Maryline Talmant

Three-dimensional simulations of ultrasonic axial transmission velocity measurement on cortical bone models

The ultrasonic axial transmission technique, used to assess cortical shells of long bones, is investigated using numerical simulations based on a three-dimensional (3D) finite difference code. We focus our interest on the effects of 3D cortical bone geometry (curvature, cortical thickness), anisotropy, and microporosity on speed of sound (SOS) measurements for different frequencies in the MHz range. We first show that SOS values measured on tubular cortical shells are identical to those measured on cortical plates of equal thickness. Anisotropy of cortical bone is then shown to have a major impact on SOS measurement as a function of cortical thickness. The range of SOS values measured on anisotropic bone is half the range found when bone is considered isotropic. Dependence of thickness occurs for cortical shell thinner than 0.5 x lambda(bone) in anisotropic bone (lambda(bone): wavelength in bone), whereas it occurs for cortical shell thinner than lambda(bone) when anisotropy is neglected. Sensitivity of SOS along the bone axis to intracortical microporosity is shown to be approximately -20 m s(-1) per percent of porosity. Using homogenized porous bone, we finally show that the cortical depth that contributes to lateral wave SOS measurement is approximately 1-1.5 mm for frequencies ranging from 500 kHz to 2 MHz under classical in vivo measurement conditions.

Effect of bone cortical thickness on velocity measurements using ultrasonic axial transmission: A 2D simulation study

In recent years, quantitative ultrasound (QUS) has played an increasing role in the assessment of bone status. The axial transmission technique allows to investigate skeletal sites such as the cortical layer of long bones (radius, tibia), inadequate to through-transmission techniques. Nevertheless, the type of propagation involved along bone specimens has not been clearly elucidated. Axial transmission is investigated here by means of two-dimensional simulations at 1 MHz. We focus our interest on the apparent speed of sound (SOS) of the first arriving signal (FAS). Its dependence on the thickness of the plate is discussed and compared to previous work. Different time criteria are used to derive the apparent SOS of the FAS as a function of source-receiver distance. Frequency-wave number analysis is performed in order to understand the type of propagation involved. For thick plates (thickness>lambdabone, longitudinal wavelength in bone), and for a limited range of source-receiver distances, the FAS corresponds to the lateral wave. Its velocity equals the longitudinal bulk velocity of the bone. For plate thickness less than lambdabone, some plate modes contribute to the FAS, and the apparent SOS decreases with the thickness in a way that depends on both the time criterion and on the source-receiver distance. The FAS corresponds neither to the lateral wave nor to a single plate mode. For very thin plates (thickness< lambdabone/4), the apparent SOS tends towards the velocity of the lowest order symmetrical vibration mode (S0 Lamb mode).

Bidirectional axial transmission can improve accuracy and precision of ultrasonic velocity measurement in cortical bone: a validation on test materials

The axial transmission technique uses a linear arrangement of ultrasonic emitters and receivers placed on a same side of a cortical bone site in contact with the skin, involving ultrasonic propagation along the axis of bone. The velocity of the waves radiated from bone has been shown to reflect bone status. The thickness and composition of soft tissue may vary along the length of the bone, between different skeletal sites, or between subjects. Hence, accurate estimates of velocity require first to eliminate the effect of the overlying soft tissue that is traversed by the ultrasound wave. To correct for such bias without measuring soft tissue properties, we designed new ultrasonic probes in the 1-2 MHz frequency range. It is based on propagation along the bone surface in two opposite directions from two sources placed on both sides of a unique group of receivers. The aim is to obtain an unbiased estimate of the velocity without any intermediate calculation of soft tissue properties, such as thickness variation or velocity. Validation tests were performed on academic material such as Perspex or aluminium. We found that head wave velocity values could be biased by more than 10% for inclination of a few degrees between the test specimen surface and the probe. On test materials, the compensation procedure implemented in our probe led to a relative precision error on velocity measurement lower than 0.2 to 0.3%. These results suggest that the correction procedure allows measuring in vivo velocities independently of soft tissue properties.

An In Vitro Study of the Ultrasonic Axial Transmission Technique at the Radius: 1-MHz Velocity Measurements Are Sensitive to Both Mineralization and Intracortical Porosity

The ultrasonic axial transmission technique allows for investigating skeletal sites such as the cortical layer of long bones (radius, tibia, phalanges). Using synchrotron radiation μCT, we investigated, in vitro, the relationships between 1‐MHz axial transmission SOS measurements at the radius and site‐matched measurements of C.Th, POR, MIN, and vBMD.

Nonlinear resonant ultrasound spectroscopy (NRUS) applied to damage assessment in bone

Nonlinear resonant ultrasound spectroscopy (NRUS) is a resonance-based technique exploiting the significant nonlinear behavior of damaged materials. In NRUS, the resonant frequency(ies) of an object is studied as a function of the excitation level. As the excitation level increases, the elastic nonlinearity is manifest by a shift in the resonance frequency. This study shows the feasibility of this technique for application to damage assessment in bone. Two samples of bovine cortical bone were subjected to progressive damage induced by application of mechanical cycling. Before cycling commenced, and at each step in the cycling process, NRUS was applied for damage assessment. For independent assessment of damage, high-energy x-ray computed tomography imaging was performed but was only useful in identifying the prominent cracks. As the integral quantity of damage increased, NRUS revealed a corresponding increase in the nonlinear response. The measured change in nonlinear response is much more sensitive than the change in linear modulus. The results suggest that NRUS could be a potential tool for micro-damage assessment in bone. Further work must be carried out for a better understanding of the physical nature of damaged bone and for the ultimate goal of the challenging in vivo implementation of the technique.

Analysis of the axial transmission technique for the assessment of skeletal status

Ultrasonic wave propagation in human cortical bone has been investigated in vitro using the so-called axial transmission technique. This technique, which relies on velocity measurement of the first arriving signal, has been used in earlier investigations to study bone status during fracture healing or osteoporosis. Two quasi-point-source elements, one transmitter and one receiver (central frequency 0.5 MHz), were used to generate a wide ultrasonic beam, part of which strikes the sample surface at the longitudinal critical angle, and to receive the signals reflected from the sample surface. The analysis of the field reflected from a fluid-solid interface for an incident spherical wave predicts the existence of a lateral wave propagating along the sample surface at a velocity close to the longitudinal velocity, in addition to the ordinary reflected wave and vibration modes. The transducer-sample and the transmitter-receiver distances were chosen such that the lateral wave is the first arriving signal. Validation of the measuring technique was performed on test materials and was followed by experiments on human cortical bones. Experimental results (arrival time and velocity) strongly suggest that the first detected signal corresponds to the lateral wave predicted by theory.

Site-matched assessment of structural and tissue properties of cortical bone using scanning acoustic microscopy and synchrotron radiation μCT

200 MHz scanning acoustic microscopy (SAM) and synchrotron radiation muCT (SR-muCT) were used to assess microstructural parameters and tissue properties in site-matched regions of interest in cortical bone. Anterior and postero-lateral regions of ten cross sections from human cortical radius were explored. Structural parameters, including diameter and number of Haversian canals per cortical area (Ca.Dm, N.Ca/Ar) and porosity Po were assessed with both methods using a custom-developed image fusion and analysis software. Acoustic impedance Z and degree of mineralization of bone DMB were extracted separately for osteonal and interstitial tissues from the fused images. Structural parameter estimations obtained from radiographic and acoustic images were almost identical. DMB and impedance values were in the range between 0.77 and 1.28 g cm(-3) and 5.13 and 12.1 Mrayl, respectively. Interindividual and regional variations were observed, whereas the strongest difference was found between osteonal and interstitial tissues (Z: 7.2 +/- 1.1 Mrayl versus 9.3 +/- 1.0 Mrayl, DMB: 1.06 +/- 0.07 g cm(-3) versus 1.16 +/- 0.05 g cm(-3), paired t-test, p < 0.05). Weak, but significant correlations between DMB and Z were obtained for the osteonal (R(2) = 0.174, p < 10(-4)) and for the pooled (osteonal and interstitial) data. The regression of the pooled osteonal and interstitial tissue data follows a second-order polynomial (R(2) = 0.39, p < 10(-4)). Both modalities fulfil the requirement for a simultaneous evaluation of cortical bone microstructure and material properties at the tissue level. While SAM inspection is limited to the evaluation of carefully prepared sample surfaces, SR-muCT provides volumetric information on the tissue without substantial preparation requirements. However, SAM provides a quantitative estimate of elastic properties at the tissue level that cannot be captured by SR-muCT.

Ultrasonically determined thickness of long cortical bones: Three-dimensional simulations of in vitro experiments

Previously it has been demonstrated that cortical bone thickness can be estimated from ultrasonic guided-wave measurements, in an axial transmission configuration, together with an appropriate analytical model. This study considers the impact of bone thickness variation within the measurement region on the ultrasonically determined thickness (UTh). To this end, wave velocities and UTh were determined from experiments and from time-domain finite-difference simulations of wave propagation, both performed on a set of ten human radius specimens (29 measurement sites). A two-dimensional numerical bone model was developed with tunable material properties and individualized geometry based on x-ray computed-tomography reconstructions of human radius. Cortical thickness (CTh) was determined from the latter. UTh data for simulations were indeed in a excellent accordance (root-mean-square error was 0.26 mm; r2=0.94, p<0.001) with average CTh within the measurement region. These results indicate that despite variations in cortical thickness along the propagation path, the measured phase velocity can be satisfactorily modeled by a simple analytical model (the A(0) plate mode in this case). Most of the variability (up to 85% when sites were carefully matched) observed in the in vitro ultrasound data was explained through simulations by variability in the cortical thickness alone.

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.

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

Recent in vitro and simulation studies have shown that guided waves measured at low ultrasound frequencies (f=200 kHz) can characterize both material properties and geometry of the cortical bone wall. In particular, a method for an accurate cortical thickness estimation from ultrasound velocity data has been presented. The clinical application remains, however, a challenge as the impact of a layer of soft tissue on top of the bone is not yet well established, and this layer is expected to affect the dispersion and relative intensities of guided modes. The present study is focused on the theoretical modeling of the impact of an overlying soft tissue. A semianalytical method and finite-difference time domain simulations were used. The models developed were shown to predict consistently real in vivo data on human radii. As a conclusion, clinical guided wave data are not consistent with in vitro data or related in vitro models, but use of an adequate in vivo model, such as the one introduced here, is necessary. A theoretical model that accounts for the impact of an overlying soft tissue could thus be used in clinical applications.