Theoretical Attenuation Coefficients Research Articles

Novel starch–tungsten (VI) oxide biocomposites: Preparation, characterization, and comparisons between experimental and theoretical photon attenuation coefficients

This study synthesized biocomposites containing starch and WO3 at varying ratios of 10 %, 20 %, 30 %, 40 %, and 50 % and assessed their thermal and radiation-shielding properties. These biocomposites were characterized using Fourier-transform infrared spectroscopy, X-ray diffraction (XRD) analysis, particle-size distribution assessments, scanning electron microscopy–energy dispersive X-ray spectroscopy, and thermogravimetric analysis–differential thermogravimetry measurements. Furthermore, the linear attenuation coefficients of the biocomposites were experimentally measured using an NaI(Tl) gamma spectrometry system and theoretically computed using XCOM and GAMOS simulations for comparisons. The XRD and particle-size distribution profiles of the WO3.2H2O powder, respectively, demonstrated evident diffraction peaks and favorable pore-size distributions. Morphological characterizations revealed that the WO3 particles were homogeneously dispersed throughout the starch matrix without any agglomeration. Comparisons of the thermal degradation rates revealed that the pure starch and starch +50%WO3 biocomposite began decomposing at approximately 200°Cand 300 °C, respectively, indicating that increasing WO3 proportions enhanced thermal stability. Furthermore, the starch +50%WO3 biocomposite demonstrated the highest experimental linear attenuation coefficient, with a value of 0.2510 ± 0.0848 cm−1 at a gamma energy of 662 keV. Meanwhile, XCOM and GAMOS simulations revealed theoretical attenuation coefficients of 0.1229 and 0.1213 cm−1 for pure starch and 0.2202 cm−1 and 0.2178 cm−1 for the starch +50%WO3 biocomposite at 662 keV, respectively.

Continuum Models for Bulk Viscosity and Relaxation in Polyatomic Gases

Bulk viscosity and acoustic wave propagation in polyatomic gases and their mixtures are studied in the frame of one-temperature and multi-temperature continuum models developed using the generalized Chapman–Enskog method. Governing equations and constitutive relations for both models are written, and the dispersion equations are derived. In the vibrationally nonequilibrium multi-component gas mixture, wave attenuation mechanisms include viscosity, thermal conductivity, bulk viscosity, diffusion, thermal diffusion, and vibrational relaxation; in the proposed approach these mechanisms are fully coupled contrarily to commonly used models based on the separation of classical Stokes–Kirchhoff attenuation and relaxation. Contributions of rotational and vibrational modes to the bulk viscosity coefficient are evaluated. In the one-temperature approach, artificial separation of rotational and vibrational modes causes great overestimation of bulk viscosity whereas using the effective internal energy relaxation time yields good agreement with experimental data and molecular-dynamic simulations. In the multi-temperature approach, the bulk viscosity is specified only by rotational modes. The developed two-temperature model provides excellent agreement of theoretical and experimental attenuation coefficients in polyatomic gases; both the location and the value of its maximum are predicted correctly. One-temperature dispersion relations do not reproduce the non-monotonic behavior of the attenuation coefficient; large bulk viscosity improves its accuracy only in the very limited frequency range. It is emphasized that implementing large bulk viscosity in the one-temperature Navier–Stokes–Fourier equations may lead to unphysical results.

Ecofriendly and radiation shielding properties of newly developed epoxy with waste marble and WO3 nanoparticles

Research into protection techniques from harmful effects of gamma radiation have increased contemporarily. The development of radiation-resistant materials having a high radiation resistance and absorption of different types of ionizing radiation could offer promising solutions to this matter. For this purpose, the preparation and examination of a novel type of polymer doped with various WO3 concentrations are presented in this study. To accomplish our main objective, we evaluated the effectiveness of their radiation shielding against gamma radiation from 137Cs, 60Co, and 241Am. At all investigated energies, the measured and theoretical linear attenuation coefficient (LAC) values are highly similar, proving that the experimental LAC values can be used to reliably predict other radiation shielding characteristics. The half value layer (HVL) values decreased as the samples' WO3 level rises indicating that increasing the amount of WO3 in these samples increases their radiation shielding effectiveness. In addition, it was found a positive correlation between radiation energy and the mean free path (MFP) values. At 0.060 MeV, the MFP values are equal to 1.374 cm, 0.691 cm, 0.521 cm, and 0.369 cm at concentrations of 0, 10, 20, and 25% WO3, respectively reflecting that the MFP is reduced by 3.7 times due to the addition of 20% WO3 nanoparticles. From the transmission factor, it was found that improving the shielding ability of the proposed materials could be achieved by increasing and adjusting the thickness of the absorber depending on the required energy range used. It is noteworthy that the present studied samples (epoxy + waste marble + nano-WO3) that have exhibited a greater shielding ability than other nanoparticles added polymers like (Epoxy + nano-MgO30), and (silicone rubber + nano-WO330).

Nonlinear Optical Limiting and Radiation Shielding Characteristics of Sm2O3 Doped Cadmium Sodium Lithium Borate Glasses.

Strong nonlinear absorption (NLA), reduced optical limiting (OL) thresholds, and high radiation shielding parameters are required for the effective use of glasses in the laser radiation and nuclear radiation protecting materials. In view of this, the efficacy of Sm2O3 on the nonlinear optical (NLO) and OL properties were ascertained (at 532 nm) along with radiation shielding characteristics. The open and closed aperture Z-scan profiles revealed the presence of positive NLA and nonlinear refraction (NLR) phenomena respectively. OL measurements showed the existence of limiting behavior in the studied glasses. The NLA and NLR coefficients were improved while the OL thresholds were decreased as the doping of Sm2O3 elevated to a higher doping level. These improvements in NLA, NLR coefficients and OL efficiencies were attributed to the non-bridging oxygens and high polarizable Sm3+ ions. The NLA and OL results clearly suggest the high (5 mol %) Sm2O3 doped glass (Sm5CNLB) glass is beneficial to protect the delicate devices and human eye by suppressing the high energy laser light. The theoretical linear attenuation coefficients (LAC) values of the presented SmxCNLB glasses were obtained with the help of Phy-X software between 0.284 and 1.333 MeV. At 0.284 MeV, the maximum values occur and take values between 0.302 (for Sm0CNLB) and 0.409 cm−1 (for Sm5CNLB). We found that the LAC for the presented SmxCNLB glasses is a function of Sm2O3 content, where the LAC tends to increase, corresponding to the high probabilities of interaction, as the content of Sm2O3 changes from 0 to 5 mol %. The effective atomic number (Zeff) for the presented SmxCNLB glasses was examined between 0.284 and 1.333 MeV. As the amount of Sm2O3 is added, the Zeff increases, and this was observed at any energy.

\\Preparation of poly(styrene-co-acrylic acid)-zinc oxide composites: Experimental and theoretical investigation of gamma radiation shielding properties

This study, it is aimed to prepare a polymer composite between styrene, acrylic acid, and ZnO and to measure the radiation shielding of the synthesized polymer composite. Firstly poly(styrene-co-acrylic acid) (P(S-co-AA)) copolymer was synthesized using the emulsion polymerization method between styrene and acrylic acid. Then, P(S-co-AA)-ZnO composites were prepared with different percentages of ZnO. For preparing these composites, the materials were mixed in a 60 °C ultrasonic bath. P(S-co-AA)-ZnO was poured into Petri dishes to form a film. When the TG curves were examined, it was not found a significant difference between the copolymer composite and the copolymer. The molecular weight of the copolymer was found to be 120000. SEM images show zinc fragments located between the polymer chains. The potential for radiation capture against gamma was determined using a NaI scintillation detector. The linear gamma attenuation coefficients for P(S-co-AA)-ZnO samples were calculated to Lambert's Beer Law and measured for 662 keV. Theoretical gamma attenuation coefficient values were calculated by multiplying the density of the composite with the mass attenuation coefficients. The absorption parameters of polymer composites are directly proportional to the increasing amount of zinc oxide. P(S-co-AA)-ZnO-15% was the best absorber at 662 keV energy compared to other polymer composites.

Tungsten-based material as promising new lead-free gamma radiation shielding material in nuclear medicine.

The main objective of this study was to evaluate the efficacy of tungsten carbide as new lead-free radiation shielding material in nuclear medicine by evaluating the attenuation properties. The elemental composition of tungsten carbide was analysed using Field-Emission Scanning Electron Microscopy (FESEM) with energy dispersive X-ray (EDX). The purity of tungsten carbide was 99.9%, APS: 40-50µm. Three discs of tungsten carbide was fabricated with thickness of 0.1cm, 0.5cm and 1.0cm. Three lead discs with similar thickness were used to compare the attenuation properties with tungsten carbide discs. Energy calibration of gamma spectroscopy was performed by using 123I, 133Ba, 152Eu, and 137Cs. Gamma radiation from these sources were irradiated on both materials at energies ranging from 0.160MeV to 0.779MeV. The experimental attenuation coefficients of lead and tungsten carbide were compared with theoretical attenuation coefficients of both materials from NIST database. The half value layer and mean free path of both materials were also evaluated in this study. This study found that the peaks obtained from gamma spectroscopy have linear relationship with all energies used in this study. The relative differences between the measured and theoretical mass attenuation coefficients are within 0.19-5.11% for both materials. Tungsten carbide has low half value layer and mean free path compared to lead for all thickness at different energies. This study shows that tungsten carbide has high potential to replace lead as new lead-free radiation shielding material in nuclear medicine.

Attenuation of gravity waves in fast ice

The attenuation coefficients of sea waves in ice in the coastal zone of the Sea of Okhotsk with periods from 4 to 30 s were estimated as a function of their wavelength based on observations. We used the model dispersion relation for these waves in ice and calculated the theoretical attenuation coefficients. We compared them with those from the data of experiments based on the relation of the spectral energies of waves in ice-free water and in ice. It is possible to use the estimated attenuation coefficients for waves of different periods to calculate the distance of wave propagation in fast ice with the critical amplitude where ice breaking is possible.

Attenuation of Gravity Waves in Fast Ice

The attenuation coefficients of sea waves in ice in the coastal zone of the Sea of Okhotsk with periods from 4 to 30 s were estimated as a function of their wavelength based on observations. We used the model dispersion relation for these waves in ice and calculated the theoretical attenuation coefficients. We compared them with those from the data of experiments based on the relation of the spectral energies of waves in ice-free water and in ice. It is possible to use the estimated attenuation coefficients for waves of different periods to calculate the distance of wave propagation in fast ice with the critical amplitude where ice breaking is possible.

The photon interaction cross sections of blood

The photon interaction cross sections which contain the photoelectric absorption, coherent (Rayleigh) and incoherent (Compton) scattering are calculated for blood in the energy range of 1–150 keV. The molecular photoelectric absorption cross section is achieved from atomic cross section data. The molecular coherent (Rayleigh) and incoherent (Compton) scattering cross sections are estimated using relativistic modified form factor and incoherent scattering function approximation, respectively. The molecular form factors updated including molecular interference effects and incoherent scattering functions were also calculated. With the inclusion of the molecular interference effects in the coherent (Rayleigh) scattering, the more accurate data of radiation scattered from blood will be provided. The results are compared with references values in literature. It is found that the theoretical attenuation coefficients are in good agreement with experimental values.

Theoretical and experimental study of PbO-SiO2-Sb2O3 glasses as gamma ray shielding materials

Investigation and application of high energy radiations require the availability of radiation shields. In this research, glasses with the composition of 0.65PbO.(0.35-x)SiO2.xSb2O3 (x = 0, 0.01, 0.02, 0.03, 0.04, 0.05) were fabricated and characterized using densitometry, XRD, UV-Vis spectrophotometry and gamma ray spectrometry. The theoretical attenuation coefficient of the samples was calculated using WinXCom software. It was observed that although PbO strongly increased the mass attenuation coefficient for Co-60 radiation of glass, its substitution by Sb2O3 initially increased the parameter from 0.0609 to 0.0621, due to the dominant effect of Sb2O3 on bubble removal. The results also showed that there was an inconsistency between the theoretical and empirical results, that is, with increasing Sb2O3 content of the samples, the attenuation coefficient initially increased and then decreased, while the theoretical calculations predicted a continuous decline. It appears that the disagreement is mainly due to the fining effect of Sb2O3 and its effects on the bubble content. The WinXCom software is designed to work solely based on the mixture law. The sample 0.65PbO.0.34SiO2.0.01Sb2O3 showed the highest mass attenuation. The coefficient was 0.0621 and 0.0609 in 1.250 MeV for the samples with x = 0 and 0.01.

Evaluation of gamma-ray attenuation properties of bismuth borate glass systems using Monte Carlo method

A Monte Carlo method was developed to investigate radiation shielding properties of bismuth borate glass. The mass attenuation coefficients and half-value layer parameters were determined for different fractional amounts of Bi2O3 in the glass samples for the 356, 662, 1173 and 1332keV photon energies. A comparison of the theoretical and experimental attenuation coefficients is presented.

Leakage monitoring research and design for natural gas pipelines based on dynamic pressure waves

Many types of gases, such as natural gas, hydrogen, and so on, are transported via pipelines using a chemical process, though leakages in these pipelines create waste and pose hazards and risks to industries, the environment and people. To monitor gas pipelines, a new leak detection and location method based on the amplitude attenuation model of dynamic pressure waves was designed and researched by experiments, compared with traditional method based on the propagation velocity and time differences as determined by the waveforms of the upstream and downstream signals. Both methods are achieved based on the propagation law of the dynamic pressure waves in the fluid flow. First, the fundamentals of the newly proposed method are clarified by considering the influence of gas flow on the waves. The experiments are then conducted in gas pipelines with 42mm internal diameters. Finally, the results of the experiments are discussed and analyzed. The results indicate that all leakages can be detected by both methods but that the largest location error of the traditional method is −0.780%, whereas the largest location errors with respect to the new method are 0.054% with the experimental attenuation coefficients and 2.055% with the theoretical attenuation coefficients. It is further determined that the influence of the gas flow effects cannot be ignored by either method. Accordingly, the conclusions drawn suggest that the proposed methods can be applied to monitor gas pipelines.

Evaluation of X-ray radiation shielding performance of barium sulphate-coated fabrics

The X-ray in the field of medical imaging is an important diagnostic tool, but it has been identified that there are potential radiation risks associated with the X-ray radiation scans. These risks have traditionally been guarded against using lead based shields. Lead has excellent radiation shielding properties, but it is also heavy and a potential health and environmental hazard due to its toxicity. Thus, there have been studies seeking to find an alternative that is as effective and yet counters the other drawbacks. In this paper, preliminary studies were conducted to assess the shielding effect of barium sulphate (BaSO4) and bismuth oxide (Bi2O3) on the coated fabric samples. X-ray transmission resulting from standard lead coated samples, uncoated fabric, BaSO4, and BaSO4/Bi2O3 coated fabrics was evaluated via measuring the penetration of primary radiation. Different properties such as mass per unit area, material thickness, and surface morphology were examined. All samples were irradiated by X-ray at 80 kVp to measure the amount of transmissions. The X-ray transmission level associated with BaSO4 ranged from 84.5 % to 70.5 %. However, this level was elevated to 55.6 % when BaSO4/Bi2O3 mixture was applied on the fabric. The theoretical attenuation coefficient values associated with different coating mixtures comprising different weight proportions of BaSO4, Bi2O3, and PVC were determined between 0 MeV and 105 MeV using XCOM code. The XCOM results implied that the X-ray attenuation coefficient among all prepared coatings should be the mixture comprising 13.3 wt% Bi2O3/20 wt% BaSO4/66.7 wt% PVC, which was in agreement with the experimental results obtained from X-ray transmission measurements.

L subshell fluorescent X-ray measurements to study CK transitions in the 66≤ Z ≤83 region

L subshell fluorescent X-rays in Dy, Ho, Er, Lu, Ta, W, Pt, Au, Hg, Pb and Bi have been measured using synchrotron with selective creation of electron vacancies in individual subshells. Coster–Kronig (CK) yields were derived from the measured intensities. Present measurements have been made at photon energies above the edges where differences between measured and theoretical attenuation coefficients are almost negligible. Parametric trends for the results with Z were developed to cover all Zs in the range of 66–83. The trends predict the switching-off of L 1–L 2, N1 transition at Z = 67. The extent of fall /rise of f Lij values corresponding to off /on of certain transitions is found inversely proportional to the difference in binding energies of two consecutive subshells involved in the transition. For Zs above /below these rises /falls, f L13 and f L12 values are almost constants. f L23 values involving no break at Zs follow the general photoionization behaviour that ionization probability is highest at the edge energy and decreases with photon energy. Yield measurements with synchrotron radiation for Dy, Ho, Lu, Hg and Bi and experimental values for f L23, f L12 in Lu and for f L13 in Ta are being quoted for the first time.

Validation of Computed Tomography-based Attenuation Correction of Deviation between Theoretical and Actual Values in Four Computed Tomography Scanners.

Objective(s):In this study, we aimed to validate the accuracy of computed tomography-based attenuation correction (CTAC), using the bilinear scaling method.Methods:The measured attenuation coefficient (μm) was compared to the theoretical attenuation coefficient (μt), using four different CT scanners and an RMI 467 phantom. The effective energy of CT beam X-rays was calculated, using the aluminum half-value layer method and was used in conjunction with an attenuation coefficient map to convert the CT numbers to μm values for the photon energy of 140 keV. We measured the CT number of RMI 467 phantom for each of the four scanners and compared the μm and μt values for the effective energies of CT beam X-rays, effective atomic numbers, and physical densities.Results:The μm values for CT beam X-rays with low effective energies decreased in high construction elements, compared with CT beam X-rays of high effective energies. As the physical density increased, the μm values elevated linearly. Compared with other scanners, the μm values obtained from the scanner with CT beam X-rays of maximal effective energy increased once the effective atomic number exceeded 10.00. The μm value of soft tissue was equivalent to the μt value. However, the ratios of maximal difference between μm and μt values were 25.4% (lung tissue) and 21.5% (bone tissue), respectively. Additionally, the maximal difference in μm values was 6.0% in the bone tissue for each scanner.Conclusion:The bilinear scaling method could accurately convert CT numbers to μ values in soft tissues.

SU-D-204-01: Dual-Energy Calibration for Breast Density Measurement Using Spectral Mammography

Purpose: To investigate the feasibility of minimizing the systematic errors in dual-energy breast density quantification induced by the use of tissue-equivalent plastic phantoms as the calibration basis materials. Methods: Dual-energy calibration using tissue-equivalent plastic phantoms was performed on a spectral mammography system based on scanning multi-slit Si strip photon-counting detectors. The plastic phantom calibration used plastic water and adipose-equivalent phantoms as the basis materials, which have different x-ray attenuation properties compared to water and lipid in actual breast tissue. Two methods were used to convert the dual-energy decomposition measurements in plastic phantom thicknesses into true water and lipid basis. The first method was based entirely on the theoretical x-ray attenuation coefficients of the investigated materials in the mammographic energy range. The conversion matrix was determined from least-squares fitting of the target material using the reported attenuation coefficients of water and lipid. The second method was developed based on experimental calibrations, which measured the low-and high-energy signals of pure water and lipid of known thicknesses. A non-linear rational function was used to correlate the decomposed thicknesses to the known values, so that the conversion coefficients can be determined. Both methods were validated using independent measurements of water and lipid mixture phantoms. The correlation of the dual-energy decomposition measurements and the known values were studied with linear regression analysis. Results: There was an excellent linear correlation between the converted water thicknesses and the known values. The slopes of the linear fits were determined to be 0.63 and 1.03 for the simulation and experimental results, respectively. The non-linear fitting in the experimental approach reduced the root-mean-square (RMS) errors from approximately 3.4 mm to 1.5 mm. Conclusion: The results suggested that conversion of the dual-energy measurements into water and lipid thicknesses minimized the systematic errors in tissue decomposition studies.

Linear attenuation coefficients of tissues from 1 keV to 150 keV

The linear attenuation coefficients and three interaction processes have been computed for liver, kidney, muscle, fat and for a range of x-ray energies from 1keV to 150keV. Molecular photoelectric absorption cross sections were calculated from atomic cross section data. Total coherent (Rayleigh) and incoherent (Compton) scattering cross sections were obtained by numerical integration over combinations of F2m(x) with the Thomson formula and Sm(x) with the Klein–Nishina formula, respectively. For the coherent (Rayleigh) scattering cross section calculations, molecular form factors were obtained from recent experimental data in the literature for values of x<1Å−1 and from the relativistic modified atomic form factors for values of x≥1Å−1. With the inclusion of molecular interference effects in the coherent (Rayleigh) scattering, more accurate knowledge of the scatter from these tissues will be provided. The number of elements involved in tissue composition is 5 for liver, 47 for kidney, 44 for muscle and 3 for fat. The results are compared with previously published experimental and theoretical linear attenuation coefficients. In general, good agreement is obtained. The molecular form factors and scattering functions and cross sections are incorporated into a Monte Carlo program. The energy distributions of x-ray photons scattered from tissues have been simulated and the results are presented.

SU-E-I-31: Evaluating Brain Imaging Material (BIM) as a Brain Tissue Surrogate for Use in Neuro-Endovascular Imaged Guided Intervention (EIGI) Research.

A brain tissue surrogate material was needed to fill the anatomical cavity of a skull to create a phantom for use in simulated Neuro-EIGI procedures. To enable diagnostic and interventional procedure simulation, the BIM must fit into and be congruous with the interior surface of the skull, be reusable, and allow the implantation of vascular phantoms. The material must reasonably reproduce the automatic technique parameter selections observed during Neuro-EIGI procedures. We formulated a putty- like material to be used as the BIM. Its x-ray attenuation properties were evaluated by comparison of the fluoroscopic and radiographic technique parameters automatically selected for a BIM-filled skull on a Toshiba Infinix angiographic C-arm unit to those of a solid anthropomorphic head phantom at various projection angles. The same comparison was made between the skull phantom without BIM in the cavity and the anthropomorphic head phantom. The BIM linear attenuation coefficient was calculated and compared to that of PMMA, a common tissue analog plastic. The BIM keeps its shape, is moldable and reusable, and is congruent to the skull's interior surfaces. It allows for insertion and interchange of various custom vascular phantoms at proper anatomic locations. Addition of the BIM to the skull cavity improves the matching of the automatically selected parameters to those of the anthropomorphic phantom by an average of 96.3% for mAs and by 4.2% for kVp in fluoroscopy mode and by 88.6% and 9.0%, respectively, in DSA mode. The BIM's experimental and theoretical linear attenuation coefficient for the RQA5 spectrum differed from PMMA's by about 30%. Despite the difference in attenuation coefficients between the PMMA and BIM, the BIM is a good surrogate material for Neuro-EIGI research as shown by its properties of congruity, reusability, and device implantation, along with the demonstrated improvement of automatically selected technique parameters. Supported in part by: NIH Grants R01-EB008425, R01-EB002873, and an equipment grant from Toshiba Medical Systems Corp.

SU-E-I-04: Implementation of a Fast Monte Carlo Scatter Correction for Cone- Beam Computed Tomography.

To improve image quality in cone-beam computed tomography (CBCT) scans by implementation of a fast and accurate MC-based scatter correction algorithm. A Solid WaterTM phantom was imaged on a Varian OBI CBCT scanner using the standard-dose head protocol (100 kVp, 151 mAs, partial-angle). A fast Monte Carlo simulation developed in the EGSnrc framework was used to transport photons through the uncorrected CBCT scan. From the simulation output, the contribution from both primary and scattered photons for each projection image was estimated. Using these estimates, a subtractive scatter correction was performed on the CBCT projection data. This correction procedure was repeated iteratively, using the previous scatter corrected scan as input to the Monte Carlo simulation. Implementation of the scatter correction algorithm on real CBCT data was shown to help mitigate scatter-induced artifacts, such as cupping and streaking. The scatter corrected images were also shown to have improved accuracy in reconstructed attenuation coefficient values. In a region of interest centered on the Solid Water phantom, the number of voxels agreeing to within 10% of the theoretical attenuation coefficient increased from 46% to 97% after two iterations of the scatter correction. These results suggest that the proposed scatter correction algorithm is successful in improving image quality in real CBCT images. The accuracy of the attenuation coefficients extracted from the corrected CBCT scan renders the data suitable for on-the-fly dose recalculations, as well as vastly improved image registration.

Dependencies of Acoustic Properties on the Frequency and the Porosity for Biot¡?s Slow Wave in Water-saturated Copper Foams

The present study investigated the dependencies of acoustic properties, such as the phase velocity and the attenuation coefficient, on the frequency and the porosity for Biot’s slow wave in 13 watersaturated copper foams used as trabecular-bone-mimicking phantoms. The acoustic properties were measured over a frequency range from 0.8 to 1.2 MHz by using a matched pair of broadband, unfocused transducers with a diameter of 12.7 mm and a center frequency of 1.0 MHz. The Biot model for elastic wave propagation in fluid-saturated porous media was employed to predict the experimental measurements in the water-saturated copper foams. A strong slow wave and a very weak fast wave were consistently observed in the transmitted signals for all the phantoms. The experimental phase velocity showed good agreement with that of the Biot model, increasing with the frequency and the porosity. The experimental and the theoretical attenuation coefficients were found to increase linearly or quasi-linearly with increasing frequency. In contrast, the porosity dependency of the experimental attenuation coefficient showed a behavior opposite to that of the Biot model. These results suggest that the Biot model can be usefully employed as a practical tool for predicting the phase velocity in trabecular bone, but is not suitable for predicting the attenuation coefficient.