HER2 classification in breast cancer cells: A new explainable machine learning application for immunohistochemistry.

The immunohistochemical (IHC) evaluation of epidermal growth factor 2 (HER2) for the diagnosis of breast cancer is still qualitative with a high degree of inter-observer variability, and thus requires the incorporation of complementary techniques such as fluorescent in situ hybridization (FISH) to resolve the diagnosis. Implementing automatic algorithms to classify IHC biomarkers is crucial for typifying the tumor and deciding on therapy for each patient with better performance. The present study aims to demonstrate that, using an explainable Machine Learning (ML) model for the classification of HER2 photomicrographs, it is possible to determine criteria to improve the value of IHC analysis. We trained a logistic regression-based supervised ML model with 393 IHC microscopy images from 131 patients, to discriminate between upregulated and normal expression of the HER2 protein. Pathologists' diagnoses (IHC only) vs. the final diagnosis complemented with FISH (IHC + FISH) were used as training outputs. Basic performance metrics and receiver operating characteristic curve analysis were used together with an explainability algorithm based on Shapley Additive exPlanations (SHAP) values to understand training differences. The model could discriminate amplified IHC from normal expression with better performance when the training output was the IHC + FISH final diagnosis (IHC vs. IHC + FISH: area under the curve, 0.94 vs. 0.81). This may be explained by the increased analytical impact of the membrane distribution criteria over the global intensity of the signal, according to SHAP value interpretation. The classification model improved its performance when the training input was the final diagnosis, downplaying the weighting of the intensity of the IHC signal, suggesting that to improve pathological diagnosis before FISH consultation, it is necessary to emphasize subcellular patterns of staining.

Bi-Directional Axial Transmission measurements applied in a clinical environment.

Accurate measurement of cortical bone parameters may improve fracture risk assessment and help clinicians on the best treatment strategy. Patients at risk of fracture are currently detected using the current X-Ray gold standard DXA (Dual XRay Absorptiometry). Different alternatives, such as 3D X-Rays, Magnetic Resonance Imaging or Quantitative Ultrasound (QUS) devices, have been proposed, the latter having advantages of being portable and sensitive to mechanical and geometrical properties. The objective of this cross-sectional study was to evaluate the performance of a Bi-Directional Axial Transmission (BDAT) device used by trained operators in a clinical environment with older subjects. The device, positioned at one-third distal radius, provides two velocities: VFAS (first arriving signal) and VA0 (first anti-symmetrical guided mode). Moreover, two parameters are obtained from an inverse approach: Ct.Th (cortical thickness) and Ct.Po (cortical porosity), along with their ratio Ct.Po/Ct.Th. The areal bone mineral density (aBMD) was obtained using DXA at the femur and spine. One hundred and six patients (81 women, 25 men) from Marien Hospital and St. Anna Hospital (Herne, Germany) were included in this study. Age ranged from 41 to 95 years, while body mass index (BMI) ranged from 16 to 47 kg.m-2. Three groups were considered: 79 non-fractured patients (NF, 75±13years), 27 with non-traumatic fractures (F, 80±9years) including 14 patients with non-vertebral fractures (NVF, 84±7years). Weak to moderate significant Spearman correlations (R ranging from 0.23 to 0.53, p < 0.05) were found between ultrasound parameters and age, BMI. Using multivariate Partial Least Square discrimination analyses with Leave-One-Out Cross-Validation (PLS-LOOCV), we found the combination of VFAS and the ratio Ct.Po/Ct.Th to be predictive for all non traumatic fractures (F) with the odds ratio (OR) equals to 2.5 [1.6-3.4] and the area under the ROC curve (AUC) equal to 0.63 [0.62-0.65]. For the group NVF, combination of four parameters VA0. Ct.Th, Ct.Po and Ct.Po/Ct.Po, along with age provides a discrimination model with OR and AUC equals to 7.5 [6.0-9.1] and 0.75 [0.73-0.76]. When restricted to a smaller population (87 patients) common to both BDAT and DXA, BDAT ORs and AUCs are comparable or slightly higher to values obtained with DXA. The fracture risk assessment by BDAT method in older patients, in a clinical setting, suggests the benefit of the affordable and transportable device for the routine use.

Can guided wave ultrasound predict bone mechanical properties at the femoral neck in patients undergoing hip arthroplasty?

The bone quality of patients undergoing hip replacement surgery is poorly predicted by radiographs alone. With better bone quality information available to a surgeon, the operation can be performed more safely. The aim of this study was to investigate whether ultrasound signals of cortical bone at peripheral sites such as the tibia and radius can be used to predict the compressive mechanical properties of cortical bone at the femoral neck. We recruited 19 patients undergoing elective hip arthroplasty and assessed the radius and tibia of these patients with the Azalée guided wave ultrasound to estimate the porosity and thickness of the cortex. Excess bone tissues were collected from the femoral neck and the compressive mechanical properties of the cortex were characterised under a mechanical loading rig to determine stiffness, ultimate strength, and density. The correlations between the ultrasound measurements and mechanical properties were analysed using linear regression, Pearson correlation statistics, and multiple regression analysis. Cortical mechanical properties were weakly to moderately correlated with the ultrasound measurements at various sites (R2 = 0.00-0.36). The significant correlations found were not consistent across all 4 peripheral measurement sites. Additionally, weak to moderate ability of the ultrasound to predict mechanical properties at the neck of femur with multiple regression analysis was found (R2 = 0.00-0.48). Again, this was inconsistent across the different anatomical sites. Overall, the results demonstrate the need for ultrasound scans to be collected directly from clinically relevant sites such as the femoral neck due to the inconsistency of mechanical properties across various sites.

Improvement of Patient Classification Using Feature Selection Applied to Bidirectional Axial Transmission.

Osteoporosis is still a worldwide problem, particularly due to associated fragility fractures. Patients at risk of fracture are currently detected using the X-Ray gold standard dual-energy X-ray absorptiometry (DXA), based on a calibrated 2-D image. Different alternatives, such as 3-D X-rays, magnetic resonance imaging (MRI) or ultrasound, have been proposed, the latter having advantages of being portable and sensitive to mechanical and geometrical properties. Bidirectional axial transmission (BDAT) has been used to classify between patients with or without nontraumatic fractures using "classical" ultrasonic parameters, such as velocities, as well as cortical thickness and porosity, obtained from an inverse problems. Recently, complementary parameters acquired with structural and textural analysis of guided wave spectrum images (GWSIs) have been introduced. These parameters are not limited by solution ambiguities, as for inverse problem. The aim of the study is to improve the patient classification using a feature selection strategy for all available ultrasound features completed by clinical parameters. To this end, three classical feature ranking methods were considered: analysis of variance (ANOVA), recursive feature elimination (RFE), and extreme gradient boosting importance feature (XGBI). In order to evaluate the performance of the feature selection techniques, three classical classification methods were used: logistic regression (LR), support vector machine (SVM), and extreme gradient boosting (XGB). The database was obtained from a previous clinical study [Minonzio et al., 2019]. Results indicate that the best accuracy of 71 [66-76]% was achieved by using RFE and SVM with 22 (out of 43) ultrasonic and clinical features. This value outperformed the accuracy of 68 [64-73]% reached with 2 (out of 6) DXA and clinical features. These values open promising perspectives toward improved and generalizable classification of patients at risk of fracture.

Using Low-Resolution Non-Invasive Infrared Sensors to Classify Activities and Falls in Older Adults.

The population is aging worldwide, creating new challenges to the quality of life of older adults and their families. Falls are an increasing, but not inevitable, threat to older adults. Information technologies provide several solutions to address falls, but smart homes and the most available solutions require expensive and invasive infrastructures. In this study, we propose a novel approach to classify and detect falls of older adults in their homes through low-resolution infrared sensors that are affordable, non-intrusive, do not disturb privacy, and are more acceptable to older adults. Using data collected between 2019 and 2020 with the eHomeseniors platform, we determine activity scores of older adults moving across two rooms in a house and represent an older adult fall through skeletonization. We find that our twofold approach effectively detects activity patterns and precisely identifies falls. Our study provides insights to physicians about the daily activities of their older adults and could potentially help them make decisions in case of abnormal behavior.

A simplified homogenization model applied to viscoelastic behavior of cortical bone at ultrasonic frequencies.

Cortical bone is a complex multiscale medium and its study is of importance for clinical fracture prevention. In particular, cortical attenuation is known to be linked with shock energy absorption and ability to resist fracture. However, the links between cortical bone absorption and its multiscale structure are still not well understood. This work is about the use of homogenized tensors in order to characterize the viscoelastic behavior of cortical bone at ultrasonic frequencies, i.e., about 0.1 to 10 MHz. Such tensors are derived from the cell problem via two-scale homogenization theory for linear elastic and Kelvin-Voigt viscoelastic descriptions. The elliptic formulations obtained from the cell problems are implemented within the range of medically-observed porosities. Microstructure is assessed considering cubic cells with cylindrical inclusion and transverse isotropic assumption. A simplified model, adding one temporal parameter τ per phase, allows a good agreement with experimental data. The corresponding attenuation is proportional to the square of the frequency, in agreement with Kramer-Kronig relations. This development is proposed in the context of robust clinical inverse problem approaches using a restricted number of parameter. Two main properties for the material filling the pores are adjusted and discussed: absorption and shear contribution. Best agreement with experimental data is observed for material inside the pores being solid and highly attenuating.

In vivopulse-echo measurement of apparent broadband attenuation andQfactor in cortical bone: a preliminary study.

Quantitative ultrasound (QUS) methods have been introduced to assess cortical bone health at the radius and tibia through the assessment of cortical thickness (Ct.Th), cortical porosity and bulk wave velocities. Ultrasonic attenuation is another QUS parameter which is not currently used. We assessed the feasibility ofin vivomeasurement of ultrasonic attenuation in cortical bone with a broadband transducer with 3.5 MHz center frequency. Echoes from the periosteal and endosteal interfaces were fitted with Gaussian pulses using sparse signal processing. Then, the slope of the broadband ultrasonic attenuation (Ct.nBUA) in cortical bone and quality factorQ11-1were calculated with a parametric approach based on the center-frequency shift. Five human subjects were measured at the one-third distal radius with pulse-echo ultrasound, and reference data was obtained with high-resolution x-ray peripheral computed tomography (Ct.Th and cortical volumetric bone mineral density (Ct.vBMD)). Ct.Th was used in the calculation of Ct.nBUA whileQ11-1is obtained solely from ultrasound data. The values of Ct.nBUA (6.7 ± 2.2 dB MHz-1.cm-1) andQ11-1(8.6 ± 3.1%) were consistent with the literature data and were correlated to Ct.vBMD (R2=0.92,p<0.01, RMSE = 0.56 dB.MHz-1.cm-1, andR2=0.93,p<0.01, RMSE = 0.76%). This preliminary study suggests that the attenuation of an ultrasound signal propagating in cortical bone can be measuredin vivoat the one-third distal radius and that it provides an information on bone quality as attenuation values were correlated to Ct.vBMD. It remains to ascertain that Ct.nBUA andQ11-1measured here exactly reflect the true (intrinsic) ultrasonic attenuation in cortical bone. Measurement of attenuation may be considered useful for assessing bone health combined with the measurement of Ct.Th, porosity and bulk wave velocities in multimodal cortical bone QUS methods.

eHomeSeniors Dataset: An Infrared Thermal Sensor Dataset for Automatic Fall Detection Research.

Automatic fall detection is a very active research area, which has grown explosively since the 2010s, especially focused on elderly care. Rapid detection of falls favors early awareness from the injured person, reducing a series of negative consequences in the health of the elderly. Currently, there are several fall detection systems (FDSs), mostly based on predictive and machine-learning approaches. These algorithms are based on different data sources, such as wearable devices, ambient-based sensors, or vision/camera-based approaches. While wearable devices like inertial measurement units (IMUs) and smartphones entail a dependence on their use, most image-based devices like Kinect sensors generate video recordings, which may affect the privacy of the user. Regardless of the device used, most of these FDSs have been tested only in controlled laboratory environments, and there are still no mass commercial FDS. The latter is partly due to the impossibility of counting, for ethical reasons, with datasets generated by falls of real older adults. All public datasets generated in laboratory are performed by young people, without considering the differences in acceleration and falling features of older adults. Given the above, this article presents the eHomeSeniors dataset, a new public dataset which is innovative in at least three aspects: first, it collects data from two different privacy-friendly infrared thermal sensors; second, it is constructed by two types of volunteers: normal young people (as usual) and performing artists, with the latter group assisted by a physiotherapist to emulate the real fall conditions of older adults; and third, the types of falls selected are the result of a thorough literature review.

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.ThAT and Ct.PoAT 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 (υFAS) and A0 mode (υA0) were also determined. Site-matched peripheral quantitative computed tomography (pQCT) provided volumetric cortical bone mineral density (Ct.vBMDpQCT) and Ct.ThpQCT. Good agreement was found between Ct.ThAT and Ct.ThpQCT (R2 = 0.62, root mean square error [RMSE] = 0.39 mm). Ct.vBMDpQCT correlated with Ct.PoAT (R2 = 0.57), υFAS (R2 = 0.43) and υA0 (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 (υFAS) and A0 mode (υA0) 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 υA0 (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.

Dispersive Radon transform.

Dispersion results in the spreading and overlapping of the wave-packets, which often limits the capability of signal interpretation; on the other hand, such a phenomenon can also be used for structure or media evaluation. In this study, the authors propose an original dispersive Radon transform (DRT), which is formulated as integration transform along a set of dispersion curves. Multichannel dispersive signals of each individual mode can be concentrated to a well localized region in the DRT domain. The proposed DRT establishes the sparse projection of the dispersive components and provides an efficient solution for mode separation, noise filtering, and missing data reconstruction. Particularly the DRT method allows projecting the temporal signals of dispersive waves on the space of parameters of interest, which can be used to solve the inverse problem for waveguide or media property estimation. The least-square procedure and sparse scheme of the DRT are introduced. A high-resolution DRT is designed based on an iterative reweighting inversion scheme, which resembles the infinite-aperture velocity gather. The proposed method is applied by analyzing ultrasonic guided waves in plate-like structures and in a human radius specimen. The results suggest that the DRT method can significantly enhance the interpretation of dispersive signals.

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.

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.

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.

Sparse SVD Method for High-Resolution Extraction of the Dispersion Curves of Ultrasonic Guided Waves.

The 2-D Fourier transform analysis of multichannel signals is a straightforward method to extract the dispersion curves of guided modes. Basically, the time signals recorded at several positions along the waveguide are converted to the wavenumber-frequency space, so that the dispersion curves (i.e., the frequency-dependent wavenumbers) of the guided modes can be extracted by detecting peaks of energy trajectories. In order to improve the dispersion curve extraction of low-amplitude modes propagating in a cortical bone, a multiemitter and multireceiver transducer array has been developed together with an effective singular vector decomposition (SVD)-based signal processing method. However, in practice, the limited number of positions where these signals are recorded results in a much lower resolution in the wavenumber axis than in the frequency axis. This prevents a clear identification of overlapping dispersion curves. In this paper, a sparse SVD (S-SVD) method, which combines the signal-to-noise ratio improvement of the SVD-based approach with the high wavenumber resolution advantage of the sparse optimization, is presented to overcome the above-mentioned limitation. Different penalty constraints, i.e., l1 -norm, Frobenius norm, and revised Cauchy norm, are compared with the sparse characteristics. The regularization parameters are investigated with respect to the convergence property and wavenumber resolution. The proposed S-SVD method is investigated using synthetic wideband signals and experimental data obtained from a bone-mimicking phantom and from an ex-vivo human radius. The analysis of the results suggests that the S-SVD method has the potential to significantly enhance the wavenumber resolution and to improve the extraction of the dispersion curves.

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.

A method for the measurement of dispersion curves of circumferential guided waves radiating from curved shells: experimental validation and application to a femoral neck mimicking phantom.

Our long-term goal is to develop an ultrasonic method to characterize the thickness, stiffness and porosity of the cortical shell of the femoral neck, which could enhance hip fracture risk prediction. To this purpose, we proposed to adapt a technique based on the measurement of guided waves. We previously evidenced the feasibility of measuring circumferential guided waves in a bone-mimicking phantom of a circular cross-section of even thickness. The goal of this study is to investigate the impact of the complex geometry of the femoral neck on the measurement of guided waves. Two phantoms of an elliptical cross-section and one phantom of a realistic cross-section were investigated. A 128-element array was used to record the inter-element response matrix of these waveguides. This experiment was simulated using a custom-made hybrid code. The response matrices were analyzed using a technique based on the physics of wave propagation. This method yields portions of dispersion curves of the waveguides which were compared to reference dispersion curves. For the elliptical phantoms, three portions of dispersion curves were determined with a good agreement between experiment, simulation and theory. The method was thus validated. The characteristic dimensions of the shell were found to influence the identification of the circumferential wave signals. The method was then applied to the signals backscattered by the superior half of constant thickness of the realistic phantom. A cut-off frequency and some portions of modes were measured, with a good agreement with the theoretical curves of a plate waveguide. We also observed that the method cannot be applied directly to the signals backscattered by the lower half of varying thicknesses of the phantom. The proposed approach could then be considered to evaluate the properties of the superior part of the femoral neck, which is known to be a clinically relevant site.

Measurement of dispersion curves of circumferential guided waves radiating from curved shells: Theory and numerical validation.

A method is proposed to evaluate in a non-contact way the phase velocity dispersion curves of circumferential waves around a shell of arbitrary shape immersed in a fluid. No assumptions are made about the thickness or the material of the shell. A geometrical model is derived to describe the shape of the radiated wavefronts in the surrounding fluid, and predict the positions of its centers of curvature. Then the time-reversal principle is applied to recover these positions and to calculate the phase velocity of the circumferential waves. Numerical finite-difference simulations are performed to evaluate the method on a circular and on an elliptic thin shell. Different dispersion curves can be recovered with an error of less than 10%.

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.