Assessment of bone density using ultrasonic backscatter

The dependence of ultrasonic backscatter on trabecular thickness in human calcaneus: theoretical and experimental results

Trabecular thickness within cancellous bone is an important determinant of osteoporotic fracture risk. Noninvasive assessment of trabecular thickness potentially could yield useful diagnostic information. Faran's theory of elastic scattering from a cylindrical object immersed in a fluid has been used to predict the dependence of ultrasonic backscatter on trabecular thickness. The theory predicts that, in the range of morphological and material properties expected for trabecular bone, the backscatter coefficient at 500 kHz should be approximately proportional to trabecular thickness to the power of 2.9. Experimental measurements of backscatter coefficient were performed on 43 human calcaneus samples in vitro. Mean trabecular thicknesses on the 43 samples were assessed using micro computed tomography (CT). A power law fit to the data showed that the backscatter coefficient empirically varied as trabecular thickness to the 2.8 power. The 95% confidence interval for this exponent was 1.7 to 3.9. The square of the correlation coefficient for the linear regression to the log transformed data was 0.40. This suggests that 40% of variations in backscatter may be attributed to variations in trabecular thickness. These results reinforce previous studies that offered validation for the Faran cylinder model for prediction of scattering properties of cancellous bone, and provide added evidence for the potential diagnostic utility of the backscatter measurement.

The effect of trabecular material properties on the frequency dependence of backscatter from cancellous bone

Previous experimental studies indicate that backscatter coefficient for human calcaneal trabecular bone varies approximately as frequency cubed. This frequency dependence has been shown to be consistent with a model in which trabeculae are thought of as long thin cylinders composed of a substance with the same material properties as hydroxyapatite. The true material properties of human trabecular bone are not known however. Based on reported measurements of material properties of many bones and bone-like substances, it is possible that the density and longitudinal sound speed of trabecular bone material are far lower than the hydroxyapatite model would suggest. In this letter, it is shown that the frequency dependence of backscatter is still expected to be approximately cubic for wide ranges for density and longitudinal sound speed (encompassing the conceivable ranges for trabecular bone).

Characterization of trabecular bone using the backscattered spectral centroid shift

Ultrasonic attenuation in bone in vivo is generally measured using a through-transmission method at the calcaneus. Although attenuation in calcaneus has been demonstrated to be a useful predictor for osteoporotic fracture risk, measurements at other clinically important sites, such as hip and spine, could potentially contain additional useful diagnostic information. Through-transmission measurements may not be feasible at these sites due to complex bone shapes and the increased amount of intervening soft tissue. Centroid shift from the backscattered signal is an index of attenuation slope and has been used previously to characterize soft tissues. In this paper, centroid shift from signals backscattered from 30 trabecular bone samples in vitro were measured. Attenuation slope also was measured using a through-transmission method. The correlation coefficient between centroid shift and attenuation slope was -0.71. The 95% confidence interval was (-0.86, -0.47). These results suggest that the backscattered spectral centroid shift may contain useful diagnostic information potentially applicable to hip and spine.

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.

Effect of marrow on the high frequency ultrasonic properties of cancellous bone

A number of investigators have performed in vitro measurements of cancellous bone to determine how various ultrasonic parameters depend on bone density and trabecular orientation. To facilitate handling and storage of bone specimens, the marrow is often removed prior to ultrasonic measurements. However, the assumption that marrow does not affect ultrasonic measurements at high frequencies (>1 MHz) has not been tested. The goal of this study is to determine the effect of marrow on the ultrasonic properties of bovine cancellous bone at frequencies greater than 1 MHz. Twelve specimens of cancellous bone were obtained from the proximal end of four bovine tibia. Ultrasonic measurements consisting of normalized broadband ultrasonic attenuation (nBUA), speed of sound (SOS) and apparent integrated backscatter (AIB) were measured in each specimen using 2.25 MHz (centre frequency) broadband ultrasonic pulses. These measurements were performed before and after marrow removal either along the superoinferior (SI) or mediolateral (ML) direction. SOS and nBUA showed no significant difference (p > 0.05) for either direction of propagation after marrow removal. AIB showed no significant difference in the SI direction. For the ML direction, a small but statistically significant difference (p = 0.044) was observed after marrow removal.

Ultrasonic characterization of human cancellous bone using transmission and backscatter measurements: relationships to density and microstructure

The present study was designed to evaluate the relationships between ultrasonic backscatter, density, and microarchitecture of cancellous bone. The slopes of the frequency-dependent attenuation coefficient (nBUA), ultrasound bone velocity (UBV), the frequency-averaged backscatter coefficient (BUB) were measured in 25 cylindrical cancellous bone cores. Bone mineral density (BMD) was determined using X-ray quantitative computed tomography. Microarchitecture was investigated with synchrotron radiation microtomography with an isotropic spatial resolution of 10 microm. Several microstructural parameters reflecting morphology, connectivity, and anisotropy of the specimens were derived from the reconstructed three-dimensional (3D) microarchitecture. The association of the ultrasonic variables with density and microarchitecture was assessed using simple and multivariate linear regression techniques. For all ultrasonic variables, a strong association was found with density (r = 0.84-0.90). We also found that, with the exception of connectivity, all microstructural parameters correlated significantly with density, with r values of 0.54-0.92. For most microstructural parameters there was a highly significant correlation with ultrasonic parameters (r = 0.33-0.91). However, the additional variance explained by microstructural parameters compared with the variance explained by BMD alone was small (Delta r(2) = 6% at best). In particular, no significant independent association was found between microstructure and backscatter coefficient (a microstructure-related ultrasonic parameter) after adjustment for density. The source for the unaccounted variance of quantitative ultrasound (QUS) parameters remains unknown.

Fundamental precision limitations for measurements of frequency dependence of backscatter: applications in tissue-mimicking phantoms and trabecular bone

Various models for ultrasonic scattering from trabecular bone have been proposed. They may be evaluated to a certain extent by comparison with experimental measurements. In order to appreciate limitations of these comparisons, it is important to understand measurement precision. In this article, an approach proposed by Lizzi and co-workers is adapted to model precision of estimates of frequency-dependent backscatter for scattering targets (such as trabecular bone) that contain many scatterers per resolution cell. This approach predicts uncertainties in backscatter due to the random nature of the interference of echoes from individual scatterers as they are summed at the receiver. The model is validated in experiments on a soft-tissue-mimicking phantom and on 24 human calcaneus samples interrogated in vitro. It is found that while random interference effects only partially explain measured variations in the magnitude of backscatter, they are virtually entirely responsible for observed variations in the frequency dependence (exponent of a power law fit) of backscatter.

Ultrasonic backscatter and transmission parameters at the os calcis in postmenopausal osteoporosis

Ultrasound technology has emerged as a new tool in the assessment of osteoporosis. Ultrasound parameters usually are measured in transmission; there is a potential for the analysis of backscattered signals to provide information on bone microarchitecture. The aim of this study was to explore a new technological development of the method, adding backscatter coefficient to transmission parameters, and to examine the appropriate thresholds to identify postmenopausal osteoporotic women. We examined 210 postmenopausal women (including 60 with osteoporotic fractures) and 30 healthy premenopausal controls. They had lumbar spine and hip bone mineral density (BMD) measurement and quantitative ultrasound (QUS) evaluation at the os calcis, measured in transmission (broadband ultrasound attenuation [BUA], speed of sound [SOS], ratio of transit time [dt] to BUA [dt/BUA], and "strength" index [STI]) and reflexion (broadband ultrasound backscattering [BUB]). The standardized CVs (sCVs) were between 2.27 % and 3.40 % for QUS measured in transmission and 4.41% for BUB. The odds ratio (OR) for fracture discrimination adjusted for age was 2.77 for hip BMD and between 1.6 and 2.9 for QUS. After adjustment for hip BMD, ORs were still highly significant for SOS, STI, and dt/BUA. According to hip BMD T score, prevalence of osteoporosis in our population was 39%. To detect the same prevalence, T scores ranged between -0.95 and -1.42 for QUS. QUS parameters have adequate ability to discriminate osteoporotic patients from controls. The World Health Organization (WHO) threshold for diagnosis of osteoporosis does not apply to this technology. The clinical utility of BUB at the os calcis, in addition to usual ultrasound parameters, is not yet proven. However, BUB evaluation, which does not require two transducers and may be implemented in conventional reflection mode systems, warrants further studies.

Relationships among calcaneal backscatter, attenuation, sound speed, hip bone mineral density, and age in normal adult women

The present study was undertaken in order to investigate the use of calcaneal ultrasonic backscatter for the application of diagnosis of osteoporosis. Broadband ultrasonic attenuation (BUA), speed of sound (SOS), the average backscatter coefficient (ABC), and the hip bone mineral density (BMD) were measured in calcanea in 47 women (average age: 58 years, standard deviation: 13 years). All three ultrasound variables had comparable correlations with hip BMD (around 0.5). As reported previously by others, BUA and SOS were rather highly correlated with each other. The logarithm of the ABC was only moderately correlated with the other two. The three ultrasound parameters exhibited similar moderate negative correlations with age. These results taken collectively suggest that the ABC may carry important diagnostic information independent of that contained in BUA and SOS and, therefore, may be useful as an adjunct measurement in the diagnosis of osteoporosis.

Frequency dependence of ultrasonic backscattering in cancellous bone: autocorrelation model and experimental results

The goal of this study is to model the frequency dependence of the ultrasonic backscatter coefficient in cancellous bone. A twofold theoretical approach has been adopted: the analytical theoretical model of Faran for spherical and cylindrical elastic scatterers, and the scattering model for weakly scattering medium in which the backscatter coefficient is related to the autocorrelation function of the propagating medium. The ultrasonic backscatter coefficient was measured in 19 bone specimens (human calcaneae) in the frequency range of 0.4-1.2 MHz. The autocorrelation function was computed from the three-dimensional (3D) microarchitecture measured using synchrotron radiation microtomography. Good agreement was found between the frequency dependence of the experimental (f3.38+/-0.31) and autocorrelation modeled (f3.48+/-0.26) backscatter coefficients. The results based on Faran theory (cylindrical Faran model: f2.89+/-0.06 and spherical Faran model: f3.91+/-0.04) show qualitative agreement with experimental data. The good prediction obtained by modeling the backscatter coefficient using the autocorrelation function of the medium opens interesting prospects for the investigation of the influence of bone microarchitecture on ultrasonic scattering.

Relationships of ultrasonic backscatter with ultrasonic attenuation, sound speed and bone mineral density in human calcaneus

Ultrasonic attenuation and sound speed have been investigated in trabecular bone by numerous authors. Ultrasonic backscatter has received much less attention. To investigate relationships among these three ultrasonic parameters and bone mineral density (BMD), 30 defatted human calcanei were investigated in vitro. Normalized broadband ultrasonic attenuation (nBUA), sound speed (SOS), and logarithm of ultrasonic backscatter coefficient (LBC) were measured. Bone mineral density was assessed using single-beam dual energy x-ray absorptiometry (DEXA). The correlation coefficients of least squares linear regressions of the three individual ultrasound (US) parameters with BMD were 0.84 (nBUA), 0.84 (SOS) and 0.79 (LBC). The 95% confidence intervals for the correlation coefficients were 0. 69-0.92 (nBUA), 0.68-0.92 (SOS) and 0.60-0.90 (LBC). The correlations among pairs of US variables ranged from 0.63-0.79. Variations in nBUA accounted for r(2) = 62% of the variations in LBC. Variations in SOS accounted for r(2) = 40% of the variations in LBC. These results suggest that ultrasonic backscattering properties may contain substantial information not already contained in nBUA and SOS. A multiple regression model including all three US variables was somewhat more predictive of BMD than a model including only nBUA and SOS.

Ultrasound shear wave imaging for bone

Recently, a computer-controlled scanning ultrasound (US) imaging system was developed in our laboratory. It includes a pair of broadband 48-MHz focusing copolymer transducers. The apertures of the transducers and their f-numbers were identically equal to 2 mm and 2.25, respectively. A specimen can be moved in a 10-microm increment in its plane and its normal direction can be rotated along the US propagation direction. It can be used to produce transmission-mode images of shear waves, as well as longitudinal waves for solid specimens. Shear waves in solids were generated by mode conversion. The results of the longitudinal and shear-wave US images for a piece of compact bovine bone obtained using this system are presented. Shear-wave images combined with longitudinal images can provide a more complete mechanical characterization of bone.

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).

Anisotropy of ultrasonic backscatter and attenuation from human calcaneus: implications for relative roles of absorption and scattering in determining attenuation

Although bone sonometry has been demonstrated to be useful in the diagnosis of osteoporosis, much remains to be learned about the processes governing the interactions between ultrasound and bone. In order to investigate these processes, ultrasonic attenuation and backscatter in two orientations were measured in 43 human calcaneal specimens in vitro at 500 kHz. In the mediolateral (ML) orientation, the ultrasound propagation direction is approximately perpendicular to the trabecular axes. In the anteroposterior (AP) orientation, a wide range of angles between the ultrasound propagation direction and trabecular axes is encountered. Average attenuation slope was 18% greater while average backscatter coefficient was 50% lower in the AP orientation compared with the ML orientation. Backscatter coefficient in both orientations approximately conformed to a cubic dependence on frequency, consistent with a previously reported model. These results support the idea that absorption is a greater component of attenuation than scattering in human calcaneal trabecular bone.

The relationship between ultrasonic backscatter and bone mineral density in human calcaneus

Backscatter and attenuation coefficients were measured from 24 human calcanei in vitro. The logarithm of the backscatter coefficient at 500 kHz showed moderate correlations with bone mineral density (r=0.81, 95% confidence interval: 0.59-0.91) and attenuation (r=0.79, 95% CI: 0.56-0.91). These results suggest that backscatter measurements may be useful in the diagnosis of osteoporosis.

Frequency dependence of ultrasonic backscatter from human trabecular bone: theory and experiment

A model describing the frequency dependence of backscatter coefficient from trabecular bone is presented. Scattering is assumed to originate from the surfaces of trabeculae, which are modeled as long thin cylinders with radii small compared with the ultrasonic wavelength. Experimental ultrasonic measurements at 500 kHz, 1 MHz, and 2.25 MHz from a wire target and from trabecular bone samples from human calcaneus in vitro are reported. In both cases, measurements are in good agreement with theory. For mediolateral insonification of calcaneus at low frequencies, including the typical diagnostic range (near 500 kHz), backscatter coefficient is proportional to frequency cubed. At higher frequencies, the frequency response flattens out. The data also suggest that at diagnostic frequencies, multiple scattering effects on the average are relatively small for the samples investigated. Finally, at diagnostic frequencies, the data suggest that absorption is likely to be a larger component of attenuation than scattering.