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Liu X, Liao J, Patel M, Miramini S, Qu J, Zhang L. Effect of uncertain clinical conditions on the early healing and stability of distal radius fractures. COMPUTER METHODS AND PROGRAMS IN BIOMEDICINE 2023; 241:107774. [PMID: 37651819 DOI: 10.1016/j.cmpb.2023.107774] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/14/2023] [Revised: 08/18/2023] [Accepted: 08/21/2023] [Indexed: 09/02/2023]
Abstract
BACKGROUND AND OBJECTIVES The healing outcomes of distal radius fracture (DRF) treated with the volar locking plate (VLP) depend on surgical strategies and postoperative rehabilitation. However, the accurate prediction of healing outcomes is challenging due to a range of certainties related to the clinical conditions of DRF patients, including fracture geometry, fixation configuration, and physiological loading. The purpose of this study is to investigate the influence of uncertainty and variability in fracture/fixation parameters on the mechano-biology and biomechanical stability of DRF, using a probabilistic numerical approach based on the results from a series of experimental tests performed in this study. METHODS Six composite radius sawboneses fitted with titanium VLP (VLP 2.0, Austofix) were loaded to failure at a rate of 2 N/s. The testing results of the elastic and plastic behaviour of the VLP were used as inputs for a probabilistic-based computational model of DRF, which simulated mechano-regulated tissue differentiation and fixation elastic capacity at the fracture site. Finally, the probability of success in early indirect healing and fracture stabilisation was predicted. RESULTS The titanium VLP is a strong and ductile fixation whose flexibility and elastic capacity are governed by flexion working length and bone-to-plate distance, respectively. A fixation with optimised designs and configurations is critical to mechanically stabilising the early fracture site. Importantly, the uncertainty and variability in fracture/fixation parameters could compromise early DRF healing. The physiological loading uncertainty is the most adverse factor, followed by the negative impact of uncertainty in fracture geometry. CONCLUSIONS The VRP 2.0 fixation made of grade II titanium is a desirable fixation that is strong enough to resist irreparable deformation during early recovery and is also ductile to deform plastically without implant failure at late rehabilitation.
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Affiliation(s)
- Xuanchi Liu
- Department of Infrastructure Engineering, The University of Melbourne, Parkville, Victoria, Australia
| | - JinJing Liao
- Department of Infrastructure Engineering, The University of Melbourne, Parkville, Victoria, Australia
| | - Minoo Patel
- Centre for Limb Lengthening & Reconstruction, Epworth Hospital Richmond, Richmond, Victoria, Australia
| | - Saeed Miramini
- Department of Infrastructure Engineering, The University of Melbourne, Parkville, Victoria, Australia
| | - Ji Qu
- UCL Queen Square Institute of Neurology, University College London, Queen Square, London, UK
| | - Lihai Zhang
- Department of Infrastructure Engineering, The University of Melbourne, Parkville, Victoria, Australia.
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2
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Hoffmeister BK, Main EN, Newman WR, Ebron SC, Huang J. Frequency dependence of the ultrasonic power reflected from the water-tissue interface of human cancellous bone in vitro. THE JOURNAL OF THE ACOUSTICAL SOCIETY OF AMERICA 2022; 152:2082. [PMID: 36319263 DOI: 10.1121/10.0014417] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/19/2022] [Accepted: 09/15/2022] [Indexed: 06/16/2023]
Abstract
Numerous studies have performed in vitro ultrasonic measurements of cancellous bone in water to develop techniques for ultrasonic bone assessment. Because cancellous bone is a highly porous medium, ultrasonic reflections at the water-bone interface may be frequency dependent. The goal of this study was to investigate the effect of porosity on the frequency dependence of the reflected power. Ultrasonic measurements were performed in a water tank at room temperature on 15 specimens of cancellous bone prepared from the proximal end of 9 human femurs using single element, broadband transducers with center frequencies of 3.5, 5, 7.5, and 10 MHz. Power spectra of pulses reflected from the water-specimen interface were corrected for the frequency response of the measurement system to obtain the reflected power in decibels RdB(f). To suppress random phase cancellation effects, RdB(f) was averaged over multiple sites on multiple specimens. A frequency dependence of RdB(f) was observed in the 2.6-10 MHz range. The frequency dependence was moderate, with a maximum change of less than 6 dB over the entire frequency range. RdB(f) was greatest for low porosity specimens. The frequency averaged intensity reflection coefficient ranged from 7.4 × 10-4 to 7.8 × 10-3 for high and low porosity specimen groups, respectively.
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Affiliation(s)
| | - Evan N Main
- Department of Physics, Rhodes College, Memphis, Tennessee 38112, USA
| | - Will R Newman
- Department of Physics, Rhodes College, Memphis, Tennessee 38112, USA
| | - Sheldon C Ebron
- Department of Physics, Rhodes College, Memphis, Tennessee 38112, USA
| | - Jinsong Huang
- College of Medicine, University of Tennessee Health Science Center, Memphis, Tennessee 38163, USA
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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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Pakula M. What kind of waves are measured in trabecular bone? ULTRASONICS 2022; 123:106692. [PMID: 35176689 DOI: 10.1016/j.ultras.2022.106692] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/28/2021] [Revised: 01/06/2022] [Accepted: 01/17/2022] [Indexed: 06/14/2023]
Abstract
The paper discusses the fundamental mechanisms underlying the interaction between ultrasound and trabecular bone, which is considered a two-phase material. When fluid-saturated cancellous bone is interrogated by ultrasound, in some cases, one or two wave modes are observed. Many authors claim that these waves correspond to the fast and slow waves predicted by Biot's theory of elastic wave propagation in fluid-saturated porous media. Within our analysis of the physical conditions, predictions of the existing two-phase models of the propagation of ultrasonic waves in the material as well as numerical simulations for fluid-saturated trabecular bone were performed. On the basis of the theoretical results (from numerical studies) and arguments presented in this paper, we aimed to answer the question of whether two waves observed in ultrasonic wave transmission studies can be interpreted as the fast and slow waves predicted by Biot's theory.
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Affiliation(s)
- Michal Pakula
- Faculty of Mechatronics, Kazimierz Wielki University in Bydgoszcz, Poland.
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5
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Xie W, Feng T, Yu D, Ta D, Cheng L, Cheng Q. Photoacoustic characterization of bone physico-chemical information. BIOMEDICAL OPTICS EXPRESS 2022; 13:2668-2681. [PMID: 35774314 PMCID: PMC9203098 DOI: 10.1364/boe.457278] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/04/2022] [Revised: 03/27/2022] [Accepted: 03/28/2022] [Indexed: 06/15/2023]
Abstract
Osteoporosis usually alters the chemical composition and physical microstructure of bone. Currently, most clinical techniques for bone assessment are focused on the either bone microstructure or bone mineral density (BMD). In this study, a novel multi-wavelength photoacoustic time-frequency spectral analysis (MWPA-TFSA) method was introduced based on the optical absorption spectra and photoacoustic effects of biological macromolecules, which evaluates changes in bone chemical composition and microstructure. The results demonstrated that osteoporotic bones had decreased BMD, more lipids, and wider trabecular separation filled with larger marrow clusters, which were consistent with multiple gold-standard results, suggesting that the MWPA-TFSA method has the potential to provide a thorough bone physico-chemical information evaluation noninvasively and nonradiatively.
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Affiliation(s)
- Weiya Xie
- Institute of Acoustics, School of Physics Science and Engineering, Tongji University, Shanghai, China
- The Key Laboratory of Spine and Spinal Cord Injury Repair and Regeneration, Ministry of Education; Department of Orthopaedics, Tongji Hospital, Tongji University School of Medicine, Shanghai, China
- These authors contributed equally to this paper
| | - Ting Feng
- Institute of Acoustics, School of Physics Science and Engineering, Tongji University, Shanghai, China
- School of Electronic and Optical Engineering, Nanjing University of Science and Technology, Nanjing, China
- These authors contributed equally to this paper
| | - Dong Yu
- Institute of Acoustics, School of Physics Science and Engineering, Tongji University, Shanghai, China
| | - Dean Ta
- Department of Electronic Engineering, Fudan University, Shanghai, China
| | - Liming Cheng
- The Key Laboratory of Spine and Spinal Cord Injury Repair and Regeneration, Ministry of Education; Department of Orthopaedics, Tongji Hospital, Tongji University School of Medicine, Shanghai, China
| | - Qian Cheng
- Institute of Acoustics, School of Physics Science and Engineering, Tongji University, Shanghai, China
- The Key Laboratory of Spine and Spinal Cord Injury Repair and Regeneration, Ministry of Education; Department of Orthopaedics, Tongji Hospital, Tongji University School of Medicine, Shanghai, China
- Shanghai Research Institute for Intelligent Autonomous Systems, Shanghai, China
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Numerical Investigations of the Fractional-Order Mathematical Model Underlying Immune-Chemotherapeutic Treatment for Breast Cancer Using the Neural Networks. FRACTAL AND FRACTIONAL 2022. [DOI: 10.3390/fractalfract6040184] [Citation(s) in RCA: 5] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 02/04/2023]
Abstract
The aim of this work is to design a stochastic framework to solve the fractional-order differential model based on the breast cancer progression during the immune-chemotherapeutic treatment phase, including certain control parameters such as anti-cancer medications, ketogenic diet and immune boosters. The developed model considers tumor density progression throughout chemotherapy treatment, as well as an immune response during normal cell–tumor cell interaction. This study’s subject seems to be to demonstrate the implications and significance of the fractional-order breast cancer mathematical model. The goal of these studies is to improve accuracy in the breast cancer model by employing fractional derivatives. This study also includes an integer, nonlinear mathematical system with immune-chemotherapeutic treatment impacts. The mathematical system divides the fractional-order breast cancer mathematical model among four manifestations: normal cell population (N), tumor cells (T), immune response class (I), and estrogen compartment (E), i.e., (NTIE). The fractional-order NTIE mathematical system is still not published previously, nor has it ever been addressed employing the stochastic solvers’ strength. To solve a fractional-order NTIE mathematical system, stochastic solvers based on the Levenberg–Marquardt backpropagation scheme (LMBS) and neural networks (NNs), namely, LMBNNs, are been constructed. To solve the fractional-order NTIE mathematical model, three cases with varying values for this same fractional order have been supplied. The statistics used to offer the numerical solutions of the fractional-order NTIE mathematical model are divided as follows: 75% in training, 15% in testing, and 10% in the authorization. The acquired numerical findings were compared using the reference solutions to determine the accuracy of the LMBNNs using Adams–Bashforth–Moulton. The numerical performances employing error histograms (EHs), state transitions (STs), regression, correlation, including mean square error (MSE) have been further supplied to authenticate overall capability, competence, validity, consistency, as well as exactness of such LMBNNs.
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Liu X, Miramini S, Patel M, Liao J, Shidid D, Zhang L. Influence of therapeutic grip exercises induced loading rates in distal radius fracture healing with volar locking plate fixation. COMPUTER METHODS AND PROGRAMS IN BIOMEDICINE 2022; 215:106626. [PMID: 35051836 DOI: 10.1016/j.cmpb.2022.106626] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/11/2021] [Revised: 12/25/2021] [Accepted: 01/07/2022] [Indexed: 06/14/2023]
Abstract
BACKGROUND AND OBJECTIVE Therapeutic exercises could potentially enhance the healing of distal radius fractures (DRFs) treated with volar locking plate (VLP). However, the healing outcomes are highly dependant on the patient-specific fracture geometries (e.g., gap size) and the loading conditions at the fracture site (e.g., loading frequency) resulted from different types of therapeutic exercises. The purpose of this study is to investigate the effects of different loading frequencies induced by therapeutic exercises on the biomechanical microenvironment of the fracture site and the transport of cells and growth factors within the fracture callus, ultimately the healing outcomes. This is achieved through numerical modelling and mechanical testing. METHODS Five radius sawbones specimens (Pacific Research Laboratories, Vashon, USA) fixed with VLP (VRP2.0+, Austofix) were mechanically tested using dynamic test instrument (INSTRON E3000, Norwood, MA). The loading protocol used in mechanical testing involved a series of cyclic axial compression tests representing hand and finger therapeutic exercises. The relationship between the dynamic loading rate (i.e., loading frequency) and dynamic stiffness of the construct was established and used as inputs to a developed numerical model for studying the dynamic loading induced cells and growth factors in fracture site and biomechanical stimuli required for healing. RESULTS There is a strong positive linear relationship between the loading rate and axial stiffness of the construct fixed with VLP. The loading rates induced by the moderate frequencies (i.e., 1-2 Hz) could promote endochondral ossification, whereas relatively high loading frequencies (i.e., over 3 Hz) may hinder the healing outcomes or lead to non-union. In addition, a dynamic loading frequency of 2 Hz in combination of a fracture gap size of 3 mm could produce a better healing outcome by enhancing the transport of cells and growth factors at the fracture site in comparison to free diffusion (i.e. without loading), and thereby produces a biomechanical microenvironment which is favourable for healing. CONCLUSION The experimentally validated numerical model presented in this study could potentially contribute to the design of effective patient-specific therapeutic exercises for better healing outcomes. Importantly, the model results demonstrate that therapeutic grip exercises induced dynamic loading could produce a better biomechanical microenvironment for healing without compromising the mechanical stability of the overall volar locking plate fixation construct.
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Affiliation(s)
- Xuanchi Liu
- Department of Infrastructure Engineering, The University of Melbourne, Parkville, Victoria, Australia
| | - Saeed Miramini
- Department of Infrastructure Engineering, The University of Melbourne, Parkville, Victoria, Australia
| | - Minoo Patel
- Centre for Limb Lengthening and Reconstruction, Epworth Hospital Richmond, Richmond, Victoria, Australia
| | - JinJing Liao
- Department of Infrastructure Engineering, The University of Melbourne, Parkville, Victoria, Australia
| | - Darpan Shidid
- RMIT Centre for Additive Manufacture, RMIT University, Melbourne, Victoria, Australia
| | - Lihai Zhang
- Department of Infrastructure Engineering, The University of Melbourne, Parkville, Victoria, Australia.
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Influence of Higher Order Viscous and Thermal Effects on an Ultrasonic Wave Reflected from the First Interface of a Porous Material. MATERIALS 2022; 15:ma15030798. [PMID: 35160744 PMCID: PMC8836579 DOI: 10.3390/ma15030798] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 12/09/2021] [Revised: 01/16/2022] [Accepted: 01/17/2022] [Indexed: 02/05/2023]
Abstract
Ultrasound propagation in porous materials involves some higher order physical parameters whose importance depends on the acoustic characteristics of the materials. This article concerns the study of the influence of two parameters recently introduced, namely, the viscous and thermal surfaces, on the acoustic wave reflected by the first interface of a porous material with a rigid structure. These two parameters describe the fluid/structure interactions in a porous medium during the propagation of the acoustic wave in the high-frequency regime. Both viscous and thermal surfaces are involved in Laurent expansion, which is limited to the dynamic tortuosity and compressibility to a higher order and corrects the visco-thermal losses. A sensitivity study is performed on the modulus of the reflection coefficient at the first interface as a function of frequency and on the waveforms reflected by the porous material in the time domain. The results of this study show that highly absorbent porous materials are the most sensitive to viscous and thermal surfaces, which makes the consideration of these two parameters paramount for the characterization of highly absorbent porous materials using the waves reflected from the first interface.
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9
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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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10
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Di Giulio E, Auriemma F, Napolitano M, Dragonetti R. Acoustic and thermoacoustic properties of an additive manufactured lattice structure. THE JOURNAL OF THE ACOUSTICAL SOCIETY OF AMERICA 2021; 149:3878. [PMID: 34241447 DOI: 10.1121/10.0005085] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/01/2021] [Accepted: 05/07/2021] [Indexed: 06/13/2023]
Abstract
With the advent of additive manufacturing, lattice structures can be printed with precisely controlled geometries. In this way, it is possible to realize porous samples with specific acoustic and thermoacoustic characteristics. However, to this aim and prior to the manufacturing process, it is fundamental to have a design tool that can predict the behaviour of the lattices. In the literature, Luu, Perrot, and Panneton [Acta Acust. United Ac. 103, 1050 (2017)] provide a model to characterize transport parameters of fibrous material with a certain fiber orientation with respect to the direction of wave propagation. In this work, finite element numerical simulations are used to improve their model in order to compute the thermoviscous functions of lattice structures composed of cylindrical struts arranged in Tetragonal Body Centred cells. New correlations for transport parameters are suggested, which are finally coupled with the semi-phenomenological model of Johnson-Champoux-Allard-Lafarge to obtain the complex density and bulk modulus of the equivalent fluid. These results are compared with the measurements carried out on two 3-dimensional-printed samples with hybrid impedance tube techniques.
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Affiliation(s)
- Elio Di Giulio
- Department of Industrial Engineering, University of Naples Federico II, 80125 Naples, Italy
| | - Fabio Auriemma
- Department of Mechanical and Industrial Engineering, Tallinn University of Technology- TalTech, 19086 Tallinn, Estonia
| | - Marialuisa Napolitano
- Department of Industrial Engineering, University of Naples Federico II, 80125 Naples, Italy
| | - Raffaele Dragonetti
- Department of Industrial Engineering, University of Naples Federico II, 80125 Naples, Italy
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11
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Xie W, Feng T, Zhang M, Li J, Ta D, Cheng L, Cheng Q. Wavelet transform-based photoacoustic time-frequency spectral analysis for bone assessment. PHOTOACOUSTICS 2021; 22:100259. [PMID: 33777692 PMCID: PMC7985564 DOI: 10.1016/j.pacs.2021.100259] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/13/2020] [Revised: 02/17/2021] [Accepted: 03/01/2021] [Indexed: 05/08/2023]
Abstract
In this study, we investigated the feasibility of using photoacoustic time-frequency spectral analysis (PA-TFSA) for evaluating the bone mineral density (BMD) and bone structure. Simulations and ex vivo experiments on bone samples with different BMDs and mean trabecular thickness (MTT) were conducted. All photoacoustic signals were processed using the wavelet transform-based PA-TFSA. The power-weighted mean frequency (PWMF) was evaluated to obtain the main frequency component at different times. The y-intercept, midband-fit, and slope of the linearly fitted curve of the PWMF over time were also quantified. The results show that the osteoporotic bone samples with lower BMD and thinner MTT have higher frequency components and lower acoustic frequency attenuation over time, thus higher y-intercept, midband-fit, and slope. The midband-fit and slope were found to be sensitive to the BMD; therefore, both parameters could be used to distinguish between osteoporotic and normal bones (p < 0.05).
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Key Words
- ARTB, area ratio of trabecular bone
- BMD, bone mineral density
- Bone assessment
- CWT, continuous wavelet transform
- DEXA, dual energy X-ray absorptiometry
- EDTA, ethylenediaminetetraacetic acid
- MTT, mean trabecular thickness
- PA, photoacoustic
- PA-TFS, photoacoustic time-frequency spectrum
- PA-TFSA, photoacoustic time-frequency spectral analysis
- PWMF, power-weighted mean frequency
- Photoacoustic measurement
- QUS, quantitative ultrasound
- ROI, region of interest
- Time-frequency spectral analysis
- US, ultrasound
- Wavelet transform
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Affiliation(s)
- Weiya Xie
- Institute of Acoustics, School of Physics Science and Engineering, Tongji University, Shanghai, PR China
- The Key Laboratory of Spine and Spinal Cord Injury Repair and Regeneration, Ministry of Education, Department of Orthopaedics, Tongji Hospital, Tongji University School of Medicine, Shanghai, PR China
| | - Ting Feng
- Institute of Acoustics, School of Physics Science and Engineering, Tongji University, Shanghai, PR China
- School of Electronic and Optical Engineering, Nanjing University of Science and Technology, Nanjing, PR China
| | - Mengjiao Zhang
- Institute of Acoustics, School of Physics Science and Engineering, Tongji University, Shanghai, PR China
| | - Jiayan Li
- Institute of Acoustics, School of Physics Science and Engineering, Tongji University, Shanghai, PR China
| | - Dean Ta
- Department of Electronic Engineering, Fudan University, Shanghai, PR China
| | - Liming Cheng
- The Key Laboratory of Spine and Spinal Cord Injury Repair and Regeneration, Ministry of Education, Department of Orthopaedics, Tongji Hospital, Tongji University School of Medicine, Shanghai, PR China
| | - Qian Cheng
- Institute of Acoustics, School of Physics Science and Engineering, Tongji University, Shanghai, PR China
- The Key Laboratory of Spine and Spinal Cord Injury Repair and Regeneration, Ministry of Education, Department of Orthopaedics, Tongji Hospital, Tongji University School of Medicine, Shanghai, PR China
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Roncen R, Fellah ZEA, Ogam E. Bayesian inference of human bone sample properties using ultrasonic reflected signals. THE JOURNAL OF THE ACOUSTICAL SOCIETY OF AMERICA 2020; 148:3797. [PMID: 33379902 DOI: 10.1121/10.0002878] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/22/2020] [Accepted: 11/15/2020] [Indexed: 06/12/2023]
Abstract
The non-intrusiveness and low cost of ultrasonic interrogation is motivating the development of new means of detection of osteoporosis and other bone deficiencies. Bone is a porous media saturated with a viscous fluid and could thus be well characterized by the Biot model. The main purpose of this work is to present an in vitro methodology for the identification of the properties and structural parameters of the bone, adopting a statistical Bayesian inference technique using ultrasonic reflected signals at normal incidence. It is, in this respect, a companion paper to a previous work [J. Acoust. Soc. Am. 146, 3 (2019), pp. 1629-1640], where ultrasonic transmitted signals were considered. This approach allows the retrieval of some important parameters that characterize the bone structure and associated uncertainties. The method was applied to seven samples of bone extracted from femoral heads, immersed in water, and exposed to ultrasonic signals with a center frequency of ≈500 kHz. For all seven samples, signals at different sites were acquired to check the method robustness. The porosity, pore mean size and standard deviation, and the porous frame bulk modulus were all successfully identified using only ultrasonic reflected signals.
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Affiliation(s)
- R Roncen
- ONERA/Département Multi-Physique pour l'Énergétique, Université de Toulouse, F-31055, Toulouse, France
| | - Z E A Fellah
- Laboratoire de Mécanique et d'Acoustique, Centre National de la Recherche Scientifique, Unité Mixte de Recherche 7031, Aix-Marseille Université, Centrale Marseille, F-13402 Marseille Cedex 20, France
| | - E Ogam
- Laboratoire de Mécanique et d'Acoustique, Centre National de la Recherche Scientifique, Unité Mixte de Recherche 7031, Aix-Marseille Université, Centrale Marseille, F-13402 Marseille Cedex 20, France
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Otero J, Felis I, Herrero A, Merchán JA, Ardid M. Bragg Peak Localization with Piezoelectric Sensors for Proton Therapy Treatment. SENSORS 2020; 20:s20102987. [PMID: 32466140 PMCID: PMC7287827 DOI: 10.3390/s20102987] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 03/20/2020] [Revised: 05/06/2020] [Accepted: 05/22/2020] [Indexed: 11/16/2022]
Abstract
A full chain simulation of the acoustic hadrontherapy monitoring for brain tumours is presented in this work. For the study, a proton beam of 100 MeV is considered. In the first stage, Geant4 is used to simulate the energy deposition and to study the behaviour of the Bragg peak. The energy deposition in the medium produces local heating that can be considered instantaneous with respect to the hydrodynamic time scale producing a sound pressure wave. The resulting thermoacoustic signal has been subsequently obtained by solving the thermoacoustic equation. The acoustic propagation has been simulated by FEM methods in the brain and the skull, where a set of piezoelectric sensors are placed. Last, the final received signals in the sensors have been processed in order to reconstruct the position of the thermal source and, thus, to determine the feasibility and accuracy of acoustic beam monitoring in hadrontherapy.
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Affiliation(s)
- Jorge Otero
- Institut d’Investigació per a la Gestió Integrada de les Zones Costaneres (IGIC), Universitat Politècnica de València (UPV), Gandia, 46730 València, Spain;
- Correspondence: ; Tel.: +34-968-197-521 (ext. 125)
| | - Ivan Felis
- Centro Tecnológico Naval y del Mar (CTN), Fuente Álamo, 30320 Murcia, Spain;
| | - Alicia Herrero
- Institut de Matemàtica Multidisciplinar, Universitat Politècnica de València (UPV), 46022 València, Spain;
| | - José A. Merchán
- Grupo de Física Nuclear Aplicada y Simulación, Universidad Pedagógica y Tecnológica de Colombia (UPTC), 150003 Tunja, Colombia;
| | - Miguel Ardid
- Institut d’Investigació per a la Gestió Integrada de les Zones Costaneres (IGIC), Universitat Politècnica de València (UPV), Gandia, 46730 València, Spain;
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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: 15] [Impact Index Per Article: 3.8] [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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Liu J, Lan L, Zhou J, Yang Y. Influence of cancellous bone microstructure on ultrasonic attenuation: a theoretical prediction. Biomed Eng Online 2019; 18:103. [PMID: 31653267 PMCID: PMC6815062 DOI: 10.1186/s12938-019-0724-4] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/08/2019] [Accepted: 10/16/2019] [Indexed: 02/07/2023] Open
Abstract
Background Quantitative ultrasound has been used for the assessment of cancellous bone status. The attenuation mechanisms of cancellous bone, however, have not been well understood, because the microstructure of cancellous bone is significantly inhomogeneous and the interaction between ultrasound and the microstructure of cancellous bone is complex. In this study, a theoretical approach was applied to investigate the influence of the microstructure of cancellous bone on ultrasonic attenuation. Results The scattering from a trabecular cylinder was significantly angle dependent. The dependencies of the ultrasonic attenuation on frequency, scatterer size, and porosity were explored from the theoretical calculation. Prediction results showed that the ultrasonic attenuation increased with the increase of frequency and decreased linearly with the increase in porosity, and the broadband ultrasound attenuation decreased with the increase in porosity. All these predicted trends were consistent with published experimental data. In addition, our model successfully explained the principle of broadband ultrasound attenuation measurement (i.e., the attenuation over the frequency range 0.3–0.65 MHz was approximately linearly proportional to frequency) by considering the contributions of scattering and absorption to attenuation. Conclusion The proposed theoretical model may be a potentially valuable tool for understanding the interaction of ultrasound with cancellous bone.
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Affiliation(s)
- Jinjin Liu
- Department of Radiology, The First Affiliated Hospital of Wenzhou Medical University, Ouhai Qu, Wenzhou, 325000, Zhejiang, China
| | - Li Lan
- Department of Ultrasonography, The First Affiliated Hospital of Wenzhou Medical University, Wenzhou, Zhejiang, China
| | - Jiafeng Zhou
- Department of Radiology, The First Affiliated Hospital of Wenzhou Medical University, Ouhai Qu, Wenzhou, 325000, Zhejiang, China
| | - Yunjun Yang
- Department of Radiology, The First Affiliated Hospital of Wenzhou Medical University, Ouhai Qu, Wenzhou, 325000, Zhejiang, China.
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16
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Roncen R, Fellah ZEA, Piot E, Ogam E. Bayesian inference of a human bone and biomaterials using ultrasonic transmitted signals. THE JOURNAL OF THE ACOUSTICAL SOCIETY OF AMERICA 2019; 146:1629. [PMID: 31590502 DOI: 10.1121/1.5125263] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/26/2019] [Accepted: 08/20/2019] [Indexed: 06/10/2023]
Abstract
Ultrasonic techniques could be good candidates to aid the assessment of osteoporosis detection, due to their non-intrusiveness and low cost. While earlier studies made use of the measured ultrasonic phase velocity and attenuation inside the bone, very few have considered an inverse identification of both the intrinsic pore microstructure and the mechanical properties of the bone, based on Biot's model. The main purpose of this work is to present an in vitro methodology for bone identification, adopting a statistical Bayesian inference technique using ultrasonic transmitted signals, which allows the retrieval of the identified parameters and their uncertainty. In addition to the bone density, Young's modulus and Poisson's ratio, the bone pore microstructure parameters (porosity, tortuosity, and viscous length) are identified. These additional microstructural terms could improve the knowledge on the correlations between bone microstructure and bone diseases, since they provide more information on the trabecular structure. In general, the exact properties of the saturating fluid are unknown (bone marrow and blood in the case of bone study) so in this work, the fluid properties (water) are identified during the inference as a proof of concept.
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Affiliation(s)
- R Roncen
- ONERA/Département Multi-Physique pour l'énergétique, Université de Toulouse, F-31055, Toulouse, France
| | - Z E A Fellah
- Laboratoire de Mécanique et d'Acoustique, Centre National de la Recherche Scientifique, Unité Mixte de Recherche 7031, Aix-Marseille Université, Centrale Marseille, F-13402 Marseille Cedex 20, France
| | - E Piot
- ONERA/Département Multi-Physique pour l'énergétique, Université de Toulouse, F-31055, Toulouse, France
| | - E Ogam
- Laboratoire de Mécanique et d'Acoustique, Centre National de la Recherche Scientifique, Unité Mixte de Recherche 7031, Aix-Marseille Université, Centrale Marseille, F-13402 Marseille Cedex 20, France
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17
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The effect of charge density on the velocity and attenuation of ultrasound waves in human cancellous bone. J Biomech 2018; 79:54-57. [PMID: 30122518 DOI: 10.1016/j.jbiomech.2018.07.048] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/30/2018] [Revised: 07/19/2018] [Accepted: 07/31/2018] [Indexed: 11/23/2022]
Abstract
Cancellous bone is a highly porous material, and two types of waves, fast and slow, are observed when ultrasound is used for detecting bone diseases. There are several possible stimuli for bone remodelling processes, including bone fluid flow, streaming potential, and piezoelectricity. Poroelasticity has been widely used for elucidating the bone fluid flow phenomenon, but the combination of poroelasticity with charge density has not been introduced. Theoretically, general poroelasticity with a varying charge density is employed for determining the relationship between wave velocity and attenuation with charge density. Fast wave velocity and attenuation are affected by porosity as well as charge density; however, for a slow wave, both slow wave velocity and attenuation are not as sensitive to the effect of charge density as they are for a fast wave. Thus, employing human femoral data, we conclude that charged ions gather on trabecular struts, and the fast wave, which moves along the trabecular struts, is significantly affected by charge density.
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18
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Krödel S, Palermo A, Daraio C. Acoustic properties of porous microlattices from effective medium to scattering dominated regimes. THE JOURNAL OF THE ACOUSTICAL SOCIETY OF AMERICA 2018; 144:319. [PMID: 30075686 DOI: 10.1121/1.5046068] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/13/2017] [Accepted: 06/24/2018] [Indexed: 06/08/2023]
Abstract
Microlattices are architected materials that allow for an unprecedented control of mechanical properties (e.g., stiffness, density, and Poisson's coefficient). In contrast to their quasi-static mechanical properties, the acoustic properties of microlattices remain largely unexplored. This paper analyzes the acoustic response of periodic millimeter-sized microlattices immersed in water using experiments and numerical simulations. Microlattices are fabricated using high-precision stereolithographic three-dimensional printing in a large variety of porosities and lattice topologies. This paper shows that the acoustic propagation undergoes a frequency dependent transition from a classic poroelastic behaviour that can be described by Biot's theory to a regime that is dominated by scattering effects. Biot's acoustic parameters are derived from direct simulations of the microstructure using coupled fluid and solid finite elements. The wave speeds predicted with Biot's theory agree well with the experimental measures. Within the scattering regime, the signals show a strong attenuation and dispersion, which is characterized by a cut-off frequency. The strong dispersion results in a frequency dependent group velocity. A simplified model of an elastic cylindrical scatterer allows predicting the signal attenuation and dispersion observed experimentally. The results in this paper pave the way for the creation of microlattice materials for the control of ultrasonic waves across a wide range of frequencies.
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Affiliation(s)
- Sebastian Krödel
- Department of Mechanical and Process Engineering, ETH Zürich, Tannenstrasse 3, 8092, Zürich, Switzerland
| | - Antonio Palermo
- Department of Civil, Chemical, Environmental and Materials Engineering, University of Bologna, Viale del Risorgimento 2, Bologna 40136, Italy
| | - Chiara Daraio
- Division of Engineering and Applied Science, California Institute of Technology, 1200 California Boulevard, Pasadena, California 91125, USA
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19
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Yoon K, Lee W, Croce P, Cammalleri A, Yoo SS. Multi-resolution simulation of focused ultrasound propagation through ovine skull from a single-element transducer. Phys Med Biol 2018; 63:105001. [PMID: 29658494 DOI: 10.1088/1361-6560/aabe37] [Citation(s) in RCA: 26] [Impact Index Per Article: 4.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/07/2023]
Abstract
Transcranial focused ultrasound (tFUS) is emerging as a non-invasive brain stimulation modality. Complicated interactions between acoustic pressure waves and osseous tissue introduce many challenges in the accurate targeting of an acoustic focus through the cranium. Image-guidance accompanied by a numerical simulation is desired to predict the intracranial acoustic propagation through the skull; however, such simulations typically demand heavy computation, which warrants an expedited processing method to provide on-site feedback for the user in guiding the acoustic focus to a particular brain region. In this paper, we present a multi-resolution simulation method based on the finite-difference time-domain formulation to model the transcranial propagation of acoustic waves from a single-element transducer (250 kHz). The multi-resolution approach improved computational efficiency by providing the flexibility in adjusting the spatial resolution. The simulation was also accelerated by utilizing parallelized computation through the graphic processing unit. To evaluate the accuracy of the method, we measured the actual acoustic fields through ex vivo sheep skulls with different sonication incident angles. The measured acoustic fields were compared to the simulation results in terms of focal location, dimensions, and pressure levels. The computational efficiency of the presented method was also assessed by comparing simulation speeds at various combinations of resolution grid settings. The multi-resolution grids consisting of 0.5 and 1.0 mm resolutions gave acceptable accuracy (under 3 mm in terms of focal position and dimension, less than 5% difference in peak pressure ratio) with a speed compatible with semi real-time user feedback (within 30 s). The proposed multi-resolution approach may serve as a novel tool for simulation-based guidance for tFUS applications.
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Affiliation(s)
- Kyungho Yoon
- Department of Radiology, Brigham and Women's Hospital, Harvard Medical School, Boston, MA, United States of America
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20
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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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21
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Dragna D, Pineau P, Blanc-Benon P. A generalized recursive convolution method for time-domain propagation in porous media. THE JOURNAL OF THE ACOUSTICAL SOCIETY OF AMERICA 2015; 138:1030-1042. [PMID: 26328719 DOI: 10.1121/1.4927553] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/05/2023]
Abstract
An efficient numerical method, referred to as the auxiliary differential equation (ADE) method, is proposed to compute convolutions between relaxation functions and acoustic variables arising in sound propagation equations in porous media. For this purpose, the relaxation functions are approximated in the frequency domain by rational functions. The time variation of the convolution is thus governed by first-order differential equations which can be straightforwardly solved. The accuracy of the method is first investigated and compared to that of recursive convolution methods. It is shown that, while recursive convolution methods are first or second-order accurate in time, the ADE method does not introduce any additional error. The ADE method is then applied for outdoor sound propagation using the equations proposed by Wilson et al. in the ground [(2007). Appl. Acoust. 68, 173-200]. A first one-dimensional case is performed showing that only five poles are necessary to accurately approximate the relaxation functions for typical applications. Finally, the ADE method is used to compute sound propagation in a three-dimensional geometry over an absorbing ground. Results obtained with Wilson's equations are compared to those obtained with Zwikker and Kosten's equations and with an impedance surface for different flow resistivities.
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Affiliation(s)
- Didier Dragna
- Laboratoire de Mécanique des Fluides et d'Acoustique, Unité Mixte de Recherche, Centre National de la Recherche Scientifique 5509, École Centrale de Lyon, Université de Lyon, 36, avenue Guy de Collongue, 69134 Écully Cedex, France
| | - Pierre Pineau
- Laboratoire de Mécanique des Fluides et d'Acoustique, Unité Mixte de Recherche, Centre National de la Recherche Scientifique 5509, École Centrale de Lyon, Université de Lyon, 36, avenue Guy de Collongue, 69134 Écully Cedex, France
| | - Philippe Blanc-Benon
- Laboratoire de Mécanique des Fluides et d'Acoustique, Unité Mixte de Recherche, Centre National de la Recherche Scientifique 5509, École Centrale de Lyon, Université de Lyon, 36, avenue Guy de Collongue, 69134 Écully Cedex, France
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22
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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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23
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Kawasaki S, Ueda R, Hasegawa A, Fujita A, Mihata T, Matsukawa M, Neo M. Ultrasonic wave properties of human bone marrow in the femur and tibia. THE JOURNAL OF THE ACOUSTICAL SOCIETY OF AMERICA 2015; 138:EL83-EL87. [PMID: 26233067 DOI: 10.1121/1.4922764] [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
Ultrasonic wave properties of human bone marrow obtained in the femur and tibia were measured using an ultrasound pulse technique. The measured frequency range was 4-10 MHz, and the temperature range was 30 °C-40 °C. The sound velocity was 1410 m/s, and the attenuation coefficient was 4.4 dB/cm at 36 °C (10 MHz). These values decreased with temperature. Site dependence and individual differences in elderly human bone marrow were negligible. The slopes of the attenuation coefficient were estimated by a power law. The values of the exponent n were 2.0 (30 °C-38 °C) and 2.3 (40 °C).
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Affiliation(s)
- Satoshi Kawasaki
- Laboratory of Ultrasonic Electronics, Doshisha University, 1-3 Tatara-Miyakodani, Kyotanabe, Kyoto 610-0321, Japan
| | - Ryohei Ueda
- Laboratory of Ultrasonic Electronics, Doshisha University, 1-3 Tatara-Miyakodani, Kyotanabe, Kyoto 610-0321, Japan
| | - Akihiko Hasegawa
- Department of Orthopedic Surgery, Daiichi Towakai Hospital, 2-17, Miyano-cho, Takatsuki, Osaka 569-0081, Japan
| | - Akifumi Fujita
- Department of Orthopedic Surgery, Daiichi Towakai Hospital, 2-17, Miyano-cho, Takatsuki, Osaka 569-0081, Japan
| | - Teruhisa Mihata
- Department of Orthopedic Surgery, Osaka Medical College, 2-7, Daigaku-machi, Takatsuki, Osaka 569-8686, Japan , , , , , ,
| | - Mami Matsukawa
- Laboratory of Ultrasonic Electronics, Doshisha University, 1-3 Tatara-Miyakodani, Kyotanabe, Kyoto 610-0321, Japan
| | - Masashi Neo
- Department of Orthopedic Surgery, Osaka Medical College, 2-7, Daigaku-machi, Takatsuki, Osaka 569-8686, Japan , , , , , ,
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24
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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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25
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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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26
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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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27
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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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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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Numerical investigation of ultrasonic attenuation through 2D trabecular bone structures reconstructed from CT scans and random realizations. Comput Biol Med 2013; 45:143-56. [PMID: 24480174 DOI: 10.1016/j.compbiomed.2013.12.005] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/11/2013] [Revised: 12/09/2013] [Accepted: 12/10/2013] [Indexed: 11/23/2022]
Abstract
In this paper, we compare ultrasound interrogations of actual CT-scanned images of trabecular bone with artificial randomly constructed bone. Even though it is known that actual bone does not have randomly distributed trabeculae, we find that the ultrasound attenuations are close enough to cast doubt on any microstructural information, such as trabeculae width and distance between trabeculae, being gleaned from such experiments. More precisely, we perform numerical simulations of ultrasound interrogation on cancellous bone to investigate the phenomenon of ultrasound attenuation as a function of excitation frequency and bone porosity. The theoretical model is based on acoustic propagation equations for a composite fluid-solid material and is solved by a staggered-grid finite-difference scheme in the time domain. Numerical experiments are performed on two-dimensional bone samples reconstructed from CT-scanned images of real human calcaneus and from random distributions of fluid-solid particles generated via the turning bands method. A detailed comparison is performed on various parameters such as the attenuation rate and speed of sound through the bone samples as well as the normalized broadband ultrasound attenuation coefficient. Comparing results from these two types of bone samples allows us to assess the role of bone microstructure in ultrasound attenuation. It is found that the random model provides suitable bone samples for ultrasound interrogation in the transverse direction of the trabecular network.
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30
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Blanc E, Chiavassa G, Lombard B. A time-domain numerical modeling of two-dimensional wave propagation in porous media with frequency-dependent dynamic permeability. THE JOURNAL OF THE ACOUSTICAL SOCIETY OF AMERICA 2013; 134:4610. [PMID: 25669273 DOI: 10.1121/1.4824832] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/04/2023]
Abstract
An explicit finite-difference scheme is presented for solving the two-dimensional Biot equations of poroelasticity across the full range of frequencies. The key difficulty is to discretize the Johnson-Koplik-Dashen (JKD) model which describes the viscous dissipations in the pores. Indeed, the time-domain version of Biot-JKD model involves order 1/2 fractional derivatives which amount to a time convolution product. To avoid storing the past values of the solution, a diffusive representation of fractional derivatives is used: The convolution kernel is replaced by a finite number of memory variables that satisfy local-in-time ordinary differential equations. The coefficients of the diffusive representation follow from an optimization procedure of the dispersion relation. Then, various methods of scientific computing are applied: The propagative part of the equations is discretized using a fourth-order finite-difference scheme, whereas the diffusive part is solved exactly. An immersed interface method is implemented to discretize the geometry on a Cartesian grid, and also to discretize the jump conditions at interfaces. Numerical experiments are proposed in various realistic configurations.
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Affiliation(s)
- Emilie Blanc
- Laboratoire de Mécanique et d'Acoustique, UPR 7051, CNRS, 31 Chemin Joseph-Aiguier, Marseille Cedex 20, 13402, France
| | - Guillaume Chiavassa
- Laboratoire de Mécanique et d'Acoustique, UPR 7051, CNRS, 31 Chemin Joseph-Aiguier, Marseille Cedex 20, 13402, France
| | - Bruno Lombard
- Laboratoire de Mécanique et d'Acoustique, UPR 7051, CNRS, 31 Chemin Joseph-Aiguier, Marseille Cedex 20, 13402, France
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31
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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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32
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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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33
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Mézière F, Muller M, Dobigny B, Bossy E, Derode A. Simulations of ultrasound propagation in random arrangements of elliptic scatterers: occurrence of two longitudinal waves. THE JOURNAL OF THE ACOUSTICAL SOCIETY OF AMERICA 2013; 133:643-652. [PMID: 23363084 DOI: 10.1121/1.4774276] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/01/2023]
Abstract
Ultrasound propagation in clusters of elliptic (two-dimensional) or ellipsoidal (three-dimensional) scatterers randomly distributed in a fluid is investigated numerically. The essential motivation for the present work is to gain a better understanding of ultrasound propagation in trabecular bone. Bone microstructure exhibits structural anisotropy and multiple wave scattering. Some phenomena remain partially unexplained, such as the propagation of two longitudinal waves. The objective of this study was to shed more light on the occurrence of these two waves, using finite-difference simulations on a model medium simpler than bone. Slabs of anisotropic, scattering media were randomly generated. The coherent wave was obtained through spatial and ensemble-averaging of the transmitted wavefields. When varying relevant medium parameters, four of them appeared to play a significant role for the observation of two waves: (i) the solid fraction, (ii) the direction of propagation relatively to the scatterers orientation, (iii) the ability of scatterers to support shear waves, and (iv) a continuity of the solid matrix along the propagation. These observations are consistent with the hypothesis that fast waves are guided by the locally plate/bar-like solid matrix. If confirmed, this interpretation could significantly help developing approaches for a better understanding of trabecular bone micro-architecture using ultrasound.
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Affiliation(s)
- Fabien Mézière
- Institut Langevin, ESPCI ParisTech, CNRS, Université Paris Diderot - Paris 7, 1 rue Jussieu, 75005, Paris
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34
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Grimes M, Bouhadjera A, Haddad S, Benkedidah T. In vitro estimation of fast and slow wave parameters of thin trabecular bone using space-alternating generalized expectation-maximization algorithm. ULTRASONICS 2012; 52:614-621. [PMID: 22284937 DOI: 10.1016/j.ultras.2012.01.001] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/06/2011] [Revised: 12/02/2011] [Accepted: 01/04/2012] [Indexed: 05/31/2023]
Abstract
In testing cancellous bone using ultrasound, two types of longitudinal Biot's waves are observed in the received signal. These are known as fast and slow waves and their appearance depend on the alignment of bone trabeculae in the propagation path and the thickness of the specimen under test (SUT). They can be used as an effective tool for the diagnosis of osteoporosis because wave propagation behavior depends on the bone structure. However, the identification of these waves in the received signal can be difficult to achieve. In this study, ultrasonic wave propagation in a 4mm thick bovine cancellous bone in the direction parallel to the trabecular alignment is considered. The observed Biot's fast and slow longitudinal waves are superimposed; which makes it difficult to extract any information from the received signal. These two waves can be separated using the space alternating generalized expectation maximization (SAGE) algorithm. The latter has been used mainly in speech processing. In this new approach, parameters such as, arrival time, center frequency, bandwidth, amplitude, phase and velocity of each wave are estimated. The B-Scan images and its associated A-scans obtained through simulations using Biot's finite-difference time-domain (FDTD) method are validated experimentally using a thin bone sample obtained from the femoral-head of a 30 months old bovine.
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Affiliation(s)
- Morad Grimes
- Electronics Department, NDT Lab, Jijel University, Ouled Aissa, Jijel 18000, Algeria.
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35
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Klinge S, Hackl K, Gilbert RP. Investigation of the influence of reflection on the attenuation of cancellous bone. Biomech Model Mechanobiol 2012; 12:185-99. [PMID: 22484789 DOI: 10.1007/s10237-012-0391-x] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/30/2011] [Accepted: 03/15/2012] [Indexed: 10/28/2022]
Abstract
The model proposed in this paper is based on the fact that the reflection might have a significant contribution to the attenuation of the acoustic waves propagating through the cancellous bone. The numerical implementation of the mentioned effect is realized by the development of a new representative volume element that includes an infinitesimally thin 'transient' layer on the contact surface of the bone and the marrow. This layer serves to model the amplitude transformation of the incident wave by the transition through media with different acoustic impedances and to take into account the energy loss due to the reflection. The proposed representative volume element together with the multiscale finite element is used to simulate the wave propagation and to evaluate the attenuation coefficient for samples with different effective densities in the dependence of the applied excitation frequency. The obtained numerical values show a very good agreement with the experimental results. Moreover, the model enables the determination of the upper and the lower bound for the attenuation coefficient.
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Affiliation(s)
- Sandra Klinge
- Institute of Mechanics, Ruhr-University Bochum, Bochum, Germany.
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36
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Wear KA, Nagaraja S, Dreher ML, Gibson SL. Relationships of quantitative ultrasound parameters with cancellous bone microstructure in human calcaneus in vitro. THE JOURNAL OF THE ACOUSTICAL SOCIETY OF AMERICA 2012; 131:1605-12. [PMID: 22352530 PMCID: PMC6931152 DOI: 10.1121/1.3672701] [Citation(s) in RCA: 38] [Impact Index Per Article: 3.2] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/23/2023]
Abstract
Ultrasound parameters (attenuation, phase velocity, and backscatter), bone mineral density (BMD), and microarchitectural features were measured on 29 human cancellous calcaneus samples in vitro. Regression analysis was performed to predict ultrasound parameters from BMD and microarchitectural features. The best univariate predictors of the ultrasound parameters were the indexes of bone quantity: BMD and bone volume fraction (BV/TV). The most predictive univariate models for attenuation, phase velocity, and backscatter coefficient yielded adjusted squared correlation coefficients of 0.69-0.73. Multiple regression models yielded adjusted correlation coefficients of 0.74-0.83. Therefore attenuation, phase velocity, and backscatter are primarily determined by bone quantity, but multiple regression models based on bone quantity plus microarchitectural features achieve slightly better predictive performance than models based on bone quantity alone.
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Affiliation(s)
- Keith A Wear
- U.S. Food and Drug Administration, Center for Devices and Radiological Health, 10903 New Hampshire Boulevard, Silver Spring, Maryland 20993, USA.
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37
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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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38
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CARDOSO LUIS, MEUNIER ALAIN, ODDOU CHRISTIAN. IN VITROACOUSTIC WAVE PROPAGATION IN HUMAN AND BOVINE CANCELLOUS BONE AS PREDICTED BY BIOT'S THEORY. J MECH MED BIOL 2011. [DOI: 10.1142/s0219519408002565] [Citation(s) in RCA: 19] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022]
Abstract
Recent in vitro studies have provided evidence of the propagation of two different longitudinal wave modes at ultrasonic frequencies in cancellous bone. The genesis of these two plane waves in fluid-saturated porous media is predicted by the poroelastic approach to wave propagation originally developed by Biot. However, wave velocity is usually analyzed as a function of bone mass density only; therefore, the influence of the cancellous bone microstructure over the wave velocity is not taken into account. In the present study, a descriptor of the microstructure is considered in Biot's theory. This model is used to evaluate the large experimental variability of both fast and slow wave velocities measured on randomly oriented human and bovine cancellous bone samples. The role of the anisotropic solid structure and fluid in the behavior of fast and slow wave velocities is examined. Experimental and theoretically predicted velocities are found in close agreement when analyzed as a function of both porosity and structural index. This model has the potential to be used to determine an acoustically derived structural index in cancellous bone.
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Affiliation(s)
- LUIS CARDOSO
- Department of Biomedical Engineering, City College of New York, City University of New York, Convent Ave at 138th Street, New York, NY 10031, USA
| | - ALAIN MEUNIER
- B2OA (Biomécanique et Biomatériaux Ostéo-articulaires) Laboratory, CNRS UMR 7052 (SPI), University of Paris VII, XII and XIII, France
- University of Paris VII, 10 Avenue de Verdun, 75010 Paris, France
| | - CHRISTIAN ODDOU
- B2OA (Biomécanique et Biomatériaux Ostéo-articulaires) Laboratory, CNRS UMR 7052 (SPI), University of Paris VII, XII and XIII, France
- University of Paris XII, 61 Avenue du Général de Gaulle, 94010 Créteil, France
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39
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Kubo T, Fujimori K, Cazier N, Saeki T, Matsukawa M. Properties of ultrasonic waves in bovine bone marrow. ULTRASOUND IN MEDICINE & BIOLOGY 2011; 37:1923-1929. [PMID: 21963039 DOI: 10.1016/j.ultrasmedbio.2011.08.005] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/10/2010] [Revised: 08/04/2011] [Accepted: 08/07/2011] [Indexed: 05/31/2023]
Abstract
We investigated the properties of ultrasonic waves in bovine bone marrow. Six bone marrow samples were obtained from different parts (proximal, middle and distal) of the shafts of two bovine femora without destruction. The measured frequency range was 3 to 10 MHz, and the temperature range was 15 to 40°C. Both wave velocity and attenuation coefficient in bone marrow always decreased as temperature increased. The velocity ranged from 1400 to 1610 m/s and attenuation coefficient ranged from 4 to 16 dB/cm. Wave velocities in bone marrow were similar to those in water, whereas the temperature dependences were different, and the wave attenuation coefficients were much higher than those in water. The dependence of velocity on temperature changed slightly around 23-24°C, where a transition from soft gel to oily liquid occurred. The transition temperature was confirmed by differential scanning calorimetry (DSC). Below this transition temperature, positive velocity dispersion was observed.
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Affiliation(s)
- Tomohiro Kubo
- Laboratory of Ultrasonic Electronics, Doshisha University, Kyoto, Japan
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40
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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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41
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Langton CM. The 25th Anniversary of BUA for the Assessment of Osteoporosis: Time for a New Paradigm? Proc Inst Mech Eng H 2011; 225:113-25. [DOI: 10.1243/09544119jeim777] [Citation(s) in RCA: 24] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022]
Abstract
The measurement of broadband ultrasonic attenuation (BUA) in cancellous bone at the calcaneus for the assessment of osteoporosis was first described within this journal 25 years ago. It was recognized in 2006 by Universities UK as being one of the ‘100 discoveries and developments in UK Universities that have changed the world’ over the past 50 years. In 2008, the UK's Department of Health also recognized BUA assessment of osteoporosis in a publication highlighting 11 projects that have contributed to ‘60 years of NHS research benefiting patients’. The BUA technique has been extensively clinically validated and is utilized worldwide, with at least seven commercial systems currently providing calcaneal BUA measurement. However, there is still no fundamental understanding of the dependence of BUA upon the material and structural properties of cancellous bone. This review aims to provide an ‘engineering in medicine’ perspective and proposes a new paradigm based upon phase cancellation due to variation in propagation transit time across the receive transducer face to explain the non-linear relationship between BUA and bone volume fraction in cancellous bone.
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Affiliation(s)
- C M Langton
- Physics, Faculty of Science & Technology and Institute of Health & Biomedical Innovation, Queensland University of Technology, Brisbane, Australia,
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42
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Buchanan JL, Gilbert RP, Ou MJY. Wavelet decomposition of transmitted ultrasound wave through a 1-D muscle-bone system. J Biomech 2010; 44:352-8. [PMID: 21092969 DOI: 10.1016/j.jbiomech.2010.10.030] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/21/2010] [Accepted: 10/21/2010] [Indexed: 11/29/2022]
Abstract
In the attempt for using ultrasound as a diagnostic device for osteoporosis, several authors have described the result of the in vitro experiment in which ultrasound is passed through a cancellous bone specimen placed in a water tank. However, in the in vivo setting, a patient's cancellous bone is surrounded by cortical and muscle layers. This paper considers in the one-dimensional case (1) what effect the cortical bone segments surrounding the cancellous segment would have on the received signal and (2) what the received signal would be when a source and receiver are placed on opposite sides of a structure consisting of a cancellous segment surrounded by cortical and muscle layers. Mathematically this is accomplished by representing the received signal as a sum of wavelets which go through different reflection-transmission histories at the muscle-cortical bone and cortical-cancellous bone interfaces. The muscle and cortical bone are modeled as elastic materials and the cancellous bone as a poroelastic material described by the Biot-Johnson-Koplik-Dashen model. The approach presented here permits the assessment of which possible paths of transmission and reflection through the cortical-cancellous or muscle-cortical-cancellous complex will result in significant contributions to the received waveform. This piece of information can be useful for solving the inverse problem of non-destructive assessment of material properties of bone. Our methodology can be generalized to three-dimensional parallelly layered structure by first applying Fourier transform in the directions perpendicular to the transverse direction.
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Affiliation(s)
- James L Buchanan
- Mathematics Department, United States Naval Academy, Annapolis, MD 21402, USA
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43
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Mizuno K, Somiya H, Kubo T, Matsukawa M, Otani T, Tsujimoto T. Influence of cancellous bone microstructure on two ultrasonic wave propagations in bovine femur: an in vitro study. THE JOURNAL OF THE ACOUSTICAL SOCIETY OF AMERICA 2010; 128:3181-9. [PMID: 21110613 DOI: 10.1121/1.3493444] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/10/2023]
Abstract
The influence of cancellous bone microstructure on the ultrasonic wave propagation of fast and slow waves was experimentally investigated. Four spherical cancellous bone specimens extracted from two bovine femora were prepared for the estimation of acoustical and structural anisotropies of cancellous bone. In vitro measurements were performed using a PVDF transducer (excited by a single sinusoidal wave at 1 MHz) by rotating the spherical specimens. In addition, the mean intercept length (MIL) and bone volume fraction (BV/TV) were estimated by X-ray micro-computed tomography. Separation of the fast and slow waves was clearly observed in two specimens. The fast wave speed was strongly dependent on the wave propagation direction, with the maximum speed along the main trabecular direction. The fast wave speed increased with the MIL. The slow wave speed, however, was almost constant. The fast wave speeds were statistically higher, and their amplitudes were statistically lower in the case of wave separation than in that of wave overlap.
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Affiliation(s)
- Katsunori Mizuno
- Laboratory of Ultrasonic Electronics, Doshisha University, 1-3 Tatara Miyakodani, Kyotanabe City 610-0321, Japan
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44
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Sai H, Iguchi G, Tobimatsu T, Takahashi K, Otani T, Horii K, Mano I, Nagai I, Iio H, Fujita T, Yoh K, Baba H. Novel ultrasonic bone densitometry based on two longitudinal waves: significant correlation with pQCT measurement values and age-related changes in trabecular bone density, cortical thickness, and elastic modulus of trabecular bone in a normal Japanese population. Osteoporos Int 2010; 21:1781-90. [PMID: 20514480 DOI: 10.1007/s00198-010-1217-2] [Citation(s) in RCA: 28] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Received: 08/20/2009] [Accepted: 02/12/2010] [Indexed: 10/19/2022]
Abstract
UNLABELLED A reference database for trabecular bone density, cortical thickness, and elastic modulus of trabecular bone for a novel ultrasonic bone densitometry system (LD-100) based on two longitudinal waves (fast and slow) was determined over a wide age range in a normal Japanese population. INTRODUCTION A novel ultrasonic bone densitometry system (LD-100 system) was applied to create a reference database for trabecular bone density (TBD), cortical thickness (CoTh), and elastic modulus of trabecular bone (EMTb) for this device over a wide age range in a normal Japanese population. METHODS In a comparative study between LD-100 and peripheral quantitative computed tomography (pQCT) systems, 52 individuals were examined by both systems at the same radius simultaneously. To create a reference database, a total of 2,380 healthy subjects (1,179 men, 1,201 women), ages 18-99 years, were examined using the LD-100 system. RESULTS Highly significant correlations between the LD-100 and pQCT systems were found in TBD (r = 0.877, p < 0.001) and CoTh (r = 0.723, p < 0.001). For the reference database, peak values of TBD, CoTh, and EMTb were observed at 30-34 years (255.09 mg/cm(3)), 20-24 years (5.23 mm), and 20-24 years (4.09 GPa) in men, and at 25-29 years (209.24 mg/cm(3)), 25-29 years (3.98 mm), and 20-24 years (3.33 GPa) in women, respectively. The TBD fell significantly (p < 0.05) beginning at 55-59 years in both sexes, with a relatively rapid decrease in women. The CoTh showed a significant decrease beginning at 40-44 years in men and 50-54 years in women. The EMTb showed a significant decrease beginning at 40-44 years in men and 55-59 years in women. CONCLUSIONS The LD-100 system is a useful bone densitometry device and the database of age-related changes in TBD, CoTh, and EMTb established in this study will provide fundamental data for future studies related to bone status.
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Affiliation(s)
- H Sai
- Department of Biosignal Pathophysiology, Kobe University Graduate School of Medicine, Kobe, Japan
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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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Bréban S, Padilla F, Fujisawa Y, Mano I, Matsukawa M, Benhamou CL, Otani T, Laugier P, Chappard C. Trabecular and cortical bone separately assessed at radius with a new ultrasound device, in a young adult population with various physical activities. Bone 2010; 46:1620-5. [PMID: 20230926 DOI: 10.1016/j.bone.2010.03.005] [Citation(s) in RCA: 36] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Received: 08/19/2009] [Revised: 01/27/2010] [Accepted: 03/04/2010] [Indexed: 11/15/2022]
Abstract
The aim was to evaluate a new ultrasound device in a young adult population and to assess its reproducibility via comparison to DXA measurements and geometrical measurements from high-resolution radiographs. Ninety-three subjects aged between 20 and 51 years were recruited and divided into four groups according to their gender and physical activity status: 22 male athletes, 19 male controls, 21 female athletes, and 31 female controls. Ultrasonic measurements were assessed by the prototype LD-100 (Oyo Electric Co., Kyoto, Japan) on the dominant distal radius. Attenuation in the radius (dB), cortical bone thickness (mm), radius thickness (mm), mass density of cancellous bone (mg/cm(3)), and elasticity (GPa) of cancellous bone were obtained. BMD was measured by DXA at the dominant distal radius. Radius images were obtained with a direct high-resolution digital X-ray device (BMA, D(3)A Medical Systems), and radius and cortical thicknesses were estimated using a specific software (ImageJ, Bethesda, USA), in an area site-matched with LD-100. There was a significant positive correlation between site-matched BMD measurement and LD-100 parameters (p<0.004), X-ray radius thickness, and LD-100 parameters except elasticity (p<0.05, r>0.32), X-ray cortical thickness and LD-100 attenuation and cortical thickness (p<0.01). A significantly higher attenuation, cortical and radius thicknesses were found in athletes compared to controls (p<0.05). The radius thickness measured on radiographs was significantly higher in athletes versus controls in both sexes, and cortical thickness was significantly higher in male athletes versus controls. These data suggest a positive influence of physical activity on bone cortical measurements. This study also confirmed the particular interest of bone assessment by ultrasound.
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Affiliation(s)
- S Bréban
- CTI, U658 Inserm, Orléans, France.
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Aygün H, Attenborough K, Lauriks W, Langton CM. Ultrasonic wave propagation in stereo-lithographical bone replicas. THE JOURNAL OF THE ACOUSTICAL SOCIETY OF AMERICA 2010; 127:3781-3789. [PMID: 20550276 DOI: 10.1121/1.3397581] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/29/2023]
Abstract
Predictions of a modified anisotropic Biot-Allard theory are compared with measurements of pulses centered on 100 kHz and 1 MHz transmitted through water-saturated stereo-lithographical bone replicas. The replicas are 13 times larger than the original bone samples. Despite the expected effects of scattering, which is neglected in the theory, at 100 kHz the predicted and measured transmitted waveforms are similar. However, the magnitude of the leading negative edge of the waveform is overpredicted, and the trailing parts of the waveforms are not predicted well. At 1 MHz, although there are differences in amplitudes, the theory predicts that the transmitted waveform is almost a scaled version of that incident in conformity with the data.
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Affiliation(s)
- Haydar Aygün
- Medical Physics, Post-Graduate Medical Institute, The University of Hull, Cottingham Road, Hull HU6 7RX, United Kingdom
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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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Aygün H, Attenborough K, Postema M, Lauriks W, Langton CM. Predictions of angle dependent tortuosity and elasticity effects on sound propagation in cancellous bone. THE JOURNAL OF THE ACOUSTICAL SOCIETY OF AMERICA 2009; 126:3286-3290. [PMID: 20000942 DOI: 10.1121/1.3242358] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/28/2023]
Abstract
The anisotropic pore structure and elasticity of cancellous bone cause wave speeds and attenuation in cancellous bone to vary with angle. Previously published predictions of the variation in wave speed with angle are reviewed. Predictions that allow tortuosity to be angle dependent but assume isotropic elasticity compare well with available data on wave speeds at large angles but less well for small angles near the normal to the trabeculae. Claims for predictions that only include angle-dependence in elasticity are found to be misleading. Audio-frequency data obtained at audio-frequencies in air-filled bone replicas are used to derive an empirical expression for the angle-and porosity-dependence of tortuosity. Predictions that allow for either angle dependent tortuosity or angle dependent elasticity or both are compared with existing data for all angles and porosities.
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Affiliation(s)
- Haydar Aygün
- Medical Physics, PGMI, The University of Hull, Cottingham Road, HU6 7RX Hull, United Kingdom.
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