Lanczos subspace filter diagonalization: Homogeneous recursive filtering and a low-storage method for the calculation of matrix elements

We develop a new iterative filter diagonalization (FD) scheme based on Lanczos subspaces and demonstrate its application to the calculation of bound-state and resonance eigenvalues. The new scheme combines the Lanczos three-term vector recursion for the generation of a tridiagonal representation of the Hamiltonian with a three-term scalar recursion to generate filtered states within the Lanczos representation. Eigenstates in the energy windows of interest can then be obtained by solving a small generalized eigenvalue problem in the subspace spanned by the filtered states. The scalar filtering recursion is based on the homogeneous eigenvalue equation of the tridiagonal representation of the Hamiltonian, and is simpler and more efficient than our previous quasi-minimum-residual filter diagonalization (QMRFD) scheme (H. G. Yu and S. C. Smith, Chem. Phys. Lett., 1998, 283, 69), which was based on solving for the action of the Green operator via an inhomogeneous equation. A low-storage method for the construction of Hamiltonian and overlap matrix elements in the filtered-basis representation is devised, in which contributions to the matrix elements are computed simultaneously as the recursion proceeds, allowing coefficients of the filtered states to be discarded once their contribution has been evaluated. Application to the HO2 system shows that the new scheme is highly efficient and can generate eigenvalues with the same numerical accuracy as the basic Lanczos algorithm.

Method for generation of homogeneous multicellular tumor spheroids applicable to a wide variety of cell types

Multicellular tumor spheroids (MCTS) are used as organotypic models of normal and solid tumor tissue. Traditional techniques for generating MCTS, such as growth on nonadherent surfaces, in suspension, or on scaffolds, have a number of drawbacks, including the need for manual selection to achieve a homogeneous population and the use of nonphysiological matrix compounds. In this study we describe a mild method for the generation of MCTS, in which individual spheroids form in hanging drops suspended from a microtiter plate. The method has been successfully applied to a broad range of cell lines and shows nearly 100% efficiency (i.e., one spheroid per drop). Using the hepatoma cell line, HepG2, the hanging drop method generated well-rounded MCTS with a narrow size distribution (coefficient of variation [CV] 10% to 15%, compared with 40% to 60% for growth on nonadherent surfaces). Structural analysis of HepG2 and a mammary gland adenocarcinoma cell line, MCF-7, composed spheroids, revealed highly organized, three-dimensional, tissue-like structures with an extensive extracellular matrix. The hanging drop method represents an attractive alternative for MCTS production, because it is mild, can be applied to a wide variety of cell lines, and can produce spheroids of a homogeneous size without the need for sieving or manual selection. The method has applications for basic studies of physiology and metabolism, tumor biology, toxicology, cellular organization, and the development of bioartificial tissue. (C) 2003 Wiley Periodicals, Inc.

Predicting composition of leg sections with anthropometry and bioelectrical impedance analysis using magnetic resonance imaging as reference

Magnetic resonance imaging (MRI) was used to evaluate and compare with anthropometry a fundamental bioelectrical impedance analysis (BIA) method for predicting muscle and adipose tissue composition in the lower limb. Healthy volunteers (eight men and eight women), aged 41 to 62 years, with mean (S.D.) body mass indices of 28.6 (5.4) kg/m(2) and 25.1 (5.4) kg/m(2) respectively, were subjected to MRI leg scans, from which 20-cm sections of thigh and IO-cm sections of lower leg (calf) were analysed for muscle and adipose tissue content, using specifically developed software. Muscle and adipose tissue were also predicted from anthropometric measurements of circumferences and skinfold thicknesses, and by use of fundamental BIA equations involving section impedance at 50 kHz and tissue-specific resistivities. Anthropometric assessments of circumferences, cross-sectional areas and volumes for total constituent tissues matched closely MRI estimates. Muscle volume was substantially overestimated (bias: thigh, -40%; calf, -18%) and adipose tissue underestimated (bias: thigh, 43%; calf, 8%) by anthropometry, in contrast to generally better predictions by the fundamental BIA approach for muscle (bias:thigh, -12%; calf, 5%) and adipose tissue (bias:thigh, 17%; calf, -28%). However, both methods demonstrated considerable individual variability (95% limits of agreement 20-77%). In general, there was similar reproducibility for anthropometric and fundamental BIA methods in the thigh (inter-observer residual coefficient of variation for muscle 3.5% versus 3.8%), but the latter was better in the calf (inter-observer residual coefficient of variation for muscle 8.2% versus 4.5%). This study suggests that the fundamental BIA method has advantages over anthropometry for measuring lower limb tissue composition in healthy individuals.

Asymmetric MRI magnet design using a hybrid numerical method

This paper describes a hybrid numerical method for the design of asymmetric magnetic resonance imaging magnet systems. The problem is formulated as a field synthesis and the desired current density on the surface of a cylinder is first calculated by solving a Fredholm equation of the first kind. Nonlinear optimization methods are then invoked to fit practical magnet coils to the desired current density. The field calculations are performed using a semi-analytical method. A new type of asymmetric magnet is proposed in this work. The asymmetric MRI magnet allows the diameter spherical imaging volume to be positioned close to one end of the magnet. The main advantages of making the magnet asymmetric include the potential to reduce the perception of claustrophobia for the patient, better access to the patient by attending physicians, and the potential for reduced peripheral nerve stimulation due to the gradient coil configuration. The results highlight that the method can be used to obtain an asymmetric MRI magnet structure and a very homogeneous magnetic field over the central imaging volume in clinical systems of approximately 1.2 m in length. Unshielded designs are the focus of this work. This method is flexible and may be applied to magnets of other geometries. (C) 1999 Academic Press.

A method for the design of MRI radiofrequency coils based on triangular and pulse basis functions

This paper presents a numerical technique for the design of an RF coil for asymmetric magnetic resonance imaging (MRI) systems. The formulation is based on an inverse approach where the cylindrical surface currents are expressed in terms of a combination of sub-domain basis functions: triangular and pulse functions. With the homogeneous transverse magnetic field specified in a spherical region, a functional method is applied to obtain the unknown current coefficients. The current distribution is then transformed to a conductor pattern by use of a stream function technique. Preliminary MR images acquired using a prototype RF coil are presented and validate the design method. (C) 2002 Elsevier Science B.V. All rights reserved.

Improved comparison plot method for pore structure characterization of MCM-41

MCM-41 samples of various pore dimensions are synthesized. Plotting of nitrogen adsorption data at 77 K versus the statistical film thickness (comparison plot) reveals three distinct stages, with a characteristic of two points of inflection. The steep intermediate stage caused by capillary condensation occurred in the highly uniform mesopores. From the slopes of the sections before and after the condensation, the surface area of the mesopores is calculated. The linear portion of the last section is extrapolated to the adsorption axis of the comparison plot, and this intercept is used to obtain the volume of the mesopores. From the surface area and pore volume, average mesopore diameter is calculated, and the value thus obtained is in good agreement with the pore dimension obtained from powder X-ray diffraction measurements. The principle of the calculation as well as problems associated are discussed in detail.

On the Hopf bifurcation in control systems with a bounded nonlinearity asymptotically homogeneous at infinity

The paper studies existence, uniqueness, and stability of large-amplitude periodic cycles arising in Hopf bifurcation at infinity of autonomous control systems with bounded nonlinear feedback. We consider systems with functional nonlinearities of Landesman-Lazer type and a class of systems with hysteresis nonlinearities. The method is based on the technique of parameter functionalization and methods of monotone concave and convex operators. (C) 2001 Academic Press.

An inverse design method for elliptical MRI magnets

An inverse, current density mapping (CDM) method has been developed for the design of elliptical cross-section MRI magnets. The method provides a rapid prototyping system for unusual magnet designs, as it generates a 3D current density in response to a set of target field and geometric constraints. The emphasis of this work is on the investigation of new elliptical coil structures for clinical MRI magnets. The effect of the elliptical aspect ratio on magnet performance is investigated. Viable designs are generated for symmetric, asymmetric and open architecture elliptical magnets using the new method. Clinically relevant attributes such as reduced stray field and large homogeneous regions relative to total magnet length are included in the design process and investigated in detail. The preliminary magnet designs have several novel features.

A design method for superconducting MRI magnets with ferromagnetic material

The emphasis of this work is on the optimal design of MRI magnets with both superconducting coils and ferromagnetic rings. The work is directed to the automated design of MRI magnet systems containing superconducting wire and both `cold' and `warm' iron. Details of the optimization procedure are given and the results show combined superconducting and iron material MRI magnets with excellent field characteristics. Strong, homogeneous central magnetic fields are produced with little stray or external field leakage. The field calculations are performed using a semi-analytical method for both current coil and iron material sources. Design examples for symmetric, open and asymmetric clinical MRI magnets containing both superconducting coils and ferromagnetic material are presented.

Asymmetric blasting: a rock mass dependent blast design method

Blasting has been the most frequently used method for rock breakage since black powder was first used to fragment rocks, more than two hundred years ago. This paper is an attempt to reassess standard design techniques used in blasting by providing an alternative approach to blast design. The new approach has been termed asymmetric blasting. Based on providing real time rock recognition through the capacity of measurement while drilling (MWD) techniques, asymmetric blasting is an approach to deal with rock properties as they occur in nature, i.e., randomly and asymmetrically spatially distributed. It is well accepted that performance of basic mining operations, such as excavation and crushing rely on a broken rock mass which has been pre conditioned by the blast. By pre-conditioned we mean well fragmented, sufficiently loose and with adequate muckpile profile. These muckpile characteristics affect loading and hauling [1]. The influence of blasting does not end there. Under the Mine to Mill paradigm, blasting has a significant leverage on downstream operations such as crushing and milling. There is a body of evidence that blasting affects mineral liberation [2]. Thus, the importance of blasting has increased from simply fragmenting and loosing the rock mass, to a broader role that encompasses many aspects of mining, which affects the cost of the end product. A new approach is proposed in this paper which facilitates this trend 'to treat non-homogeneous media (rock mass) in a non-homogeneous manner (an asymmetrical pattern) in order to achieve an optimal result (in terms of muckpile size distribution).' It is postulated there are no logical reasons (besides the current lack of means to infer rock mass properties in the blind zones of the bench and onsite precedents) for drilling a regular blast pattern over a rock mass that is inherently heterogeneous. Real and theoretical examples of such a method are presented.

Calculation of bound and resonance states of HO2 for nonzero total angular momentum

Bound and resonance states of HO2 have been calculated quantum mechanically by the Lanczos homogeneous filter diagonalization method [Zhang and Smith, Phys. Chem. Chem. Phys. 3, 2282 (2001); J. Chem. Phys. 115, 5751 (2001)] for nonzero total angular momentum J = 1,2,3. For lower bound states, agreement between the results in this paper and previous work is quite satisfactory; while for high lying bound states and resonances these are the first reported results. A helicity quantum number V assignment (within the helicity conserving approximation) is performed and the results indicate that for lower bound states it is possible to assign the V quantum numbers unambiguously, but for resonances it is impossible to assign the V helicity quantum numbers due to strong mixing. In fact, for the high-lying bound states, the mixing has already appeared. These results indicate that the helicity conserving approximation is not good for the resonance state calculations and exact quantum calculations are needed to accurately describe the reaction dynamics for HO2 system. Analysis of the resonance widths shows that most of the resonances are overlapping and the interferences between them lead to large fluctuations from one resonance to another. In accord with the conclusions from earlier J = 0 calculations, this indicates that the dissociation of HO2 is essentially irregular. (C) 2003 American Institute of Physics.

Application of X-ray microtomography to numerical simulations of agglomerate breakage by distinct element method

Computer-aided tomography has been used for many years to provide significant information about the internal properties of an object, particularly in the medical fraternity. By reconstructing one-dimensional (ID) X-ray images, 2D cross-sections and 3D renders can provide a wealth of information about an object's internal structure. An extension of the methodology is reported here to enable the characterization of a model agglomerate structure. It is demonstrated that methods based on X-ray microtomography offer considerable potential in the validation and utilization of distinct element method simulations also examined.

Adsorption of argon on homogeneous graphitized thermal carbon black and heterogeneous carbon surface

In this paper we investigate the effects of surface mediation on the adsorption behavior of argon at different temperatures on homogeneous graphitized thermal carbon black and on heterogeneous nongraphitized carbon black surface. The grand canonical Monte Carlo (GCMC) simulation is used to study the adsorption, and its performance is tested against a number of experimental data on graphitized thermal carbon black (which is known to be highly homogeneous) that are available in the literature. The surface-mediation effect is shown to be essential in the correct description of the adsorption isotherm because without accounting for that effect the GCMC simulation results are always greater than the experimental data in the region where the monolayer is being completed. This is due to the overestimation of the fluid–fluid interaction between particles in the first layer close to the solid surface. It is the surface mediation that reduces this fluid–fluid interaction in the adsorbed layers, and therefore the GCMC simulation results accounting for this surface mediation that are presented in this paper result in a better description of the data. This surface mediation having been determined, the surface excess of argon on heterogeneous carbon surfaces having solid–fluid interaction energies different from the graphite can be readily obtained. Since the real heterogeneous carbon surface is not the same as the homogeneous graphite surface, it can be described by an area distribution in terms of the well depth of the solid–fluid energy. Assuming a patchwise topology of the surface with patches of uniform well depth of solid–fluid interaction, the adsorption on a real carbon surface can be determined as an integral of the local surface excess of each patch with respect to the differential area. When this is matched against the experimental data of a carbon surface, we can derive the area distribution versus energy and hence the geometrical surface area. This new approach will be illustrated with the adsorption of argon on a nongraphitized carbon at 87.3 and 77 K, and it is found that the GCMC surface area is different from the BET surface area by about 7%. Furthermore, the description of the isotherm in the region of BET validity of 0.06 to 0.2 is much better with our method than with the BET equation.

Unlocking pathology archives for molecular genetic studies: a reliable method to generate probes for chromogenic and fluorescent in situ hybridization

Chromogenic (CISH) and fluorescent ( FISH) in situ hybridization have emerged as reliable techniques to identify amplifications and chromosomal translocations. CISH provides a spatial distribution of gene copy number changes in tumour tissue and allows a direct correlation between copy number changes and the morphological features of neoplastic cells. However, the limited number of commercially available gene probes has hindered the use of this technique. We have devised a protocol to generate probes for CISH that can be applied to formalin-fixed, paraffin-embedded tissue sections (FFPETS). Bacterial artificial chromosomes ( BACs) containing fragments of human DNA which map to specific genomic regions of interest are amplified with phi 29 polymerase and random primer labelled with biotin. The genomic location of these can be readily confirmed by BAC end pair sequencing and FISH mapping on normal lymphocyte metaphase spreads. To demonstrate the reliability of the probes generated with this protocol, four strategies were employed: (i) probes mapping to cyclin D1 (CCND1) were generated and their performance was compared with that of a commercially available probe for the same gene in a series of 10 FFPETS of breast cancer samples of which five harboured CCND1 amplification; (ii) probes targeting cyclin-dependent kinase 4 were used to validate an amplification identified by microarray-based comparative genomic hybridization (aCGH) in a pleomorphic adenoma; (iii) probes targeting fibroblast growth factor receptor 1 and CCND1 were used to validate amplifications mapping to these regions, as defined by aCGH, in an invasive lobular breast carcinoma with FISH and CISH; and (iv) gene-specific probes for ETV6 and NTRK3 were used to demonstrate the presence of t(12; 15)(p12; q25) translocation in a case of breast secretory carcinoma with dual colour FISH. In summary, this protocol enables the generation of probes mapping to any gene of interest that can be applied to FFPETS, allowing correlation of morphological features with gene copy number.

An inverse method for designing loaded RF coils in MRI

Radio-frequency ( RF) coils are designed such that they induce homogeneous magnetic fields within some region of interest within a magnetic resonance imaging ( MRI) scanner. Loading the scanner with a patient disrupts the homogeneity of these fields and can lead to a considerable degradation of the quality of the acquired image. In this paper, an inverse method is presented for designing RF coils, in which the presence of a load ( patient) within the MRI scanner is accounted for in the model. To approximate the finite length of the coil, a Fourier series expansion is considered for the coil current density and for the induced fields. Regularization is used to solve this ill-conditioned inverse problem for the unknown Fourier coefficients. That is, the error between the induced and homogeneous target fields is minimized along with an additional constraint, chosen in this paper to represent the curvature of the coil windings. Smooth winding patterns are obtained for both unloaded and loaded coils. RF fields with a high level of homogeneity are obtained in the unloaded case and a limit to the level of homogeneity attainable is observed in the loaded case.