Propagation of acoustic waves in a one-dimensional macroscopically inhomogeneous poroelastic material.

Wave propagation in macroscopically inhomogeneous porous materials has received much attention in recent years. The wave equation, derived from the alternative formulation of Biot's theory of 1962, was reduced and solved recently in the case of rigid frame inhomogeneous porous materials. This paper focuses on the solution of the full wave equation in which the acoustic and the elastic properties of the poroelastic material vary in one-dimension. The reflection coefficient of a one-dimensional macroscopically inhomogeneous porous material on a rigid backing is obtained numerically using the state vector (or the so-called Stroh) formalism and Peano series. This coefficient can then be used to straightforwardly calculate the scattered field. To validate the method of resolution, results obtained by the present method are compared to those calculated by the classical transfer matrix method at both normal and oblique incidence and to experimental measurements at normal incidence for a known two-layers porous material, considered as a single inhomogeneous layer. Finally, discussion about the absorption coefficient for various inhomogeneity profiles gives further perspectives.

Analytical method for the ultrasonic characterization of homogeneous rigid porous materials from transmitted and reflected coefficients.

A frequency domain method dedicated to the analytic recovery of the four relevant parameters of macroscopically homogeneous rigid frame porous materials, e.g., plastic foams, at the high frequency range of the Johnson-Champoux-Allard model is developed and presented. The reconstructions appeal to experimental data concerning time domain measurements of the ultrasonic fields reflected and transmitted by a plate of the material at normal incidence. The effective density and bulk modulus of the material are first reconstructed from the frequency domain reflection and transmission coefficients. From the latter, the porosity, tortuosity, and thermal and viscous characteristic lengths are recovered. In a sense, the method presented herein is quite similar in the ultrasonic range, but also quite complementary, to the method developed by Panneton and Olny [J. Acoust. Soc. Am. 119, 2027-2040 (2006); 123, 814-824 (2008)] at low frequency, which appeal to experimental data measured in an impedance tube.

Acoustic response of a rigid-frame porous medium plate with a periodic set of inclusions.

The acoustic response of a rigid-frame porous plate with a periodic set of inclusions is investigated by a multipole method. The acoustic properties, in particular, the absorption, of such a structure are then derived and studied. Numerical results together with a modal analysis show that the addition of a periodic set of high-contrast inclusions leads to the excitation of the modes of the plate and to a large increase in the acoustic absorption.

Reconstruction of material properties profiles in one-dimensional macroscopically inhomogeneous rigid frame porous media in the frequency domain.

The present paper deals with the inverse scattering problem involving macroscopically inhomogeneous rigid frame porous media. It consists of the recovery, from acoustic measurements, of the profiles of spatially varying material parameters by means of an optimization approach. The resolution is based on the modeling of acoustic wave propagation in macroscopically inhomogeneous rigid frame porous materials, which was recently derived from the generalized Biot's theory. In practice, the inverse problem is solved by minimizing an objective function defined in the least-square sense by the comparison of the calculated reflection (and transmission) coefficient(s) with the measured or synthetic one(s), affected or not by additive Gaussian noise. From an initial guess, the profiles of the x-dependent material parameters are reconstructed iteratively with the help of a standard conjugate gradient method. The convergence rate of the latter and the accuracy of the reconstructions are improved by the availability of an analytical gradient.

Estradiol entry into endometrial cells in suspension.

Cells from a human endometrial adenocarcinoma cell line (HEC-50) were superfused with mixtures of [3H]E2 and [14C]E1 in order to estimate rates of entry and exit of E1 and E2 into and out of cells according to previously published procedures (J. steroid Biochem., 13 (1980) 1379). Proportionality between rates of entry and concentrations of E2 outside the cells, indicative of passive diffusion, was found at levels of E2 ranging from 1 to 100 ng/ml. Effects of albumin and of pure human sex steroid binding protein (SBP) on the rate of entry of E2 were also evaluated in parallel superfusions. In other single tracer experiments, [3H]E2 was used at concentrations as low as 100 pg/ml and the effects of plasma proteins on entry were evaluated by measuring steady-state concentrations of E2 and E1 in cells and superfusate. Results from these experiments indicate that albumin, and to a larger extent SBP, reduced the entry of E2 into HEC-50 cells. Similar results were obtained when CG-5 cells, a variant of the human breast cancer cell line MCF-7, were superfused with [3H]E2. Further experiments are needed, however, to determine the physiologic role of plasma estrogen binding proteins on the entry and metabolism of E1 and E2 into target cells.

Superfusion of normal and neoplastic mouse mammary tissue with estrogens.

Slices of normal mammary tissue from pregnant and lactating mice and slices of neoplastic (MXT) mouse mammary tissue were superfused with estradiol (E2) and estrone (E1) each labeled with a different isotope. Isotope concentrations in tissue and perfusate at the steady state were used to calculate fractions and rates of uptake, metabolism and release of estrogens by the tissue perfused. Both E2 and E1 entered equally well and were concentrated to the same extent by normal and neoplastic mammary tissue. However, much smaller tissue to medium ratios and larger diffusible fractions of estrogens were found in tumor slices as compared to mammary tissue from both pregnant and lactating mice, the uptake being the highest in pregnancy mammary glands. The interconversion between E1 and E2 was found to favor the formation of E2 in normal mammary tissue, the metabolic activity being the highest in lactating glands. In the MXT tumor slices the conversion of E1 into E2 was predominant as well but in contrast to the almost negligible metabolism of E2 in normal mammary tissue, a large fraction of E2 was converted into E1. The observed differences in estrogen uptake and metabolism between pregnant and lactating mammary glands were in concordance with the functional characteristics of the tissues. Furthermore, E1 was shown to play an important role in the mouse mammary gland as a metabolic precursor of E2. A different metabolic pattern was found in neoplastic mammary tissue.