2D-3D Rigid-Body Registration of X-Ray Fluoroscopy and CT Images

The registration of pre-operative volumetric datasets to intra- operative two-dimensional images provides an improved way of verifying patient position and medical instrument loca- tion. In applications from orthopedics to neurosurgery, it has a great value in maintaining up-to-date information about changes due to intervention. We propose a mutual information- based registration algorithm to establish the proper align- ment. For optimization purposes, we compare the perfor- mance of the non-gradient Powell method and two slightly di erent versions of a stochastic gradient ascent strategy: one using a sparsely sampled histogramming approach and the other Parzen windowing to carry out probability density approximation. Our main contribution lies in adopting the stochastic ap- proximation scheme successfully applied in 3D-3D registra- tion problems to the 2D-3D scenario, which obviates the need for the generation of full DRRs at each iteration of pose op- timization. This facilitates a considerable savings in compu- tation expense. We also introduce a new probability density estimator for image intensities via sparse histogramming, de- rive gradient estimates for the density measures required by the maximization procedure and introduce the framework for a multiresolution strategy to the problem. Registration results are presented on uoroscopy and CT datasets of a plastic pelvis and a real skull, and on a high-resolution CT- derived simulated dataset of a real skull, a plastic skull, a plastic pelvis and a plastic lumbar spine segment.

Geometric and Algebraic Aspects of 3D Affine and Projective Structures from Perspective 2D Views

We investigate the differences --- conceptually and algorithmically --- between affine and projective frameworks for the tasks of visual recognition and reconstruction from perspective views. It is shown that an affine invariant exists between any view and a fixed view chosen as a reference view. This implies that for tasks for which a reference view can be chosen, such as in alignment schemes for visual recognition, projective invariants are not really necessary. We then use the affine invariant to derive new algebraic connections between perspective views. It is shown that three perspective views of an object are connected by certain algebraic functions of image coordinates alone (no structure or camera geometry needs to be involved).

Impact of mass lumping on gravity and Rossby waves in 2D finite-element shallow-water models

The goal of this study is to evaluate the effect of mass lumping on the dispersion properties of four finite-element velocity/surface-elevation pairs that are used to approximate the linear shallow-water equations. For each pair, the dispersion relation, obtained using the mass lumping technique, is computed and analysed for both gravity and Rossby waves. The dispersion relations are compared with those obtained for the consistent schemes (without lumping) and the continuous case. The P0-P1, RT0 and P-P1 pairs are shown to preserve good dispersive properties when the mass matrix is lumped. Test problems to simulate fast gravity and slow Rossby waves are in good agreement with the analytical results.

A new porous 2D coordination polymer built by copper(II) and trimesic acid

A 2D porous material, Cu-3(tmen)(3)(tma)(2)(H2O)(2)(.)6.5H(2)O [tmen = N,N,N',N'-tetramethylethane-1,2-diamine; tmaH(3) = 1,3,5-benzenetricarboxylic acid/trimesic acid], has been synthesized and characterized by X-ray single crystal analysis, variable temperature magnetic measurements, IR spectra and XRPD pattern. The complex consists of 2D layers built by three crystallographically independent Cu(tmen) moieties bridged by tma anions. Of the three copper ions, Cu(1) and Cu(2) present distorted square pyramidal coordination geometry, while the third exhibits a severely distorted octahedral environment. The Cu(1)(tmen) and Cu(2)(tmen) building blocks bridged by tma anions give rise to chains with a zig-zag motif, which are cross-connected by Cu(3)(tmen)-tma polymers sharing metal ions Cu(2) through pendant tma carboxylates. The resulting 2D architecture extends in the crystallographic ab-plane. The adjacent sheets are embedded through the Cu(3)(tmen) tma chains, leaving H2O-filled channels. There are 6.5 lattice water molecules per formula unit, some of which are disordered. Upon heating, the lattice water molecules get eliminated without destroying the crystal morphology and the compound rehydrated reversibly on exposure to humid atmosphere. Magnetic data of the complex have been fitted considering isolated irregular Cu-3 triangles (three different J parameters) by applying the CLUMAG program. The best fit indicates three close comparable J parameters and very weak antiferromagnetic interactions are operative between the metal centers. (C) 2004 Elsevier B.V. All rights reserved.

2D parallel interpenetration of [M-2(bpp)(4)X-4] [M, Fe(II)/Co(II); bpp, 4,4 '-trimethylenedipyridine; X, SCN-SeCN- and N-3(-)] complexes: pseudohalide-dependent conformation of bpp

Three coordination complexes of Co(II)/Fe(II) with 4,4'-trimethylenedipyridine (bpp) and pseudohalides (SCN-, SeCN- and N-3(-)) have been synthesized. The complexes have been characterized by X-ray single crystal structure determination. They are isomorphous having 2D layers in which two independent wavy nets display parallel interwoven structures. Pseudohalide binds metal centers through N terminal and occupies the trans axial positions of the octahedral metal coordination environment. Pseudohalide remains pendant on both sides of the polymeric layer and help the stacking through hydrogen bonding. The conformation of bpp in the interpenetrated nets is observed to be dependent on the choice of pseudohalide. (C) 2008 Elsevier Inc. All rights reserved.

Two new mu-(1,3-azido)-bridged polymers: alternating single and double bridges in a 1D nickel(II) complex and uniform bridge in a 2D copper(II) complex: Syntheses, single-crystal structures and magnetic studies

Two polymeric azido bridged complexes [Ni2L2(N-3)(3)](n)(ClO4). (1) and [Cu(bpdS)(2)(N-3)],(ClO4),(H2O)(2.5n) (2) [L = Schiff base, obtained from the condensation of pyridine-2-aldehyde with N,N,2,2-tetramethyl-1,3-propanediamine; bpds = 4,4'-bipyridyl disulfide] have been synthesized and their crystal structures have been determined. Complex 1, C26H42ClN15Ni2O4, crystallizes in a triclinic system, space group P1 with a 8.089(13), b = 9.392(14), c = 12.267(18) angstrom, a = 107.28(l), b 95.95(1), gamma = 96.92(1)degrees and Z = 2; complex 2, C20H21ClCuN7O6.5S4, crystallizes in an orthorhombic system, space group Pnna with a = 10.839(14), b = 13.208(17), c = 19.75(2) angstrom and Z = 4. The crystal structure of I consists of 1D polymers of nickel(L) units, alternatively connected by single and double bridging mu-(1,3-N-3) ligand with isolated perchlorate anions. Variable temperature magnetic susceptibility data of the complex have been measured and the fitting,of magnetic data was carried out applying the Borris-Almenar formula for such types of alternating one-dimensional S = 1 systems, based on the Hamiltonian H = -J Sigma(S2iS2i-1 + aS(2i)S(2i+1)). The best-fit parameters obtained are J = -106.7 +/- 2 cm(-1); a = 0.82 +/- 0.02; g = 2.21 +/- 0.02. Complex 2 is a 2D network of 4,4 topology with the nodes occupied by the Cu-II ions, and the edges formed by single azide and double bpds connectors. The perchlorate anions are located between pairs of bpds. The magnetic data have been fitted considering the complex as a pseudo-one-dimensional system, with all copper((II)) atoms linked by [mu(1,3-azido) bridging ligands at axial positions (long Cu...N-3 distances) since the coupling through long bpds is almost nil. The best-fit parameters obtained with this model are J = -1.21 +/- 0.2 cm(-1), g 2.14 +/- 0.02. (c) Wiley-VCH Verlag GmbH & Co. KGaA, 69451 Weinheim, Germany, 2005).

Synthesis and structural characterization of two nostoclide analogues

The vinylogous aldol reaction between appropriate aldehydes and furan-based silyloxy diene synthon generated from 3-benzyl-5H-furan-2-one (3) afforded two truncated lactone analogues [compounds (4) and (5)] of nostoclides (2). The compounds were fully characterized by IR, NMR (H-1 and C-13), 2D NMR spectroscopy experiments (HMBC, HSQC and NOESY), MS spectrometry and X-ray crystallography. Compounds (4) and (5) crystallized in the space group P2(1)2(1)2(1) and P2(1)/c, respectively. Although expected correlations between hydrogen atoms in spatial close proximity were not observed for compound (5) using NMR, the stereochemistry of the exocyclic double bond of both (4) and (5) was unambiguously determined to be Z and E, respectively, using X-ray crystallography. The packing of both compounds within the crystal are stabilized by non-classical inter-molecular hydrogen bonds. DFT calculations (B3LYP/6-31+G* level) confirmed that the crystal structures possessed the lowest energies in the gas phase when compared to their geometric isomers. (c) 2006 Elsevier B.V. All rights reserved.

Fracture toughness and cutting

An exploratory model for cutting is presented which incorporates fracture toughness as well as the commonly considered effects of plasticity and friction. The periodic load fluctuations Been in cutting force dynamometer tests are predicted, and considerations of chatter and surface finish follow. A non-dimensional group is put forward to classify different regimes of material response to machining. It leads to tentative explanations for the difficulties of cutting materials such as ceramics and brittlo polymers, and also relates to the formation of discontinuous chips. Experiments on a range of solids with widely varying toughness/strength ratios generally agree with the analysis.

Toughness & cutting: A new way of determining ductile fracture toughness and strength

A review is given of the mechanics of cutting, ranging from the slicing of thin floppy offcuts (where there is negligible elasticity and no permanent deformation of the offcut) to the machining of ductile metals (where there is severe permanent distortion of the offcut/chip). Materials scientists employ the former conditions to determine the fracture toughness of ‘soft’ solids such as biological materials and foodstuffs. In contrast, traditional analyses of metalcutting are based on plasticity and friction only, and do not incorporate toughness. The machining theories are inadequate in a number of ways but a recent paper has shown that when ductile work of fracture is included many, if not all, of the shortcomings are removed. Support for the new analysis is given by examination of FEM simulations of metalcutting which reveal that a ‘separation criterion’ has to be employed at the tool tip. Some consideration shows that the separation criteria are versions of void-initiation-growth-and-coalescence models employed in ductile fracture mechanics. The new analysis shows that cutting forces for ductile materials depend upon the fracture toughness as well as plasticity and friction, and reveals a simple way of determining both toughness and flow stress from cutting experiments. Examples are given for a wide range of materials including metals, polymers and wood, and comparison is made with the same properties independently determined using conventional testpieces. Because cutting can be steady state, a new way is presented for simultaneously measuring toughness and flow stress at controlled speeds and strain rates.

Cutting, by 'pressing and slicing,' of thin floppy slices of materials illustrated by experiments on cheddar cheese and salami

Why it is easier to cut with even the sharpest knife when 'pressing down and sliding' than when merely 'pressing down alone' is explained. A variety of cases of cutting where the blade and workpiece have different relative motions is analysed and it is shown that the greater the 'slice/push ratio' xi given by ( blade speed parallel to the cutting edge/blade speed perpendicular to the cutting edge), the lower the cutting forces. However, friction limits the reductions attainable at the highest.. The analysis is applied to the geometry of a wheel cutting device (delicatessan slicer) and experiments with a cheddar cheese and a salami using such an instrumented device confirm the general predictions. (C) 2004 Kluwer Academic Publishers.

Ocean acoustic models for low frequency propagation in 2D and 3D environments

In this paper we are mainly concerned with the development of efficient computer models capable of accurately predicting the propagation of low-to-middle frequency sound in the sea, in axially symmetric (2D) and in fully 3D environments. The major physical features of the problem, i.e. a variable bottom topography, elastic properties of the subbottom structure, volume attenuation and other range inhomogeneities are efficiently treated. The computer models presented are based on normal mode solutions of the Helmholtz equation on the one hand, and on various types of numerical schemes for parabolic approximations of the Helmholtz equation on the other. A new coupled mode code is introduced to model sound propagation in range-dependent ocean environments with variable bottom topography, where the effects of an elastic bottom, of volume attenuation, surface and bottom roughness are taken into account. New computer models based on finite difference and finite element techniques for the numerical solution of parabolic approximations are also presented. They include an efficient modeling of the bottom influence via impedance boundary conditions, they cover wide angle propagation, elastic bottom effects, variable bottom topography and reverberation effects. All the models are validated on several benchmark problems and versus experimental data. Results thus obtained were compared with analogous results from standard codes in the literature.