A free plate model can predict guided modes propagating in tubular bone-mimicking phantoms

Minonzio, Jean‐Gabriel; Foiret, Josquin; Moilanen, Petro; Pirhonen, Jalmari; Zhao, Zuomin; Talmant, Maryline; Timonen, J.; Laugier, Pascal

doi:10.1121/1.4903920

Cited by 27 publications

(24 citation statements)

References 20 publications

(40 reference statements)

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“…Consequently, this study does not come down for or against the validity of the plate model in its forward use, but on the correctness of the model parameters inferred by the inverse problem. For the frequency-thickness product range considered here, the obtained estimates close to the reference values suggest that when studied axially and over a relatively short receivers distance, the Lamb wave theory in plates represents a good approximation to explain GWs propagating in the radius, as shown in our previous work [20,40].…”

Section: Discussionsupporting

confidence: 82%

“…In the present study, a two-dimensional (2-D) transverse isotropic non absorbing free plate waveguide model is used to fit the experimental dispersion curves. This choice is motivated by our previous studies, which showed that the propagation of guided waves into tubular-shaped samples could be explained by a 2-D free plate model [40] and that a 2-D transverse isotropic free plate model, despite its simplicity, provided reliable cortical thickness estimates [20].…”

Section: Forward Calculation Of the Lamb Modesmentioning

confidence: 99%

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Genetic algorithms-based inversion of multimode guided waves for cortical bone characterization

et al. 2016

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Recent progress in quantitative ultrasound has exploited the multimode waveguide response of long bones. Measurements of the guided modes, along with suitable waveguide modeling, have the potential to infer strength-related factors such as stiffness (mainly determined by cortical porosity) and cortical thickness. However, the development of such model-based approaches is challenging, in particular because of the multiparametric nature of the inverse problem. Current estimation methods in the bone field rely on a number of assumptions for pairing the incomplete experimental data with the theoretical guided modes (e.g. semi-automatic selection and classification of the data). The availability of an alternative inversion scheme that is user-independent is highly desirable. Thus, this paper introduces an efficient inversion method based on genetic algorithms using multimode guided waves, in which the mode-order is kept blind. Prior to its evaluation on bone, our proposal is validated using laboratory-controlled measurements on isotropic plates and bone-mimicking phantoms. The results show that the model parameters (i.e. cortical thickness and porosity) estimated from measurements on a few ex vivo human radii are in good agreement with the reference values derived from x-ray micro-computed tomography. Further, the cortical thickness estimated from in vivo measurements at the third from the distal end of the radius is in good agreement with the values delivered by site-matched high-resolution x-ray peripheral computed tomography.

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Section: Discussionsupporting

confidence: 82%

Section: Forward Calculation Of the Lamb Modesmentioning

confidence: 99%

Genetic algorithms-based inversion of multimode guided waves for cortical bone characterization

et al. 2016

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“…Given the rather limited length of the ROI (20 mm), we assume a uniform cortical thickness in the measurement region [27]; and (iii) given our probe configuration (the elements width is much larger than the pitch) and its central frequency (1-MHz), bone curvature is negligible and guided waves mostly propagate in the axial direction. The tubular bone shape can thus be locally approximated by a plate [28].…”

Section: A Forward Problemmentioning

confidence: 99%

Bone cortical thickness and porosity assessment using ultrasound guided waves: An ex vivo validation study

Minonzio

Bochud

Vallet

et al. 2018

Bone

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Several studies showed the ability of the cortex of long bones such as the radius and tibia to guide mechanical waves. Such experimental evidence has given rise to the emergence of a category of quantitative ultrasound techniques, referred to as the axial transmission, specifically developed to measure the propagation of ultrasound guided waves in the cortical shell along the axis of long bones. An ultrasound axial transmission technique, with an automated approach to quantify cortical thickness and porosity is described. The guided modes propagating in the cortex are recorded with a 1-MHz custom made linear transducer array. Measurement of the dispersion curves is achieved using a two-dimensional spatio-temporal Fourier transform combined with singular value decomposition. Automatic parameters identification is obtained through the solution of an inverse problem in which the dispersion curves are predicted with a two-dimensional transverse isotropic free plate model. Thirty-one radii and fifteen tibiae harvested from human cadavers underwent axial transmission measurements. Estimates of cortical thickness and porosity were obtained on 40 samples out of 46. The reproducibility, given by the root mean square error of the standard deviation of estimates, was 0.11 mm for thickness and 1.9% for porosity. To assess accuracy, site-matched micro-computed tomography images of the bone specimens imaged at 9 μm voxel size served as the gold standard. Agreement between micro-computed tomography and axial transmission for quantification of thickness and porosity at the radius and tibia ranged from R=0.63 for porosity (root mean square error RMSE=1.8%) to 0.89 for thickness (RMSE=0.3 mm). Despite an overall good agreement for porosity, the method performs less well for porosities lower than 10%. The heterogeneity and general complexity of cortical bone structure, which are not fully accounted for by our model, are suspected to weaken the model approximation. This study presents the first validation study for assessing cortical thickness and porosity using the axial transmission technique. The automatic signal processing minimizes operator-dependent errors for parameters determination. Recovering the waveguide characteristics, that is to say cortical thickness and porosity, could provide reliable information about skeletal status and future fracture risk.

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“…to simplify the interpretation of ultrasonic responses obtained numerically or experimentally (Kilappa et al, 2015;Le et al, 2010;Minonzio et al, 2015;Xu et al, 2016). Recently, more comprehensive numerical approaches were explored with the aim of improving the realism of the effect of cortical bone features on the axial transmission propagation expected in vivo.…”

Section: Introductionmentioning

confidence: 99%

Effect of intracortical bone properties on the phase velocity and cut-off frequency of low-frequency guided wave modes (20–85 kHz)

Pereira

Haïat²,

Fernandes

et al. 2019

The Journal of the Acoustical Society of America

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Manuscript (TeX or Word only) Click here to access/download;Manuscript (TeX or Word only);Manuscript.tex JASA/Sample JASA Article The assessment of intracortical bone properties is of interest since early-stage osteoporosis is associated with resorption in the endosteal region. However, understanding the interaction between ultrasonic guided waves and the cortical bone structure remains challenging. The purpose of this work is to investigate the effect of intracortical bone properties on the ultrasonic response obtained at low-frequency (<100 kHz) using an axial transmission configuration. The semi-analytical finite element method was used to simulate the propagation of guided waves in a waveguide with realistic geometry and material properties. An array of 20 receivers was used to calculate the phase velocity and cutoff frequency of the excited modes using the 2D Fourier transform. The results show that the position of the emitter around the circumference of the bone is an important parameter to control since it can lead to variations of up to 10 dB in the amplitude of the transmitted modes. The cutoff frequency of the high order modes was, however, only slightly affected by the circunferential position of the emitter, and was sensitive mainly to the axial shear modulus. The phase velocity and cutoff frequency in the 20-85 kHz range are promising parameters for the assessment of intracortical properties.

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A free plate model can predict guided modes propagating in tubular bone-mimicking phantoms

Cited by 27 publications

References 20 publications

Genetic algorithms-based inversion of multimode guided waves for cortical bone characterization

Genetic algorithms-based inversion of multimode guided waves for cortical bone characterization

Bone cortical thickness and porosity assessment using ultrasound guided waves: An ex vivo validation study

Effect of intracortical bone properties on the phase velocity and cut-off frequency of low-frequency guided wave modes (20–85 kHz)

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