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.

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

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 R2=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.

Assessment of trabecular bone tissue elasticity with resonant ultrasound spectroscopy.

The material properties of the trabeculae (tissue-level properties), together with the trabecular architecture and the bone volume fraction determine the apparent millimetre-scale bone mechanical properties. We present a novel method to measure trabecular tissue elastic modulus Et using resonant ultrasound spectroscopy (RUS). The first mechanical resonance frequency fe of a freestanding cuboid specimen is measured and used to back-calculate Et. The steps of the back-calculation are (1) the apparent stiffness tensors C(Et˜) is computed using micro-finite elements for a set of trial values of tissue Young's modulus Et˜ based on the computed tomography image of the specimen; (2) the modeled free-vibration resonance frequencies fm(Et˜) of the specimen is calculated with the Rayleigh-Ritz method using C(Et˜); (3) finally, Et is obtained by interpolation using fe and fm(Et˜). Four bovine bone specimens were tested (nominal size 5×6 ×6mm3). Average (standard deviation) of Et was 13.12 (1.06)GPa. The measurement of a single resonance frequency enabled an estimation of tissue elasticity in line with available data. RUS is a non destructive technique relatively easy to implement compared to traditional mechanical testing. The novel method could contribute to a better documentation of bone tissue elasticity which is an important parameter of micro-finite element analyses for the clinical assessment of bone strength.

A critical assessment of the in-vitro measurement of cortical bone stiffness with ultrasound.

Elasticity assessment based on bulk wave velocity (BWV) measurements is the most popular technique to characterize the anisotropic stiffness tensor in cortical bone. Typically, a cuboid bone specimen is cut with its sides along the different anatomical directions. Then, the velocity of shear and longitudinal waves propagating along different directions are assessed, from which stiffness coefficients are calculated. Despite the importance of obtaining accurate elasticity values for bone research, there is no generally accepted protocol to measure BWV and the precision of the technique has been seldom investigated. The purpose of this work is to critically assess the method to measure BWV on cuboid specimens in terms of ultrasound frequency, specimen size and signal processing technique. In this study, we measured polycarbonate specimens of different dimensions and 55 human bone specimens with different transducers using frequencies ranging from 2.25 to 10MHz and 1-5MHz for longitudinal and shear waves, respectively. We compared four signal processing methods to detect the wave arrival time. The main results are that, (1) the measurement of shear waves is more complex than that of longitudinal wave, being less precise and more sensitive to sample size; (2) the estimated stiffness depends on the signal processing technique used (up to 10% variation for shear coefficients of bone); and (3) bone stiffness assessed from BWV using the first arrival of the signal to determine the time-of-flight is not different from stiffness assessed using resonant ultrasound spectroscopy (RUS). These results evidence that the measurement method can have an effect on the stiffness values estimates and hence, a well-defined protocol is needed to accurately measure bone stiffness coefficients based on BWV.

Cortical bone elasticity measured by resonant ultrasound spectroscopy is not altered by defatting and synchrotron X-ray imaging.

In the study of mechanical properties of human bone, specimens may be defatted before experiments to prevent contamination and the risk of infections. High energy synchrotron radiation micro-computed tomography (SR-µCT) is a popular technique to study bone microstructure. However, little is known about the effects of defatting or irradiation during SR-µCT imaging on different elastic coefficients including shear and longitudinal moduli in different anatomical directions. In this work, these effects are evaluated on a set of 24 samples using resonant ultrasound spectroscopy (RUS), which allows one to accurately measure the complete set of elastic coefficients of cortical bone non destructively. The results show that defatting with diethylether and methanol and irradiation up to 2.5kGy has no detectable effect on any of the elastic coefficients of human cortical bone.

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

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.

Anisotropy of dynamic acoustoelasticity in limestone, influence of conditioning, and comparison with nonlinear resonance spectroscopy.

Anisotropy of wave velocity and attenuation induced by a dynamic uniaxial strain is investigated by dynamic acoustoelastic testing in limestone. Nonlinear resonance spectroscopy is performed simultaneously for comparison. A compressional resonance of the sample at 6.8 kHz is excited to produce a dynamic strain with an amplitude varied from 10(-7) to 10(-5). A sequence of ultrasound pulses tracks variations in ultrasonic velocity and attenuation. Variations measured when the ultrasound pulses propagate in the direction of the uniaxial strain are 10 times larger than when the ultrasound propagation occurs perpendicularly. Variations consist of a "fast" variation at 6.8 kHz and an offset. Acoustically induced conditioning is found to reduce wave velocity and enhance attenuation (offset). It also modifies "fast" nonlinear elastodynamics, i.e., wave amplitude dependencies of ultrasonic velocity and attenuation. At the onset of conditioning and beyond, different excitation amplitudes bring the material to non-equilibrium states. After conversion of velocity-strain dynamic relations into elastic modulus-strain dynamic relations and integration with respect to strain, the dynamic stress-strain relation is obtained. Analysis of stress-strain hysteresis shows that hysteretic nonlinear elasticity is not a significant source of the amplitude-dependent dissipation measured by nonlinear resonance spectroscopy. Mechanisms causing conditioning are likely producing amplitude-dependent dissipation as well.

Nonlinear elastodynamics in micro-inhomogeneous solids observed by head-wave based dynamic acoustoelastic testing.

Dynamic acoustoelastic testing provides a more complete insight into the acoustic nonlinearity exhibited by micro-inhomogeneous media like granular and cracked materials. This method consists of measuring time of flight and energy modulations of pulsed ultrasonic waves induced by a low-frequency standing wave. Here pulsed ultrasonic head waves were employed to assess elastic and dissipative nonlinearities in a region near the surface of a solid. Synchronization of the ultrasound pulse sequence with the low-frequency excitation provided instantaneous variations in the elastic modulus and the attenuation as functions of the instantaneous low-frequency strain. Weak quadratic elastic nonlinearity and no dissipative nonlinearity were detected in duralumin. In limestone, distinction between tensile and compressive behaviors revealed an asymmetry in the acoustic nonlinearity and hysteresis in both the elastic modulus and the attenuation variations. Measured nonlinear acoustical parameters are in good agreement with values obtained by different techniques. Reversible acoustically induced conditioning modified the acoustic nonlinearity both quantitatively and qualitatively. It reduced tension-compression asymmetry, suggesting a nonequilibrium modification of the sources of acoustic nonlinearity. Additionally to the metrology of the acoustic nonlinearity, head wave based dynamic acoustoelastic testing may be a useful tool to monitor changes in the microstructure or the accumulation of damage in solids.

Trabecular and cortical bone separately assessed at radius with a new ultrasound device, in a young adult population with various physical activities.

The aim was to evaluate a new ultrasound device in a young adult population and to assess its reproducibility via comparison to DXA measurements and geometrical measurements from high-resolution radiographs. Ninety-three subjects aged between 20 and 51 years were recruited and divided into four groups according to their gender and physical activity status: 22 male athletes, 19 male controls, 21 female athletes, and 31 female controls. Ultrasonic measurements were assessed by the prototype LD-100 (Oyo Electric Co., Kyoto, Japan) on the dominant distal radius. Attenuation in the radius (dB), cortical bone thickness (mm), radius thickness (mm), mass density of cancellous bone (mg/cm(3)), and elasticity (GPa) of cancellous bone were obtained. BMD was measured by DXA at the dominant distal radius. Radius images were obtained with a direct high-resolution digital X-ray device (BMA, D(3)A Medical Systems), and radius and cortical thicknesses were estimated using a specific software (ImageJ, Bethesda, USA), in an area site-matched with LD-100. There was a significant positive correlation between site-matched BMD measurement and LD-100 parameters (p<0.004), X-ray radius thickness, and LD-100 parameters except elasticity (p<0.05, r>0.32), X-ray cortical thickness and LD-100 attenuation and cortical thickness (p<0.01). A significantly higher attenuation, cortical and radius thicknesses were found in athletes compared to controls (p<0.05). The radius thickness measured on radiographs was significantly higher in athletes versus controls in both sexes, and cortical thickness was significantly higher in male athletes versus controls. These data suggest a positive influence of physical activity on bone cortical measurements. This study also confirmed the particular interest of bone assessment by ultrasound.

Simultaneous determination of acoustic velocity and density of a cortical bone slab: ultrasonic model-based approach.

An ultrasonic setup coupled to a 1-D mathematical model of wave propagation is used to determine the material properties of elastic solids. A maximum likelihood fit of the acoustic response with the model response in the frequency domain enables the simultaneous determination of acoustic velocity, mass density, damping, and sample thickness. The method, previously tested with homogeneous materials, has been applied to compact bone despite the fact that it is a highly attenuating material.

Femur ultrasound (FemUS)--first clinical results on hip fracture discrimination and estimation of femoral BMD.

SUMMARY: A quantitative ultrasound (QUS) device for measurements at the proximal femur was developed and tested in vivo (Femur Ultrasound Scanner, FemUS). Hip fracture discrimination was as good as for DXA, and a high correlation with hip BMD was achieved. Our results show promise for enhanced QUS-based assessment of osteoporosis. INTRODUCTION: Dual X-ray absorptiometry (DXA) at the femur is the best predictor of hip fractures, better than DXA measurements at other sites. Calcaneal quantitative ultrasound (QUS) can be used to estimate the general osteoporotic fracture risk, but no femoral QUS measurement has been introduced yet. We developed a QUS scanner for measurements at the femur (Femur Ultrasound Scanner, FemUS) and tested its in vivo performance. METHODS: Using the FemUS device, we obtained femoral QUS and DXA on 32 women with recent hip fractures and 30 controls. Fracture discrimination and the correlation with femur bone mineral density (BMD) were assessed. RESULTS: Hip fracture discrimination using the FemUS device was at least as good as with hip DXA and calcaneal QUS. Significant correlations with total hip bone mineral density were found with a correlation coefficient R (2) up to 0.72 and a residual error of about one half of a T-score in BMD. CONCLUSIONS: QUS measurements at the proximal femur are feasible and show a good performance for hip fracture discrimination. Given the promising results, this laboratory prototype should be reengineered to a clinical applicable instrument. Our results show promise for further enhancement of QUS-based assessment of osteoporosis.

Relationship between ultrasonic parameters and apparent trabecular bone elastic modulus: a numerical approach.

The physical principles underlying quantitative ultrasound (QUS) measurements in trabecular bone are not fully understood. The translation of QUS results into bone strength remains elusive. However, ultrasound being mechanical waves, it is likely to assess apparent bone elasticity. The aim of this study is to derive the sensitivity of QUS parameters to variations of apparent bone elasticity, a surrogate for strength. The geometry of 34 human trabecular bone samples cut in the great trochanter was reconstructed using 3-D synchrotron micro-computed tomography. Finite-difference time-domain simulations coupled to 3-D micro-structural models were performed in the three perpendicular directions for each sample and each direction. A voxel-based micro-finite element linear analysis was employed to compute the apparent Young's modulus (E) of each sample for each direction. For the antero-posterior direction, the predictive power of speed of sound and normalized broadband ultrasonic attenuation to assess E was equal to 0.9 and 0.87, respectively, which is better than what is obtained using bone density alone or coupled with micro-architectural parameters and of the same order of what can be achieved with the fabric tensor approach. When the direction of testing is parallel to the main trabecular orientation, the predictive power of QUS parameters decreases and the fabric tensor approach always gives the best results. This decrease can be explained by the presence of two longitudinal wave modes. Our results, which were obtained using two distinct simulation tools applied on the same set of samples, highlight the potential of QUS techniques to assess bone strength.

In vivo performance evaluation of bi-directional ultrasonic axial transmission for cortical bone assessment.

Our objective was to assess a new quantitative ultrasound device suitable for the measurement of speed of sound in radius. The so-called "bidirectional" technique allows an accurate estimation of velocity based on a compensation for soft tissue effects implemented directly inside the probe. Velocity measurements at 1 MHz of the first arriving signal were performed at the one third distal radius in 358 enrolled women. The average velocity by age decade increases to a peak velocity of 4043 m/s in the class 30-39 y (n = 19) and decreases thereafter. Fracture discrimination was investigated on the subset of the population for which dual-energy x-ray absorptiometry measurement was available, in addition to first arriving signal velocity measurements. The study group consisted of 122 postmenopausal women without history of fracture (group NF) and 44 postmenopausal patients (group F) with osteoporotic fractures (hip, spine, Colles fracture). When adjusted for age and bone mass index, the odds ratio (OR) for fracture prediction by ultrasound velocity, was 1.81 (1.21; 2.70) and OR associated to neck femur BMD was 2.07 (1.31-3.29). For the full model including age and body mass index as cofactors, the area under the receiver operating characteristic curve was 0.77, either for ultrasound velocity or neck femur bone mineral density. Despite the small population and the variety of fractures in the fracture group, our data indicate that the velocity of the first arriving signal measured by bidirectional technique discriminates patients with osteoporotic fracture from controls.

Comparative ultrasound evaluation of human trabecular bone graft properties after treatment with different sterilization procedures.

New sterilization methods for human bone are likely to affect the mechanical properties of human cancellous grafts. These mechanical properties dictate the short- and mid-term results of the orthopedic procedure. The aim of this study was to compare the effects on bone mechanical properties, as assessed by ultrasound velocity, of different sterilization methods used under similar conditions: bleach and sublimation, humid heat, successive baths of physiological saline with osmotic detersion, and CO(2) in the supercritical phase. Alterations in mechanical properties were small with CO(2) (velocity change: -2%) and humid heat (-2.5%). Osmotic detersion had a significant but moderate effect (-4.7%). The -9% change with the protocol involving bleach suggested a greater than 30% decrease in load to failure, based on earlier studies. Gamma irradiation of defatted trabecular allografts, in a dose of 10 or 25 KGy, produced no significant changes in ultrasound velocity. Powerful protein denaturants used in sterilization protocols substantially alter the mechanical resistance of the grafts, which may jeopardize the orthopedic procedure.

Sensitivity of qus parameters to controlled variations of bone strength assessed with a cellular model.

The physical principles underlying quantitative ultrasound (QUS) measurements are not fully understood yet. Therefore, the translation of QUS results into bone strength remains elusive. In the present study, we derive the sensitivity of broadband ultrasonic attenuation (BUA) and speed of sound (SOS) to variations of bone strength. For this purpose, a mechanical cellular model is combined to a multiple regression resulting from the analysis of finite-difference time domain (FDTD) simulations. Specifically, we investigate how QUS variables respond to a variation in strength of 10%, realized either by a change in material properties or a change in bone volume fraction (BV/TV). The results show that except when BV/TV is high, the variations of BUA in response to a variation in strength realized by a pure change of BV/TV exceeds the technique imprecision and thus can be detected. When the variation of strength is realized by changes of compressive or shear stiffness, the response in QUS properties is dominated by the variation in C(11), whereas changes in C(44), remaining below the precision error, cannot be detected. The interpretation of these data, however, is not straightforward due to sparse description of elastic properties at the tissue level. To overcome the limitation of the cellular model, more realistic computational models such as micro- finite element analysis have to be considered.

Spatial distribution of anisotropic acoustic impedance assessed by time-resolved 50-MHz scanning acoustic microscopy and its relation to porosity in human cortical bone.

We used quantitative scanning acoustic microscopy (SAM) to assess tissue acoustic impedance and microstructure of cortical bone of human radii with the aim to provide data on regional distribution of acoustic impedance along the circumferential and across the radial directions in the entire cross-section of the radius diaphysis as well as to determine the range of impedance values in transverse (perpendicular to bone axis) and longitudinal (parallel to bone axis) cross-sections. Several microstructural features related to cortical porosity were analyzed in order to determine whether these features differ in different parts of the cortex and to assess the relationship between the microstructure and tissue acoustic impedance. Fifteen fresh bone specimens (human radius) were investigated using a SAM (center frequency of 50 MHz and -6 dB lateral resolution of approximately 23 microm). The sample acoustic impedance was obtained by means of a calibration curve correlating the reflected signal amplitude of reference materials with their corresponding well-known acoustic impedance. Tissue acoustic impedance and microstructural features were derived from the morphometric analysis of the segmented impedance images. A higher porosity was found in the inner cortical layer (mean+/-SD=8.9+/-2.3%) compared to the peripheral layer (2.7+/-1.5%) (paired t-test, p<10(-5)). ANOVA showed that most of the variance can be explained by the regional effect across the radial direction with a minor contribution due to between-sample variability. Similar to porosity, the number and diameter of pores were greater in the inner layer. In contrast to porosity, ANOVA showed that impedance variability can mostly be explained by between-specimen variability. Two-way ANOVA revealed that after compensation for the between-sample variability the variation in acoustic impedance across the radial direction was much larger than that along the circumferential direction. In addition to the significant difference between the inner cortical layer (8.25+/-0.4 Mrayl) and peripheral layer (8.0+/-0.5 Mrayl) (unilateral paired t-test, p<10(-4)), the values in the anterior region (8.2+/-0.5 Mrayl) were found to be significantly higher than those of the posterior region (7.9+/-0.6 Mrayl). Impedance mean value of longitudinal sections was lower than mean value measured in transverse cross-sections, resulting in an impedance acoustic anisotropy ratio of 1.17+/-0.03 in the inner cortical layer and 1.19+/-0.02 in the peripheral layer. SAM is a valuable tool to provide data on the spatial distribution of microstructural and microelastic bone properties that is useful to improve our understanding of the impact of bone microstructure on tissue material properties.

Relationships of trabecular bone structure with quantitative ultrasound parameters: in vitro study on human proximal femur using transmission and backscatter measurements.

The present study was designed to assess the relationships between QUS parameters and bone density or microarchitecture on samples of human femoral trabecular bone. The normalized slope of the frequency-dependent attenuation (nBUA), the speed of sound (SOS) and the broadband ultrasound backscatter coefficient (BUB) were measured on 37 specimens of pure trabecular bones removed from upper parts of fresh human femurs. Bone mineral density (BMD) was assessed using a clinical scanner. Finally, 8 mm diameter cylindrical cores were extracted from the specimens and their microarchitecture was reconstructed after synchrotron radiation microtomography experiments (isotropic resolution of 10 microm). A large number of microarchitectural parameters were computed, describing morphology, connectivity and geometry of the specimens. BMD correlated with all the microarchitectural parameters and the number of significant correlations was found among the architectural parameters themselves. All QUS parameters were significantly correlated to BMD (R=0.83 for nBUA, R=0.81 for SOS and R=0.69 for BUB) and to microarchitectural parameters (R=-0.79 between nBUA and Tb.Sp, R=-0.81 between SOS and Tb.Sp, R=-0.65 between BUB and BS/BV). Using multivariate model, it was found that microstructural parameters adds 10%, 19%, and 4% to the respective BMD alone contribution for the three variables BUA, SOS and BUB. Moreover, the RMSE was reduced by up to 50% for SOS, by up to 21% for nBUA and up to 11% when adding structural variables to BMD in explaining QUS results. Given the sample, which is not osteoporosis-enriched, the added contribution is quite substantial. The variability of SOS was indeed completely explained by a multivariate model including BMD and independent structural parameters (R(2)=0.94). The inverse problem on the data presented here has been addressed using simple and multiple linear regressions. It was shown that the predictions (in terms of R(2) or RMSE) of microarchitectural parameters was not enhanced when combining 2 or 3 QUS in multiple linear regressions compared to the prediction obtained with one QUS parameter alone. The best model was found for the prediction of Tb.Th() from BUA (R(2)=0.58, RMSE=17 microm). Given the high values of RMSE, these linear models appear of limited clinical value, suggesting that appropriate models have to be derived in order to solve the inverse problem. In this regard, a very interesting multivariate model was found for nBUA and BUB with Tb.Th and Tb.N, in agreement with single scattering theories by random medium. However, the source of residual variability of nBUA and BUB (15% and 45% respectively) remained unexplained.

Fast wave ultrasonic propagation in trabecular bone: numerical study of the influence of porosity and structural anisotropy.

Our goal is to assess the potential of computational methods as an alternative to analytical models to predict the two longitudinal wave modes observed in cancellous bone and predicted by the Biot theory. A three-dimensional (3D) finite-difference time-domain method is coupled with 34 human femoral trabecular microstructures measured using microcomputed tomography. The main trabecular alignment (MTA) and the degree of anisotropy (DA) were assessed for all samples. DA values were comprised between 1.02 and 1.9. The influence of bone volume fraction (BV/TV) between 5% and 25% on the properties of the fast and slow waves was studied using a dedicated image processing algorithm to modify the initial 3D microstructures. A heuristic method was devised to determine when both wave modes are time separated. The simulations (performed in three perpendicular directions) predicted that both waves generally overlap in time for a direction of propagation perpendicular to the MTA. When these directions are parallel, both waves are separated in time for samples with high DA and BV/TV values. A relationship was found between the least bone volume fraction required for the observation of nonoverlapping waves and the degree of anisotropy: The higher the DA, the lower the least BV/TV.

Nonlinear ultrasound can detect accumulated damage in human bone.

Bone micro-damage is commonly accepted as a relevant parameter for fracture risk assessment, but there is no available technique for its non-invasive characterization. The objective of this work is to study the potential of nonlinear ultrasound for damage detection in human bone. Ultrasound is particularly desirable due to its non-invasive and non-ionizing characteristics. We show results illustrating the correlation of progressive fatigue of human bone samples to their nonlinear dynamical response. In our experiments, damage was induced in 30 samples of diaphyseal human femur using fatigue cycling. At intervals in the cycling, the nonlinear response of the samples was assessed applying Nonlinear Resonant Ultrasound Spectroscopy (NRUS). The nonlinear parameter alpha, which in other materials correlates with the quantity of damage, dramatically increased with the number of mechanical testing cycles. We find a large spread in alpha in the pristine samples and infer that the spread is due to damage differences in the sample population. As damage accumulates during cycling, we find that alpha is much more sensitive to damage than other quantities measured, including the slope and hysteresis of the load/displacement curve, and the dynamic wavespeed. To our knowledge, this study represents the first application of the concept of nonlinear dynamic elasticity to human bone. The results are promising, suggesting the value of further work on this topic. Ultimately, the approach may have merit for in vivo bone damage characterization.

Prediction of bone mechanical properties using QUS and pQCT: study of the human distal radius.

The objective was to compare the prediction of bone mechanical properties provided by axial transmission to that provided by peripheral quantitative computed tomography (pQCT) at the distal radius. The distal radius is the location for Colles' fractures, a common osteoporosis related trauma situation. Measurements of the radial speed of sound were performed using three axial transmission devices: a commercial device (Sunlight Omnisense, 1.25 MHz), a bi-directional axial transmission prototype (1 MHz), both measuring the velocity of the first arriving signal (FAS), and a low frequency (200 kHz) device, measuring the velocity of a slower wave. Co-localized pQCT measurements of bone mineral density and cortical thickness were performed. Ultrasound and pQCT parameters were compared to mechanical parameters such as failure load and Young's modulus, obtained using quasistatic compressive mechanical testing and finite elements modelling (FEM). Correlations of the ultrasound and pQCT parameters to mechanical parameters were comparable. The best predictor of failure load was the pQCT measured cortical thickness. The best predictor of Young's modulus was the bi-directional SOS. The low frequency device significantly correlated to cortical thickness and failure load. The results suggest that different axial transmission approaches give access to different bone mechanical parameters. The association of different axial transmission techniques should be able to provide a good prediction of bone mechanical parameters, and should therefore be helpful for fracture risk prediction.