On the design of spherical gradient index lenses

Classical spherical gradient index (GRIN) lenses (such as Maxwell Fish Eye lens, Eaton lens, Luneburg lens, etc.) design procedure using the Abel integral equation is reviewed and reorganized. Each lens is fully defined by a function called the angle of flight which describes the ray deflection through the lens. The radial refractive index distribution is obtained by applying a linear integral transformation to the angle of flight. The interest of this formulation is in the linearity of the integral transformation which allows us to derive new solutions from linear combinations of known lenses. Beside the review of the classical GRIN designs, we present a numerical method for GRIN lenses defined by the Abel integral equation with fixed limits, which is an ill-posed problem.

Two-dimensional isostatic meshes in the finite element method

In a Finite Element (FE) analysis of elastic solids several items are usually considered, namely, type and shape of the elements, number of nodes per element, node positions, FE mesh, total number of degrees of freedom (dot) among others. In this paper a method to improve a given FE mesh used for a particular analysis is described. For the improvement criterion different objective functions have been chosen (Total potential energy and Average quadratic error) and the number of nodes and dof's of the new mesh remain constant and equal to the initial FE mesh. In order to find the mesh producing the minimum of the selected objective function the steepest descent gradient technique has been applied as optimization algorithm. However this efficient technique has the drawback that demands a large computation power. Extensive application of this methodology to different 2-D elasticity problems leads to the conclusion that isometric isostatic meshes (ii-meshes) produce better results than the standard reasonably initial regular meshes used in practice. This conclusion seems to be independent on the objective function used for comparison. These ii-meshes are obtained by placing FE nodes along the isostatic lines, i.e. curves tangent at each point to the principal direction lines of the elastic problem to be solved and they should be regularly spaced in order to build regular elements. That means ii-meshes are usually obtained by iteration, i.e. with the initial FE mesh the elastic analysis is carried out. By using the obtained results of this analysis the net of isostatic lines can be drawn and in a first trial an ii-mesh can be built. This first ii-mesh can be improved, if it necessary, by analyzing again the problem and generate after the FE analysis the new and improved ii-mesh. Typically, after two first tentative ii-meshes it is sufficient to produce good FE results from the elastic analysis. Several example of this procedure are presented.

Method for the characterization of Fresnel lens flux transfer performance

Fresnel lenses and other faceted or micro-optic devices are increasingly used in multiple applications like solar light concentrators and illumination devices, just to name some representative. However, it seems to be a certain lack of adequate techniques for the assessment of the performance of final fabricated devices. As applications are more exigent this characterization is a must. We provide a technique to characterize the performance of Fresnel lenses, as light collection devices. The basis for the method is a configuration where a camera images the Fresnel lens aperture. The entrance pupil of the camera is situated at the focal spot or the conjugate of a simulated solar source. In this manner, detailed maps of the performance of different Fresnel lenses are obtained for different acceptance angles.

Method for determining reaction rate of mild steel containers during melting of magnesium-aluminium alloys and effect of aluminium content on directionally solidified microstructures

A magnesium alloy of eutectic composition (33 wt-'%Al) was directionally solidified in mild steel tubes at two growth rates, 32 and 580 mum s(-1,) in a temperature gradient between 10 and 20 K mm(-1). After directional solidification, the composition of each specimen varied dramatically, from 32'%Al in the region that had remained solid to 18%Al (32 mum s(-1) specimen) and 13%Al (580 mum s(-1) specimen) at the plane that had been quenched from the eutectic temperature. As the aluminium content decreased, the microstructure contained an increasing volume fraction of primary magnesium dendrites and the eutectic morphology gradually changed from lamellar to partially divorced. The reduction in aluminium content was caused by the growth of an Al-Fe phase ahead of the Mg-Al growth front. Most of the growth of the Al-Fe phase occurred during the remelting period before directional solidification. The thickness of the Al-Fe phase increased with increased temperature and time of contact with the molten Mg-Al alloy. (C) 2003 Maney Publishing.

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.

An FDTD model for calculation of gradient-induced eddy currents in MRI system

In most magnetic resonance imaging (MRI) systems, pulsed magnetic gradient fields induce eddy currents in the conducting structures of the superconducting magnet. The eddy currents induced in structures within the cryostat are particularly problematic as they are characterized by long time constants by virtue of the low resistivity of the conductors. This paper presents a three-dimensional (3-D) finite-difference time-domain (FDTD) scheme in cylindrical coordinates for eddy-current calculation in conductors. This model is intended to be part of a complete FDTD model of an MRI system including all RF and low-frequency field generating units and electrical models of the patient. The singularity apparent in the governing equations is removed by using a series expansion method and the conductor-air boundary condition is handled using a variant of the surface impedance concept. The numerical difficulty due to the asymmetry of Maxwell equations for low-frequency eddy-current problems is circumvented by taking advantage of the known penetration behavior of the eddy-current fields. A perfectly matched layer absorbing boundary condition in 3-D cylindrical coordinates is also incorporated. The numerical method has been verified against analytical solutions for simple cases. Finally, the algorithm is illustrated by modeling a pulsed field gradient coil system within an MRI magnet system. The results demonstrate that the proposed FDTD scheme can be used to calculate large-scale eddy-current problems in materials with high conductivity at low frequencies.

A gradient descent algorithm for minimizing amino acid coupling reactions when synthesizing cyclic-peptide libraries

Combinatorial chemistry has become an invaluable tool in medicinal chemistry for the identification of new drug leads. For example, libraries of predetermined sequences and head-to-tail cyclized peptides are routinely synthesized in our laboratory using the IRORI approach. Such libraries are used as molecular toolkits that enable the development of pharmacophores that define activity and specificity at receptor targets. These libraries can be quite large and difficult to handle, due to physical and chemical constraints imposed by their size. Therefore, smaller sub-libraries are often targeted for synthesis. The number of coupling reactions required can be greatly reduced if the peptides having common amino acids are grouped into the same sub-library (batching). This paper describes a schedule optimizer to minimize the number of coupling reactions by rotating and aligning sequences while simultaneously batching. The gradient descent method thereby reduces the number of coupling reactions required for synthesizing cyclic peptide libraries. We show that the algorithm results in a 75% reduction in the number of coupling reactions for a typical cyclic peptide library.

A wave equation technique for designing compact gradient coils

A primary purpose of this research is to design a gradient coil that is planar in construction and can be inserted within existing infrastructure. The proposed wave equation method for the design of gradient coils is novel within the field. it is comprehensively shown how this method can be used to design the planar x-, y-, and z-gradient wire windings to produce the required magnetic fields within a certain domain. The solution for the cylindrical gradient coil set is also elucidated. The wave equation technique is compared with the well-known target held method to gauge the quality of resultant design. In the case of the planar gradient coil design, it is shown that using the new method, a set of compact gradient coils with large field of view can be produced. The final design is considerably smaller in dimension when compared with the design obtained using the target field method, and therefore the manufacturing costs and materials required are somewhat reduced.

A method for screening the temperature dependence of three-dimensional crystal formation

Temperature is an important parameter controlling protein crystal growth. A new temperature-screening system (Thermo-screen) is described consisting of a gradient thermocycler fitted with a special crystallization-plate adapter onto which a 192-well sitting-drop crystallization plate can be mounted (temperature range 277-372 K; maximum temperature gradient 20 K; interval precision 0.3 K). The system allows 16 different conditions to be monitored simultaneously over a range of 12 temperatures and is well suited to conduct wide (similar to 20 K) and fine (similar to 3 K) temperature-optimization screens. It can potentially aid in the determination of temperature phase diagrams and run more complex temperature-cycling experiments for seeding and crystal growth.

Analysis of transient eddy currents in MRI using a cylindrical FDTD method

Most magnetic resonance imaging (MRI) spatial encoding techniques employ low-frequency pulsed magnetic field gradients that undesirably induce multiexponentially decaying eddy currents in nearby conducting structures of the MRI system. The eddy currents degrade the switching performance of the gradient system, distort the MRI image, and introduce thermal loads in the cryostat vessel and superconducting MRI components. Heating of superconducting magnets due to induced eddy currents is particularly problematic as it offsets the superconducting operating point, which can cause a system quench. A numerical characterization of transient eddy current effects is vital for their compensation/control and further advancement of the MRI technology as a whole. However, transient eddy current calculations are particularly computationally intensive. In large-scale problems, such as gradient switching in MRI, conventional finite-element method (FEM)-based routines impose very large computational loads during generation/solving of the system equations. Therefore, other computational alternatives need to be explored. This paper outlines a three-dimensional finite-difference time-domain (FDTD) method in cylindrical coordinates for the modeling of low-frequency transient eddy currents in MRI, as an extension to the recently proposed time-harmonic scheme. The weakly coupled Maxwell's equations are adapted to the low-frequency regime by downscaling the speed of light constant, which permits the use of larger FDTD time steps while maintaining the validity of the Courant-Friedrich-Levy stability condition. The principal hypothesis of this work is that the modified FDTD routine can be employed to analyze pulsed-gradient-induced, transient eddy currents in superconducting MRI system models. The hypothesis is supported through a verification of the numerical scheme on a canonical problem and by analyzing undesired temporal eddy current effects such as the B-0-shift caused by actively shielded symmetric/asymmetric transverse x-gradient head and unshielded z-gradient whole-body coils operating in proximity to a superconducting MRI magnet.

Tailoring magnetic field gradient design to magnet cryostat geometry

Eddy currents induced within a magnetic resonance imaging (MRI) cryostat bore during pulsing of gradient coils can be applied constructively together with the gradient currents that generate them, to obtain good quality gradient uniformities within a specified imaging volume over time. This can be achieved by simultaneously optimizing the spatial distribution and temporal pre-emphasis of the gradient coil current, to account for the spatial and temporal variation of the secondary magnetic fields due to the induced eddy currents. This method allows the tailored design of gradient coil/magnet configurations and consequent engineering trade-offs. To compute the transient eddy currents within a realistic cryostat vessel, a low-frequency finite-difference time-domain (FDTD) method using total-field scattered-field (TFSF) scheme has been performed and validated

Natural gradient matrix momentum

Natural gradient learning is an efficient and principled method for improving on-line learning. In practical applications there will be an increased cost required in estimating and inverting the Fisher information matrix. We propose to use the matrix momentum algorithm in order to carry out efficient inversion and study the efficacy of a single step estimation of the Fisher information matrix. We analyse the proposed algorithm in a two-layer network, using a statistical mechanics framework which allows us to describe analytically the learning dynamics, and compare performance with true natural gradient learning and standard gradient descent.

Dual affinity method for plasmid DNA purification in aqueous two-phase systems

The DNA binding fusion protein, LacI-His6-GFP, together with the conjugate PEG-IDA-Cu(II) (10 kDa) was evaluated as a dual affinity system for the pUC19 plasmid extraction from an alkaline bacterial cell lysate in poly(ethylene glycol) (PEG)/dextran (DEX) aqueous two-phase systems (ATPS). In a PEG 600-DEX 40 ATPS containing 0.273 nmol of LacI fusion protein and 0.14% (w/w) of the functionalised PEG-IDA-Cu(II), more than 72% of the plasmid DNA partitioned to the PEG phase, without RNA or genomic DNA contamination as evaluated by agarose gel electrophoresis. In a second extraction stage, the elution of pDNA from the LacI binding complex proved difficult using either dextran or phosphate buffer as second phase, though more than 75% of the overall protein was removed in both systems. A maximum recovery of approximately 27% of the pCU19 plasmid was achieved using the PEG-dextran system as a second extraction system, with 80-90% of pDNA partitioning to the bottom phase. This represents about 7.4 microg of pDNA extracted per 1 mL of pUC19 desalted lysate.

Solid phase synthesis of a metronidazole oligonucleotide conjugate

Direct, solid phase synthesis of an oligonucleotide conjugate of the antibiotic drug metronidazole was accomplished by the phosphoramidite method. Removal of protecting groups and cleavage from the controlled pore glass (CPG) solid support was successful using mild conditions (20% EtN in pyridine, then conc. NH (aq) at rt for 30 min) whereas standard conditions (conc. NH (aq) at 55°C for 16 h) cleaved the drug. © 2006 by MDPI.

A simple bioanalytical method for the quantification of antiepileptic drugs in dried blood spots

An increasing number of publications on the dried blood spot (DBS) sampling approach for the quantification of drugs and metabolites have been spurred on by the inherent advantages of this sampling technique. In the present research, a selective and sensitive high-performance liquid chromatography method for the concurrent determination of multiple antiepileptic drugs (AEDs) [levetiracetam (LVT), lamotrigine (LTG), phenobarbital (PHB)], carbamazepine (CBZ) and its active metabolite carbamazepine-10,11 epoxide (CBZE)] in a single DBS has been developed and validated. Whole blood was spotted onto Guthrie cards and dried. Using a standard punch (6 mm diameter), a circular disc was punched from the card and extracted with methanol: acetonitrile (3:1, v/v) containing hexobarbital (Internal Standard) and sonicated prior to evaporation. The extract was then dissolved in water and vortex mixed before undergoing solid phase extraction using HLB cartridges. Chromatographic separation of the AEDs was achieved using Waters XBridge™ C18 column with a gradient system. The developed method was linear over the concentration ranges studied with r ≥ 0.995 for all compounds. The lower limits of quantification (LLOQs) were 2, 1, 2, 0.5 and 1 μg/mL for LVT, LTG, PHB, CBZE and CBZ, respectively. Accuracy (%RE) and precision (%CV) values for within and between day were <20% at the LLOQs and <15% at all other concentrations tested. This method was successfully applied to the analysis of the AEDs in DBS samples taken from children with epilepsy for the assessment of their adherence to prescribed treatments.