Reconstruction of viscoelastic tissue properties from MR elastography-type measurements

This study is concerned with an optimization-based approach to the identification of “background” viscoelastic properties of soft tissues from magnetic resonance (MR) elastography-type measurements. In this approach, the triaxial tissue displacements, captured by the MR scanner over a suitable subdomain that is free of major heterogeneities, are split into (i) a boundary subset that is used to formulate the forward (Dirichlet) problem, and (ii) an internal subset, employed as “the data” for the inverse (material characterization) problem. For an elevated performance of the minimization scheme, material sensitivities of the featured cost functional are computed semi-analytically via a boundary-integral formulation, resulting in alternative “direct” and adjoint-field sensitivity formulas. The numerical results, obtained assuming input parameters that are relevant to MR elastography, indicate that the proposed approach may provide an effective means for comprehensive multi-frequency characterization of the “background” viscoelasticity of soft tissues.     

<Emphasis Type="Italic">L</Emphasis><Superscript>1</Superscript>-minimization methods for Hamilton–Jacobi equations: the one-dimensional case

A new approximation technique based on L ¹-minimization is introduced. It is proven that the approximate solution converges to the viscosity solution in the case of one-dimensional stationary Hamilton–Jacobi equation with convex Hamiltonian. This material is based upon work supported by the National Science Foundation grant DMS-0510650. J.-L. Guermond is on leave from LIMSI, UPRR 3251 CNRS, BP 133, 91403 Orsay Cedex, France.     

Branched coverings

Basic results on combinatorial branched coverings between relative geometric cycles are given. It is shown that every geometricn-cycle is a branched covering overS. If the downstairs space of a branched covering is locally simply connected then the branched set is a pure subcomplex of codimension 2. Finally, several Hurwitz-like theorems on existence and representation of branched coverings between relative geometric cycles are derived.This work was supported in part by the Research Council of Slovenia, Yugoslavia.     

Square-planar copper(II) complexes with a novel tetradentate amido-carboxylate ligand. Crystal structure of [Co(H2O)6][Cu(mda)] · 2H2O

A novel O—N—N—O-type tetradentate ligand H₄mda (H₄mda = malamido-N,N-diacetic acid) and the corresponding square-planar copper(II) complexes have been prepared and characterized. The mda^4– ligand coordinates to the copper(II) ion via two pairs of deprotonated ligating atoms (two carboxylate oxygens and two deprotonated amide nitrogens) with in-plane square chelation. A four-coordinate, square-planar geometry has been established crystallographically for the [Co(H₂O)₆][Cu(mda)] · 2H₂O complex. Structural data correlating the square-planar geometry of the [Cu(mda)]^2– unit are discussed in relation to information obtained for similar complexes. The i.r., electronic, absorption and reflectance spectra of the complexes are analysed in comparison with related complexes of known geometries.     

Phosphorescent excited state of [Au2[(Ph2Sb)2O]3]2+: Jahn-Teller distortion at only one gold(I) center

Dinuclear three-coordinate Au(I) complex [Au2{(Ph2Sb)2O}3](ClO4)2 1 displays an interesting phosphorescent behavior in which a large Stokes' shift is observed. Ab initio calculations show that the main distortion for the first triplet excited state, which is responsible for the luminescence behavior of complex 1, is a Jahn-Teller distortion for only one of the Au(I) centers together with a gold-gold distance shortening. This behavior could be extrapolated to other phosphorescent dinuclear three-coordinate Au(I) complexes.     

Folding probabilities: a novel approach to folding transitions and the two-dimensional Ising-model

The theoretical concept of folding probability, p(fold), has proven to be a useful means to characterize the kinetics of protein folding. Here, we illustrate the practical importance of p(fold) and demonstrate how it can be determined theoretically. We derive a general analytical expression for p(fold) and show how it can be estimated from simulations for systems where the transition rates between the relevant microstates are not known. By analyzing the Ising model we are able to determine the scaling behavior of the numerical error in the p(fold) estimate as function of the number of analyzed Monte Carlo runs. We apply our method to a simple, newly developed protein folding model for the formation of alpha helices. It is demonstrated that our technique highly parallelizes the calculation of p(fold) and that it is orders of magnitude more efficient than conventional approaches.     

Vibrational Studies of Palladium(II) Acetate Compounds Ii. Infrared Spectra of the Diethylamine Adduct of Palladium(II) Acetate

Recorded and discussed are the infrared spectra of the diethylamine adduct of palladium(II) acetate. An empirical assignment of the spectra is proposed. The palladium-oxygen bonds in the adduct are not much different in strength from those in hexa-μ-acetato-triangulo-tripalladium(II)-water (2/1). The diethylanine molecules are present as such, as evidenced by the appearance of a rather strong band attributed to the N-H stretching vibrations.     

Direct measurements of controlled aerodynamic forces on a wire-suspended axisymmetric body

A novel in-line miniature force transducer is developed for direct measurements of the net aerodynamic forces and moments on a bluff body. The force transducers are integrated into each of the eight mounting wires that are utilized for suspension of an axisymmetric model in a wind tunnel having minimal wake interference. The aerodynamic forces and moments on the model are altered by induced active local attachment of the separated base flow. Fluidic control is effected by an array of four integrated aft-facing synthetic jet actuators that emanate from narrow, azimuthally segmented slots, equally distributed around the perimeter of the circular tail end. The jet orifices are embedded within a small backward-facing step that extends into a Coanda surface. The altered flow dynamics associated with both quasi-steady and transitory asymmetric activation of the flow control effect is characterized by direct force and PIV measurements.     

From imaging to material identification: A generalized concept of topological sensitivity

To establish a compact analytical framework for the preliminary stress-wave identification of material defects, the focus of this study is an extension of the concept of topological derivative, rooted in elastostatics and the idea of cavity nucleation, to 3D elastodynamics involving germination of solid obstacles. The main result of the proposed generalization is an expression for topological sensitivity, explicit in terms of the elastodynamic Green's function, obtained by an asymptotic expansion of a misfit-type cost functional with respect to the nucleation of a dissimilar elastic inclusion in a defect-free “reference” solid. The featured formula, consisting of an inertial-contrast monopole term and an elasticity-contrast dipole term, is shown to be applicable to a variety of reference solids (semi-infinite and infinite domains with constant or functionally graded elastic properties) for which the Green's functions are available. To deal with situations when the latter is not the case (e.g. finite reference bodies or those with pre-existing defects), an adjoint field approach is employed to derive an alternative expression for topological sensitivity that involves the contraction of two (numerically computed) elastodynamic states. A set of numerical results is included to demonstrate the potential of generalized topological derivative as an efficient tool for exposing not only the geometry, but also material characteristics of subsurface material defects through a local, point-wise identification of “optimal” inclusion properties that minimize the topological sensitivity at sampling location. Beyond the realm of non-invasive characterization of engineered materials, the proposed developments may be relevant to medical diagnosis and in particular to breast cancer detection where focused ultrasound waves show a promise of superseding manual palpation.