations tested. Realignment substantially increased the variance of the measurements. Angular misalignment can result in significant errors, particularly in the determination of coma. These findings are important when assessing highly aberrated eyes during follow-up or before surgery. © 2007 ASCRS and ESCRS.

Poly(methyl methacrylate) model study of optical surface quality after excimer laser photorefractive keratectomy

Purpose: To evaluate lenses produced by excimer laser ablation of poly(methyl methacrylate) (PMMA) plates. Setting: University research laboratory. Methods: Two Nidek EC-5000 scanning-slit excimer laser systems were used to ablate plane-parallel plates of PMMA. The ablated lenses were examined by focimetry, interferometry, and mechanical surface profiling. Results: The spherical optical powers of the lenses matched the expected values, but the cylindrical powers were generally lower than intended. Interferometry revealed marked irregularity in the surface of negative corrections, which often had a positive “island” at their center. Positive corrections were generally smoother. These findings were supported by the results of mechanical profiling. Contrast sensitivity measurements carried out when observing through ablated lenses whose power had been neutralized with a suitable spectacle lens of opposite sign confirmed that the surface irregularities of the ablated lenses markedly reduced contrast sensitivity over a range of spatial frequencies. Conclusion: Improvements in beam delivery systems seem desirable.

The tetrahexahedric angular Calogero model

The spherical reduction of the rational Calogero model (of type A n−1 and after removing the center of mass) is considered as a maximally superintegrable quantum system, which describes a particle on the (n−2)-sphere subject to a very particular potential. We present a detailed analysis of the simplest non-separable case, n=4, whose potential is singular at the edges of a spherical tetrahexahedron. A complete set of independent conserved charges and of Hamiltonian intertwiners is constructed, and their algebra is elucidated. They arise from the ring of polynomials in Dunkl-deformed angular momenta, by classifying the subspaces invariant and antiinvariant under all Weyl reflections, respectively.

The Traceless Oldroyd viscoelastic model

In the traceless Oldroyd viscoelastic model, the viscoelastic extra stress tensor is decomposed into its traceless (deviatoric) and spherical parts, leading to a reformulation of the classical Oldroyd model. The equivalence of the two models is established comparing model predictions for simple test cases. The new model is validated using several 2D benchmark problems. The structure and behavior of the new model are discussed and the future use of the new model in envisioned, both on the theoretical and numerical perspectives.

A traceless variant of the Johnson-Segalman viscoelastic model

A traceless variant of the Johnson-Segalman viscoelastic model is presented. The viscoelastic extra stress tensor is de composed into its traceless (deviatoric) and spherical parts, leading to a reformulation of the classical Johnson-Segalman model. The equivalente of the two models is established comparing model predictions for simple test cases. The new model is validated using several 2D benchmark problems.The structure and behavior of the new model are discussed.

An approximate method for the solution of an influence function foil rolling model

Fleck and Johnson (Int. J. Mech. Sci. 29 (1987) 507) and Fleck et al. (Proc. Inst. Mech. Eng. 206 (1992) 119) have developed foil rolling models which allow for large deformations in the roll profile, including the possibility that the rolls flatten completely. However, these models require computationally expensive iterative solution techniques. A new approach to the approximate solution of the Fleck et al. (1992) Influence Function Model has been developed using both analytic and approximation techniques. The numerical difficulties arising from solving an integral equation in the flattened region have been reduced by applying an Inverse Hilbert Transform to get an analytic expression for the pressure. The method described in this paper is applicable to cases where there is or there is not a flat region.