A model for ultrasonic scattering in cancellous bone based on velocity fluctuations in a binary mixture

Mechanisms of Interaction of Ultrasound With Cancellous Bone: A Review

Ultrasound is now a clinically accepted modality in the management of osteoporosis. The most common commercial clinical devices assess fracture risk from measurements of attenuation and sound speed in cancellous bone. This review discusses fundamental mechanisms underlying the interaction between ultrasound and cancellous bone. Because of its two-phase structure (mineralized trabecular network embedded in soft tissue-marrow), its anisotropy, and its inhomogeneity, cancellous bone is more difficult to characterize than most soft tissues. Experimental data for the dependencies of attenuation, sound speed, dispersion, and scattering on ultrasound frequency, bone mineral density, composition, microstructure, and mechanical properties are presented. The relative roles of absorption, scattering, and phase cancellation in determining attenuation measurements in vitro and in vivo are delineated. Common speed of sound metrics, which entail measurements of transit times of pulse leading edges (to avoid multipath interference), are greatly influenced by attenuation, dispersion, and system properties, including center frequency and bandwidth. However, a theoretical model has been shown to be effective for correction for these confounding factors in vitro and in vivo. Theoretical and phantom models are presented to elucidate why cancellous bone exhibits negative dispersion, unlike soft tissue, which exhibits positive dispersion. Signal processing methods are presented for separating "fast" and "slow" waves (predicted by poroelasticity theory and supported in cancellous bone) even when the two waves overlap in time and frequency domains. Models to explain dependencies of scattering on frequency and mean trabecular thickness are presented and compared with measurements. Anisotropy, the effect of the fluid filler medium (marrow in vivo or water in vitro), phantoms, computational modeling of ultrasound propagation, acoustic microscopy, and nonlinear properties in cancellous bone are also discussed.

Influence of cancellous bone microstructure on ultrasonic attenuation: a theoretical prediction

Background

Quantitative ultrasound has been used for the assessment of cancellous bone status. The attenuation mechanisms of cancellous bone, however, have not been well understood, because the microstructure of cancellous bone is significantly inhomogeneous and the interaction between ultrasound and the microstructure of cancellous bone is complex. In this study, a theoretical approach was applied to investigate the influence of the microstructure of cancellous bone on ultrasonic attenuation.

Results

The scattering from a trabecular cylinder was significantly angle dependent. The dependencies of the ultrasonic attenuation on frequency, scatterer size, and porosity were explored from the theoretical calculation. Prediction results showed that the ultrasonic attenuation increased with the increase of frequency and decreased linearly with the increase in porosity, and the broadband ultrasound attenuation decreased with the increase in porosity. All these predicted trends were consistent with published experimental data. In addition, our model successfully explained the principle of broadband ultrasound attenuation measurement (i.e., the attenuation over the frequency range 0.3–0.65 MHz was approximately linearly proportional to frequency) by considering the contributions of scattering and absorption to attenuation.

Conclusion

The proposed theoretical model may be a potentially valuable tool for understanding the interaction of ultrasound with cancellous bone.

Correlations of the frequency dependence of the ultrasonic backscatter coefficient with the bone volume fraction and the trabecular thickness in bovine trabecular bone: Application of the binary mixture model

The ultrasonic backscatter coefficient and the exponent n (frequency dependence of the backscatter coefficient) were measured in 24 bovine femoral trabecular bone samples. The binary mixture model for ultrasonic scattering from trabecular bone was applied to predict the variations of the ultrasound parameters with the bone volume fraction (BV/TV) and the trabecular thickness (Tb.Th) in trabecular bone. The backscatter coefficient exhibited significant, positive correlations with the BV/TV (R = 0.82) and the Tb.Th (R = 0.79). In contrast, the exponent n was found to be significantly, negatively correlated with the BV/TV (R = -0.77) and the Tb.Th, (R = -0.71).

Solid volume fraction estimation of bone:marrow replica models using ultrasound transit time spectroscopy

The acceptance of broadband ultrasound attenuation (BUA) for the assessment of osteoporosis suffers from a limited understanding of both ultrasound wave propagation through cancellous bone and its exact dependence upon the material and structural properties. It has recently been proposed that ultrasound wave propagation in cancellous bone may be described by a concept of parallel sonic rays; the transit time of each ray defined by the proportion of bone and marrow propagated. A Transit Time Spectrum (TTS) describes the proportion of sonic rays having a particular transit time, effectively describing the lateral inhomogeneity of transit times over the surface aperture of the receive ultrasound transducer. The aim of this study was to test the hypothesis that the solid volume fraction (SVF) of simplified bone:marrow replica models may be reliably estimated from the corresponding ultrasound transit time spectrum. Transit time spectra were derived via digital deconvolution of the experimentally measured input and output ultrasonic signals, and compared to predicted TTS based on the parallel sonic ray concept, demonstrating agreement in both position and amplitude of spectral peaks. Solid volume fraction was calculated from the TTS; agreement between true (geometric calculation) with predicted (computer simulation) and experimentally-derived values were R(2)=99.9% and R(2)=97.3% respectively. It is therefore envisaged that ultrasound transit time spectroscopy (UTTS) offers the potential to reliably estimate bone mineral density and hence the established T-score parameter for clinical osteoporosis assessment.

Numerical investigation of ultrasound reflection and backscatter measurements in cancellous bone on various receiving areas

In this study, new ultrasound reflection and backscatter measurements in cancellous bone using a membrane-type hydrophone are proposed. A membrane hydrophone made of a piezoelectric polymer film mounted on an annular frame allows an incident ultrasound wave to pass through its aperture because it has no backing material. Therefore, in measurements using the membrane hydrophone, the receiving area could be located independently from the transmitting area. In addition, the size and shape of the receiving area, which corresponded to those of the electrode deposited on the piezoelectric film, could be arranged in various ways. To investigate the validity of the proposed measurements, before bench-top experiments, the reflected and backscattered waves from cancellous bone were numerically simulated using a finite-difference time-domain method. The reflection and backscatter parameters were measured on various receiving areas, and their correlation coefficients with the structural parameters in the cancellous bone were derived. The simulated results suggested that appropriate receiving areas for the reflection and backscatter measurements could exist and that the proposed measurements could be more effective for evaluating bone properties than conventional measurements.

A deconvolution method for deriving the transit time spectrum for ultrasound propagation through cancellous bone replica models

The acceptance of broadband ultrasound attenuation for the assessment of osteoporosis suffers from a limited understanding of ultrasound wave propagation through cancellous bone. It has recently been proposed that the ultrasound wave propagation can be described by a concept of parallel sonic rays. This concept approximates the detected transmission signal to be the superposition of all sonic rays that travel directly from transmitting to receiving transducer. The transit time of each ray is defined by the proportion of bone and marrow propagated. An ultrasound transit time spectrum describes the proportion of sonic rays having a particular transit time, effectively describing lateral inhomogeneity of transit times over the surface of the receiving ultrasound transducer. The aim of this study was to provide a proof of concept that a transit time spectrum may be derived from digital deconvolution of input and output ultrasound signals. We have applied the active-set method deconvolution algorithm to determine the ultrasound transit time spectra in the three orthogonal directions of four cancellous bone replica samples and have compared experimental data with the prediction from the computer simulation. The agreement between experimental and predicted ultrasound transit time spectrum analyses derived from Bland–Altman analysis ranged from 92% to 99%, thereby supporting the concept of parallel sonic rays for ultrasound propagation in cancellous bone. In addition to further validation of the parallel sonic ray concept, this technique offers the opportunity to consider quantitative characterisation of the material and structural properties of cancellous bone, not previously available utilising ultrasound.

The 25th Anniversary of BUA for the Assessment of Osteoporosis: Time for a New Paradigm?

The measurement of broadband ultrasonic attenuation (BUA) in cancellous bone at the calcaneus for the assessment of osteoporosis was first described within this journal 25 years ago. It was recognized in 2006 by Universities UK as being one of the ‘100 discoveries and developments in UK Universities that have changed the world’ over the past 50 years. In 2008, the UK's Department of Health also recognized BUA assessment of osteoporosis in a publication highlighting 11 projects that have contributed to ‘60 years of NHS research benefiting patients’. The BUA technique has been extensively clinically validated and is utilized worldwide, with at least seven commercial systems currently providing calcaneal BUA measurement. However, there is still no fundamental understanding of the dependence of BUA upon the material and structural properties of cancellous bone. This review aims to provide an ‘engineering in medicine’ perspective and proposes a new paradigm based upon phase cancellation due to variation in propagation transit time across the receive transducer face to explain the non-linear relationship between BUA and bone volume fraction in cancellous bone.

Effect of bone marrow on acoustic properties of trabecular bone--3D finite difference modeling study

The composition of bone marrow is influenced by many factors, such as age and diseases. The present numerical study investigates the contribution of marrow on the acoustic measurements of trabecular bone. Cylindrical bone samples (n = 11), extracted from three anatomical sites of human cadaver knees, were imaged with a high-resolution microtomography (microCT). Three-dimensional finite difference time domain (FDTD) models (Wave 3000 Pro 2.2, Cyberlogic Inc., NY, USA) were created using the segmented microCT images of each sample. First, we evaluated the effect of voxel size on the computer resource requirements, morphological parameters and acoustic simulations. Second, the effect of bone marrow on ultrasonic measurements was assessed. The simulations were repeated with two voxel sizes before and after substitution of bone marrow (i.e., fat) with water. The voxel size of the FDTD mesh controlled the fine structure of the modeled calcified matrix and significantly affected the simulation results. However, present simulations showed that the effect of bone marrow on ultrasound parameters can be reliably simulated with the applied voxel sizes of 72 and 90 microm. Ultrasound attenuation and speed were found (p < 0.01) to decrease and increase, respectively, when bone marrow was substituted with water. Moreover, reflection from the surface of the sample increased (p < 0.01) and backscatter from internal structures decreased (p < 0.01) after removal of marrow. The effect of bone marrow on the acoustic properties was stronger in samples with low bone volume fraction. The present results indicate that the amount and quality of bone marrow significantly influence the acoustic properties of trabecular bone. Possible interindividual differences in the composition of bone marrow may increase uncertainty in clinical ultrasound diagnostics of osteoporosis. Importantly, the effect is most significant in osteoporotic low-density bone.

Mechanisms for attenuation in cancellous-bone-mimicking phantoms

Broadband ultrasound attenuation (BUA) in cancellous bone is useful for prediction of osteoporotic fracture risk, but its causes are not well understood. To investigate attenuation mechanisms, 9 cancellous-bone-mimicking phantoms containing nylon filaments (simulating bone trabeculae) embedded within soft-tissue-mimicking fluid (simulating marrow) were interrogated. The measurements of frequency-dependent attenuation coefficient had 3 separable components: 1) a linear (with frequency) component attributable to absorption in the soft-tissue-mimicking fluid, 2) a quasilinear (with frequency) component, which may include absorption in and longitudinal-shear mode conversion by the nylon filaments, and 3) a nonlinear (with frequency) component, which may be attributable to longitudinal-longitudinal scattering by the nylon filaments. The slope of total linear (with frequency) attenuation coefficient (sum of components #1 and #2) versus frequency was found to increase linearly with volume fraction, consistent with reported measurements on cancellous bone. Backscatter coefficient measurements in the 9 phantoms supported the claim that the nonlinear (with frequency) component of attenuation coefficient (component #3) was closely associated with longitudinal-longitudinal scattering. This work represents the first experimental separation of these 3 components of attenuation in cancellous bone-mimicking phantoms.

Ultrasonic scattering from cancellous bone: a review

This paper reviews theory, measurements, and computer simulations of scattering from cancellous bone reported by many laboratories. Three theoretical models (binary mixture, Faran cylinder, and weak scattering) for scattering from cancellous bone have demonstrated some consistency with measurements of backscatter. Backscatter is moderately correlated with bone mineral density in human calcaneus in vitro (r(2) = 0.66 - 0.68). Backscatter varies approximately as frequency cubed and trabecular thickness cubed in human calcaneus and femur in vitro. Backscatter from human calcaneus and bovine tibia exhibits substantial anisotropy. So far, backscatter has demonstrated only modest clinical utility. Computer simulation models have helped to elucidate mechanisms underlying scattering from cancellous bones.

The measurement of broadband ultrasonic attenuation in cancellous bone--a review of the science and technology

The measurement of broadband ultrasonic attenuation (BUA) in cancellous bone at the calcaneus was first described in 1984. The assessment of osteoporosis by BUA has recently been recognized by Universities UK, within its EurekaUK book, as being one of the "100 discoveries and developments in UK Universities that have changed the world" over the past 50 years, covering the whole academic spectrum from the arts and humanities to science and technology. Indeed, BUA technique has been clinically validated and is utilized worldwide, with at least seven commercial systems providing calcaneal BUA measurement. However, a fundamental understanding of the dependence of BUA upon the material and structural properties of cancellous bone is still lacking. This review aims to provide a science- and technology-orientated perspective on the application of BUA to the medical disease of osteoporosis.

Predictions of the modified Biot-Attenborough model for the dependence of phase velocity on porosity in cancellous bone

The modified Biot-Attenborough (MBA) model for acoustic wave propagation in porous media has been found useful to predict wave properties in cancellous bone. The present study is aimed at applying the MBA model to predict the dependence of phase velocity on porosity in cancellous bone. The MBA model predicts a phase velocity that decreases nonlinearly with porosity. The optimum values for input parameters of the MBA model, such as compressional speed c(m) of solid bone and phase velocity parameter s(2), were determined by comparing the predictions with previously published measurements in human calcaneus and bovine cancellous bone. The value of the phase velocity parameter s(2)=1.23 was obtained by curve fitting to the experimental data for 53 human calcaneus samples only, assuming a compressional speed c(m)=2500 m/s of solid bone. The root-mean-square error (RMSE) of the curve fit was 15.3m/s. The optimized value of s(2) for all 75 cancellous bone samples including 22 bovine samples was 1.42 with a value of 55 m/s for the RMSE of the curve fit. The latter fit was obtained by using of a value of c(m)=3200 m/s. Although the MBA model relies on the empirical parameters determined from experimental data, it is expected that the model can be usefully employed as a practical tool in the field of clinical ultrasonic bone assessment.

Characterization of dense bovine cancellous bone tissue microstructure by ultrasonic backscattering using weak scattering models

A weak scattering model was proposed for the ultrasonic frequency-dependent backscatter in dense bovine cancellous bone, using two autocorrelation functions to describe the medium: one with discrete homogeneities (spherical distribution of equal spheres) and another, which considers tissue as an inhomogeneous continuum (densely populated medium). The inverse problem to estimate trabecular thickness of bone tissue has been addressed. A combination of the two autocorrelation functions was required to closely approximate the backscatter from bovine bone with various microarchitecture, given that the shape of trabeculae ranges from a rodlike to a platelike shape. Because of the large variation in trabecular thickness, both at an intraspecimen and an interspecimen level, thickness distributions for individual trabeculae for each bone specimen were obtained, and dominant trabecular sizes were determined. Comparison of backscatter measurements to theoretical predictions indicated that there were more than one dominant trabecular sizes that scatter sound for most specimens. Linear regression, performed between dominant trabecular thickness and estimated correlation length, showed significant linear correlation (R(2)=0.81). Attenuation due to scattering by a continuous distribution of scatterers was predicted to be linear over a frequency range from 0.3 to 0.9 MHz, suggesting a possibility that scattering may be a significant source of attenuation.

Evaluation of ultrasonic scattering in human cancellous bone by using a binary mixture model

A weak scattering model based on small perturbations in a binary mixture is developed to estimate the ultrasonic scattering from human cancellous bone, which is modelled as a random isotropic continuum containing identical scatters. Ultrasonic scattering is determined by both velocity fluctuation and density fluctuation, when k(2)a(2) << 1 is satisfied. Two kinds of trabeculae thickness distributions, i.e. even distribution and Gauss distribution, are applied in the calculation of attenuation and backscattering. Frequency dependence of the backscatter coefficient is found to be Af(3.13) and Af(2.84) with the Gauss distribution and an even distribution, respectively. Both backscattering and attenuation change significantly against porosity for the case of high porosity. The predicted results are close to the measured ones from the literature. The errors of this theoretical model are also discussed in this paper.

What is ultrasound?

This paper is based on material presented at the start of a Health Protection Agency meeting on ultrasound and infrasound. In answering the question 'what is ultrasound?', it shows that the simple description of a wave which transports mechanical energy through the local vibration of particles at frequencies of 20 kHz or more, with no net transport of the particles themselves, can in every respect be misleading or even incorrect. To explain the complexities responsible for this, the description of ultrasound is first built up from the fundamental properties of these local particle vibrations. This progresses through an exposition of the characteristics of linear waves, in order to explain the propensity for, and properties of, the nonlinear propagation which occurs in many practical ultrasonic fields. Given the Health Protection environment which framed the original presentation, explanation and examples are given of how these complexities affect issues of practical importance. These issues include the measurement and description of fields and exposures, and the ability of ultrasound to affect tissue (through microstreaming, streaming, cavitation, heating, etc.). It is noted that there are two very distinct regimes, in terms of wave characteristics and potential for bioeffect. The first concerns the use of ultrasound in liquids/solids, for measurement or material processing. For biomedical applications (where these two processes are termed diagnosis and therapy, respectively), the issue of hazard has been studied in depth, although this has not been done to such a degree for industrial uses of ultrasound in liquids/solids (sonar, non-destructive testing, ultrasonic processing etc.). However, in the second regime, that of the use of ultrasound in air, although the waves in question tend to be of much lower intensities than those used in liquids/solids, there is a greater mismatch between the extent to which hazard has been studied, and the growth in commercial applications for airborne ultrasound.

Comparison of acoustic characteristics predicted by Biot's theory and the modified Biot-Attenborough model in cancellous bone

Biot's theory and the modified Biot-Attenborough (MBA) model are applied to predict the dependences of acoustic characteristics on frequency and on porosity in cancellous bone. The phase velocities and the attenuation coefficients predicted by both theories are compared with the experimental data of bovine cancellous bone specimens published in the literature. Biot's theory successfully predicts the dependences of the phase velocity on frequency and on porosity in cancellous bone, whereas a significant discrepancy is observed between the predicted and the measured attenuation coefficients. The MBA model agrees well with the frequency and the porosity dependences of the phase velocity and the attenuation coefficient experimentally measured in bovine bones. Although the MBA model relies on phenomenological parameters derived from the experimental data, its approach to cancellous bone can be usefully employed in the field of clinical ultrasonic bone assessment.

Acoustic wave propagation in bovine cancellous bone: application of the Modified Biot-Attenborough model

Acoustic wave propagation in bovine cancellous bone is experimentally and theoretically investigated in the frequency range of 0.5-1 MHz. The phase velocity, attenuation coefficient, and broadband ultrasonic attenuation (BUA) of bovine cancellous bone are measured as functions of frequency and porosity. For theoretical estimation, the Modified Biot-Attenborough (MBA) model is employed with three new phenomenological parameters: the boundary condition, phase velocity, and impedance parameters. The MBA model is based on the idealization of cancellous bone as a nonrigid porous medium with circular cylindrical pores oriented normal to the surface. It is experimentally observed that the phase velocity is approximately nondispersive and the attenuation coefficient linearly increases with frequency. The MBA model predicts a slightly negative dispersion of phase velocity linearly with frequency and the nonlinear relationships of attenuation and BUA with porosity. The experimental results are in good agreement with the theoretical results estimated with the MBA model. It is expected that the MBA model can be usefully employed in the field of clinical bone assessment for the diagnosis of osteoporosis.

Prediction of frequency-dependent ultrasonic backscatter in cancellous bone using statistical weak scattering model

The goal of this study was to propose a model for the ultrasonic frequency-dependent backscatter coefficient in cancellous bone. This model allows us to address the inverse problem and to predict the mean trabecular thickness. A weak scattering model is used and the backscatter coefficient is expressed in terms of an autocorrelation function of the medium. Different autocorrelation functions (Gaussian, exponential and densely populated media) were used to compute the backscatter coefficient and comparison is made with experimental data for 19 specimens and for frequency ranging from 0.4 to 1.2 MHz. For each specimen, a nonlinear regression was performed and the mean trabecular thickness is estimated. Experimental data and theoretical predictions were averaged over the 19 specimens. A good agreement between experimental data and predictions was found for both the magnitude and the frequency-dependence of the backscatter coefficient. We also found a good agreement between the experimental mean trabecular thickness (Tb. Th = 130 +/- 6.5 micro m) derived from the analysis of bone 3-D microarchitecture using high-resolution microtomography and theoretical predictions (d(Gauss) = 140 +/- 10 micro m, d(exponential) = 153 +/- 12.5 micro m and d(dense) = 138 +/- 6.5 micro m). These results open interesting prospects for the estimation of the mean trabecular thickness from in vivo measurements.

Prediction of backscatter coefficient in trabecular bones using a numerical model of three-dimensional microstructure

A model of ultrasonic backscattering for cancellous bone saturated by water is proposed. This model assumes that scattering is caused by the solid trabeculae and describes the cancellous bone as a weak scattering medium. The backscatter coefficient is related to the spatial Fourier transform of bone microarchitecture and to the density and compressibility fluctuations between the solid trabeculae and the saturating fluid. The computations of the model make use of three-dimensional numerical images of bone microarchitecture, obtained by tomographic reconstructions with a 10 microm spatial resolution. With this model, the predictions of the frequency dependence and of the magnitude of the backscatter coefficient are reasonably accurate. The theoretical predictions are compared to experimental data obtained on 19 specimens. An accuracy error of approximately 1 dB was found (difference between the averaged experimental values and theoretical predictions). One limit of the model may come from inaccurate values of trabecular bone characteristics needed for the computations (density and longitudinal velocity), which are yet to be precisely determined for human trabecular bone. However, the model is only slightly sensitive to variations of bone material properties. It was found that an accuracy error of 2.2 dB at maximum resulted from inaccurate a priori values of bone material properties. A computation of the elastic mean free path in the medium suggests that multiple scattering plays a minor role in the working frequency bandwidth (0.4-1.2 MHz). It follows from these results that a weak scattering medium model may be appropriate to describe scattering from trabecular bone.

Age, gender, and fragility fractures are associated with differences in quantitative ultrasound independent of bone mineral density

Bone strength is determined by bone mineral density (BMD) and bone structure. Dual-energy X-ray absorptiometry (DXA) measures BMD. Whether quantitative ultrasound (qUS) measures a property of bone distinct from BMD is uncertain. To evaluate this, DXA and qUS were measured in 58 fracture patients and 428 controls. To study the independent effects of age and gender on qUS measurements and control for BMD by study design rather than statistical methods, subgroups from the normative database were created and intentionally matched by the same femoral neck (FN) BMD. Speed of sound (SOS; m/sec), broadband ultrasound attenuation (BUA; dB/MHz), and stiffness index (SI) were then compared in individuals matched by FN BMD but differing in age, gender, and presence or absence of fractures. The results are presented as percentage difference (mean +/- SD). Elderly women with the same FN BMD as young women had 1 +/- 2% lower SOS (p < 0.05), 8 +/- 15% lower SI (p < 0.05), and 4 +/- 9% lower BUA (p = 0.07). Elderly women with the same FN BMD as elderly men had 5 +/- 9% lower BUA (p < 0.05). Elderly men with the same FN BMD as young men had 1 +/- 2% lower SOS (p = 0.1), 5 +/- 14% lower SI (p = 0.2), and 1 +/- 9% lower BUA (n.s.). Young women with the same FN BMD as young men had 2 +/- 7% lower BUA (n.s.). Women with fragility fractures had 8 +/- 11% lower BUA (p < 0.001) and 13 +/- 22% lower SI (p < 0.01) than controls with no fractures matched by FN BMD, age, and gender. Men with fragility fractures had 13 +/- 12% lower BUA (p < 0.01) and 16 +/- 19% lower SI (p < 0.05) than controls with no fractures matched by FN BMD, age, and gender. Despite comparable femoral neck BMD, qUS measurements differed according to age, gender, and fracture status, suggesting that qUS may provide additional information independent of femoral neck BMD, such as differences in connectivity or other properties yet to be identified.

Quantitative ultrasound does not reflect mechanically induced damage in human cancellous bone

This study investigated the ability of quantitative ultrasound (QUS) to detect reductions in the elastic modulus of cancellous bone caused by mechanical damage. Ultrasonic velocity and attenuation were measured using an in-house parametric imaging system in 46 cancellous bone cores from the human calcaneus. Each core was subjected to a mechanical testing regime to (a) determine the predamage elastic modulus, (b) induce damage by applying specified strains in excess of the yield strain, and (c) measure the postdamage elastic modulus. The specimens were divided into four groups: a control group subjected to a nominally nondestructive 0.7% maximum strain (epsilonm) and three damage groups subjected to increasing strain levels (epsilonm = 1.5, 3.0, and 4.5%). QUS measurements before and after the mechanical testing showed no significant differences between the control group and damage groups, despite highly significant (p < 0.001) reductions in the elastic modulus of up to 72%. These results indicate that current QUS techniques do not intrinsically reflect the elastic properties of cancellous bone. This is consistent with ultrasonic properties being determined by other factors (apparent density and/or architecture), which normally are associated strongly with elastic properties, but only when bone is mechanically intact. Clinically, this implies that ultrasound cannot be expected to detect bone fragility in the absence of major changes in bone density and/or trabecular architecture.

Low-megahertz ultrasonic properties of bovine cancellous bone

Ultrasound offers a noninvasive means to detect changes that occur to the density of cancellous bone as a result of degenerative diseases such as osteoporosis. Techniques based on the velocity and frequency dependence of attenuation of ultrasonic pulses propagated through cancellous bone have proven sensitive to bone density. Most previous studies have investigated these two parameters in the frequency range of 0.1-1.0 MHz. The present study had two goals. The first was to measure three ultrasonic parameters: longitudinal mode velocity; broadband ultrasonic attenuation (BUA); and apparent integrated backscatter (AIB), at higher frequencies using a broadband 2.25 MHz measurement system. The second goal was to assess the dependence of these parameters on bone density. Twenty-one specimens of cancellous bone acquired from the proximal end of four bovine tibiae were investigated in this study. The apparent density of the specimens (determined with the bone marrow removed and the specimens thoroughly dry) ranged between 0.3 and 0.9 g/cm(3). Ultrasonic measurements were performed along three mutually perpendicular directions corresponding to the anteroposterior (AP), mediolateral (ML), and superoinferior (SI) axes of the tibia. A linear regression was used to analyze the results of these measurements as a function of apparent density. Velocity demonstrated a highly significant linear increase with density for all three directions (AP: p < 0.001; ML: p < 0.001; SI: p < 0.01). AIB decreased with density in all three directions; however, only the ML and SI directions demonstrated a significant linear correlation (AP: p = n.s.; ML: p < 0.05; SI: p < 0.05). In the frequency range 0.5-1.0 MHz, BUA exhibited a significant linear increase in the AP and ML directions, but not the SI direction (AP: p < 0.05; ML: p < 0.01; SI: p = n.s.). In contrast, in the frequency range 1.0-2.0 MHz, BUA exhibited a highly significant increase with density in the SI direction, but no significant change in the AP and ML directions (AP: p = n.s., ML: p = n.s., SI: p < 0.001).

Scattering of ultrasound in cancellous bone: predictions from a theoretical model

An understanding of the interaction between acoustic waves and cancellous bone is needed in order to realize the full clinical potential of ultrasonic bone measurements. Scattering is likely to be of central importance but has received little attention to date. In this study, we adopted a theoretical model from the literature in which scattering was assumed to be proportional to the mean fluctuation in sound speed, and bone was considered to be a random continuum containing identical scatterers. The model required knowledge only of sound speeds in bone and marrow, porosity, and scatter size. Predicted attenuation, broadband ultrasonic attenuation (BUA) and backscatter coefficient were obtained for a range of porosities and scatterer sizes, and were found to be comparable to published values for cancellous bone. Trends in predicted BUA with porosity agreed with previous experimental observations. All three predicted acoustic parameters showed a non-linear dependence on scatterer size which was independent of porosity. These data confirm the value of the scattering approach and provide the first quantitative predictions of the independent influence of structure and porosity on bone acoustic properties.

Bone properties as estimated by mineral density, ultrasound attenuation, and velocity

Quantitative ultrasound (QUS) analysis of bone has been suggested to have a level of performance equal to dual-energy X-ray absorptiometry (DXA) for the assessment of fracture risk. In this study, QUS and DXA measurements were conducted on bovine trabecular bone in vitro using commercially available clinical instruments. The samples were then mechanically tested to obtain Young's modulus and ultimate strength. In addition, QUS and DXA parameters of the human calcaneus (n = 34) were measured in vivo. The measurements revealed a significant effect of bovine bone size on broadband ultrasound attenuation (BUA) and speed of sound (SOS) in vitro. By normalizing the DXA and QUS results with bone thickness we could systematically improve their ability to predict bone strength. However, in bovine trabecular bone, BUA showed no significant linear correlation with either bone mineral density (BMD), Young's modulus, or ultimate strength. This finding may be typical of only high-density and low-porosity bovine bone. We significantly improved prediction of ultimate strength by combining density and ultrasound velocity results as compared with assessments of volumetric BMDvol (p < 0.05) or SOS (p < 0.001) alone. However, the improvement was not significant if BMDvol, instead of wet density, was used. Altogether, 88% of the variation in the ultimate strength of bovine bone could be explained by combined density and ultrasound velocity. In vivo, SOS showed a weak negative correlation with heel width (r = -1.350). The in vivo measurements also showed a close correlation for BUA with BMD in the human calcaneus. This suggests that BUA is more suitable for quantitative analysis of low-density trabecular bone.