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Chen G, Zhang Y, Abraham O, Pageot D, Chekroun M, Tournat V. Numerical parametric study of Nonlinear Coda Wave Interferometry sensitivity to microcrack size in a multiple scattering medium. ULTRASONICS 2021; 116:106483. [PMID: 34126405 DOI: 10.1016/j.ultras.2021.106483] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/06/2020] [Revised: 05/26/2021] [Accepted: 05/26/2021] [Indexed: 06/12/2023]
Abstract
This paper reports a numerical study of the sensitivity and applicability of the Nonlinear Coda Wave Interferometry (NCWI) method in a heterogeneous material with a localized microcracked zone. We model the influence of a strong pump wave on the localized microcracked zone as a small average increase in the length of each crack. Further probing of this microcracked zone with a multiply scattered ultrasonic wave induces small changes to the coda-type signal, which are quantified with coda wave interferometry. A parametric sensitivity study of the CWI observables with respect to the changes in crack length is established via numerical simulations of the problem using a 2D spectral element method (SEM2D). The stretching of the signal, proportional to the relative variation in effective velocity, is found to be linearly proportional to the global change in crack length, while the other CWI parameter, the remnant decorrelation coefficient, is found to be quadratically proportional to the crack length change. The NCWI method is shown to be relevant for the detection of different damaged material states in complex solids. The reported numerical results are especially significant in the context of quantitative nondestructive evaluation of micro-damage level of a heterogeneous materials using nonlinear ultrasound signals.
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Affiliation(s)
- Guangzhi Chen
- Acoustic Science and Technology Laboratory, Harbin Engineering University, Harbin 150001, China; Key Laboratory of Marine Information Acquisition and Security (Harbin Engineering University), Ministry of Industry and Information Technology, Harbin 150001, China; College of Underwater Acoustic Engineering, Harbin Engineering University, Harbin 150001, China
| | - Yuxiang Zhang
- Acoustic Science and Technology Laboratory, Harbin Engineering University, Harbin 150001, China; Key Laboratory of Marine Information Acquisition and Security (Harbin Engineering University), Ministry of Industry and Information Technology, Harbin 150001, China; College of Underwater Acoustic Engineering, Harbin Engineering University, Harbin 150001, China.
| | - Odile Abraham
- GERS-GeoEND, Univ Gustave Eiffel, IFSTTAR, F-44344 Bouguenais, France.
| | - Damien Pageot
- GERS-GeoEND, Univ Gustave Eiffel, IFSTTAR, F-44344 Bouguenais, France
| | - Mathieu Chekroun
- Laboratoire d'Acoustique de l'Université du Mans (LAUM), UMR 6613, Institut d'Acoustique - Graduate School (IA-GS), CNRS, Le Mans Université, France
| | - Vincent Tournat
- Laboratoire d'Acoustique de l'Université du Mans (LAUM), UMR 6613, Institut d'Acoustique - Graduate School (IA-GS), CNRS, Le Mans Université, France
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Pasquinelli C, Montanaro H, Lee HJ, Hanson LG, Kim H, Kuster N, Siebner HR, Neufeld E, Thielscher A. Transducer modeling for accurate acoustic simulations of transcranial focused ultrasound stimulation. J Neural Eng 2020; 17:046010. [DOI: 10.1088/1741-2552/ab98dc] [Citation(s) in RCA: 15] [Impact Index Per Article: 3.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/12/2022]
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Wear KA. Mechanisms of Interaction of Ultrasound With Cancellous Bone: A Review. IEEE TRANSACTIONS ON ULTRASONICS, FERROELECTRICS, AND FREQUENCY CONTROL 2020; 67:454-482. [PMID: 31634127 PMCID: PMC7050438 DOI: 10.1109/tuffc.2019.2947755] [Citation(s) in RCA: 41] [Impact Index Per Article: 10.3] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/17/2023]
Abstract
Ultrasound is now a clinically accepted modality in the management of osteoporosis. The most common commercial clinical devices assess fracture risk from measurements of attenuation and sound speed in cancellous bone. This review discusses fundamental mechanisms underlying the interaction between ultrasound and cancellous bone. Because of its two-phase structure (mineralized trabecular network embedded in soft tissue-marrow), its anisotropy, and its inhomogeneity, cancellous bone is more difficult to characterize than most soft tissues. Experimental data for the dependencies of attenuation, sound speed, dispersion, and scattering on ultrasound frequency, bone mineral density, composition, microstructure, and mechanical properties are presented. The relative roles of absorption, scattering, and phase cancellation in determining attenuation measurements in vitro and in vivo are delineated. Common speed of sound metrics, which entail measurements of transit times of pulse leading edges (to avoid multipath interference), are greatly influenced by attenuation, dispersion, and system properties, including center frequency and bandwidth. However, a theoretical model has been shown to be effective for correction for these confounding factors in vitro and in vivo. Theoretical and phantom models are presented to elucidate why cancellous bone exhibits negative dispersion, unlike soft tissue, which exhibits positive dispersion. Signal processing methods are presented for separating "fast" and "slow" waves (predicted by poroelasticity theory and supported in cancellous bone) even when the two waves overlap in time and frequency domains. Models to explain dependencies of scattering on frequency and mean trabecular thickness are presented and compared with measurements. Anisotropy, the effect of the fluid filler medium (marrow in vivo or water in vitro), phantoms, computational modeling of ultrasound propagation, acoustic microscopy, and nonlinear properties in cancellous bone are also discussed.
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Mueller JK, Ai L, Bansal P, Legon W. Numerical evaluation of the skull for human neuromodulation with transcranial focused ultrasound. J Neural Eng 2018; 14:066012. [PMID: 28777075 DOI: 10.1088/1741-2552/aa843e] [Citation(s) in RCA: 68] [Impact Index Per Article: 11.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/18/2022]
Abstract
OBJECTIVE Transcranial focused ultrasound is an emerging field for human non-invasive neuromodulation, but its dosing in humans is difficult to know due to the skull. The objective of the present study was to establish modeling methods based on medical images to assess skull differences between individuals on the wave propagation of ultrasound. APPROACH Computational models of transcranial focused ultrasound were constructed using CT and MR scans to solve for intracranial pressure. We explored the effect of including the skull base in models, different transducer placements on the head, and differences between 250 kHz or 500 kHz acoustic frequency for both female and male models. We further tested these features using linear, nonlinear, and elastic simulations. To better understand inter-subject skull thickness and composition effects we evaluated the intracranial pressure maps between twelve individuals at two different skull sites. MAIN RESULTS Nonlinear acoustic simulations resulted in virtually identical intracranial pressure maps with linear acoustic simulations. Elastic simulations showed a difference in max pressures and full width half maximum volumes of 15% at most. Ultrasound at an acoustic frequency of 250 kHz resulted in the creation of more prominent intracranial standing waves compared to 500 kHz. Finally, across twelve model human skulls, a significant linear relationship to characterize intracranial pressure maps was not found. SIGNIFICANCE Despite its appeal, an inherent problem with the use of a noninvasive transcranial ultrasound method is the difficulty of knowing intracranial effects because of the skull. Here we develop detailed computational models derived from medical images of individuals to simulate the propagation of neuromodulatory ultrasound across the skull and solve for intracranial pressure maps. These methods allow for a much better understanding of the intracranial effects of ultrasound for an individual in order to ensure proper targeting and more tightly control dosing.
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Affiliation(s)
- Jerel K Mueller
- Department of Rehabilitation Medicine, Division of Physical Therapy and Division of Rehabilitation Science, Medical School, University of Minnesota, Minneapolis, MN, United States of America
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Bai L, Xu K, Li D, Ta D, Le LH, Wang W. Fatigue evaluation of long cortical bone using ultrasonic guided waves. J Biomech 2018; 77:83-90. [PMID: 29961583 DOI: 10.1016/j.jbiomech.2018.06.015] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/27/2017] [Revised: 06/08/2018] [Accepted: 06/19/2018] [Indexed: 10/28/2022]
Abstract
Bone fatigue fracture is a progressive disease due to stress concentration. This study aims to evaluate the long bone fatigue damage using the ultrasonic guided waves. Two-dimensional finite-difference time-domain method was employed to simulate the ultrasonic guided wave propagation in the long bone under different elastic modulus. The experiment was conducted on a 3.8 mm-thick bovine bone plate. The phase velocities of two fundamental guided modes, A1 and S1, were measured by using the axial transmission technique. Simulation shows that the phase velocities of guided modes A1 and S1 decrease with the increasing of the fatigue damage. After 20,000 cycles of fatigue loading on the bone plate, the average phase velocities of A1 and S1 modes were 6.6% and 5.3% respectively, lower than those of the intact bone. The study suggests that ultrasonic guided waves can be potentially used to evaluate the fatigue damage in long bones.
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Affiliation(s)
- Liang Bai
- Department of Electronic Engineering, Fudan University, Shanghai 200433, China
| | - Kailiang Xu
- Institut Langevin, ESPCI Paris, CNRS UMR 7587, INSERM U979, 17 Rue Moreau, 75012 Paris, France.
| | - Dan Li
- Department of Electronic Engineering, Fudan University, Shanghai 200433, China
| | - Dean Ta
- Department of Electronic Engineering, Fudan University, Shanghai 200433, China; State Key Laboratory of ASIC and System, Fudan University, Shanghai 200433, China; Key Laboratory of Medical Imaging Computing and Computer Assisted Intervention (MICCAI) of Shanghai, Shanghai 200032, China.
| | - Lawrence H Le
- Department of Radiology and Diagnostic Imaging, University of Alberta, Edmonton, Alberta, Canada
| | - Weiqi Wang
- Department of Electronic Engineering, Fudan University, Shanghai 200433, China
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Lee KI. Relationships of linear and nonlinear ultrasound parameters with porosity and trabecular spacing in trabecular-bone-mimicking phantoms. THE JOURNAL OF THE ACOUSTICAL SOCIETY OF AMERICA 2016; 140:EL528. [PMID: 28040043 DOI: 10.1121/1.4972530] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/10/2023]
Abstract
The speed of sound (SOS), the normalized broadband ultrasound attenuation (nBUA), and the nonlinear parameter (B/A) were measured in 18 trabecular-bone-mimicking phantoms consisting of water-saturated aluminum foams. The strong slow wave and the very weak fast wave were consistently observed in the signals transmitted through all of the phantoms. It was found that the SOS increased as the porosity and the trabecular spacing increased. In contrast, both the nBUA and the B/A showed opposite dependences on the porosity and the trabecular spacing. All three ultrasound parameters exhibited high correlation coefficients with the porosity and the trabecular spacing.
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Affiliation(s)
- Kang Il Lee
- Department of Physics, Kangwon National University, Chuncheon 24341, Republic of Korea
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Eiras JN, Vu QA, Lott M, Payá J, Garnier V, Payan C. Dynamic acousto-elastic test using continuous probe wave and transient vibration to investigate material nonlinearity. ULTRASONICS 2016; 69:29-37. [PMID: 27018754 DOI: 10.1016/j.ultras.2016.03.008] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/16/2015] [Revised: 02/15/2016] [Accepted: 03/11/2016] [Indexed: 06/05/2023]
Abstract
This study demonstrates the feasibility of the dynamic acousto-elastic effect of a continuous high frequency wave for investigating the material nonlinearity upon transient vibration. The approach is demonstrated on a concrete sample measuring 15×15×60cm(3). Two ultrasonic transducers (emitter and receiver) are placed at its middle span. A continuous high frequency wave of 500kHz propagates through the material and is modulated with a hammer blow. The position of the hammer blow on the sample is configured to promote the first bending mode of vibration. The use of a continuous wave allows discrete time extraction of the nonlinear behavior by a short-time Fourier transform approach, through the simultaneous comparison of a reference non-modulated signal and an impact-modulated signal. The hammer blow results in phase shifts and variations of signal amplitude between reference and perturbed signals, which are driven by the resonant frequency of the sample. Finally, a comprehensive analysis of the relaxation mechanisms (modulus and attenuation recovery) is conducted to untangle the coupled fast and slow hysteretic effects.
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Affiliation(s)
- J N Eiras
- Instituto de Ciencia y Tecnología del Hormigón (ICITECH), Universitat Politècnica de València, Camino de Vera s/n, 46022 València, Spain.
| | - Q A Vu
- Aix-Marseille Université, LMA UPR 7051, IUT, 413 Av. Gaston Berger, 13100 Aix-en-Provence, France
| | - M Lott
- Aix-Marseille Université, LMA UPR 7051, IUT, 413 Av. Gaston Berger, 13100 Aix-en-Provence, France
| | - J Payá
- Instituto de Ciencia y Tecnología del Hormigón (ICITECH), Universitat Politècnica de València, Camino de Vera s/n, 46022 València, Spain
| | - V Garnier
- Aix-Marseille Université, LMA UPR 7051, IUT, 413 Av. Gaston Berger, 13100 Aix-en-Provence, France
| | - C Payan
- Aix-Marseille Université, LMA UPR 7051, IUT, 413 Av. Gaston Berger, 13100 Aix-en-Provence, France
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8
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Renaud G, Bosch JG, van der Steen AFW, de Jong N. Dynamic acousto-elastic testing applied to a highly dispersive medium and evidence of shell buckling of lipid-coated gas microbubbles. THE JOURNAL OF THE ACOUSTICAL SOCIETY OF AMERICA 2015; 138:2668-2677. [PMID: 26627744 DOI: 10.1121/1.4932587] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/05/2023]
Abstract
Dynamic acousto-elastic testing is applied to a mixture of lipid-coated microbubbles in water. A dynamic change of ambient pressure is produced by a 16 kHz pressure wave having a peak pressure amplitude of 28 kPa. The induced changes of phase velocity and attenuation are captured by a sequence of short ultrasound pulses with a center frequency of 4 MHz. As a consequence of the dispersion brought about by the resonance of microbubbles at a frequency close to 2 MHz, time-domain approaches like the cross-correlation method are shown to be unsuited to determine the variation in ultrasound wavespeed. A frequency-domain analysis shows that the acousto-elastic effect (first order pressure derivative of ultrasound phase velocity) depends on the ultrasound frequency. The acousto-elastic effect tends to that measured in water for an ultrasound frequency above the resonance frequency of microbubbles, while it is two orders of magnitude larger for an ultrasound frequency close to or below the resonance frequency of microbubbles. Besides the large magnitude of the acousto-elastic effect observed for an ultrasound frequency below the resonance frequency of microbubbles, the first order pressure derivative of ultrasound phase velocity is negative. This supports the occurrence of shell buckling of lipid-coated microbubbles induced by the 16 kHz pressure wave.
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Affiliation(s)
- Guillaume Renaud
- Sorbonne Universités, UPMC Univ Paris 06, CNRS UMR 7371, INSERM UMR S 1146, Laboratoire d'Imagerie Biomédicale, 15 rue de l'école de médecine, 75006 Paris, France
| | - Johan G Bosch
- Department of Biomedical Engineering, ThoraxCenter, Erasmus Medical Center, P.O. Box 2040, 3000 CA Rotterdam, The Netherlands
| | - Antonius F W van der Steen
- Department of Biomedical Engineering, ThoraxCenter, Erasmus Medical Center, P.O. Box 2040, 3000 CA Rotterdam, The Netherlands
| | - Nico de Jong
- Department of Biomedical Engineering, ThoraxCenter, Erasmus Medical Center, P.O. Box 2040, 3000 CA Rotterdam, The Netherlands
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Callé S, Moreschi H, Renaud G, Defontaine M. Ultrasound propagation in trabecular bone: a numerical study of the influence of microcracks. ULTRASONICS 2014; 54:1231-1236. [PMID: 24041497 DOI: 10.1016/j.ultras.2013.08.003] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/31/2013] [Revised: 07/24/2013] [Accepted: 08/06/2013] [Indexed: 06/02/2023]
Abstract
The accumulation of microdamage in trabecular bone tissue is suspected of being a predictive indicator of osteoporosis diagnosis. To quantify this microdamage, the Dynamic AcoustoElastic Testing (DAET) method measures the Time Of Flight (TOF) and amplitude variations of transmitted ultrasound (US) pulses, while the bone sample is submitted to a low frequency sinusoidal hydrostatic pressure (opening/closing of microcracks). However, DAET is both sensitive to viscoelastic properties changes and microcracks density. To verify the microcracks density contribution on DAET results, a numerical approach is proposed. Multliple configurations of microdamaged trabecular bone-tissue-like mesh have been simulated. A 2D pseudo-spectral time domain numerical model was then developed to simulate linear wave propagation in heterogeneous solids. The influence of the microcracks number and orientation on the US TOF was particularly investigated. Results are discussed and compared with experimental data obtained from DAET measurements in trabecular bone samples.
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Affiliation(s)
- Samuel Callé
- Université François-Rabelais de Tours, UMR INSERM U930, 10 boulevard Tonnellé, 37032 Tours Cedex, France.
| | - Hélène Moreschi
- Université François-Rabelais de Tours, UMR INSERM U930, 10 boulevard Tonnellé, 37032 Tours Cedex, France
| | - Guillaume Renaud
- Department of Biomedical Engineering, Thoraxcenter, Erasmus MC, P.O. Box 2040, 3000 CA Rotterdam, The Netherlands
| | - Marielle Defontaine
- Université François-Rabelais de Tours, UMR INSERM U930, 10 boulevard Tonnellé, 37032 Tours Cedex, France
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Zhang Z, Liu D, Deng M, Ta D, Wang W. Experimental observation of cumulative second-harmonic generation of lamb waves propagating in long bones. ULTRASOUND IN MEDICINE & BIOLOGY 2014; 40:1660-1670. [PMID: 24726796 DOI: 10.1016/j.ultrasmedbio.2014.01.004] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/19/2013] [Revised: 12/26/2013] [Accepted: 01/06/2014] [Indexed: 06/03/2023]
Abstract
The experimental observation of cumulative second-harmonic generation of fundamental Lamb waves in long bones is reported. Based on the modal expansion approach to waveguide excitation and the dispersion characteristics of Lamb waves in long bones, the mechanism underlying the generation and accumulation of second harmonics by propagation of the fundamental Lamb waves was investigated. An experimental setup was established to detect the second-harmonic signals of Lamb wave propagation in long bones in vitro. Through analysis of the group velocities of the received signals, the appropriate fundamental Lamb wave modes and the duration of the second-harmonic signals could be identified. The integrated amplitude of the time-domain second-harmonic signal was introduced and used to characterize the efficiency of second-harmonic generation by fundamental Lamb wave propagation. The results indicate that the second-harmonic signal generated by fundamental Lamb waves propagating in long bones can be observed clearly, and the effect was cumulative with propagation distance when the fundamental Lamb wave mode and the double-frequency Lamb wave mode had the same phase velocities. The present results may be important in the development of a new method to evaluate the status of long bones using the cumulative second harmonic of ultrasonic Lamb waves.
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Affiliation(s)
- Zhenggang Zhang
- Department of Electronic Engineering, Fudan University, Shanghai, China
| | - Dan Liu
- Department of Electronic Engineering, Fudan University, Shanghai, China
| | - Mingxi Deng
- Department of Physics, Logistics Engineering University, Chongqing, China.
| | - Dean Ta
- Department of Electronic Engineering, Fudan University, Shanghai, China; Key Laboratory of Medical Imaging Computing and Computer Assisted Intervention (MICCAI) of Shanghai, Shanghai, China.
| | - Weiqi Wang
- Department of Electronic Engineering, Fudan University, Shanghai, China
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Ellwood R, Stratoudaki T, Sharples SD, Clark M, Somekh MG. Determination of the acoustoelastic coefficient for surface acoustic waves using dynamic acoustoelastography: an alternative to static strain. THE JOURNAL OF THE ACOUSTICAL SOCIETY OF AMERICA 2014; 135:1064-1070. [PMID: 24606250 DOI: 10.1121/1.4864308] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/03/2023]
Abstract
The third-order elastic constants of a material are believed to be sensitive to residual stress, fatigue, and creep damage. The acoustoelastic coefficient is directly related to these third-order elastic constants. Several techniques have been developed to monitor the acoustoelastic coefficient using ultrasound. In this article, two techniques to impose stress on a sample are compared, one using the classical method of applying a static strain using a bending jig and the other applying a dynamic stress due to the presence of an acoustic wave. Results on aluminum samples are compared. Both techniques are found to produce similar values for the acoustoelastic coefficient. The dynamic strain technique however has the advantages that it can be applied to large, real world components, in situ, while ensuring the measurement takes place in the nondestructive, elastic regime.
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Affiliation(s)
- R Ellwood
- Electrical Systems and Optics Research Division, Faculty of Engineering, University of Nottingham, University Park, Nottingham NG7 2RD, United Kingdom
| | - T Stratoudaki
- Electrical Systems and Optics Research Division, Faculty of Engineering, University of Nottingham, University Park, Nottingham NG7 2RD, United Kingdom
| | - S D Sharples
- Electrical Systems and Optics Research Division, Faculty of Engineering, University of Nottingham, University Park, Nottingham NG7 2RD, United Kingdom
| | - M Clark
- Electrical Systems and Optics Research Division, Faculty of Engineering, University of Nottingham, University Park, Nottingham NG7 2RD, United Kingdom
| | - M G Somekh
- Electrical Systems and Optics Research Division, Faculty of Engineering, University of Nottingham, University Park, Nottingham NG7 2RD, United Kingdom
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Haupert S, Guérard S, Peyrin F, Mitton D, Laugier P. Non destructive characterization of cortical bone micro-damage by nonlinear resonant ultrasound spectroscopy. PLoS One 2014; 9:e83599. [PMID: 24392089 PMCID: PMC3879251 DOI: 10.1371/journal.pone.0083599] [Citation(s) in RCA: 29] [Impact Index Per Article: 2.9] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/21/2013] [Accepted: 11/05/2013] [Indexed: 01/22/2023] Open
Abstract
The objective of the study was to evaluate the ability of a nonlinear ultrasound technique, the so-called nonlinear resonant ultrasound spectroscopy (NRUS) technique, for detecting early microdamage accumulation in cortical bone induced by four-point bending fatigue. Small parallelepiped beam-shaped human cortical bone specimens were subjected to cyclic four-point bending fatigue in several steps. The specimens were prepared to control damage localization during four-point bending fatigue cycling and to unambiguously identify resonant modes for NRUS measurements. NRUS measurements were achieved to follow the evolution of the nonlinear hysteretic elastic behavior during fatigue-induced damage. After each fatigue step, a small number of specimens was removed from the protocol and set apart to quantitatively assess the microcrack number density and length using synchrotron radiation micro-computed tomography (SR-µCT). The results showed a significant effect of damage steps on the nonlinear hysteretic elastic behavior. No significant change in the overall length of microcracks was observed in damaged regions compared to the load-free control regions. Only an increased number of shortest microcracks, those in the lowest quartile, was noticed. This was suggestive of newly formed microcracks during the early phases of damage accumulation. The variation of nonlinear hysteretic elastic behavior was significantly correlated to the variation of the density of short microcracks. Our results suggest that the nonlinear hysteretic elastic behavior is sensitive to early bone microdamage. Therefore NRUS technique can be used to monitor fatigue microdamage progression in in vitro experiments.
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Affiliation(s)
- Sylvain Haupert
- UPMC Univ Paris 06, CNRS UMR7623, Laboratoire d’Imagerie Paramétrique, Paris, France
- * E-mail:
| | | | - Françoise Peyrin
- CREATIS, INSERM U1044, CNRS 5220, INSA Lyon, Université Lyon 1, Lyon, France
- European Synchrotron Radiation Facility, Grenoble, France
| | - David Mitton
- Université de Lyon, IFSTTAR, LBMC, UMR_T 9406, Université Lyon 1, Lyon, France
| | - Pascal Laugier
- UPMC Univ Paris 06, CNRS UMR7623, Laboratoire d’Imagerie Paramétrique, Paris, France
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Lee KI. Correlations of linear and nonlinear ultrasound parameters with density and microarchitectural parameters in trabecular bone. THE JOURNAL OF THE ACOUSTICAL SOCIETY OF AMERICA 2013; 134:EL381-EL386. [PMID: 24181979 DOI: 10.1121/1.4822420] [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
In the present study, correlations of linear and nonlinear ultrasound parameters (speed of sound, normalized broadband ultrasound attenuation, and nonlinear parameter B/A) with bone mineral density and microarchitectural parameters were investigated in 28 bovine femoral trabecular bone samples in vitro. All three ultrasound parameters exhibited relatively high correlation coefficients with the indexes of bone quantity (bone mineral density and bone volume fraction) and lower correlation coefficients with the remaining microarchitectural parameters. These results suggest that B/A, in addition to speed of sound and attenuation, may have potential as an index for the assessment of bone status and osteoporosis.
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Affiliation(s)
- Kang Il Lee
- Department of Physics, Kangwon National University, Chuncheon 200-701, Republic of Korea
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Bochud N, Rus G. Probabilistic inverse problem to characterize tissue-equivalent material mechanical properties. IEEE TRANSACTIONS ON ULTRASONICS, FERROELECTRICS, AND FREQUENCY CONTROL 2012; 59:1443-1456. [PMID: 22828840 DOI: 10.1109/tuffc.2012.2345] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/01/2023]
Abstract
The understanding of internal processes that affect the changes of consistency of soft tissue is a challenging problem. An ultrasound-monitoring Petri dish has been designed to monitor the evolution of relevant mechanical parameters during engineered tissue formation processes in real time. A better understanding of the measured ultrasonic signals required the use of numerical models of the ultrasound-tissue interactions. The extraction of relevant data and its evolution with sufficient sensitivity and accuracy is addressed by applying well-known signal processing techniques to both the experimental and numerically predicted measurements. In addition, a stochastic model-class selection formulation is used to rank which of the proposed interaction models are more plausible. The sensitivity of the system is verified by monitoring a gelation process.
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Affiliation(s)
- Nicolas Bochud
- Department of Structural Mechanics, University of Granada, Politecnico de Fuentenueva, Granada, Spain
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15
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Scalerandi M, Gliozzi AS, Bruno CLE, Antonaci P. Nonequilibrium phenomena in damaged media and their effects on the elastic properties. THE JOURNAL OF THE ACOUSTICAL SOCIETY OF AMERICA 2012; 131:4304-4315. [PMID: 22712905 DOI: 10.1121/1.4707529] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/01/2023]
Abstract
Concrete, particularly if damaged, exhibits a peculiar nonlinear elastic behavior, which is mainly due to the coupling between nonequilibrium and nonlinear features, the two of which are intrinsically connected. More specifically, the formulation of a constitutive equation able to properly predict the dynamic behavior of damaged concrete is made difficult by the concomitant presence of two mechanisms: The modification of the microstructure of the medium and the transition to a new elastic state caused by a finite amplitude excitation (conditioning). Memory of that new state is kept when the excitation is removed, before relaxation back to the original elastic state takes place. Indeed, besides accounting for linear and nonlinear parameters, a realistic constitutive equation to be used in reliable prediction models should take into account nonequilibrium effects. Specific parameters, sensitive to finite amplitude excitations, should be introduced to provide information about conditioning effects. In this paper, experimental results indicating that nonlinearity of damaged concrete is memory-dependent will be presented and the implications of such findings in the development of physical models, with relevant outcomes for the characterization of hysteretical features, will be discussed.
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Affiliation(s)
- M Scalerandi
- Department of Applied Science and Technology, Institute of Physics of Condensed Matter and Complex Systems-Politecnico di Torino, C.so Duca degli Abruzzi 24 10129 Torino, Italy.
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Détection du micro-endommagement dans le tissu osseux trabéculaire par une méthode d’acousto-élasticité dynamique. Ing Rech Biomed 2011. [DOI: 10.1016/j.irbm.2011.09.009] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/23/2022]
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Haupert S, Renaud G, Rivière J, Talmant M, Johnson PA, Laugier P. High-accuracy acoustic detection of nonclassical component of material nonlinearity. THE JOURNAL OF THE ACOUSTICAL SOCIETY OF AMERICA 2011; 130:2654-2661. [PMID: 22087892 DOI: 10.1121/1.3641405] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/31/2023]
Abstract
The aim is to assess the nonclassical component of material nonlinearity in several classes of materials with weak, intermediate, and high nonlinear properties. In this contribution, an optimized nonlinear resonant ultrasound spectroscopy (NRUS) measuring and data processing protocol applied to small samples is described. The protocol is used to overcome the effects of environmental condition changes that take place during an experiment, and that may mask the intrinsic nonlinearity. External temperature fluctuation is identified as a primary source of measurement contamination. For instance, a variation of 0.1 °C produced a frequency variation of 0.01%, which is similar to the expected nonlinear frequency shift for weakly nonlinear materials. In order to overcome environmental effects, the reference frequency measurements are repeated before each excitation level and then used to compute nonlinear parameters. Using this approach, relative resonant frequency shifts of 10(-5) can be measured, which is below the limit of 10(-4) often considered as the limit of NRUS sensitivity under common experimental conditions. Due to enhanced sensitivity resulting from the correction procedure applied in this work, nonclassical nonlinearity in materials that before have been assumed to only be classically nonlinear in past work (steel, brass, and aluminum) is reported.
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Affiliation(s)
- Sylvain Haupert
- Laboratoire d'Imagerie Paramétrique, UPMC Univ Paris 06, CNRS, UMR 7623, Paris, France.
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Faez T, Renaud G, Defontaine M, Calle S, de Jong N. Dynamic manipulation of the subharmonic scattering of phospholipid-coated microbubbles. Phys Med Biol 2011; 56:6459-73. [PMID: 21934190 DOI: 10.1088/0031-9155/56/19/018] [Citation(s) in RCA: 16] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022]
Abstract
In this paper, the influence of a dynamic variation in the ambient pressure on the subharmonic response of phospholipid-coated microbubbles was investigated. The ambient pressure in water was modulated by a 2.5 kHz acoustic wave with a peak amplitude of 15 kPa. We investigated the fundamental and subharmonic emissions at two driving frequencies: 5 and 10 MHz. The modulation of the bubble radius induced by the dynamic variation in the liquid ambient pressure subsequently causes modulations of the scattered acoustic pressure at the fundamental and subharmonic frequencies (half the fundamental frequency). As a first result, we measured that the variation in the ambient pressure of 15 kPa can modulate the subharmonic amplitude up to 10 dB as compared to the static atmospheric pressure condition. As a second result, we noticed that the relative subharmonic amplitude modulation as a function of the LF acoustic pressure was symmetrical for the 5 MHz driving frequency but asymmetric for 10 MHz. In the latter case, the subharmonic amplitude was more enhanced for an ambient overpressure than reduced for an ambient depression of the same amplitude likely due to the buckling of the lipid shell. However, the fundamental amplitude was symmetrically modulated during bubble compression and expansion. Moreover, subharmonic and fundamental amplitude modulations were found to be either in phase or out of phase with the low-frequency acoustic pressure. Numerical simulations showed that this behavior can be obtained depending on the bubbles' diameter. The highest subharmonic amplitude was measured when microbubbles were insonified at 10 MHz. This fact together with the asymmetry observed in the subharmonic modulation suggests that smaller bubbles with a buckling shell are excited at 10 MHz compared to 5 MHz. These results present new potentials for in vitro characterization of contrast agent microbubbles and possibly a new imaging modality.
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Affiliation(s)
- Telli Faez
- Biomedical Engineering Thoraxcenter, Erasmus Medical Center, PO Box 2040, 3000 CA Rotterdam, The Netherlands.
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Jing Y, Tao M, Clement GT. Evaluation of a wave-vector-frequency-domain method for nonlinear wave propagation. THE JOURNAL OF THE ACOUSTICAL SOCIETY OF AMERICA 2011; 129:32-46. [PMID: 21302985 PMCID: PMC3055284 DOI: 10.1121/1.3504705] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/02/2009] [Revised: 09/24/2010] [Accepted: 09/24/2010] [Indexed: 05/08/2023]
Abstract
A wave-vector-frequency-domain method is presented to describe one-directional forward or backward acoustic wave propagation in a nonlinear homogeneous medium. Starting from a frequency-domain representation of the second-order nonlinear acoustic wave equation, an implicit solution for the nonlinear term is proposed by employing the Green's function. Its approximation, which is more suitable for numerical implementation, is used. An error study is carried out to test the efficiency of the model by comparing the results with the Fubini solution. It is shown that the error grows as the propagation distance and step-size increase. However, for the specific case tested, even at a step size as large as one wavelength, sufficient accuracy for plane-wave propagation is observed. A two-dimensional steered transducer problem is explored to verify the nonlinear acoustic field directional independence of the model. A three-dimensional single-element transducer problem is solved to verify the forward model by comparing it with an existing nonlinear wave propagation code. Finally, backward-projection behavior is examined. The sound field over a plane in an absorptive medium is backward projected to the source and compared with the initial field, where good agreement is observed.
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Affiliation(s)
- Yun Jing
- Department of Radiology, Harvard Medical School, Brigham and Women's Hospital, Boston, Massachusetts 02115, USA
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Renaud G, Callé S, Defontaine M. Dynamic acoustoelastic testing of weakly pre-loaded unconsolidated water-saturated glass beads. THE JOURNAL OF THE ACOUSTICAL SOCIETY OF AMERICA 2010; 128:3344-3354. [PMID: 21218868 DOI: 10.1121/1.3502461] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/30/2023]
Abstract
Dynamic acoustoelastic testing is applied to weakly pre-loaded unconsolidated water-saturated glass beads. The gravitational acceleration produces, on the probed beads, a static stress of order 130 Pa, thus the granular medium is close to the jamming transition. A low-frequency (LF) acoustic wave gently disturbs the medium, inducing successively slight expansion and compaction of the granular packing expected to modulate the number of contacts between beads. Ultrasound (US) pulses are emitted simultaneously to dynamically detect the induced modification of the granular skeleton. US propagation velocity and attenuation both increase when the LF pressure increases. The quadratic nonlinear elastic parameter β, related to the pressure dependence of US propagation velocity, was measured in the range 60-530 if water-saturated glass beads are considered as an effective medium. A dynamic modification of US scattering induced by beads is proposed to modulate US attenuation. Complex hysteretic behaviors and tension-compression asymmetry are also observed and analyzed by time-domain and spectral analyses. Furthermore acoustic nonlinearities are measured in cases of quasi-static and dynamic variations of the LF wave amplitude, providing quantitatively similar acoustic nonlinearities but qualitatively different.
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Affiliation(s)
- Guillaume Renaud
- INSERM U930-CNRS ERL3106-Université François Rabelais UFR Médecine, 10 boulevard Tonnellé, 37000 Tours, France.
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Dazel O, Tournat V. Nonlinear Biot waves in porous media with application to unconsolidated granular media. THE JOURNAL OF THE ACOUSTICAL SOCIETY OF AMERICA 2010; 127:692-702. [PMID: 20136191 DOI: 10.1121/1.3277190] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/28/2023]
Abstract
The nonlinear propagation through porous media is investigated in the framework of Biot theory. For illustration, and considering the current interest for the determination of the elastic properties of granular media, the case of nonlinear propagation in "model" granular media (disordered packings of noncohesive elastic beads of the same size embedded in a visco-thermal fluid) is considered. The solutions of linear Biot waves are first obtained, considering the appropriate geometrical and physical parameters of the medium. Then, making use of the method of successive approximations of nonlinear acoustics, the solutions for the second harmonic Biot waves are derived by considering a quadratic nonlinearity in the solid frame constitutive law (which takes its origin from the high nonlinearity of contacts between grains). The propagation in a semi-infinite medium with velocity dispersion, frequency dependent dissipation, and nonlinearity is first analyzed. The case of a granular medium slab with rigid boundaries, often considered in experiments, is then presented. Finally, the importance of mode coupling between solid and fluid waves is evaluated, depending on the actual fluid, the bead diameter, or the applied static stress on the beads. The application of these results to other media supporting Biot waves (porous ceramics, polymer foams, etc.) is straightforward.
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Affiliation(s)
- Olivier Dazel
- LAUM, CNRS, Universite du Maine, Avenue Olivier Messiaen, 72085 Le Mans, France
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Microdamage evaluation in human trabecular bone based on nonlinear ultrasound vibro-modulation (NUVM). J Biomech 2009; 42:581-6. [DOI: 10.1016/j.jbiomech.2008.12.018] [Citation(s) in RCA: 14] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/18/2008] [Revised: 12/16/2008] [Accepted: 12/17/2008] [Indexed: 11/21/2022]
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Gluer CC. A new quality of bone ultrasound research. IEEE TRANSACTIONS ON ULTRASONICS, FERROELECTRICS, AND FREQUENCY CONTROL 2008; 55:1524-1528. [PMID: 18986942 DOI: 10.1109/tuffc.2008.828] [Citation(s) in RCA: 17] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/27/2023]
Abstract
Quantitative ultrasound (QUS) methods have strong power to predict osteoporotic fractures, but they are also very relevant for the assessment of bone quality. A representative sample of recent studies addressing these topics can be found in this special issue. Further pursuit of these methods will establish micro-QUS imaging methods as tools for measuring specific aspects of bone quality. Once this is achieved, we will be able to link such data to the clinical QUS methods used in vivo to determine which aspects of bone quality cause QUS to be a predictor of fracture risk that is independent of bone mineral density (BMD). Potentially this could lead to the development of a new generation of QUS devices for improved and expanded clinical assessment. Good quality of basic science work will thus lead to good quality of clinical patient examinations on the basis of a more detailed assessment of bone quality.
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Affiliation(s)
- C C Gluer
- Medizinische Phys., Univ. Schleswig-Holstein, Kiel, Germany.
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