How reproducible is the acoustical characterization of porous media?

There is a considerable number of research publications on the characterization of porous media that is carried out in accordance with ISO 10534-2 (International Standards Organization, Geneva, Switzerland, 2001) and/or ISO 9053 (International Standards Organization, Geneva, Switzerland, 1991). According to the Web of ScienceTM (last accessed 22 September 2016) there were 339 publications in the Journal of the Acoustical Society of America alone which deal with the acoustics of porous media. However, the reproducibility of these characterization procedures is not well understood. This paper deals with the reproducibility of some standard characterization procedures for acoustic porous materials. The paper is an extension of the work published by Horoshenkov, Khan, Bécot, Jaouen, Sgard, Renault, Amirouche, Pompoli, Prodi, Bonfiglio, Pispola, Asdrubali, Hübelt, Atalla, Amédin, Lauriks, and Boeckx [J. Acoust. Soc. Am. 122(1), 345-353 (2007)]. In this paper, independent laboratory measurements were performed on the same material specimens so that the naturally occurring inhomogeneity in materials was controlled. It also presented the reproducibility data for the characteristic impedance, complex wavenumber, and for some related pore structure properties. This work can be helpful to better understand the tolerances of these material characterization procedures so improvements can be developed to reduce experimental errors and improve the reproducibility between laboratories.

Fast and accurate specimen-specific simulation of trabecular bone elastic modulus using novel beam-shell finite element models.

Elastic modulus and strength of trabecular bone are negatively affected by osteoporosis and other metabolic bone diseases. Micro-computed tomography-based beam models have been presented as a fast and accurate way to determine bone competence. However, these models are not accurate for trabecular bone specimens with a high number of plate-like trabeculae. Therefore, the aim of this study was to improve this promising methodology by representing plate-like trabeculae in a way that better reflects their mechanical behavior. Using an optimized skeletonization and meshing algorithm, voxel-based models of trabecular bone samples were simplified into a complex structure of rods and plates. Rod-like and plate-like trabeculae were modeled as beam and shell elements, respectively, using local histomorphometric characteristics. To validate our model, apparent elastic modulus was determined from simulated uniaxial elastic compression of 257 cubic samples of trabecular bone (4mm×4mm×4mm; 30µm voxel size; BIOMED I project) in three orthogonal directions using the beam-shell models and using large-scale voxel models that served as the gold standard. Excellent agreement (R(2)=0.97) was found between the two, with an average CPU-time reduction factor of 49 for the beam-shell models. In contrast to earlier skeleton-based beam models, the novel beam-shell models predicted elastic modulus values equally well for structures from different skeletal sites. It allows performing detailed parametric analyses that cover the entire spectrum of trabecular bone microstructures.

Ultrasonic wave propagation in stereo-lithographical bone replicas.

Predictions of a modified anisotropic Biot-Allard theory are compared with measurements of pulses centered on 100 kHz and 1 MHz transmitted through water-saturated stereo-lithographical bone replicas. The replicas are 13 times larger than the original bone samples. Despite the expected effects of scattering, which is neglected in the theory, at 100 kHz the predicted and measured transmitted waveforms are similar. However, the magnitude of the leading negative edge of the waveform is overpredicted, and the trailing parts of the waveforms are not predicted well. At 1 MHz, although there are differences in amplitudes, the theory predicts that the transmitted waveform is almost a scaled version of that incident in conformity with the data.

Comparison of three measurement techniques for the normal absorption coefficient of sound absorbing materials in the free field.

Three different techniques for evaluating the absorption coefficient of sound absorbing materials in free field conditions are discussed. One technique measures the acoustic impedance at one point nearby a specimen, the other two techniques evaluate the impedance from the transfer function of two sound pressures and two particle velocities at two points. These are called "PU-method," "PP-method," and "UU-method," respectively. An iterative algorithm to estimate the acoustic impedance of the locally reactive specimen in the spherical wave field is also applied. First, the effect of receiver positions, specimen areas, and source heights to the measured normal absorption coefficient is investigated by the boundary element method. According to these investigations, the PU-method is most stable against the effect of specimen area, and the UU-method is easily affected by that effect. Closer source to the specimen distance is advantageous for the signal to noise ratio of these measurement techniques, but correction for the effect of the spherical wave field has to be applied. As a finding, the iterative algorithm works for all of three techniques. Finally, the PU-method is applied experimentally with a pressure-velocity sensor and a loudspeaker in a hemi-anechoic room. As a result, the calculated results have been verified.

Predictions of angle dependent tortuosity and elasticity effects on sound propagation in cancellous bone.

The anisotropic pore structure and elasticity of cancellous bone cause wave speeds and attenuation in cancellous bone to vary with angle. Previously published predictions of the variation in wave speed with angle are reviewed. Predictions that allow tortuosity to be angle dependent but assume isotropic elasticity compare well with available data on wave speeds at large angles but less well for small angles near the normal to the trabeculae. Claims for predictions that only include angle-dependence in elasticity are found to be misleading. Audio-frequency data obtained at audio-frequencies in air-filled bone replicas are used to derive an empirical expression for the angle-and porosity-dependence of tortuosity. Predictions that allow for either angle dependent tortuosity or angle dependent elasticity or both are compared with existing data for all angles and porosities.

A fast convolution-based methodology to simulate 2-D/3-D cardiac ultrasound images.

This paper describes a fast convolution-based methodology for simulating ultrasound images in a 2-D/3-D sector format as typically used in cardiac ultrasound. The conventional convolution model is based on the assumption of a space-invariant point spread function (PSF) and typically results in linear images. These characteristics are not representative for cardiac data sets. The spatial impulse response method (IRM) has excellent accuracy in the linear domain; however, calculation time can become an issue when scatterer numbers become significant and when 3-D volumetric data sets need to be computed. As a solution to these problems, the current manuscript proposes a new convolution-based methodology in which the data sets are produced by reducing the conventional 2-D/3-D convolution model to multiple 1-D convolutions (one for each image line). As an example, simulated 2-D/3-D phantom images are presented along with their gray scale histogram statistics. In addition, the computation time is recorded and contrasted to a commonly used implementation of IRM (Field II). It is shown that COLE can produce anatomically plausible images with local Rayleigh statistics but at improved calculation time (1200 times faster than the reference method).

The correlation between the SOS in trabecular bone and stiffness and density studied by finite-element analysis.

For the clinical assessment of osteoporosis (i.e., a degenerative bone disease associated with increased fracture risk), ultrasound has been proposed as an alternative or supplement to the dual-energy X-ray absorptiometry (DEXA) technique. However, the interaction of ultrasound waves with (trabecular) bone remains relatively poorly understood. The present study aimed to improve this understanding by simulating ultrasound wave propagation in 15 trabecular bone samples from the human lumbar spine, using microcomputed tomography-based finite-element modeling. The model included only the solid bone, without the bone marrow. Two structural parameters were calculated: the bone volume fraction (BV/TV) and the structural (apparent) elastic modulus (E(s)), and the ultrasound propagation parameter speed of sound (SOS). Relations between BV/TV and E(s) were similar to published experimental relations. At 1 MHz, correlations between SOS and the structural parameters BV/TV and Es were rather weak, but the results can be explained from the specific features of the trabecular structure and the intrinsic material elastic modulus E(i). In particular, the systematic differences between the three main directions provide information on the trabecular structure. In addition, at 1 MHz the correlation found between the simulated SOS values and those calculated from the simple bar equation was poor when the three directions are considered separately. Hence, under these conditions, the homogenization approach-including the bar equation-is not valid. However, at lower frequencies (50-300 kHz) this correlation significantly improved. It is concluded that detailed analysis of ultrasound wave propagation through the solid structure in various directions and with various frequencies, can yield much information on the structural and mechanical properties of trabecular bone.

Reproducibility experiments on measuring acoustical properties of rigid-frame porous media (round-robin tests).

This paper reports the results of reproducibility experiments on the interlaboratory characterization of the acoustical properties of three types of consolidated porous media: granulated porous rubber, reticulated foam, and fiberglass. The measurements are conducted in several independent laboratories in Europe and North America. The studied acoustical characteristics are the surface complex acoustic impedance at normal incidence and plane wave absorption coefficient which are determined using the standard impedance tube method. The paper provides detailed procedures related to sample preparation and installation and it discusses the dispersion in the acoustical material property observed between individual material samples and laboratories. The importance of the boundary conditions, homogeneity of the porous material structure, and stability of the adopted signal processing method are highlighted.

Acoustical measurement of the shear modulus for thin porous layers.

Simulations performed with the Biot theory show that for thin porous layers, a shear mode of the structure can be induced by a point-source in air located close to the layer. The simulations show that this mode is present around frequencies where the quarter wavelength of the shear Biot wave is equal to the thickness of the samples and show that it can be acoustically detected from the fast variations with frequency of the location of a pole of the reflection coefficient close to grazing incidence. The mode has been detected with this method for two reticulated plastic foams. For one of the foams studied, the velocity and the damping of the Rayleigh wave have been measured on a thicker layer of the same medium at higher frequencies, giving a real part of the shear modulus close to the one obtained from the measured location of the pole. The strong coupling of the shear mode with the acoustic field in air allows the measurement of the shear modulus without mechanical excitation.

Impedance measurements around grazing incidence for nonlocally reacting thin porous layers.

For locally reacting materials with a constant surface impedance, a classical method based on the work of Chien and Soroka [J. Sound Vib. 43, 9-20 (1975)] for measuring this impedance in situ around grazing incidence is currently used. A generalization of this work to include thin nonlocally reacting materials with a surface impedance noticeably dependent on the angle of incidence is performed. It is shown that the model by Chien and Soroka can be used, though the constant surface impedance must be replaced by the impedance at grazing incidence for the evaluation of the numerical distance. Measurements performed on a thin porous layer using this method are compared with measurements performed using the near-field acoustical holography method [M. Tamura, J. Acoust. Soc. Am. 88, 2259-2264 (1990)]. Other measurements performed on a fibrous layer are in good agreement with the predicted values of the impedance at grazing incidence.

Experimental investigation of leaky lamb modes by an optically induced grating.

By removing the symmetry of a free plate configuration, fluid loading significantly modifies the nature of acoustic waves travelling along a plate, and it even gives existence to new acoustic modes. We present theoretical predictions for the existence, dispersive behavior, and spatial distribution of leaky Lamb waves in a fluid-loaded film. Although Lamb modes are often investigated by studying the radiated fluid waves resulting from their leakage, here their properties are assessed by detecting the wave displacements directly using laser beam deflection. By using crossed laser beam excitation, the detection and analysis of the different modes is done at a fixed wavelength, allowing one to verify the existence, the velocity, and the damping of each predicted mode in a simple and unambiguous way. Our theoretical predictions for the nature of the modes in a water-loaded Plexiglas film, including parts of looping modes, are experimentally confirmed.

Nonlinearity of acoustic waves at solid-liquid interfaces.

The small-amplitude and finite-amplitude propagation characteristics of laser line source excited and laser detected Scholte waves are investigated. Acoustic waves with Mach numbers up to 0.054 are observed at the interface between water and glass. In our case of a hard solid-liquid interface, the Scholte wave propagates very much like a bulk wave, for which the simple-wave equation holds. The experimental results are well fitted with this model, extended with an attenuation term. An anomalously large (compared with low amplitude viscous effects) attenuation reveals possible leakage of energy from the Scholte wave to bulk waves, through a mechanism of nonlinear mixing between the different wave modes and viscosity induced turbulence.