Modeling the impact of soft tissue on axial transmission measurements of ultrasonic guided waves in human radius

Photoacoustic Imaging and Characterization of Bone in Medicine: Overview, Applications, and Outlook

Photoacoustic techniques have shown promise in identifying molecular changes in bone tissue and visualizing tissue microstructure. This capability represents significant advantages over gold standards (i.e., dual-energy X-ray absorptiometry) for bone evaluation without requiring ionizing radiation. Instead, photoacoustic imaging uses light to penetrate through bone, followed by acoustic pressure generation, resulting in highly sensitive optical absorption contrast in deep biological tissues. This review covers multiple bone-related photoacoustic imaging contributions to clinical applications, spanning bone cancer, joint pathologies, spinal disorders, osteoporosis, bone-related surgical guidance, consolidation monitoring, and transsphenoidal and transcranial imaging. We also present a summary of photoacoustic-based techniques for characterizing biomechanical properties of bone, including temperature, guided waves, spectral parameters, and spectroscopy. We conclude with a future outlook based on the current state of technological developments, recent achievements, and possible new directions.

Meta-Learning Analysis of Ultrasonic Guided Waves for Coated Cortical Bone Characterization

Due to its sensitivity to geometrical and mechanical properties of waveguides, ultrasonic guided waves (UGWs) propagating in cortical bones play an important role in the early diagnosis of osteoporosis. However, as impacts of overlaid soft tissues are complex, it remains challenging to retrieve bone properties accurately. Meta-learning, i.e., learning to learn, is capable of extracting transferable features from a few data and, thus, suitable to capture potential characteristics, leading to accurate bone assessment. In this study, we investigate the feasibility to apply the multichannel identification neural network (MCINN) to estimate the thickness and bulk velocities of coated cortical bone. It minimizes the effects of soft tissue by extracting specific features of UGW, which shares the same cortical properties, while the overlaid soft tissue varies. Distinguished from most reported methods, this work moves from the hand-design inversion scheme to data-driven assessment by automatically mapping features of UGW to the space of bone properties. The MCINN was trained and validated using simulated datasets produced by the finite-difference time-domain (FDTD) method and then applied to experimental data obtained from cortical bovine bone plates overlaid with soft tissue mimics. A good match was found between experimental trajectories and theoretical dispersion curves. The results demonstrated that the proposed method was feasible to assess the thickness of coated cortical bone plates.

Analysis of Ultrasonic Guided Wave Propagation in Multilayered Bone Structure With Varying Soft-Tissue Thickness in View of Cortical Bone Characterization

Noninvasive characterization of cortical long bones using axial transmission ultrasound is a promising diagnostic technology for osteoporotic cortical thinning assessment. However, the soft tissue-bone coupling effect remains to be a challenge and an ambiguity especially in vivo. The influence of the overlying soft tissue layer with a varying thickness on the propagation of ultrasonic guided waves in cortical bone is studied experimentally and theoretically in this article. The wave propagation is characterized based on waveform comparison, spectral density and decomposition, dispersion energy imaging, and particle displacement analysis. Good agreement between experimental observations with theoretical predictions by semi-analytical finite element simulations is observed. The sensitivity of propagation characteristics in response to the coupled tissue thickness is elucidated. As the thickness of the loading soft tissue grows, the guided wave signals exhibit greater attenuated amplitude and delayed arrival time; more complex dispersive wave patterns emerge; and the modal number and density increase. The research findings advance the fundamental comprehension of ultrasonic-guided-wave excitation and interaction in long bones and facilitate further technical development and clinical utility of quantitative guided-wave ultrasonography in routine healthcare services as a nondestructive imaging modality for cortical bone examination.

Estimation of Thickness and Speed of Sound in Cortical Bone Using Multifocus Pulse-Echo Ultrasound

Most bone loss during the development of osteoporosis occurs in cortical bone at the peripheral skeleton. Decreased cortical thickness (Ct.Th) and the prevalence of large pores at the tibia are associated with reduced bone strength at the hip. Ct.Th and cortical sound velocity, i.e., a surrogate marker for changes of cortical porosity (Ct.Po), are key biomarkers for the identification of patients at high fracture risk. In this study, we have developed a method using a conventional ultrasound array transducer to determine thickness (Ct.Th) and the compressional sound velocity propagating in the radial bone direction (Ct. ν₁₁ ) using a refraction-corrected multifocus imaging approach. The method was validated in-silico on porous bone plate models using a 2-D finite-difference time-domain method and ex vivo on plate-shaped plastic reference materials and on plate-shaped cortical bovine tibia samples. Plane-wave pulse-echo measurements provided reference values to assess precision and accuracy of our method. In-silico results revealed the necessity to account for inclination-dependent transmission losses at the bone surface. Moreover, the dependence of Ct. ν₁₁ on both porosity and pore density was observed. Ct.Th and Ct. ν₁₁ obtained ex vivo showed a high correlation ) with reference values. The ex-vivo accuracy and precision for Ct. ν₁₁ were 29.9 m/s and 0.94%, respectively, and those for Ct.Th were 0.04 mm and 1.09%, respectively. In conclusion, this numerical and experimental study demonstrates an accurate and precise estimation of Ct.Th and Ct. ν₁₁ . The developed multifocus technique may have high clinical potential to improve fracture risk prediction using noninvasive and nonionizing conventional ultrasound technology with image guidance.

Ultrasound-Based Estimates of Cortical Bone Thickness and Porosity Are Associated With Nontraumatic Fractures in Postmenopausal Women: A Pilot Study

Recent ultrasound (US) axial transmission techniques exploit the multimode waveguide response of long bones to yield estimates of cortical bone structure characteristics. This pilot cross-sectional study aimed to evaluate the performance at the one-third distal radius of a bidirectional axial transmission technique (BDAT) to discriminate between fractured and nonfractured postmenopausal women. Cortical thickness (Ct.Th) and porosity (Ct.Po) estimates were obtained for 201 postmenopausal women: 109 were nonfractured (62.6 ± 7.8 years), 92 with one or more nontraumatic fractures (68.8 ± 9.2 years), 17 with hip fractures (66.1 ± 10.3 years), 32 with vertebral fractures (72.4 ± 7.9 years), and 17 with wrist fractures (67.8 ± 9.6 years). The areal bone mineral density (aBMD) was obtained using DXA at the femur and spine. Femoral aBMD correlated weakly, but significantly with Ct.Th (R = 0.23, p < 0.001) and Ct.Po (R = -0.15, p < 0.05). Femoral aBMD and both US parameters were significantly different between the subgroup of all nontraumatic fractures combined and the control group (p < 0.05). The main findings were that (1) Ct.Po was discriminant for all nontraumatic fractures combined (OR = 1.39; area under the receiver operating characteristic curve [AUC] equal to 0.71), for vertebral (OR = 1.96; AUC = 0.84) and wrist fractures (OR = 1.80; AUC = 0.71), whereas Ct.Th was discriminant for hip fractures only (OR = 2.01; AUC = 0.72); there was a significant association (2) between increased Ct.Po and vertebral and wrist fractures when these fractures were not associated with any measured aBMD variables; (3) between increased Ct.Po and all nontraumatic fractures combined independently of aBMD neck; and (4) between decreased Ct.Th and hip fractures independently of aBMD femur. BDAT variables showed comparable performance to that of aBMD neck with all types of fractures (OR = 1.48; AUC = 0.72) and that of aBMD femur with hip fractures (OR = 2.21; AUC = 0.70). If these results are confirmed in prospective studies, cortical BDAT measurements may be considered useful for assessing fracture risk in postmenopausal women. © 2019 American Society for Bone and Mineral Research.

Influence of guided waves in bone on pulse-inversion contrast-enhanced ultrasound

PURPOSE

Guided waves generated from bone cortex inevitably act on microbubbles flowing through skeletal muscle capillaries in contrast-enhanced ultrasound (CEUS) and might influence the image quality. However, the action mechanism underlying the guided waves influence is still unknown, especially under contrast pulse-inversion transmission mode. This study aimed to clarify the influence of guided waves on pulse-inversion CEUS, which was investigated via in vitro infusion experiments.

METHOD

Tibia guided waves were detected at pulse-inversion transmission and then characterized by using a short-time Fourier transform energy distribution. Using results at normal incidence as a baseline, the influence of guided wave dispersion on the contrast and resolution of pulse-inversion CEUS was investigated at an oblique incidence through continuous microbubbles infusion experiments in a vessel-tibia flow phantom.

RESULTS

Frequency-dispersive property of tibia guided waves was observed at phases 0° and 180°, which improved the contrast of CEUS and reduced its resolution. Pulse-inversion CEUS balanced the contrast enhancement and resolution degeneration induced by guided waves. By contrast, contrast-to-tissue ratio of pulse-inversion CEUS increased by up to 109.1 ± 13.2% (P < 0.05) due to guided waves and its resolution was up to 0.9 ± 0.1 times that of baseline.

CONCLUSIONS

Alterations of contrast and resolution in pulse-inversion CEUS induced by guided waves might provide an additional assessment for the capillary perfusion in the skeletal muscle near the bone cortex.

In Vivo Measurements of Cortical Thickness and Porosity at the Proximal Third of the Tibia Using Guided Waves: Comparison with Site-Matched Peripheral Quantitative Computed Tomography and Distal High-Resolution Peripheral Quantitative Computed Tomography

The aim of this study was to estimate cortical porosity (Ct.Po) and cortical thickness (Ct.Th) using 500-kHz bi-directional axial transmission (AT). Ct.Th_AT and Ct.Po_AT were obtained at the tibia in 15 patients from a 2-D transverse isotropic free plate model fitted to measured guided wave dispersion curves. The velocities of the first arriving signal (υ_FAS) and A₀ mode (υ_A0) were also determined. Site-matched peripheral quantitative computed tomography (pQCT) provided volumetric cortical bone mineral density (Ct.vBMD_pQCT) and Ct.Th_pQCT. Good agreement was found between Ct.Th_AT and Ct.Th_pQCT (R² = 0.62, root mean square error [RMSE] = 0.39 mm). Ct.vBMD_pQCT correlated with Ct.Po_AT (R² = 0.57), υ_FAS (R² = 0.43) and υ_A0 (R² = 0.28). Furthermore, a significant correlation was found between AT and distal high-resolution pQCT. The measurement ofcortical parameters at the tibia using guided waves might improve the prediction of bone fractures in a cost-effective and radiation-free manner.

Ex vivo cortical porosity and thickness predictions at the tibia using full-spectrum ultrasonic guided-wave analysis

The estimation of cortical thickness (Ct.Th) and porosity (Ct.Po) at the tibia using axial transmission ultrasound was successfully validated ex vivo against site-matched micro-computed tomography. The assessment of cortical parameters based on full-spectrum guided-wave analysis might improve the prediction of bone fractures in a cost-effective and radiation-free manner.

PURPOSE

Cortical thickness (Ct.Th) and porosity (Ct.Po) are key parameters for the identification of patients with fragile bones. The main objective of this ex vivo study was to validate the measurement of Ct.Po and Ct.Th at the tibia using a non-ionizing, low-cost, and portable 500-kHz ultrasound axial transmission system. Additional ultrasonic velocities and site-matched reference parameters were included in the study to broaden the analysis.

METHODS

Guided waves were successfully measured ex vivo in 17 human tibiae using a novel 500-kHz bi-directional axial transmission probe. Theoretical dispersion curves of a transverse isotropic free plate model with invariant matrix stiffness were fitted to the experimental dispersion curves in order to estimate Ct.Th and Ct.Po. In addition, the velocities of the first arriving signal (υ_FAS) and A₀ mode (υ_A0) were measured. Reference Ct.Po, Ct.Th, and vBMD were obtained from site-matched micro-computed tomography. Scanning acoustic microscopy (SAM) provided the acoustic impedance of the axial cortical bone matrix.

RESULTS

The best predictions of Ct.Po (R² = 0.83, RMSE = 2.2%) and Ct.Th (R² = 0.92, RMSE = 0.2 mm, one outlier excluded) were obtained from the plate model. The second best predictors of Ct.Po and Ct.Th were vBMD (R² = 0.77, RMSE = 2.6%) and υ_A0 (R² = 0.28, RMSE = 0.67 mm), respectively.

CONCLUSIONS

Ct.Th and Ct.Po were accurately predicted at the human tibia ex vivo using a transverse isotropic free plate model with invariant matrix stiffness. The model-based predictions were not further enhanced when we accounted for variations in axial tissue stiffness as reflected by the acoustic impedance from SAM.

Dispersion characteristics of the flexural wave assessed using low frequency (50-150kHz) point-contact transducers: A feasibility study on bone-mimicking phantoms

Guided waves-based techniques are currently under development for quantitative cortical bone assessment. However, the signal interpretation is challenging due to multiple mode overlapping. To overcome this limitation, dry point-contact transducers have been used at low frequencies for a selective excitation of the zeroth order anti-symmetric Lamb A0 mode, a mode whose dispersion characteristics can be used to infer the thickness of the waveguide. In this paper, our purpose was to extend the technique by combining a dry point-contact transducers approach to the SVD-enhanced 2-D Fourier transform in order to measure the dispersion characteristics of the flexural mode. The robustness of our approach is assessed on bone-mimicking phantoms covered or not with soft tissue-mimicking layer. Experiments were also performed on a bovine bone. Dispersion characteristics of measured modes were extracted using a SVD-based signal processing technique. The thickness was obtained by fitting a free plate model to experimental data. The results show that, in all studied cases, the estimated thickness values are in good agreement with the actual thickness values. From the results, we speculate that in vivo cortical thickness assessment by measuring the flexural wave using point-contact transducers is feasible. However, this assumption has to be confirmed by further in vivo studies.

Semi-analytical finite-element modeling approach for guided wave assessment of mechanical degradation in bones

Numerical models based on the Semi Analytical Finite-Element method are used to study the characteristics of guided wave modes supported by bone-like multi-layered tubular structures. The method is first validated using previous literature and experimental studies on phantoms mimicking healthy and osteoporotic conditions of cortical bone, and later used to study a trilayer marrow–bone–tissue system at varying mechanical degradation levels. The results show that bone condition strongly affects the modal properties of axially propagating guided waves and indicates that L(0,3) and F(1,6) are suitable modes for assessing the mechanical condition of the bone. The work here reports suitable modal selection and their dispersion properties which would the aid in development of a transduction mechanism for mechanical assessment of bones.

Predicting bone strength with ultrasonic guided waves

Recent bone quantitative ultrasound approaches exploit the multimode waveguide response of long bones for assessing properties such as cortical thickness and stiffness. Clinical applications remain, however, challenging, as the impact of soft tissue on guided waves characteristics is not fully understood yet. In particular, it must be clarified whether soft tissue must be incorporated in waveguide models needed to infer reliable cortical bone properties. We hypothesize that an inverse procedure using a free plate model can be applied to retrieve the thickness and stiffness of cortical bone from experimental data. This approach is first validated on a series of laboratory-controlled measurements performed on assemblies of bone- and soft tissue mimicking phantoms and then on in vivo measurements. The accuracy of the estimates is evaluated by comparison with reference values. To further support our hypothesis, these estimates are subsequently inserted into a bilayer model to test its accuracy. Our results show that the free plate model allows retrieving reliable waveguide properties, despite the presence of soft tissue. They also suggest that the more sophisticated bilayer model, although it is more precise to predict experimental data in the forward problem, could turn out to be hardly manageable for solving the inverse problem.

In Vivo Characterization of Cortical Bone Using Guided Waves Measured by Axial Transmission

Cortical bone loss is not fully assessed by the current X-ray methods, and there is an unmet need in identifying women at risk of osteoporotic fracture, who should receive a treatment. The last decade has seen the emergence of the ultrasound (US) axial transmission (AT) techniques to assess a cortical bone. Recent AT techniques exploit the multimode waveguide response of the long bones such as the radius. A recent ex vivo study by our group evidenced that a multimode AT approach can yield simultaneous estimates of cortical thickness (Ct.Th) and stiffness. The aim of this paper is to move one step forward to evaluate the feasibility of measuring multimode guided waves (GW) in vivo and to infer from it cortical thickness. Measurements were taken on the forearm of 14 healthy subjects with the goal to test the accuracy of the estimated thickness using the bidirectional AT method implemented on a dedicated 1-MHz linear US array. This setup allows determining in vivo the dispersion curves of GW transmitted in the cortical layer of the radius. An inverse procedure based on the comparison between the measured and modeled dispersion curves predicted by a 2-D transverse isotropic free plate waveguide model allowed an estimation of cortical thickness, despite the presence of soft tissue. The Ct.Th values were validated by comparison with the site-matched estimates derived from X-ray high-resolution peripheral quantitative computed tomography. Results showed a significant correlation between both measurements ( r² = 0.7 , , and [Formula: see text] mm). This pilot study demonstrates the potential of bidirectional AT for the in vivo assessment of cortical thickness, a bone strength-related factor.

Multichannel processing for dispersion curves extraction of ultrasonic axial-transmission signals: Comparisons and case studies

Some pioneering studies have shown the clinical feasibility of long bones evaluation using ultrasonic guided waves. Such a strategy is typically designed to determine the dispersion information of the guided modes to infer the elastic and structural characteristics of cortical bone. However, there are still some challenges to extract multimode dispersion curves due to many practical limitations, e.g., high spectral density of modes, limited spectral resolution and poor signal-to-noise ratio. Recently, two representative signal processing methods have been proposed to improve the dispersion curves extraction. The first method is based on singular value decomposition (SVD) with advantages of multi-emitter and multi-receiver configuration for enhanced mode extraction; the second one uses linear Radon transform (LRT) with high-resolution imaging of the dispersion curves. To clarify the pros and cons, a face to face comparison was performed between the two methods. The results suggest that the LRT method is suitable to separate the guided modes at low frequency-thickness-product ( fh) range; for multimode signals in broadband fh range, the SVD-based method shows more robust performances for weak mode enhancement and noise filtering. Different methods are valuable to cover the entire fh range for processing ultrasonic axial transmission signals measured in long cortical bones.

Tailoring the excitation of fundamental flexural guide waves in coated bone by phase-delayed array: two-dimensional simulations

The fundamental flexural guided wave (FFGW) enables ultrasonic assessment of cortical bone thickness. In vivo, it is challenging to detect this mode, as its power ratio with respect to disturbing ultrasound is reduced by soft tissue covering the bone. A phase-delayed ultrasound source is proposed to tailor the FFGW excitation in order to improve its power ratio. This situation is analyzed by 2D finite-element simulations. The soft tissue coating (7-mm thick) was simulated as a fluid covering an elastic plate (bone, 2-6 mm thick). A six-element array of emitters on top of the coating was excited by 50-kHz tone bursts so that each emitter was appropriately delayed from the previous one. Response was recorded by an array of receivers on top of the coating, 20-50 mm away from the closest emitter. Simulations predicted that such tailored/phase-delayed excitations should improve the power ratio of FFGW by 23 ± 5 dB, independent of the number of emitters (N). On the other hand, the FFGW magnitude should increase by 5.8 ± 0.5 dB for each doubling of N. This suggests that mode tailoring based on phase-delayed excitation may play a key role in the development of an in vivo FFGW assessment.

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

The goal of this work was to show that a non-absorbing free plate model can predict with a reasonable accuracy guided modes measured in bone-mimicking phantoms that have circular cross-section. Experiments were carried out on uncoated and coated phantoms using a clinical axial transmission setup. Adjustment of the plate model to the experimental data yielded estimates for the waveguide characteristics (thickness, bulk wave velocities). Fair agreement was achieved over a frequency range of 0.4 to 1.6 MHz. A lower accuracy observed for the thinnest bone-mimicking phantoms was caused by limitations in the wave number measurements rather than by the model itself.

On ultrasound waves guided by bones with coupled soft tissues: a mechanism study and in vitro calibration

The influence of soft tissues coupled with cortical bones on precision of quantitative ultrasound (QUS) has been an issue in the clinical bone assessment in conjunction with the use of ultrasound. In this study, the effect arising from soft tissues on propagation characteristics of guided ultrasound waves in bones was investigated using tubular Sawbones phantoms covered with a layer of mimicked soft tissue of different thicknesses and elastic moduli, and an in vitro porcine femur in terms of the axial transmission measurement. Results revealed that presence of soft tissues can exert significant influence on the propagation of ultrasound waves in bones, leading to reduced propagation velocities and attenuated wave magnitudes compared with the counterparts in a free bone in the absence of soft tissues. However such an effect is not phenomenally dependent on the variations in thickness and elastic modulus of the coupled soft tissues, making it possible to compensate for the coupling effect regardless of the difference in properties of the soft tissues. Based on an in vitro calibration, this study proposed quantitative compensation for the effect of soft tissues on ultrasound waves in bones, facilitating development of high-precision QUS.

Photo-acoustic excitation and optical detection of fundamental flexural guided wave in coated bone phantoms

Photo-acoustic (PA) imaging was combined with skeletal quantitative ultrasound (QUS) for assessment of human long bones. This approach permitted low-frequency excitation and detection of ultrasound so as to efficiently receive the thickness-sensitive fundamental flexural guided wave (FFGW) through a coating of soft tissue. The method was tested on seven axisymmetric bone phantoms, whose 1- to 5-mm wall thickness and 16-mm diameter mimicked those of the human radius. Phantoms were made of a composite material and coated with a 2.5- to 7.5-mm layer of soft material that mimicked soft tissue. Ultrasound was excited with a pulsed Nd:YAG laser at 1064-nm wavelength and received on the same side of the coated phantom with a heterodyne interferometer. The FFGW was detected at 30-kHz frequency. Fitting the FFGW phase velocity by the FLC(1,1) tube mode provided an accurate (9.5 ± 4.0%) wall thickness estimate. Ultrasonic in vivo characterization of cortical bone thickness may thus become possible.

Accurate measurement of guided modes in a plate using a bidirectional approach

Measuring guided wave propagation in long bones is of interest to the medical community. When an inclination exists between the probe and the tested specimen surface, a bias is introduced on the guided mode wavenumbers. The aim of this study was to generalize the bidirectional axial transmission technique initially developed for the first arriving signal. Validation tests were performed on academic materials such a bone-mimicking plate covered with either a silicon or fat-mimicking layer. For any inclination, the wavenumbers measured with the probe parallel to the waveguide surface can be obtained by averaging the wavenumbers measured in two opposite directions.

Analysis of ultrasonic waves propagating in a bone plate over a water half-space with and without overlying soft tissue

Recent in vitro studies have shown that guided waves can characterize bone properties. However, for clinical applications to be viable, the soft-tissue layer should be considered. This study examined the effect of soft tissue on guided waves using a bovine bone plate over a water half-space and overlaid by a 4-mm gelatin-based soft-tissue mimic. The data (with and without soft tissue) clearly show a high-frequency, fast-propagating wave packet and a low-frequency, delayed phase group. The presence of soft tissue attenuates the signals significantly and increases mode density and number as predicted by theory. The data retain higher frequency content than the bone-plate data at large offsets. Using theoretical dispersion curves, the guided modes can be identified with mode 1 (similar to the A0 Lamb mode) minimally affected by the addition of soft tissue. There is infiltration of high-frequency, late-arriving energy within the low-velocity guided-wave regime. Results of travel-time calculation suggest that P-wave and PP-reflections/multiples within the soft tissue may be responsible for the high-frequency oscillations.

Assessment of the fundamental flexural guided wave in cortical bone by an ultrasonic axial-transmission array transducer

The fundamental flexural guided wave (FFGW), as modeled, for example, by the A0 Lamb mode, is a clinically useful indicator of cortical bone thickness. In the work described in this article, we tested so-called multiridge-based analysis, based on the crazy climber algorithm and short-time Fourier transform, for assessment of the FFGW component recorded by a clinical array transducer featuring a limited number of elements. Methods included numerical finite-element simulations and experiments in bone phantoms and human radius specimens (n = 41). The proposed approach enabled extraction of the FFGW component and determination of its group velocity. This group velocity was in good agreement with theoretical predictions and possessed reasonable sensitivity to cortical width (r(2) = 0.51, p < 0.001) in the in vitro experiments. It is expected that the proposed approach enables related clinical application. Further work is still needed to analyze in more detail the challenges related to the impact of the overlying soft tissue.

Modeling elastic waves in coupled media: Estimate of soft tissue influence and application to quantitative ultrasound

The effect of medium coupling on propagation of elastic waves is a general concern in a variety of engineering and bio-medical applications. Although some theories and analytical models are available for describing waves in multi-layered engineering structures, they do not focus on canvassing ultrasonic waves in human bones with coupled soft tissues, where the considerable differences in acoustic impedance between bone and soft tissue may pose a challenge in using these models (the soft tissues having an acoustic impedance around 80% less than that of a typical bone). Without proper treatment of this coupling effect, the precision of quantitative ultrasound (QUS) for clinical bone assessment can be compromised. The coupling effect of mimicked soft tissues on the first-arriving signal (FAS) and second-arriving signal (SAS) in a series of synthesized soft-tissue-bone phantoms was investigated experimentally and calibrated quantitatively. Understanding of the underlying mechanism of the coupling effect was supplemented by a dedicated finite element analysis. As revealed, the medium coupling impacts influence on different wave modes to different degrees: for FAS and SAS, the most significant changes take place when the soft tissues are initially introduced, and the decrease in signal peak energy continues with increase in the thickness or elastic modulus of the soft tissues, but the changes in propagation velocity fluctuate within 5% regardless of further increase in the thickness or elastic modulus of the soft tissues. As an application, the calibrated effects were employed to enhance the precision of SAS-based QUS when used for predicting the simulated healing status of a mimicked bone fracture, to find prediction of healing progress of bone fracture based on changes in velocity of the FAS or the SAS is inaccurate without taking into account the effect of soft tissue coupling, entailing appropriate compensation for the coupling effect.

Using the gradient of human cortical bone properties to determine age-related bone changes via ultrasonic guided waves

Bone fragility depends not only on bone mass but also on bone quality (structure and material). To accurately evaluate fracture risk or propose therapeutic treatment, clinicians need a criterion, which reflects the determinants of bone strength: geometry, structure and material. In human long bone, the changes due to aging, accentuated by osteoporosis are often revealed through the trabecularization of cortical bone, i.e., increased porosity of endosteal bone inducing a thinning of the cortex. Consequently, the intracortical porosity gradient corresponding to the spatial variation in porosity across the cortical thickness is representative of loss of mass, changes in geometry (thinning) and variations in structure (porosity). This article examines the gradient of material properties and its age-related evolution as a relevant parameter to assess bone geometry, structure and material. By applying a homogenization process, cortical bone can be considered as an anisotropic functionally graded material with variations in material properties. A semi-analytical method based on the sextic Stroh formalism is proposed to solve the wave equation in an anisotropic functionally graded waveguide for two geometries, a plate and a tube, without using a multilayered model to represent the structure. This method provides an analytical solution called the matricant and explicitly expressed under the Peano series expansion form. Our findings indicate that ultrasonic guided waves are sensitive to the age-related evolution of realistic gradients in human bone properties across the cortical thickness and have their place in a multimodal clinical protocol.

Correlations between ultrasonic guided wave velocities and bone properties in bovine tibia in vitro

Correlations between ultrasonic guided wave velocities and bone properties were investigated in bovine tibia in vitro. The velocities of the first arriving signal and the slow guided wave, termed V(FAS) and V(SGW), along the long axis of the tibia were measured at 200 kHz in 20 bovine tibiae using the axial transmission technique. V(FAS) yielded significant negative correlation coefficients of -0.54 to -0.66 with the bone properties. In contrast, V(SGW) yielded strong positive correlation coefficients of 0.68-0.84. The best univariate predictor of V(FAS) and V(SGW) was the cortical thickness yielding adjusted squared correlation coefficients of 0.41 and 0.69, respectively.

Impact of attenuation on guided mode wavenumber measurement in axial transmission on bone mimicking plates

Robust signal processing methods adapted to clinical measurements of guided modes are required to assess bone properties such as cortical thickness and porosity. Recently, an approach based on the singular value decomposition (SVD) of multidimensional signals recorded with an axial transmission array of emitters and receivers has been proposed for materials with negligible absorption, see Minonzio et al. [J. Acoust. Soc. Am. 127, 2913-2919 (2010)]. In presence of absorption, the ability to extract guided mode degrades. The objective of the present study is to extend the method to the case of absorbing media, considering attenuated plane waves (complex wavenumber). The guided mode wavenumber extraction is enhanced and the order of magnitude of the attenuation of the guided mode is estimated. Experiments have been carried out on 2 mm thick plates in the 0.2-2 MHz bandwidth. Two materials are inspected: polymethylacrylate (PMMA) (isotropic with absorption) and artificial composite bones (Sawbones, Pacific Research Laboratory Inc, Vashon, WA) which is a transverse isotropic absorbing medium. Bulk wave velocities and bulk attenuation have been evaluated from transmission measurements. These values were used to compute theoretical Lamb mode wavenumbers which are consistent with the experimental ones obtained with the SVD-based approach.

Analysis of superimposed ultrasonic guided waves in long bones by the joint approximate diagonalization of eigen-matrices algorithm

The parameters of ultrasonic guided waves (GWs) are very sensitive to mechanical and structural changes in long cortical bones. However, it is a challenge to obtain the group velocity and other parameters of GWs because of the presence of mixed multiple modes. This paper proposes a blind identification algorithm using the joint approximate diagonalization of eigen-matrices (JADE) and applies it to the separation of superimposed GWs in long bones. For the simulation case, the velocity of the single mode was calculated after separation. A strong agreement was obtained between the estimated velocity and the theoretical expectation. For the experiments in bovine long bones, by using the calculated velocity and a theoretical model, the cortical thickness (CTh) was obtained. For comparison with the JADE approach, an adaptive Gaussian chirplet time-frequency (ACGTF) method was also used to estimate the CTh. The results showed that the mean error of the CTh acquired by the JADE approach was 4.3%, which was smaller than that of the ACGTF method (13.6%). This suggested that the JADE algorithm may be used to separate the superimposed GWs and that the JADE algorithm could potentially be used to evaluate long bones.

Experimental and simulation results on the effect of cortical bone mineralization in ultrasound axial transmission measurements: a model for fracture healing ultrasound monitoring

Ultrasound axial transmission (UAT), a technique using propagation of ultrasound waves along the cortex of cortical bones, has been proposed as a diagnostic technique for the evaluation of fracture healing. Quantitative ultrasound parameters have been reported to be sensitive to callus changes during the regeneration process. The aim of this work was to identify the specific effect of cortical bone mineralization on UAT measurements by means of numerical simulations and experiments using a reverse fracture healing approach. A cortical bovine femur sample was used, in which a 3mm fracture gap was drilled. A 3mm thick cortical bone slice, extracted from another location in the bone sample, was submitted to a progressive demineralization process with EDTA during 12 days. UAT measurements and simulations using a 1MHz probe were performed with the demineralized slice placed into the fracture gap to mimic different stages of mineralization during the healing process. The calcium loss of the slice due to the EDTA treatment was recorded everyday, and its temporal evolution could be modeled by an exponential law. A 50MHz scanning acoustic microscopy was also used to assess the mineralization degree of the bone slice at the end of the intervention. These data were used in the numerical simulations to derive a model of the time evolution of bone slice mechanical properties. From both the experiments and the simulations, a significant and progressive increase in the time of flight (TOF; p<0.001) of the propagating waves measured by UAT was observed during the beginning of the demineralization process (first 4 days). Although the simulated TOF values were slightly larger than the experimental ones, they both exhibited a similar time-dependence, validating the simulation approach. Our results suggest that TOF measured in axial transmission is affected by local changes of speed of sound induced by changes in local mineralization. TOF may be an appropriate indicator to monitor callus maturation.

Propagation of elastic waves in an anisotropic functionally graded hollow cylinder in vacuum

As a non-destructive, non-invasive and non-ionizing evaluation technique for heterogeneous media, the ultrasonic method is of major interest in industrial applications but especially in biomedical fields. Among the unidirectionally heterogeneous media, the continuously varying media are a particular but widespread case in natural materials. The first studies on laterally varying media were carried out by geophysicists on the Ocean, the atmosphere or the Earth, but the teeth, the bone, the shells and the insects wings are also functionally graded media. Some of them can be modeled as planar structures but a lot of them are curved media and need to be modeled as cylinders instead of plates. The present paper investigates the influence of the tubular geometry of a waveguide on the propagation of elastic waves. In this paper, the studied structure is an anisotropic hollow cylinder with elastic properties (stiffness coefficients c(ij) and mass density ρ) functionally varying in the radial direction. An original method is proposed to find the eigenmodes of this waveguide without using a multilayered model for the cylinder. This method is based on the sextic Stroh's formalism and an analytical solution, the matricant, explicitly expressed under the Peano series expansion form. This approach has already been validated for the study of an anisotropic laterally-graded plate (Baron et al., 2007; Baron and Naili, 2010) [6,5]. The dispersion curves obtained for the radially-graded cylinder are compared to the dispersion curves of a corresponding laterally-graded plate to evaluate the influence of the curvature. Preliminary results are presented for a tube of bone in vacuum modelling the in vitro conditions of bone strength evaluation.

Guided wave phase velocity measurement using multi-emitter and multi-receiver arrays in the axial transmission configuration

This paper is devoted to a method of extraction of guided waves phase velocities from experimental signals. Measurements are performed using an axial transmission device consisting of a linear arrangement of emitters and receivers placed on the surface of the inspected specimen. The technique takes benefit of using both multiple emitters and receivers and is validated on a reference wave guide. The guided mode phase velocities are obtained using a projection in the singular vectors basis. The singular vectors are determined by the singular values decomposition (SVD) of the response matrix between the two arrays in the frequency domain. This technique enables to recover accurately guided wave phase velocity dispersion curves. The SVD based approach was designed to overcome limitations of spatio-temporal Fourier transform for receiver array of limited spatial extent as in the case of clinical assessment of cortical bone in axial transmission.

Potential of first arriving signal to assess cortical bone geometry at the Hip with QUS: a model based study

There is evidence that quantitative ultrasound (QUS) at the proximal femur involves waves propagating circumferentially in the cortical shell. These waves, in theory, convey information on bone geometrical and material characteristics and thus have the potential to improve fracture risk prediction. In this work, the time-of-flight (TOF) of the first arriving signal (FAS) that corresponds to waves propagating circumferentially is considered. The relationships between the TOF of the FAS and geometrical features of the femoral neck are investigated. Five neck cross-sections from 11 human femurs from females (>65y) were extracted from 3-D X-ray quantitative computed tomography (XR-QCT) datasets. Geometrical parameters including cross-sectional area (CSA), minimum moment of inertia (I(min)) and section modulus (Z) were computed from femoral neck cross-section images. Two-dimensional numerical simulation of US propagation through femoral neck was performed and TOF of the FAS was estimated. TOF was best correlated with I(min): R(2)=0.82 (p=10(-4); RMSE=1390mm(4) [13%]) in the region between proximal and mid-femoral neck and with Z: R(2)=0.55 (p<10(-2); RMSE=480mm(3) [17%]) and CSA: R(2)=0.62 (p<5.10(-3); RMSE=22mm(2) [7%]) in the mid-femoral neck. The results suggest that QUS has the potential to assess proximal femur strength based on estimates of geometrical properties of the cortical shell.

Analysis of the most energetic late arrival in axially transmitted signals in cortical bone

Axial transmission techniques are particularly suitable for the ultrasonic assessment of cortical bone. The generic term "axial transmission technique" indicates a measurement configuration in which emitters and receivers are placed on the same side of the skeletal site, along the bone axis. Whereas axially transmitted signals are composed of several contributions, only the first arriving signal was shown to be a robust indicator of bone status, because its velocity discriminates osteoporotic from healthy patients in clinical studies. Later arrivals may provide additional bone indicators enhancing diagnostic value, but the precise determination of their velocities is challenging. In this paper, we focus on the most energetic contribution and we applied a singular-value decomposition-based extraction method not yet employed in the domain of bone assessment with the aim of determining the velocity of this contribution. Signals acquired in vitro on human radii, together with academic models, were used to reveal the relationship between the velocity of the most energetic component and bone properties. The velocity of the most energetic component is highly correlated to cortical layer thickness in the in vitro database (R(2)= 0.6, P < 10(-5) compared with R(2)= 0.20, P < 10-(2) for the first arriving signal), consistent with a flexural type of wave on regular tubes or plates. Conclusions are in agreement with published papers based on other axial transmission and signal processing approaches.