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Transient Propagation of Longitudinal and Transverse Waves in Cancellous Bone: Application of Biot Theory and Fractional Calculus. Symmetry (Basel) 2022. [DOI: 10.3390/sym14101971] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/16/2022] Open
Abstract
In this paper, the influence of the transverse wave on sound propagation in a porous medium with a flexible structure is considered. The study is carried out in the time domain using the modified Biot theory obtained by the symmetry of the Lagrangian (invariance by translation and rotation). The viscous exchanges between the fluid and the structure are described by fractional calculus. When a sound pulse arrives at normal incidence on a porous material with a flexible structure, the transverse waves interfere with the longitudinal waves during propagation because of the viscous interactions that appear between the fluid and the structure. By performing a calculation in the Laplace domain, the reflection and transmission operators are derived. Their time domain expressions depend on the Green functions of the longitudinal and transverse waves. In order to study the effects of the transverse wave on the transmitted longitudinal waves, numerical simulations of the transmitted waves in the time domain by varying the characteristic parameters of the medium are realized whether the transverse wave is considered or not.
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Measurement of Ultrasound Parameters of Bovine Cancellous Bone as a Function of Frequency for a Range of Porosities via Through-Transmission Ultrasonic Spectroscopy. ACOUSTICS 2022. [DOI: 10.3390/acoustics4020025] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 02/04/2023]
Abstract
The relationship between ultrasonic parameters (attenuation coefficients and velocity) and bone porosity in bovine cancellous bone is explored to understand the possibility of fracture risk diagnosis associated with osteoporosis by applying ultrasound. In vitro measurements of ultrasonic parameters on twenty-one bovine cancellous bone samples from tibia were conducted, using ultrasonic spectroscopy in the through-transmission mode. Transducers of three different center frequencies were used to cover a wide diagnostic frequency range between 1.0–7.8 MHz. The nonlinear relationship of porosity and normalized attenuation coefficient (nATTN) and normalized broadband attenuation coefficient (nBUA) were well described by a third-order polynomial fit, whereas porosity and the phase velocity (UV) were found to be negatively correlated with the linear correlation coefficients of −0.93, −0.89 and −0.83 at 2.25, 5.00 and 7.50 MHz, respectively. The results imply that the ultrasound parameters attain maximum values for the bone sample with the lowest porosity, and then decrease for samples with greater porosity for the range of porosities in our samples for all frequencies. Spatial variation in the ultrasound parameters was found to be caused by non-uniform pore size distribution, which was examined at five different locations within the same bone specimen. However, it did not affect the relationship of ultrasound parameters and porosity at these frequencies.
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Xu R, O'Reilly MA. Establishing density-dependent longitudinal sound speed in the vertebral lamina. THE JOURNAL OF THE ACOUSTICAL SOCIETY OF AMERICA 2022; 151:1516. [PMID: 35364923 DOI: 10.1121/10.0009316] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/18/2021] [Accepted: 12/26/2021] [Indexed: 06/14/2023]
Abstract
Focused ultrasound treatments of the spinal cord may be facilitated using a phased array transducer and beamforming to correct spine-induced focal aberrations. Simulations can non-invasively calculate aberration corrections using x-ray computed tomography (CT) data that are correlated to density (ρ) and longitudinal sound speed (cL). We aimed to optimize vertebral lamina-specific cL(ρ) functions at a physiological temperature (37 °C) to maximize time domain simulation accuracy. Odd-numbered ex vivo human thoracic vertebrae were imaged with a clinical CT-scanner (0.511 × 0.511 × 0.5 mm), then sonicated with a transducer (514 kHz) focused on the canal via the vertebral lamina. Vertebra-induced signal time shifts were extracted from pressure waveforms recorded within the canals. Measurements were repeated 5× per vertebra, with 2.5 mm vertical vertebra shifts between measurements. Linear functions relating cL with CT-derived density were optimized. The optimized function was cL(ρ)=0.35(ρ-ρw)+ cL,w m/s, where w denotes water, giving the tested laminae a mean bulk density of 1600 ± 30 kg/m3 and a mean bulk cL of 1670 ± 60 m/s. The optimized lamina cL(ρ) function was accurate to λ/16 when implemented in a multi-layered ray acoustics model. This modelling accuracy will improve trans-spine ultrasound beamforming.
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Affiliation(s)
- Rui Xu
- Department of Medical Biophysics, University of Toronto, 101 College Street, Suite 15-701, Toronto, Ontario, M5G 1L7, Canada
| | - Meaghan A O'Reilly
- Physical Sciences Platform, Sunnybrook Research Institute, 2075 Bayview Avenue, Toronto, Ontario, M4N 3M5, Canada
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4
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Clinical Devices for Bone Assessment. ADVANCES IN EXPERIMENTAL MEDICINE AND BIOLOGY 2022; 1364:35-53. [DOI: 10.1007/978-3-030-91979-5_3] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 10/18/2022]
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5
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Ultrasonic Assessment of Cancellous Bone Based on the Two-Wave Phenomenon. ADVANCES IN EXPERIMENTAL MEDICINE AND BIOLOGY 2022; 1364:119-143. [DOI: 10.1007/978-3-030-91979-5_6] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
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6
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Wear K. Scattering in Cancellous Bone. ADVANCES IN EXPERIMENTAL MEDICINE AND BIOLOGY 2022; 1364:163-175. [DOI: 10.1007/978-3-030-91979-5_8] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 10/18/2022]
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Wear KA. Mechanisms of Interaction of Ultrasound With Cancellous Bone: A Review. IEEE TRANSACTIONS ON ULTRASONICS, FERROELECTRICS, AND FREQUENCY CONTROL 2020; 67:454-482. [PMID: 31634127 PMCID: PMC7050438 DOI: 10.1109/tuffc.2019.2947755] [Citation(s) in RCA: 41] [Impact Index Per Article: 10.3] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/17/2023]
Abstract
Ultrasound is now a clinically accepted modality in the management of osteoporosis. The most common commercial clinical devices assess fracture risk from measurements of attenuation and sound speed in cancellous bone. This review discusses fundamental mechanisms underlying the interaction between ultrasound and cancellous bone. Because of its two-phase structure (mineralized trabecular network embedded in soft tissue-marrow), its anisotropy, and its inhomogeneity, cancellous bone is more difficult to characterize than most soft tissues. Experimental data for the dependencies of attenuation, sound speed, dispersion, and scattering on ultrasound frequency, bone mineral density, composition, microstructure, and mechanical properties are presented. The relative roles of absorption, scattering, and phase cancellation in determining attenuation measurements in vitro and in vivo are delineated. Common speed of sound metrics, which entail measurements of transit times of pulse leading edges (to avoid multipath interference), are greatly influenced by attenuation, dispersion, and system properties, including center frequency and bandwidth. However, a theoretical model has been shown to be effective for correction for these confounding factors in vitro and in vivo. Theoretical and phantom models are presented to elucidate why cancellous bone exhibits negative dispersion, unlike soft tissue, which exhibits positive dispersion. Signal processing methods are presented for separating "fast" and "slow" waves (predicted by poroelasticity theory and supported in cancellous bone) even when the two waves overlap in time and frequency domains. Models to explain dependencies of scattering on frequency and mean trabecular thickness are presented and compared with measurements. Anisotropy, the effect of the fluid filler medium (marrow in vivo or water in vitro), phantoms, computational modeling of ultrasound propagation, acoustic microscopy, and nonlinear properties in cancellous bone are also discussed.
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8
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Taki H, Nagatani Y, Matsukawa M, Kanai H, Izumi SI. Fast decomposition of two ultrasound longitudinal waves in cancellous bone using a phase rotation parameter for bone quality assessment: Simulation study. THE JOURNAL OF THE ACOUSTICAL SOCIETY OF AMERICA 2017; 142:2322. [PMID: 29092537 DOI: 10.1121/1.5008502] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/07/2023]
Abstract
Ultrasound signals that pass through cancellous bone may be considered to consist of two longitudinal waves, which are called fast and slow waves. Accurate decomposition of these fast and slow waves is considered to be highly beneficial in determination of the characteristics of cancellous bone. In the present study, a fast decomposition method using a wave transfer function with a phase rotation parameter was applied to received signals that have passed through bovine bone specimens with various bone volume to total volume (BV/TV) ratios in a simulation study, where the elastic finite-difference time-domain method is used and the ultrasound wave propagated parallel to the bone axes. The proposed method succeeded to decompose both fast and slow waves accurately; the normalized residual intensity was less than -19.5 dB when the specimen thickness ranged from 4 to 7 mm and the BV/TV value ranged from 0.144 to 0.226. There was a strong relationship between the phase rotation value and the BV/TV value. The ratio of the peak envelope amplitude of the decomposed fast wave to that of the slow wave increased monotonically with increasing BV/TV ratio, indicating the high performance of the proposed method in estimation of the BV/TV value in cancellous bone.
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Affiliation(s)
- Hirofumi Taki
- Graduate School of Biomedical Engineering, Tohoku University, Sendai 980-8575, Japan
| | - Yoshiki Nagatani
- Department of Electronics, Kobe City College of Technology, Kobe 651-2194, Japan
| | - Mami Matsukawa
- Faculty of Science and Engineering, Doshisha University, Kyotanabe 610-0321, Japan
| | - Hiroshi Kanai
- Graduate School of Engineering, Tohoku University, Sendai 980-8579, Japan
| | - Shin-Ichi Izumi
- Graduate School of Biomedical Engineering, Tohoku University, Sendai 980-8575, Japan
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9
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Wear KA, Nagaraja S, Dreher ML, Sadoughi S, Zhu S, Keaveny TM. Relationships among ultrasonic and mechanical properties of cancellous bone in human calcaneus in vitro. Bone 2017; 103:93-101. [PMID: 28666970 PMCID: PMC6941483 DOI: 10.1016/j.bone.2017.06.021] [Citation(s) in RCA: 16] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Received: 04/07/2017] [Revised: 06/01/2017] [Accepted: 06/26/2017] [Indexed: 11/15/2022]
Abstract
Clinical bone sonometers applied at the calcaneus measure broadband ultrasound attenuation and speed of sound. However, the relation of ultrasound measurements to bone strength is not well-characterized. Addressing this issue, we assessed the extent to which ultrasonic measurements convey in vitro mechanical properties in 25 human calcaneal cancellous bone specimens (approximately 2×4×2cm). Normalized broadband ultrasound attenuation, speed of sound, and broadband ultrasound backscatter were measured with 500kHz transducers. To assess mechanical properties, non-linear finite element analysis, based on micro-computed tomography images (34-micron cubic voxel), was used to estimate apparent elastic modulus, overall specimen stiffness, and apparent yield stress, with models typically having approximately 25-30 million elements. We found that ultrasound parameters were correlated with mechanical properties with R=0.70-0.82 (p<0.001). Multiple regression analysis indicated that ultrasound measurements provide additional information regarding mechanical properties beyond that provided by bone quantity alone (p≤0.05). Adding ultrasound variables to linear regression models based on bone quantity improved adjusted squared correlation coefficients from 0.65 to 0.77 (stiffness), 0.76 to 0.81 (apparent modulus), and 0.67 to 0.73 (yield stress). These results indicate that ultrasound can provide complementary (to bone quantity) information regarding mechanical behavior of cancellous bone.
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Affiliation(s)
- Keith A Wear
- U.S. Food and Drug Administration, Center for Devices and Radiological Health, 10903 New Hampshire Blvd., Silver Spring, MD 20993, USA.
| | - Srinidhi Nagaraja
- U.S. Food and Drug Administration, Center for Devices and Radiological Health, 10903 New Hampshire Blvd., Silver Spring, MD 20993, USA.
| | - Maureen L Dreher
- U.S. Food and Drug Administration, Center for Devices and Radiological Health, 10903 New Hampshire Blvd., Silver Spring, MD 20993, USA.
| | - Saghi Sadoughi
- Orthopaedic Biomechanics Laboratory, Department of Mechanical Engineering, 5124 Etcheverry Hall, Mailstop 1740, University of California at Berkeley, Berkeley, CA 94720-1740, USA.
| | - Shan Zhu
- Orthopaedic Biomechanics Laboratory, Department of Mechanical Engineering, 5124 Etcheverry Hall, Mailstop 1740, University of California at Berkeley, Berkeley, CA 94720-1740, USA.
| | - Tony M Keaveny
- Orthopaedic Biomechanics Laboratory, Department of Mechanical Engineering, 5124 Etcheverry Hall, Mailstop 1740, University of California at Berkeley, Berkeley, CA 94720-1740, USA; Department of Bioengineering, University of California, Berkeley, CA, USA.
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10
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Wille ML, Langton CM. Solid volume fraction estimation of bone:marrow replica models using ultrasound transit time spectroscopy. ULTRASONICS 2016; 65:329-337. [PMID: 26455950 DOI: 10.1016/j.ultras.2015.09.009] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/27/2015] [Revised: 08/31/2015] [Accepted: 09/15/2015] [Indexed: 06/05/2023]
Abstract
The acceptance of broadband ultrasound attenuation (BUA) for the assessment of osteoporosis suffers from a limited understanding of both ultrasound wave propagation through cancellous bone and its exact dependence upon the material and structural properties. It has recently been proposed that ultrasound wave propagation in cancellous bone may be described by a concept of parallel sonic rays; the transit time of each ray defined by the proportion of bone and marrow propagated. A Transit Time Spectrum (TTS) describes the proportion of sonic rays having a particular transit time, effectively describing the lateral inhomogeneity of transit times over the surface aperture of the receive ultrasound transducer. The aim of this study was to test the hypothesis that the solid volume fraction (SVF) of simplified bone:marrow replica models may be reliably estimated from the corresponding ultrasound transit time spectrum. Transit time spectra were derived via digital deconvolution of the experimentally measured input and output ultrasonic signals, and compared to predicted TTS based on the parallel sonic ray concept, demonstrating agreement in both position and amplitude of spectral peaks. Solid volume fraction was calculated from the TTS; agreement between true (geometric calculation) with predicted (computer simulation) and experimentally-derived values were R(2)=99.9% and R(2)=97.3% respectively. It is therefore envisaged that ultrasound transit time spectroscopy (UTTS) offers the potential to reliably estimate bone mineral density and hence the established T-score parameter for clinical osteoporosis assessment.
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Affiliation(s)
- Marie-Luise Wille
- Biomedical Engineering & Medical Physics Discipline, Science & Engineering Faculty and Institute of Health & Biomedical Innovation, Queensland University of Technology, Brisbane, QLD, Australia.
| | - Christian M Langton
- Biomedical Engineering & Medical Physics Discipline, Science & Engineering Faculty and Institute of Health & Biomedical Innovation, Queensland University of Technology, Brisbane, QLD, Australia
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11
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Groopman AM, Katz JI, Holland MR, Fujita F, Matsukawa M, Mizuno K, Wear KA, Miller JG. Conventional, Bayesian, and Modified Prony's methods for characterizing fast and slow waves in equine cancellous bone. THE JOURNAL OF THE ACOUSTICAL SOCIETY OF AMERICA 2015; 138:594-604. [PMID: 26328678 PMCID: PMC4529434 DOI: 10.1121/1.4923366] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/19/2015] [Revised: 06/16/2015] [Accepted: 06/21/2015] [Indexed: 05/28/2023]
Abstract
Conventional, Bayesian, and the modified least-squares Prony's plus curve-fitting (MLSP + CF) methods were applied to data acquired using 1 MHz center frequency, broadband transducers on a single equine cancellous bone specimen that was systematically shortened from 11.8 mm down to 0.5 mm for a total of 24 sample thicknesses. Due to overlapping fast and slow waves, conventional analysis methods were restricted to data from sample thicknesses ranging from 11.8 mm to 6.0 mm. In contrast, Bayesian and MLSP + CF methods successfully separated fast and slow waves and provided reliable estimates of the ultrasonic properties of fast and slow waves for sample thicknesses ranging from 11.8 mm down to 3.5 mm. Comparisons of the three methods were carried out for phase velocity at the center frequency and the slope of the attenuation coefficient for the fast and slow waves. Good agreement among the three methods was also observed for average signal loss at the center frequency. The Bayesian and MLSP + CF approaches were able to separate the fast and slow waves and provide good estimates of the fast and slow wave properties even when the two wave modes overlapped in both time and frequency domains making conventional analysis methods unreliable.
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Affiliation(s)
- Amber M Groopman
- Department of Physics, Washington University in St. Louis, St. Louis, Missouri 63130, USA
| | - Jonathan I Katz
- Department of Physics, Washington University in St. Louis, St. Louis, Missouri 63130, USA
| | - Mark R Holland
- Department of Radiology and Imaging Sciences, Indiana University-Purdue University School of Medicine, Indianapolis, Indiana 46202, USA
| | - Fuminori Fujita
- Laboratory of Ultrasonic Electronics, Research Center for Wave Electronics, Doshisha University, Kyotanabe, 610-0321 Kyoto, Japan
| | - Mami Matsukawa
- Laboratory of Ultrasonic Electronics, Research Center for Wave Electronics, Doshisha University, Kyotanabe, 610-0321 Kyoto, Japan
| | - Katsunori Mizuno
- Underwater Technology Research Center, The University of Tokyo, Meguro-ku, Tokyo 153-8505, Japan
| | - Keith A Wear
- Center for Devices and Radiological Health, Food and Drug Administration, Silver Spring, Maryland 20993, USA
| | - James G Miller
- Department of Physics, Washington University in St. Louis, St. Louis, Missouri 63130, USA
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Taki H, Nagatani Y, Matsukawa M, Mizuno K, Sato T. Fast characterization of two ultrasound longitudinal waves in cancellous bone using an adaptive beamforming technique. THE JOURNAL OF THE ACOUSTICAL SOCIETY OF AMERICA 2015; 137:1683-1692. [PMID: 25920821 DOI: 10.1121/1.4916276] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/04/2023]
Abstract
The received signal in through-transmission ultrasound measurements of cancellous bone consists of two longitudinal waves, called the fast and slow waves. Analysis of these fast and slow waves may reveal characteristics of the cancellous bone that would be good indicators of osteoporosis. Because the two waves often overlap, decomposition of the received signal is an important problem in the characterization of bone quality. This study proposes a fast and accurate decomposition method based on the frequency domain interferometry imaging method with a modified wave transfer function that uses a phase rotation parameter. The proposed method accurately characterized the fast and slow waves in the experimental study, and the residual intensity, which was normalized with respect to the received signal intensity, was less than -20 dB over the bone specimen thickness range from 6 to 15 mm. In the simulation study, the residual intensity was less than -20 dB over the specimen thickness range from 3 to 8 mm. Decomposition of a single received signal takes only 5 s using a laptop personal computer with a single central processing unit. The proposed method has great potential to provide accurate and rapid measurements of indicators of osteoporosis in cancellous bone.
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Affiliation(s)
- Hirofumi Taki
- Graduate School of Engineering, Tohoku University, Sendai 980-8579, Japan
| | - Yoshiki Nagatani
- Department of Electronics, Kobe City College of Technology, Kobe 651-2194, Japan
| | - Mami Matsukawa
- Faculty of Science and Engineering, Doshisha University, Kyotanabe 610-0321, Japan
| | - Katsunori Mizuno
- Institute of Industrial Science, The University of Tokyo, Tokyo 113-8654, Japan
| | - Toru Sato
- Graduate School of Informatics, Kyoto University, Kyoto 606-8501, Japan
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13
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Wear KA. Nonlinear attenuation and dispersion in human calcaneus in vitro: statistical validation and relationships to microarchitecture. THE JOURNAL OF THE ACOUSTICAL SOCIETY OF AMERICA 2015; 137:1126-1133. [PMID: 25786928 PMCID: PMC9204557 DOI: 10.1121/1.4908310] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/28/2023]
Abstract
Through-transmission measurements were performed on 30 human calcaneus samples in vitro. Nonlinear attenuation and dispersion measurements were investigated by estimating 95% confidence intervals of coefficients of polynomial expansions of log magnitude and phase of transmission coefficients. Bone mineral density (BMD) was measured with dual x-ray absorptiometry. Microarchitecture was measured with microcomputed tomography. Statistically significant nonlinear attenuation and nonzero dispersion were confirmed for a clinical bandwidth of 300-750 kHz in 40%-43% of bone samples. The mean linear coefficient for attenuation was 10.3 dB/cm MHz [95% confidence interval (CI): 9.0-11.6 dB/cm MHz]. The mean quadratic coefficient for attenuation was 1.6 dB/cm MHz(2) (95% CI: 0.4-2.8 dB/cm MHz(2)). Nonlinear attenuation provided little information regarding BMD or microarchitecture. The quadratic coefficient for phase (which is related to dispersion) showed moderate correlations with BMD (r = -0.65; 95% CI: -0.82 to -0.36), bone surface-to-volume ratio (r = 0.47; 95% CI: 0.12-0.72) and trabecular thickness (r = -0.40; 95% CI: -0.67 to -0.03). Dispersion was proportional to bone volume fraction raised to an exponent of 2.1 ± 0.2, which is similar to the value for parallel nylon-wire phantoms (2.4 ± 0.2) and supports a multiple-scattering model for dispersion.
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Affiliation(s)
- Keith A Wear
- United States Food and Drug Administration, Center for Devices and Radiological Health, Silver Spring, Maryland 20993
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14
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Wear K, Nagatani Y, Mizuno K, Matsukawa M. Fast and slow wave detection in bovine cancellous bone in vitro using bandlimited deconvolution and Prony's method. THE JOURNAL OF THE ACOUSTICAL SOCIETY OF AMERICA 2014; 136:2015-24. [PMID: 25324100 PMCID: PMC8240127 DOI: 10.1121/1.4895668] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/10/2023]
Abstract
Fast and slow waves were detected in a bovine cancellous bone sample for thicknesses ranging from 7 to 12 mm using bandlimited deconvolution and the modified least-squares Prony's method with curve fitting (MLSP + CF). Bandlimited deconvolution consistently isolated two waves with linear-with-frequency attenuation coefficients as evidenced by high correlation coefficients between attenuation coefficient and frequency: 0.997 ± 0.002 (fast wave) and 0.986 ± 0.013 (slow wave) (mean ± standard deviation). Average root-mean-squared (RMS) differences between the two algorithms for phase velocities were 5 m/s (fast wave, 350 kHz) and 13 m/s (slow wave, 750 kHz). Average RMS differences for signal loss were 1.6 dB (fast wave, 350 kHz) and 0.4 dB (slow wave, 750 kHz). Phase velocities for thickness = 10 mm were 1726 m/s (fast wave, 350 kHz) and 1455 m/s (slow wave, 750 kHz). Results show support for the model of two waves with linear-with frequency attenuation, successful isolation of fast and slow waves, good agreement between bandlimited deconvolution and MLSP + CF as well as with a Bayesian algorithm, and potential variations of fast and/or slow wave properties with bone sample thickness.
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Affiliation(s)
- Keith Wear
- U.S. Food and Drug Administration, Silver Spring, Maryland 20993
| | - Yoshiki Nagatani
- Department of Electronics, Kobe City College of Technology 8-3, Gakuen Higashi-cho, Nishiku, Kobe, 651-2194 Japan
| | - Katsunori Mizuno
- Underwater Technology Collaborative Research Center, Institute of Industrial Science, University of Tokyo, 4-6-1 Komaba Meguro-ku, Tokyo, 153-8505, Japan
| | - Mami Matsukawa
- Laboratory of Ultrasonic Electronics, Faculty of Science and Engineering, Doshisha University 1-3, Tatara Miyakodani, Kyotanabe, 610-0321, Kyoto, Japan
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15
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Potsika VT, Grivas KN, Protopappas VC, Vavva MG, Raum K, Rohrbach D, Polyzos D, Fotiadis DI. Application of an effective medium theory for modeling ultrasound wave propagation in healing long bones. ULTRASONICS 2014; 54:1219-1230. [PMID: 24091149 DOI: 10.1016/j.ultras.2013.09.002] [Citation(s) in RCA: 15] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/04/2013] [Revised: 08/14/2013] [Accepted: 09/01/2013] [Indexed: 06/02/2023]
Abstract
Quantitative ultrasound has recently drawn significant interest in the monitoring of the bone healing process. Several research groups have studied ultrasound propagation in healing bones numerically, assuming callus to be a homogeneous and isotropic medium, thus neglecting the multiple scattering phenomena that occur due to the porous nature of callus. In this study, we model ultrasound wave propagation in healing long bones using an iterative effective medium approximation (IEMA), which has been shown to be significantly accurate for highly concentrated elastic mixtures. First, the effectiveness of IEMA in bone characterization is examined: (a) by comparing the theoretical phase velocities with experimental measurements in cancellous bone mimicking phantoms, and (b) by simulating wave propagation in complex healing bone geometries by using IEMA. The original material properties of cortical bone and callus were derived using serial scanning acoustic microscopy (SAM) images from previous animal studies. Guided wave analysis is performed for different healing stages and the results clearly indicate that IEMA predictions could provide supplementary information for bone assessment during the healing process. This methodology could potentially be applied in numerical studies dealing with wave propagation in composite media such as healing or osteoporotic bones in order to reduce the simulation time and simplify the study of complicated geometries with a significant porous nature.
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Affiliation(s)
- Vassiliki T Potsika
- Unit of Medical Technology and Intelligent Information Systems, Department of Materials Science and Engineering, University of Ioannina, GR 45110 Ioannina, Greece
| | - Konstantinos N Grivas
- Department of Mechanical Engineering and Aeronautics, University of Patras, GR 26500 Patras, Greece
| | - Vasilios C Protopappas
- Unit of Medical Technology and Intelligent Information Systems, Department of Materials Science and Engineering, University of Ioannina, GR 45110 Ioannina, Greece
| | - Maria G Vavva
- Department of Mechanical Engineering and Aeronautics, University of Patras, GR 26500 Patras, Greece
| | - Kay Raum
- Julius Wolff Institute, Berlin-Brandenburg School for Regenerative Therapies, Charité-Universitätsmedizin Berlin, Augustenburger Platz 1, 13353 Berlin, Germany
| | - Daniel Rohrbach
- Julius Wolff Institute, Berlin-Brandenburg School for Regenerative Therapies, Charité-Universitätsmedizin Berlin, Augustenburger Platz 1, 13353 Berlin, Germany
| | - Demosthenes Polyzos
- Department of Mechanical Engineering and Aeronautics, University of Patras, GR 26500 Patras, Greece
| | - Dimitrios I Fotiadis
- Unit of Medical Technology and Intelligent Information Systems, Department of Materials Science and Engineering, University of Ioannina, GR 45110 Ioannina, Greece.
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Mézière F, Muller M, Bossy E, Derode A. Measurements of ultrasound velocity and attenuation in numerical anisotropic porous media compared to Biot's and multiple scattering models. ULTRASONICS 2014; 54:1146-54. [PMID: 24125533 DOI: 10.1016/j.ultras.2013.09.013] [Citation(s) in RCA: 24] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/27/2013] [Revised: 07/31/2013] [Accepted: 09/10/2013] [Indexed: 05/23/2023]
Abstract
This article quantitatively investigates ultrasound propagation in numerical anisotropic porous media with finite-difference simulations in 3D. The propagation media consist of clusters of ellipsoidal scatterers randomly distributed in water, mimicking the anisotropic structure of cancellous bone. Velocities and attenuation coefficients of the ensemble-averaged transmitted wave (also known as the coherent wave) are measured in various configurations. As in real cancellous bone, one or two longitudinal modes emerge, depending on the micro-structure. The results are confronted with two standard theoretical approaches: Biot's theory, usually invoked in porous media, and the Independent Scattering Approximation (ISA), a classical first-order approach of multiple scattering theory. On the one hand, when only one longitudinal wave is observed, it is found that at porosities higher than 90% the ISA successfully predicts the attenuation coefficient (unlike Biot's theory), as well as the existence of negative dispersion. On the other hand, the ISA is not well suited to study two-wave propagation, unlike Biot's model, at least as far as wave speeds are concerned. No free fitting parameters were used for the application of Biot's theory. Finally we investigate the phase-shift between waves in the fluid and the solid structure, and compare them to Biot's predictions of in-phase and out-of-phase motions.
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Affiliation(s)
- Fabien Mézière
- Institut Langevin, ESPCI ParisTech, CNRS UMR7587, INSERM U979, Université Paris Diderot - Paris 7, 1 rue Jussieu, 75005 Paris, France.
| | - Marie Muller
- Institut Langevin, ESPCI ParisTech, CNRS UMR7587, INSERM U979, Université Paris Diderot - Paris 7, 1 rue Jussieu, 75005 Paris, France.
| | - Emmanuel Bossy
- Institut Langevin, ESPCI ParisTech, CNRS UMR7587, INSERM U979, Université Paris Diderot - Paris 7, 1 rue Jussieu, 75005 Paris, France
| | - Arnaud Derode
- Institut Langevin, ESPCI ParisTech, CNRS UMR7587, INSERM U979, Université Paris Diderot - Paris 7, 1 rue Jussieu, 75005 Paris, France
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17
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Wear KA. Time-domain separation of interfering waves in cancellous bone using bandlimited deconvolution: simulation and phantom study. THE JOURNAL OF THE ACOUSTICAL SOCIETY OF AMERICA 2014; 135:2102-12. [PMID: 25235007 PMCID: PMC8317067 DOI: 10.1121/1.4868473] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/10/2023]
Abstract
In through-transmission interrogation of cancellous bone, two longitudinal pulses ("fast" and "slow" waves) may be generated. Fast and slow wave properties convey information about material and micro-architectural characteristics of bone. However, these properties can be difficult to assess when fast and slow wave pulses overlap in time and frequency domains. In this paper, two methods are applied to decompose signals into fast and slow waves: bandlimited deconvolution and modified least-squares Prony's method with curve-fitting (MLSP + CF). The methods were tested in plastic and Zerdine(®) samples that provided fast and slow wave velocities commensurate with velocities for cancellous bone. Phase velocity estimates were accurate to within 6 m/s (0.4%) (slow wave with both methods and fast wave with MLSP + CF) and 26 m/s (1.2%) (fast wave with bandlimited deconvolution). Midband signal loss estimates were accurate to within 0.2 dB (1.7%) (fast wave with both methods), and 1.0 dB (3.7%) (slow wave with both methods). Similar accuracies were found for simulations based on fast and slow wave parameter values published for cancellous bone. These methods provide sufficient accuracy and precision for many applications in cancellous bone such that experimental error is likely to be a greater limiting factor than estimation error.
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Affiliation(s)
- Keith A Wear
- Center for Devices and Radiological Health, U.S. Food and Drug Administration, Bldg. 62, Room 3108, 10903 New Hampshire Boulevard, Silver Spring, Maryland 20993
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18
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Wear KA. Estimation of fast and slow wave properties in cancellous bone using Prony's method and curve fitting. THE JOURNAL OF THE ACOUSTICAL SOCIETY OF AMERICA 2013; 133:2490-501. [PMID: 23556613 PMCID: PMC8243208 DOI: 10.1121/1.4792935] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/25/2023]
Abstract
The presence of two longitudinal waves in poroelastic media is predicted by Biot's theory and has been confirmed experimentally in through-transmission measurements in cancellous bone. Estimation of attenuation coefficients and velocities of the two waves is challenging when the two waves overlap in time. The modified least squares Prony's (MLSP) method in conjuction with curve-fitting (MLSP + CF) is tested using simulations based on published values for fast and slow wave attenuation coefficients and velocities in cancellous bone from several studies in bovine femur, human femur, and human calcaneus. The search algorithm is accelerated by exploiting correlations among search parameters. The performance of the algorithm is evaluated as a function of signal-to-noise ratio (SNR). For a typical experimental SNR (40 dB), the root-mean-square errors (RMSEs) for one example (human femur) with fast and slow waves separated by approximately half of a pulse duration were 1 m/s (slow wave velocity), 4 m/s (fast wave velocity), 0.4 dB/cm MHz (slow wave attenuation slope), and 1.7 dB/cm MHz (fast wave attenuation slope). The MLSP + CF method is fast (requiring less than 2 s at SNR = 40 dB on a consumer-grade notebook computer) and is flexible with respect to the functional form of the parametric model for the transmission coefficient. The MLSP + CF method provides sufficient accuracy and precision for many applications such that experimental error is a greater limiting factor than estimation error.
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Affiliation(s)
- Keith A Wear
- U.S. Food and Drug Administration, 10903 New Hampshire Avenue, Building 62, Room 3108, Silver Spring, Maryland 20993-0002, USA.
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19
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Fellah M, Fellah ZEA, Mitri FG, Ogam E, Depollier C. Transient ultrasound propagation in porous media using Biot theory and fractional calculus: application to human cancellous bone. THE JOURNAL OF THE ACOUSTICAL SOCIETY OF AMERICA 2013; 133:1867-1881. [PMID: 23556556 DOI: 10.1121/1.4792721] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/02/2023]
Abstract
A temporal model based on the Biot theory is developed to describe the transient ultrasonic propagation in porous media with elastic structure, in which the viscous exchange between fluid and structure are described by fractional derivatives. The fast and slow waves obey a fractional wave equation in the time domain. The solution of Biot's equations in time depends on the Green functions of each of the waves (fast and slow), and their fractional derivatives. The reflection and transmission operators for a slab of porous materials are derived in the time domain, using calculations in the Laplace domain. Their analytical expressions, depend on Green's function of fast and slow waves. Experimental results for slow and fast waves transmitted through human cancellous bone samples are given and compared with theoretical predictions.
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Affiliation(s)
- M Fellah
- Laboratoire de Physique Théorique, Faculté de Physique, USTHB, BP 32 El Alia, Bab Ezzouar 16111, Algeria
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20
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Hoffman JJ, Nelson AM, Holland MR, Miller JG. Cancellous bone fast and slow waves obtained with Bayesian probability theory correlate with porosity from computed tomography. THE JOURNAL OF THE ACOUSTICAL SOCIETY OF AMERICA 2012; 132:1830-7. [PMID: 22978910 PMCID: PMC3460989 DOI: 10.1121/1.4739455] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/10/2023]
Abstract
A Bayesian probability theory approach for separating overlapping ultrasonic fast and slow waves in cancellous bone has been previously introduced. The goals of this study were to investigate whether the fast and slow waves obtained from Bayesian separation of an apparently single mode signal individually correlate with porosity and to isolate the fast and slow waves from medial-lateral insonification of the calcaneus. The Bayesian technique was applied to trabecular bone data from eight human calcanei insonified in the medial-lateral direction. The phase velocity, slope of attenuation (nBUA), and amplitude were determined for both the fast and slow waves. The porosity was assessed by micro-computed tomography (microCT) and ranged from 78.7% to 94.1%. The method successfully separated the fast and slow waves from medial-lateral insonification of the calcaneus. The phase velocity for both the fast and slow wave modes showed an inverse correlation with porosity (R(2) = 0.73 and R(2) = 0.86, respectively). The slope of attenuation for both wave modes also had a negative correlation with porosity (fast wave: R(2) = 0.73, slow wave: R(2) = 0.53). The fast wave amplitude decreased with increasing porosity (R(2) = 0.66). Conversely, the slow wave amplitude modestly increased with increasing porosity (R(2) = 0.39).
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Affiliation(s)
- Joseph J Hoffman
- Department of Physics, Washington University in St. Louis, St. Louis, Missouri 63139, USA
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21
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Cardoso L, Cowin SC. Role of structural anisotropy of biological tissues in poroelastic wave propagation. MECHANICS OF MATERIALS : AN INTERNATIONAL JOURNAL 2012; 44:174-188. [PMID: 22162897 PMCID: PMC3233242 DOI: 10.1016/j.mechmat.2011.08.007] [Citation(s) in RCA: 11] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/10/2023]
Abstract
Ultrasound waves have a broad range of clinical applications as a non-destructive testing approach in imaging and in the diagnoses of medical conditions. Generally, biological tissues are modeled as an homogenized equivalent medium with an apparent density through which a single wave propagates. Only the first wave arriving at the ultrasound probe is used for the measurement of the speed of sound. However, the existence of a second wave in tissues such as cancellous bone has been reported and its existence is an unequivocal signature of Biot type poroelastic media. To account for the fact that ultrasound is sensitive to microarchitecture as well as density, a fabric-dependent anisotropic poroelastic ultrasound (PEU) propagation theory was recently developed. Key to this development was the inclusion of the fabric tensor - a quantitative stereological measure of the degree of structural anisotropy of bone - into the linear poroelasticity theory. In the present study, this framework is extended to the propagation of waves in several soft and hard tissues. It was found that collagen fibers in soft tissues and the mineralized matrix in hard tissues are responsible for the anisotropy of the solid tissue constituent through the fabric tensor in the model.
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Affiliation(s)
- Luis Cardoso
- The Department of Biomedical Engineering, The City University of New York, New York, NY 10031
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22
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Lee KI. Correlations of group velocity, phase velocity, and dispersion with bone density in bovine trabecular bone. THE JOURNAL OF THE ACOUSTICAL SOCIETY OF AMERICA 2011; 130:EL399-EL404. [PMID: 22225133 DOI: 10.1121/1.3662007] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/31/2023]
Abstract
The present study investigated the correlations of the group velocity, the phase velocity, and the velocity dispersion with the apparent bone density in bovine trabecular bone in vitro. The phase velocity exhibited the negative dispersion, consistent with the behavior in human trabecular bone. The group and the phase velocities were found to increase with increasing apparent bone density, respectively, exhibiting similar high correlations of r=0.94 and 0.96. The negative dispersion rate exhibited a decreasing dependence on the apparent bone density, with a significant correlation of r=-0.86.
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Affiliation(s)
- Kang Il Lee
- Department of Physics, Kangwon National University, Chuncheon 200-701, Republic of Korea.
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23
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Nelson AM, Hoffman JJ, Anderson CC, Holland MR, Nagatani Y, Mizuno K, Matsukawa M, Miller JG. Determining attenuation properties of interfering fast and slow ultrasonic waves in cancellous bone. THE JOURNAL OF THE ACOUSTICAL SOCIETY OF AMERICA 2011; 130:2233-40. [PMID: 21973378 PMCID: PMC3206914 DOI: 10.1121/1.3625241] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/05/2023]
Abstract
Previous studies have shown that interference between fast waves and slow waves can lead to observed negative dispersion in cancellous bone. In this study, the effects of overlapping fast and slow waves on measurements of the apparent attenuation as a function of propagation distance are investigated along with methods of analysis used to determine the attenuation properties. Two methods are applied to simulated data that were generated based on experimentally acquired signals taken from a bovine specimen. The first method uses a time-domain approach that was dictated by constraints imposed by the partial overlap of fast and slow waves. The second method uses a frequency-domain log-spectral subtraction technique on the separated fast and slow waves. Applying the time-domain analysis to the broadband data yields apparent attenuation behavior that is larger in the early stages of propagation and decreases as the wave travels deeper. In contrast, performing frequency-domain analysis on the separated fast waves and slow waves results in attenuation coefficients that are independent of propagation distance. Results suggest that features arising from the analysis of overlapping two-mode data may represent an alternate explanation for the previously reported apparent dependence on propagation distance of the attenuation coefficient of cancellous bone.
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Affiliation(s)
- Amber M Nelson
- Department of Physics, Washington University in Saint Louis, Saint Louis, Missouri 63130, USA
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24
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Kimura M. Velocity dispersion and attenuation in granular marine sediments: comparison of measurements with predictions using acoustic models. THE JOURNAL OF THE ACOUSTICAL SOCIETY OF AMERICA 2011; 129:3544-3561. [PMID: 21682381 DOI: 10.1121/1.3585841] [Citation(s) in RCA: 24] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/30/2023]
Abstract
The large velocity dispersion recently reported could be explained by a gap stiffness model incorporated into the Biot model (the BIMGS model) proposed by the author. However, at high frequencies, some measured results have been reported for negative velocity dispersion and attenuation proportional to the first to fourth power of frequency. In this study, first, it is shown that the results of velocity dispersion and attenuation calculated using the BIMGS model are consistent with the results measured in two kinds of water-saturated sands with different grain sizes, except in the high-frequency range. Then, the velocity dispersion and attenuation in six kinds of water-saturated glass beads and four kinds of water-saturated silica sands with different grain sizes are measured in the frequency ranges of 80-140 and 300-700 kHz. The measured results are compared with those calculated using the BIMGS model plus some acoustic models. It is shown that the velocity dispersion and attenuation are well predicted by using the BIMGS model in the range of kd ≤ 0.5 (k: wavenumber in water, d: grain diameter) and by using the BIMGS model plus multiple scattering effects in the range of kd ≥ 0.5 in which negative velocity dispersion appears.
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Affiliation(s)
- Masao Kimura
- Poro-Acoustics Laboratory, 1115-22 Miyakami, Shimizu, Shizuoka, Shizuoka 424-0911, Japan.
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25
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Zhang C, Le LH, Zheng R, Ta D, Lou E. Measurements of ultrasonic phase velocities and attenuation of slow waves in cellular aluminum foams as cancellous bone-mimicking phantoms. THE JOURNAL OF THE ACOUSTICAL SOCIETY OF AMERICA 2011; 129:3317-26. [PMID: 21568432 DOI: 10.1121/1.3562560] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/10/2023]
Abstract
The water-saturated aluminum foams with an open network of interconnected ligaments were investigated by ultrasonic transmission technique for the suitability as cancellous bone-mimicking phantoms. The phase velocities and attenuation of nine samples covering three pores per inch (5, 10, and 20 PPI) and three aluminum volume fractions (5, 8, and 12% AVF) were measured over a frequency range of 0.7-1.3 MHz. The ligament thickness and pore sizes of the phantoms and low-density human cancellous bones are similar. A strong slow wave and a weak fast wave are observed for all samples while the latter is not visible without significant amplification (100x). This study reports the characteristics of slow wave, whose speeds are less than the sound speed of the saturating water and decrease mildly with AVF and PPI with an average 1469 m/s. Seven out of nine samples show positive dispersion and the rest show minor negative dispersion. Attenuation increases with AVF, PPI, and frequency except for the 20 PPI samples, which exhibit non-increasing attenuation level with fluctuations due to scattering. The phase velocities agree with Biot's porous medium theory. The RMSE is 16.0 m/s (1%) at n = 1.5. Below and above this value, the RMSE decreases mildly and rises sharply, respectively.
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Affiliation(s)
- Chan Zhang
- Department of Radiology and Diagnostic Imaging, University of Alberta, Edmonton, Alberta T6G 2B7, Canada
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26
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Cardoso L, Cowin SC. Fabric dependence of quasi-waves in anisotropic porous media. THE JOURNAL OF THE ACOUSTICAL SOCIETY OF AMERICA 2011; 129:3302-16. [PMID: 21568431 PMCID: PMC3115277 DOI: 10.1121/1.3557032] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/01/2010] [Revised: 01/14/2011] [Accepted: 01/19/2011] [Indexed: 05/20/2023]
Abstract
Assessment of bone loss and osteoporosis by ultrasound systems is based on the speed of sound and broadband ultrasound attenuation of a single wave. However, the existence of a second wave in cancellous bone has been reported and its existence is an unequivocal signature of poroelastic media. To account for the fact that ultrasound is sensitive to microarchitecture as well as bone mineral density (BMD), a fabric-dependent anisotropic poroelastic wave propagation theory was recently developed for pure wave modes propagating along a plane of symmetry in an anisotropic medium. Key to this development was the inclusion of the fabric tensor--a quantitative stereological measure of the degree of structural anisotropy of bone--into the linear poroelasticity theory. In the present study, this framework is extended to the propagation of mixed wave modes along an arbitrary direction in anisotropic porous media called quasi-waves. It was found that differences between phase and group velocities are due to the anisotropy of the bone microarchitecture, and that the experimental wave velocities are more accurately predicted by the poroelastic model when the fabric tensor variable is taken into account. This poroelastic wave propagation theory represents an alternative for bone quality assessment beyond BMD.
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Affiliation(s)
- Luis Cardoso
- The Department of Biomedical Engineering, The City University of New York, New York, New York 10031, USA.
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27
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Aly AH, Ginsberg HJ, Cobbold RSC. On ultrasound imaging for guided screw insertion in spinal fusion surgery. ULTRASOUND IN MEDICINE & BIOLOGY 2011; 37:651-664. [PMID: 21376451 DOI: 10.1016/j.ultrasmedbio.2011.01.011] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/21/2010] [Revised: 01/10/2011] [Accepted: 01/14/2011] [Indexed: 05/30/2023]
Abstract
Spinal fusion surgery generally involves the insertion of screws in the pedicle, a three-dimensional (3-D) process that requires great skill if serious consequences are to be avoided. This article describes an image guidance technique based on generating B‑mode images from within a small bore hole in the pedicle's trabecular bone. The purpose is to determine the viability and safety of the hole placement for subsequent insertion of the screw. Toward this end, this article endeavours to understand the factors that govern B-mode image quality. Specifically, the results of numerical simulations on the effects of transducer frequency and bone volume on image quality are presented along with demonstrations of B-mode image formation obtained in vitro on human pedicles using a 3.2 MHz probe. The results of the numerical simulations suggest that high frequency and high bone volume generally reduce the image quality. The in vitro experiments showed that the trabecular and cortical bone can be detected in the B-mode images.
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Affiliation(s)
- Al-Hassan Aly
- Institute of Biomaterials and Biomedical Engineering, University of Toronto, Toronto, Canada
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28
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Pichardo S, Sin VW, Hynynen K. Multi-frequency characterization of the speed of sound and attenuation coefficient for longitudinal transmission of freshly excised human skulls. Phys Med Biol 2010; 56:219-50. [PMID: 21149950 DOI: 10.1088/0031-9155/56/1/014] [Citation(s) in RCA: 160] [Impact Index Per Article: 11.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/25/2023]
Abstract
For medical applications of ultrasound inside the brain, it is necessary to understand the relationship between the apparent density of skull bone and its corresponding speed of sound and attenuation coefficient. Although there have been previous studies exploring this phenomenon, there is still a need to extend the measurements to cover more of the clinically relevant frequency range. The results of measurements of the longitudinal speed of sound and attenuation coefficient are presented for specimens of human calvaria. The study was performed for the frequencies of 0.27, 0.836, 1.402, 1.965 and 2.525 MHz. Specimens were obtained from fresh cadavers through a protocol with the Division of Anatomy of the University of Toronto. The protocol was approved by the Research Ethics Board of Sunnybrook Health Sciences Centre. The specimens were mounted in polycarbonate supports that were marked for stereoscopic positioning. Computer tomography (CT) scans of the skulls mounted on their supports were performed, and a three-dimensional skull surface was reconstructed. This surface was used to guide a positioning system to ensure the normal sound incidence of an acoustic signal. This signal was produced by a focused device with a diameter of 5 cm and a focal length of 10 cm. Measurements of delay in time of flight were carried out using a needle hydrophone. Measurements of effective transmitted energy were carried out using a radiation force method with a 10 µg resolution scale. Preliminary functions of speed of sound and attenuation coefficient, both of which are related to apparent density, were established using a multi-layer propagation model that takes into account speed of sound, density and thickness of the layer. An optimization process was executed from a large set of random functions and the best functions were chosen for those ones that closest reproduced the experimental observations. The final functions were obtained after a second pass of the optimization process was executed, but this time using a finite-difference time-difference solution of the Westervelt equation, which is more precise than the multi-layer model but much more time consuming for computation. For six of seven specimens, measurements were carried out on five locations on the calvaria, and for the other specimen three measurements were made. In total, measurements were carried out on 33 locations. Results indicated the presence of dispersion effects and that these effects are different according to the type of bone in the skull (cortical and trabecular). Additionally, both the speed of sound and attenuation showed dependence on the skull density that varied with the frequency. Using the optimal functions and the information of density from the CT scans, the average values (±s.d.) of the speed of sound for cortical bone were estimated to be 2384(± 130), 2471(± 90), 2504(± 120), 2327(± 90) and 2053(± 40) m s(-1) for the frequencies of 270, 836, 1402, 1965 and 2526 kHz, respectively. For trabecular bone, and in the same order of frequency values, the speeds of sound were 2140(± 130), 2300(± 100), 2219(± 200), 2133(± 130) and 1937(± 40) m s(-1), respectively. The average values of the attenuation coefficient for cortical bone were 33(± 9), 240(± 9) and 307(± 30) Np m(-1) for the frequencies of 270, 836, and 1402, respectively. For trabecular bone, and in the same order of frequency values, the average values of the attenuation coefficient were 34(± 13), 216(± 16) and 375(± 30) Np m(-1), respectively. For frequencies of 1.965 and 2.525 MHz, no measurable radiation force was detected with the setup used.
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Affiliation(s)
- Samuel Pichardo
- Department of Electrical Engineering, Lakehead University and Image-guided Interventions, Thunder Bay Regional Research Institute, 980 Oliver Road, Thunder Bay, ON, P7B 6V4, Canada.
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29
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Anderson CC, Bauer AQ, Holland MR, Pakula M, Laugier P, Bretthorst GL, Miller JG. Inverse problems in cancellous bone: estimation of the ultrasonic properties of fast and slow waves using Bayesian probability theory. THE JOURNAL OF THE ACOUSTICAL SOCIETY OF AMERICA 2010; 128:2940-8. [PMID: 21110589 PMCID: PMC3003723 DOI: 10.1121/1.3493441] [Citation(s) in RCA: 26] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/10/2010] [Revised: 08/23/2010] [Accepted: 08/31/2010] [Indexed: 05/05/2023]
Abstract
Quantitative ultrasonic characterization of cancellous bone can be complicated by artifacts introduced by analyzing acquired data consisting of two propagating waves (a fast wave and a slow wave) as if only one wave were present. Recovering the ultrasonic properties of overlapping fast and slow waves could therefore lead to enhancement of bone quality assessment. The current study uses Bayesian probability theory to estimate phase velocity and normalized broadband ultrasonic attenuation (nBUA) parameters in a model of fast and slow wave propagation. Calculations are carried out using Markov chain Monte Carlo with simulated annealing to approximate the marginal posterior probability densities for parameters in the model. The technique is applied to simulated data, to data acquired on two phantoms capable of generating two waves in acquired signals, and to data acquired on a human femur condyle specimen. The models are in good agreement with both the simulated and experimental data, and the values of the estimated ultrasonic parameters fall within expected ranges.
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Affiliation(s)
- Christian C Anderson
- Department of Physics, Washington University in St Louis, St Louis, Missouri 63130, USA
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30
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Wear KA. Cancellous bone analysis with modified least squares Prony's method and chirp filter: phantom experiments and simulation. THE JOURNAL OF THE ACOUSTICAL SOCIETY OF AMERICA 2010; 128:2191-203. [PMID: 20968389 PMCID: PMC9130964 DOI: 10.1121/1.3478779] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/10/2023]
Abstract
The presence of two longitudinal waves in porous media is predicted by Biot's theory and has been confirmed experimentally in cancellous bone. When cancellous bone samples are interrogated in through-transmission, these two waves can overlap in time. Previously, the Modified Least-Squares Prony's (MLSP) method was validated for estimation of amplitudes, attenuation coefficients, and phase velocities of fast and slow waves, but tended to overestimate phase velocities by up to about 5%. In the present paper, a pre-processing chirp filter to mitigate the phase velocity bias is derived. The MLSP/chirp filter (MLSPCF) method was tested for decomposition of a 500 kHz-center-frequency signal containing two overlapping components: one passing through a low-density-polyethylene plate (fast wave) and another passing through a cancellous-bone-mimicking phantom material (slow wave). The chirp filter reduced phase velocity bias from 100 m/s (5.1%) to 69 m/s (3.5%) (fast wave) and from 29 m/s (1.9%) to 10 m/s (0.7%) (slow wave). Similar improvements were found for 1) measurements in polycarbonate (fast wave) and a cancellous-bone-mimicking phantom (slow wave), and 2) a simulation based on parameters mimicking bovine cancellous bone. The MLSPCF method did not offer consistent improvement in estimates of attenuation coefficient or amplitude.
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Affiliation(s)
- Keith A Wear
- Center for Devices and Radiological Health, U.S. Food and Drug Administration, Room 3108, Building 62, 10903 New Hampshire Boulevard, Silver Spring, Maryland 20993, USA.
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31
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Hosokawa A. Effect of porosity distribution in the propagation direction on ultrasound waves through cancellous bone. IEEE TRANSACTIONS ON ULTRASONICS, FERROELECTRICS, AND FREQUENCY CONTROL 2010; 57:1320-8. [PMID: 20529708 DOI: 10.1109/tuffc.2010.1552] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/10/2023]
Abstract
Cancellous bone is a porous material composed of numerous trabecular elements, and its porosity changes according to its position within a bone. In this study, the effect of porosity distribution in the propagation direction on ultrasound waves through cancellous bone was numerically investigated using finite-difference time-domain (FDTD) simulations. Fifty four numerical models of cancellous bone were reconstructed from 3-D X-ray microcomputed tomographic (microCT) images at 6 positions in a bovine femoral bone. To generate trabecular structures with distinct porosity distributions, 3 erosion procedures were performed in which the trabecular elements in each cancellous bone model were eroded. In one procedure, erosion was uniformly distributed over the whole spatial region of the cancellous bone model, but in the other 2 procedures, the spatial distribution of erosion was changed in a specific direction. Fast and slow waves propagating through the 3-D microCT cancellous bone models in the porosity-distributed direction were simulated using the viscoelastic FDTD method. The wave amplitudes and propagation speeds of the fast and slow waves were measured for the cancellous bone models eroded by each procedure, and the effect of porosity distribution was investigated in terms of change in the trabecular microstructure. The results suggest that both wave amplitudes increased when porosity distribution was low and when trabecular structure was more uniform, but that the speed of the fast wave increased when porosity distribution was high and when longer trabecular elements were present.
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Affiliation(s)
- Atsushi Hosokawa
- Department of Electrical and Computer Engineering, Akashi National College of Technology, Hyogo, Japan.
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32
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Haïat G, Naili S. Independent scattering model and velocity dispersion in trabecular bone: comparison with a multiple scattering model. Biomech Model Mechanobiol 2010; 10:95-108. [PMID: 20490887 DOI: 10.1007/s10237-010-0220-z] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/05/2009] [Accepted: 04/26/2010] [Indexed: 10/19/2022]
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33
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Wear KA. Decomposition of two-component ultrasound pulses in cancellous bone using modified least squares prony method--phantom experiment and simulation. ULTRASOUND IN MEDICINE & BIOLOGY 2010; 36:276-87. [PMID: 20113862 PMCID: PMC9180631 DOI: 10.1016/j.ultrasmedbio.2009.06.1092] [Citation(s) in RCA: 16] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/26/2009] [Revised: 05/27/2009] [Accepted: 06/08/2009] [Indexed: 05/22/2023]
Abstract
Porous media such as cancellous bone often support the simultaneous propagation of two compressional waves. When small bone samples are interrogated in through-transmission with broadband sources, these two waves often overlap in time. The modified least-squares Prony's (MLSP) method was tested for decomposing a 500 kHz-center-frequency signal containing two overlapping components: one passing through a polycarbonate plate (to produce the "fast" wave) and another passing through a cancellous-bone-mimicking phantom (to produce the "slow" wave). The MLSP method yielded estimates of attenuation slopes accurate to within 7% (polycarbonate plate) and 2% (cancellous bone phantom). The MLSP method yielded estimates of phase velocities accurate to within 1.5% (both media). The MLSP method was also tested on simulated data generated using attenuation slopes and phase velocities corresponding to bovine cancellous bone. Throughout broad ranges of signal-to-noise ratio (SNR), the MLSP method yielded estimates of attenuation slope that were accurate to within 1.0% and estimates of phase velocity that were accurate to within 4.3% (fast wave) and 1.3% (slow wave).
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Affiliation(s)
- Keith A Wear
- Center for Devices and Radiological Health, U.S. Food and Drug Administration, Silver Spring, MD 20993, USA.
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Wear KA. Frequency dependence of average phase shift from human calcaneus in vitro. THE JOURNAL OF THE ACOUSTICAL SOCIETY OF AMERICA 2009; 126:3291-300. [PMID: 20000943 DOI: 10.1121/1.3257550] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/10/2023]
Abstract
If dispersion in a medium is weak and approximately linear with frequency (over the experimental band of frequencies), then it can be shown that the constant term in a polynomial representation of phase shift as a function of frequency can produce errors in measurements of phase-velocity differences in through-transmission, substitution experiments. A method for suppressing the effects of the constant phase shift in the context of the single-wave-model was tested on measurements from 30 cancellous human calcaneus samples in vitro. Without adjustment for constant phase shifts, the estimated phase velocity at 500 kHz was 1516+/-6 m/s (mean+/-standard error), and the estimated dispersion was -24+/-4 m/s MHz (mean+/-standard error). With adjustment for constant phase shifts, the estimated mean velocity decreased by 4-9 m/s, and the estimated magnitude of mean dispersion decreased by 50%-100%. The average correlation coefficient between the measured attenuation coefficient and frequency was 0.997+/-0.0026 (mean+/-standard deviation), suggesting that the signal for each sample was dominated by one wave. A single-wave, linearly dispersive model conformed to measured complex transfer functions from the 30 cancellous-bone samples with an average root-mean-square error of 1.9%+/-1.0%.
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Affiliation(s)
- Keith A Wear
- Center for Devices and Radiological Health, U. S. Food and Drug Administration, Silver Spring, Maryland 20993, USA.
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Pakula M, Padilla F, Laugier P. Influence of the filling fluid on frequency-dependent velocity and attenuation in cancellous bones between 0.35 and 2.5 MHz. THE JOURNAL OF THE ACOUSTICAL SOCIETY OF AMERICA 2009; 126:3301-10. [PMID: 20000944 DOI: 10.1121/1.3257233] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/10/2023]
Abstract
The paper is focused on experiments on human cancellous bones filled with different fluids with the goal of evaluating their contribution to velocity dispersion, absorption, and scattering mechanisms. The specimens were measured first filled with marrow and subsequently, after marrow removal, with water and alcohol. No significant influence of the fluids was evidenced on the attenuation coefficient. Given the absence of impact of viscosity of the saturating fluid, the authors hypothesized that the source of attenuation is associated with viscoelastic absorption in the solid trabeculae and with scattering. Alteration of scattering obtained by changing the acoustic impedance mismatch between the fluid (alcohol vs water) and the trabeculae was reflected neither in the attenuation nor in its slope. This led the authors to suggest that longitudinal-to-shear scattering together with absorption in the solid phase are candidates as main sources for the attenuation. The differences in velocity values indicate that the elastic properties of the fluid are main determinants of the phase velocity. This finding is particularly significant in the context of /in vivo/ measurements, because it demonstrates that the subject-dependent properties of marrow may partly explain the inter-subject variability of speed of sound values.
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Affiliation(s)
- Michal Pakula
- Institute of Mechanics and Applied Computer Science, Kazimierz Wielki University, 85-064 Bydgoszcz, Poland.
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Application of the multiscale FEM to the modeling of cancellous bone. Biomech Model Mechanobiol 2009; 9:87-102. [DOI: 10.1007/s10237-009-0161-6] [Citation(s) in RCA: 41] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/06/2009] [Accepted: 06/15/2009] [Indexed: 11/25/2022]
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Wear KA. The dependencies of phase velocity and dispersion on volume fraction in cancellous-bone-mimicking phantoms. THE JOURNAL OF THE ACOUSTICAL SOCIETY OF AMERICA 2009; 125:1197-201. [PMID: 19206892 PMCID: PMC9125424 DOI: 10.1121/1.3050310] [Citation(s) in RCA: 13] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/25/2023]
Abstract
Frequency-dependent phase velocity was measured in eight cancellous-bone-mimicking phantoms consisting of suspensions of randomly oriented nylon filaments (simulating trabeculae) in a soft-tissue-mimicking medium (simulating marrow). Trabecular thicknesses ranged from 152 to 356 mum. Volume fractions of nylon filament material ranged from 0% to 10%. Phase velocity varied approximately linearly with frequency over the range from 300 to 700 kHz. The increase in phase velocity (compared with phase velocity in a phantom containing no filaments) at 500 kHz was approximately proportional to volume fraction occupied by nylon filaments. The derivative of phase velocity with respect to frequency was negative and exhibited nonlinear, monotonically decreasing dependence on volume fraction. The dependencies of phase velocity and its derivative on volume fraction in these phantoms were similar to those reported in previous studies on (1) human cancellous bone and (2) phantoms consisting of parallel nylon wires immersed in water.
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Affiliation(s)
- Keith A Wear
- US Food and Drug Administration, Center for Devices and Radiological Health, HFZ-142, Rockville, Maryland 20852, USA.
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