The effect of cortical endplates on ultrasound velocity through the calcaneus: an in vitro study

A feasibility study on microwave imaging of bone for osteoporosis monitoring

The dielectric properties of bones are found to be influenced by the demineralisation of bones. Therefore, microwave imaging (MWI) can be used to monitor in vivo dielectric properties of human bones and hence aid in the monitoring of osteoporosis. This paper presents the feasibility analysis of the MWI device for monitoring osteoporosis. Firstly, the dielectric properties of tissues present in the human heel are analysed. Secondly, a transmission line (TL) formalism approach is adopted to examine the feasible frequency band and the matching medium for MWI of trabecular bone. Finally, simplified numerical modelling of the human heel was set to monitor the penetration of E-field, the received signal strength, and the power loss in a numerical model of the human heel. Based on the TL formalism approach, 0.6-1.9-GHz frequency band is found to feasible for bone imaging purpose. The relative permittivity of the matching medium can be chosen between 15 and 40. The average percentage difference between the received signal for feasible and inconvenient frequency band was found to be 82%. The findings based on the dielectric contrast of tissues in the heel, the feasible frequency band, and the finite difference time domain simulations support the development of an MWI prototype for monitoring osteoporosis.

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.

Relationships among ultrasonic and mechanical properties of cancellous bone in human calcaneus in vitro

Clinical bone sonometers applied at the calcaneus measure broadband ultrasound attenuation and speed of sound. However, the relation of ultrasound measurements to bone strength is not well-characterized. Addressing this issue, we assessed the extent to which ultrasonic measurements convey in vitro mechanical properties in 25 human calcaneal cancellous bone specimens (approximately 2×4×2cm). Normalized broadband ultrasound attenuation, speed of sound, and broadband ultrasound backscatter were measured with 500kHz transducers. To assess mechanical properties, non-linear finite element analysis, based on micro-computed tomography images (34-micron cubic voxel), was used to estimate apparent elastic modulus, overall specimen stiffness, and apparent yield stress, with models typically having approximately 25-30 million elements. We found that ultrasound parameters were correlated with mechanical properties with R=0.70-0.82 (p<0.001). Multiple regression analysis indicated that ultrasound measurements provide additional information regarding mechanical properties beyond that provided by bone quantity alone (p≤0.05). Adding ultrasound variables to linear regression models based on bone quantity improved adjusted squared correlation coefficients from 0.65 to 0.77 (stiffness), 0.76 to 0.81 (apparent modulus), and 0.67 to 0.73 (yield stress). These results indicate that ultrasound can provide complementary (to bone quantity) information regarding mechanical behavior of cancellous bone.

Numerical investigation of ultrasonic attenuation through 2D trabecular bone structures reconstructed from CT scans and random realizations

In this paper, we compare ultrasound interrogations of actual CT-scanned images of trabecular bone with artificial randomly constructed bone. Even though it is known that actual bone does not have randomly distributed trabeculae, we find that the ultrasound attenuations are close enough to cast doubt on any microstructural information, such as trabeculae width and distance between trabeculae, being gleaned from such experiments. More precisely, we perform numerical simulations of ultrasound interrogation on cancellous bone to investigate the phenomenon of ultrasound attenuation as a function of excitation frequency and bone porosity. The theoretical model is based on acoustic propagation equations for a composite fluid-solid material and is solved by a staggered-grid finite-difference scheme in the time domain. Numerical experiments are performed on two-dimensional bone samples reconstructed from CT-scanned images of real human calcaneus and from random distributions of fluid-solid particles generated via the turning bands method. A detailed comparison is performed on various parameters such as the attenuation rate and speed of sound through the bone samples as well as the normalized broadband ultrasound attenuation coefficient. Comparing results from these two types of bone samples allows us to assess the role of bone microstructure in ultrasound attenuation. It is found that the random model provides suitable bone samples for ultrasound interrogation in the transverse direction of the trabecular network.

Influence of cortical endplate on speed of sound in bovine femoral trabecular bone in vitro

Speed of sound (SOS) was measured in 14 bovine femoral trabecular bone samples with and without the cortical endplates with various thicknesses of 1.00, 1.31, 1.47, 1.75, and 2.00 mm. The presence of the cortical endplates resulted in an increase in the mean SOS of 16 m/s (+0.9%) to 91 m/s (+5.3%). The mean SOS measured in the samples with and without the cortical endplates exhibited similar significant correlations with apparent bone density (r = 0.86-0.91). All the SOS measurements were also found to be highly correlated with each other (r = 0.89-0.99).

Ultrasonic properties in marrow-filled and water-filled bovine femoral trabecular bones in vitro

Phase velocity and normalized broadband ultrasound attenuation (nBUA) were measured in 22 marrow-filled and water-filled bovine femoral trabecular bone samples. Replacement of marrow by water led to a significant increase in the mean phase velocity of 47 ± 12 m/s (+3.1%), but a decrease in the mean nBUA of 10.4 ± 2.9 dB/cm/MHz (-38.9%). All the ultrasonic properties in the marrow-filled and water-filled samples exhibited significant negative Pearson's correlation coefficients of r = -0.87 to -0.92 with porosity. High correlations were also observed between pairs of the ultrasonic properties, with r = 0.85 to 0.93.

Relationships of quantitative ultrasound parameters with cancellous bone microstructure in human calcaneus in vitro

Ultrasound parameters (attenuation, phase velocity, and backscatter), bone mineral density (BMD), and microarchitectural features were measured on 29 human cancellous calcaneus samples in vitro. Regression analysis was performed to predict ultrasound parameters from BMD and microarchitectural features. The best univariate predictors of the ultrasound parameters were the indexes of bone quantity: BMD and bone volume fraction (BV/TV). The most predictive univariate models for attenuation, phase velocity, and backscatter coefficient yielded adjusted squared correlation coefficients of 0.69-0.73. Multiple regression models yielded adjusted correlation coefficients of 0.74-0.83. Therefore attenuation, phase velocity, and backscatter are primarily determined by bone quantity, but multiple regression models based on bone quantity plus microarchitectural features achieve slightly better predictive performance than models based on bone quantity alone.

Calcaneal quantitative ultrasound value for middle-aged and elderly Malaysian Chinese men and its association with age and body anthropometry

Quantitative ultrasound (QUS) is a relatively easy, reliable, and safe method for bone status assessment, but reference data for Asian males remain scarce. Our study aimed to determine the values for one QUS parameter, the speed of sound (SOS) at the calcaneus, in Malaysian Chinese men and to determine the association between the SOS and several demographic characteristics, such as age, weight, height, and body mass index. Three hundred forty-eight Malaysian Chinese men aged 40 yr and older were recruited, and their calcaneal QUS value was determined using the CM-200 densitometer (Furuno Electric, Nishinomiya City, Japan). The results indicated a significant correlation between SOS and age, and multiple stepwise regression analysis indicated that age and height were important predictors of SOS. A significant reduction in SOS value was observed when men 60 yr and older were compared with men aged 40-49 yr. Compared with the reference data for Japanese males, Chinese men in Malaysia showed higher SOS values across all the age groups studied. In conclusion, there is an age-related decrease in SOS values in Malaysian Chinese men, and the SOS values established in this study can be used as a reference for future studies.

Is low-intensity pulsed ultrasound effective for revitalizing a severely necrotic small bone? An experimental rabbit model

Previously, we successfully applied a new method composed of drilling, bone marrow transplantation (BMT), external fixation and low-intensity pulsed ultrasound (LIPUS) for the clinical treatment of Kienböck's disease. The purpose of this study was to investigate whether bone regeneration can be induced by LIPUS and/or multiple drilling and/or BMT within a severely necrotic small-bone rabbit model. Eighteen rabbits were divided into three groups (BMT, drilling and control) and LIPUS stimulation was introduced daily for 8 weeks post-transplantation. Next, 12 additional rabbits were produced for the BMT group and LIPUS stimulation was introduced daily for 4 and 12 weeks (n = 6 for each). Histopathologically, new bone formations were rarely observed in the drilling and control groups. In the BMT group, the mineralizing surface areas of LIPUS(+) showed a significant increase compared with LIPUS(-) for 8 weeks. LIPUS treatment alone did not accelerate the revitalization of necrotic bones. However, LIPUS combined with BMT tended to promote new bone formation.

Influence of the filling fluid on frequency-dependent velocity and attenuation in cancellous bones between 0.35 and 2.5 MHz

The paper is focused on experiments on human cancellous bones filled with different fluids with the goal of evaluating their contribution to velocity dispersion, absorption, and scattering mechanisms. The specimens were measured first filled with marrow and subsequently, after marrow removal, with water and alcohol. No significant influence of the fluids was evidenced on the attenuation coefficient. Given the absence of impact of viscosity of the saturating fluid, the authors hypothesized that the source of attenuation is associated with viscoelastic absorption in the solid trabeculae and with scattering. Alteration of scattering obtained by changing the acoustic impedance mismatch between the fluid (alcohol vs water) and the trabeculae was reflected neither in the attenuation nor in its slope. This led the authors to suggest that longitudinal-to-shear scattering together with absorption in the solid phase are candidates as main sources for the attenuation. The differences in velocity values indicate that the elastic properties of the fluid are main determinants of the phase velocity. This finding is particularly significant in the context of /in vivo/ measurements, because it demonstrates that the subject-dependent properties of marrow may partly explain the inter-subject variability of speed of sound values.

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.

A method for improved standardization of in vivo calcaneal time-domain speed-of-sound measurements

Although calcaneal speed of sound (SOS) is an effective predictor of osteoporotic fracture risk, clinical SOS measurements exhibit a high degree of inter-system variability. Calcaneal SOS is usually computed from time-of-flight measurements of broadband ultrasound pulses that propagate through the foot. In order to minimize the effects of multi-path interference, many investigators measure time-of-flight from markers near the leading edge of the pulse. The calcaneus is a highly attenuating, highly inhomogeneous bone that distorts propagating ultrasound pulses via frequency-dependent attenuation, reverberation, dispersion, multiple scattering, and refraction. This pulse distortion can produce errors in leading-edge transit-time marker-based SOS measurements. In this paper, an equation to predict dependence of time-domain SOS measurements on system parameters (center frequency and bandwidth), transit-time marker location, and bone properties (attenuation coefficient and thickness) is validated with through-transmission measurements in a bone-mimicking phantom and in 73 women in vivo, using a clinical bone sonometer. In order to test the utility of the formula for suppressing system dependence of SOS measurements, a wideband laboratory data acquisition system was used to make a second set of through-transmission measurements on the phantom. The compensation formula reduced system-dependent leading-edge transit-time marker-based SOS measurements in the phantom from 41 m/s to 5 m/s and reduced average transit-time marker-related SOS variability in 73 women from 40 m/s to 10 m/s. The compensation formula can be used to improve standardization in bone sonometry.

Instrumentation for in vivo ultrasonic characterization of bone strength

Although it has been more than 20 years since the first recorded use of a quantitative ultrasound (QUS) technology to predict bone fragility, the field has not yet reached its maturity. QUS has the potential to predict fracture risk in several clinical circumstances and has the advantages of being nonionizing, inexpensive, portable, highly acceptable to patients, and repeatable. However, the wide dissemination of QUS in clinical practice is still limited and suffering from the absence of clinical consensus on how to integrate QUS technologies in bone densitometry armamentarium. Several critical issues need to be addressed to develop the role of QUS within rheumatology. These include issues of technologies adapted to measure the central skeleton, data acquisition, and signal processing procedures to reveal bone properties beyond bone mineral quantity and elucidation of the complex interaction between ultrasound and bone structure. This article reviews the state-of-the art in technological developments applied to assess bone strength in vivo. We describe generic measurement and signal processing methods implemented in clinical ultrasound devices, the devices and their practical use, and performance measures. The article also points out the present limitations, especially those related to the absence of standardization, and the lack of comprehensive theoretical models. We conclude with suggestions of future lines and trends in technology challenges and research areas such as new acquisition modes, advanced signal processing techniques, and modelization.

The dependence of time-domain speed-of-sound measurements on center frequency, bandwidth, and transit-time marker in human calcaneus in vitro

Time-domain speed-of-sound (SOS) measurements in calcaneus are effective predictors of osteoporotic fracture risk. High attenuation and dispersion in bone, however, produce severe distortion of transmitted pulses that leads to ambiguity of time-domain SOS measurements. An equation to predict the effects of system parameters (center frequency and bandwidth), algorithm parameters (pulse arrival-time marker), and bone properties (attenuation coefficient and thickness) on time-domain SOS estimates is derived for media with attenuation that varies linearly with frequency. The equation is validated using data from a bone-mimicking phantom and from 30 human calcaneus samples in vitro. The data suggest that the effects of dispersion are small compared with the effects of frequency-dependent attenuation. The equation can be used to retroactively compensate data. System-related variations in SOS are shown to decrease as the pulse-arrival-time marker is moved toward the pulse center. Therefore, compared with other time-domain measures of SOS, group velocity exhibits the minimum system dependence.

Variation of ultrasonic parameters with microstructure and material properties of trabecular bone: a 3D model simulation

This study determined the influence of trabecular bone microstructure and material properties on QUS parameters using numerical simulations coupled with high-resolution synchrotron radiation microCT.

INTRODUCTION

Finite-difference time domain (FDTD) simulations coupled to 3D microstructural models of trabecular bone reconstructed from synchrotron radiation microtomography (SR-microCT) were used herein to compare and quantify the effects of bone volume fraction, microstructure, and material properties on QUS parameters.

MATERIALS AND METHODS

3D SR-microCT datasets of 30 trabecular human femoral bone specimens were used to create binary digital 3D models. We studied the sensitivity of quantitative ultrasound (QUS) to bone volume fraction by examining QUS parameters at different stages of trabecular thinning or thickening using an iterative dedicated algorithm. The sensitivity to bone material properties was also assessed by analyzing different scenarios in which density and stiffness could be varied independently. The effect of microstructure was qualitatively assessed by producing virtual bone specimens of identical bone volume fraction. Simulations of ultrasonic wave propagation through the trabecular bone volumes were performed using the FDTD simulation software SimSonic developed by our group. For each structure, both broadband ultrasonic attenuation (BUA) and speed of sound (SOS) were computed.

RESULTS

BUA and SOS showed a strong correlation with BV/TV (r(2)=0.94, p<10(-4)) and varied quasi-linearly with BV/TV at an approximate rate of 2 dB/cm.MHz and 11 m/s per percent increase of BV/TV, respectively. Bone alterations caused by variation in BV/TV between 5% and 25% had a greater impact on QUS variables (variation of BUA: 40 dB/cm.MHz; variation of SOS: 200 m/s) than variations caused by alterations of material properties realized either by a 30% change of density or 40% change of stiffness (BUA: 1.7 dB/cm.MHz; SOS: 43 m/s) or than diversity in microarchitecture (BUA:7.8 dB/cm.MHz; SOS: 36 m/s). Moreover, the sensitivity of BUA and SOS to changes in BMD by a given amount realized by a pure change in bone mass (or BV/TV) was found to be predominant over a pure change of mineralization, except for low BV/TV values, where both effects are comparable.

CONCLUSIONS

Trabecular bone microstructure (i.e., trabecular thickness) and material properties were changed to quantify the impact of specific determinants on QUS variables. In this sample of unselected autopsies, specimen variability in bone volume seemed to have a somewhat larger impact on QUS variables than the variability of the other determinants assessed. Whether this is also the case for osteoporotic patients remains to be studied.

The temperature dependence of the speed of sound in bovine bone marrow at 750 kHz

We present values for the speed of sound (SOS) in bovine bone marrow as a function of temperature between 17 degrees C and 44 degrees C. The measurements were made using a time-of-flight approach on a volume of roughly 10 mL, at 750 kHz. The equipment was validated using both distilled water and castor oil. The results show a linear response with SOS changing from 1456.23 ms(-1) at 17 degrees C to 1342.40 ms(-1) at 44 degrees C. The mean value at 37 degrees C was (1371.91 ms(-1)). The temperature coefficient of the SOS was found to be -4.21 +/- 0.19 ms(-1) degrees C(-1). This was well fitted to a least squares model with R2 = 0.88.

Effects of frequency-dependent attenuation and velocity dispersion on in vitro ultrasound velocity measurements in intact human femur specimens

Numerous studies have shown that ultrasonic velocity measured in bone provides a good assessment of osteoporotic fracture risk. However, a lack of standardization of signal processing techniques used to compute the speed of sound (SOS) complicates the comparison between data obtained with different commercial devices. In this study, 38 intact femurs were tested using a through-transmission technique and SOS determined using different techniques. The resulting difference in measured SOS was determined as functions of the attenuation and the velocity dispersion. A numerical simulation was used to explain how attenuation and dispersion impact two different SOS measurements (group velocity, velocity based on the first zero crossing of the signal). A new method aimed at compensating for attenuation was devised and led to a significant reduction in the difference between SOS obtained with both signal processing techniques. A comparison between SOS and X-ray density measurements indicated that the best correlation was reached for SOS based on the first zero crossing apparently because it used a marker located in the early part of the signal and was less sensitive to multipath interference. The conclusion is that first zero crossing velocity may be preferred to group velocity for ultrasonic assessment at this potential fracture site.

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.

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.

Bone marrow influences quantitative ultrasound measurements in human cancellous bone

Quantitative ultrasound (QUS) transmission and backscatter measurements were made in 46 human cancellous bone specimens from the calcaneus. All QUS measurements were made at 35 degrees C, initially with marrow filling the pores and then repeated after substituting water for marrow. Bone mineral density (BMD) was determined using x-ray absorptiometry. Marrow significantly decreased ultrasound (US) velocity, but increased attenuation, attenuation slope and backscatter (p < 0.001 for all) compared to the water-saturated state. The impact of marrow on QUS measurements was greater at lower BMD values (p < 0.05), and was greater in women than in men (p < 0.05). QUS measurements in marrow-saturated specimens correlated less strongly with BMD than did corresponding measurements in water-saturated specimens (p < 0.05), consistent with interspecimen marrow heterogeneity. These data indicate that the potential impact of marrow should be considered when interpreting clinical QUS measurements. Understanding and exploiting these effects could lead to novel approaches for ultrasonic characterisation of both bone and marrow.

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.

A stratified model to predict dispersion in trabecular bone

Frequency-dependent phase velocity (dispersion) has previously been measured in trabecular bone by several groups. In contrast to most biologic tissues, phase velocity in trabecular bone tends to decrease with frequency. A stratified model, consisting of alternating layers of bone and marrow (in vivo) or water (in vitro), has been employed in an attempt to explain this phenomenon. Frequency-dependent phase velocity was measured from 300 to 700 kHz in 1) phantoms consisting of regularly spaced thin parallel layers of polystyrene sheets in water and 2) 30 calcaneus samples in vitro. For the polystyrene phantoms, the agreement between theory and experiment was good. For the calcaneus samples, the model has some limited usefulness (uncertainty of about 5%) in predicting average phase velocity. More importantly, the model seems to perform consistently well for predicting the frequency dependence of phase velocity in calcaneus.

Ultrasonic attenuation in human calcaneus from 0.2 to 1.7 MHz

Ultrasonic attenuation has been demonstrated to be a useful measurement in the diagnosis of osteoporosis. Most studies have employed ultrasound in a range of frequencies from about 200 kHz-300 kHz to 600 kHz-1 MHz, and many have assumed a linear dependence of attenuation on frequency. In order to investigate the attenuation properties of human calcaneus at higher frequencies, 16 defatted human calcanea were interrogated in vitro using two matched pairs of transducers with center frequencies of 500 kHz and 2.25 MHz. The linear dependence of attenuation on frequency seems to extend up to at least 1.7 MHz. The correlation between attenuation coefficient and frequency from 400 kHz to 1.7 MHz was r = 0.999 (95% confidence interval, CI, = 0.998-1.00). The measurements suggest that some deviations from linear frequency dependence of attenuation may occur at lower frequencies (below 400 kHz), however.

The prospects of estimating trabecular bone tissue properties from the combination of ultrasound, dual-energy X-ray absorptiometry, microcomputed tomography, and microfinite element analysis

Osteoporosis commonly is assessed by bone quantity, using bone mineral density (BMD) measurements from dual-energy X-ray absorptiometry (DXA). However, such a measure gives neither information about the integrity of the trabecular architecture nor about the mechanical properties of the constituting trabeculae. We investigated the feasibility of deriving the elastic modulus of the trabeculae (the tissue modulus) from computer simulation of mechanical testing by microfinite element analysis (muFEA) in combination with measurements of ultrasound speed of sound (SOS) and BMD measurements. This approach was tested on 15 postmortem bovine bone cubes. The apparent elastic modulus of the specimens was estimated from SOS measurements in combination with BMD. Then the trabecular morphology was reconstructed using microcomputed tomography (muCT). From the reconstruction a mesh for muFEA was derived, used to simulate mechanical testing. The tissue modulus was found by correlating the apparent moduli of the specimens as assessed by ultrasound with the ones as determined with muFEA. A mean tissue modulus of 4.5 GPa (SD, 0.69) was found. When adjusting the muFEA-determined elastic moduli of the entire specimens with their calculated tissue modulus, an overall correlation of R2 = 96% with ultrasound-predicted values was obtained. We conclude that the apparent elastic stiffness characteristics as determined from ultrasound correlate linearly with those from muFEA. From both methods in combination, the elastic stiffness of the mineralized tissue can be determined as an estimator for mechanical tissue quality. This method can already be used for biopsy specimens, and potentially could be applicable in vivo as well, when clinical CT or magnetic resonance imaging (MRI) tools with adequate resolution reach the market. In this way, mechanical bone quality could be estimated more accurately in clinical practice.

A numerical method to predict the effects of frequency-dependent attenuation and dispersion on speed of sound estimates in cancellous bone

Many studies have demonstrated that time-domain speed-of-sound (SOS) measurements in calcaneus are predictive of osteoporotic fracture risk. However, there is a lack of standardization for this measurement. Consequently, different investigators using different measurement systems and analysis algorithms obtain disparate quantitative values for calcaneal SOS, impairing and often precluding meaningful comparison and/or pooling of measurements. A numerical method has been developed to model the effects of frequency-dependent attenuation and dispersion on transit-time-based SOS estimates. The numerical technique is based on a previously developed linear system analytic model for Gaussian pulses propagating through linearly attenuating, weakly dispersive media. The numerical approach is somewhat more general in that it can be used to predict the effects of arbitrary pulse shapes and dispersion relationships. The numerical technique, however, utilizes several additional assumptions (compared with the analytic model) which would be required for the practical task of correcting existing clinical databases. These include a single dispersion relationship for all calcaneus samples, a simple linear model relating phase velocity to broadband ultrasonic attenuation, and a constant calcaneal thickness. Measurements on a polycarbonate plate and 30 human calcaneus samples were in good quantitative agreement with numerical predictions. In addition, the numerical approach predicts that in cancellous bone, frequency-dependent attenuation tends to be a greater contributor to variations in transit-time-based SOS estimates than dispersion. This approach may be used to adjust previously acquired individual measurements so that SOS data recorded with different devices using different algorithms may be compared in a meaningful fashion.

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.

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.

Measurements of phase velocity and group velocity in human calcaneus

Ultrasonic velocity in calcaneus correlates highly with bone mineral density, which is a good predictor of osteoporotic fracture risk. Several commercial bone sonometers perform a velocity measurement based on the transit time of a broadband pulse to assess skeletal status. This approach is somewhat problematic, however, because several authors have reported ambiguities in measurements in calcaneus. Phase velocity is an alternative that may be less dependent on device spectral characteristics. In addition, dispersion (the frequency-dependence of phase velocity) is a fundamental property worth investigating to increase understanding of interaction between ultrasound and bone. To compare two group-velocity measurement methods and one phase-velocity measurement method, a polycarbonate sample (for method validation) and 24 human calcanei were investigated in vitro. Phase velocity in calcaneus at 500 kHz was 1511 m/s +/- 30 m/s (mean +/- standard deviation). Average phase velocity decreased approximately linearly with frequency (-18 m/s MHz). The two group velocity measurements were comparable and tended to be slightly lower than phase velocity. The magnitude of dispersion showed little correlation with bone mineral density.

Speed of sound reflects Young's modulus as assessed by microstructural finite element analysis

We analyzed the ability of the quantitative ultrasound (QUS) parameter, speed of sound (SOS), and bone mineral density (BMD), as measured by dual-energy X-ray absorptiometry (DXA), to predict Young's modulus, as assessed by microstructural finite element analysis (muFEA) from microcomputed tomography (muCT) reconstructions. With muFEA simulation, all bone elements in the model can be assigned the same isotropic Young's modulus; therefore, in contrast to mechanical tests, only the trabecular structure plays a role in the determination of the elastic properties of the specimen. SOS, BMD, and microCT measurements were performed in 15 cubes of pure trabecular bovine bone in three orthogonal directions: anteroposterior (AP); mediolateral (ML); and craniocaudal (CC). The anisotropy of the architecture was determined using mean intercept length (MIL) measurements. SOS, MIL, and Young's modulus (E) values were significantly different in all three directions (p < 0.001), with the highest values in the CC direction. There was a strong linear relationship between E and SOS in each of the three orthogonal directions, with r(2) being 0.88, 0.92, and 0.84 (all p < 0.0001) for the CC, ML, and AP directions, respectively. The relationship between E and BMD was less strong, with r(2) being between 0.66 and 0.85 (all p < 0.0001) in the different directions. There was also a significant, positive correlation between SOS and BMD in each of the three axes (r(2) being 0.81, 0.42, and 0.92 in the CC, ML, and AP directions, respectively; p < 0.0001). After correction for BMD, the correlations between SOS and E in each of the three directions remained highly significant (r(2) = 0.77, p < 0. 0001 for the AP direction; r(2) = 0.48, p < 0.001 for the CC direction; r(2) = 0.52, p < 0.005 for the ML direction). After correction for SOS, BMD remained significantly correlated with Young's modulus in the AP and CC directions (r(2) = 0.52, p < 0.005; r(2) = 0.30, p < 0.05, respectively), but the correlation in the ML direction was no longer statistically significant. In a stepwise regression model, E was best predicted by SOS in each of the orthogonal directions. These observations illustrate the ability of the SOS technique to assess the architectural mechanical quality of trabecular bone.

Speed of sound, bone mineral density and bone strength in oophorectomized rats

BACKGROUND

The aim of this study was to determine the sensitivity of bone mineral density (BMD), ultrasounds (SOS) and resistance to torsion (T) to detect experimental osteopenia induced in rats 3 and 6 months after ooforectomy.

MATERIALS AND METHODS

Seventy-four rats were used, divided into four groups, ooforectomized rats analysed 3 and 6 months after the operation and their respective control groups, in which BMD (Hologic QDR 1000 S/N 277), SOS (DBM Sonic 1200) and T (adapted test machine) were determined in the right femur.

RESULTS

The results of the three techniques distinguished the ooforectomized groups from the controls, both 3 and 6 months after the ooforectomy, obtaining more significant differences with BMD (P = 0.0006, P = 0. 001, respectively) than SOS and T, where a significance of only P = 0.05 was obtained. In the correlation study among the three techniques, a significant correlation was observed between BMD and SOS (r = 0.39, P = 0.0008), as well as between BMD and T (r = 0.31, P = 0.03). However, significance was not observed between the SOS and T tests.

CONCLUSION

In the study of sensitivity and specificity of the techniques used to detect the osteopenia caused by the ooforectomy, by means of calculation of the area under the receiver operation characteristic (ROC) curve, it was proven that although the three techniques distinguished between the two analysed populations, BMD presented an area under the ROC curve that was superior (0.87, 0.85) to that obtained with SOS (0.73, 0.67) and T (0.73, 0.68), both 3 and 6 months after the operation.

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.

The effects of frequency-dependent attenuation and dispersion on sound speed measurements: applications in human trabecular bone

Sound speed may be measured by comparing the transit time of a broadband ultrasonic pulse transmitted through an object with that transmitted through a reference water path. If the speed of sound in water and the thickness of the sample are known, the speed of sound in the object may be computed. To measure the transit time differential, a marker such as a zero-crossing, may be used. A sound speed difference between the object and water shifts all markers backward or forward. Frequency-dependent attenuation and dispersion may alter the spectral characteristics of the waveform, thereby distorting the locations of markers and introducing variations in sound-speed estimates. Theory is derived to correct for this distortion for Gaussian pulses propagating through linearly attenuating, weakly dispersive media. The theory is validated using numerical analysis, measurements on a tissue mimicking phantom, and on 24 human calcaneus samples in vitro. Variations in soft tissue-like media are generally not exceptionally large for most applications but can be substantial, particularly for high bandwidth pulses propagating through media with high attenuation coefficients. At 500 kHz, variations in velocity estimates in bone can be very substantial, on the order of 40 to 50 m/s because of the high attenuation coefficient of bone. In trabecular bone, the effects of frequency-dependent attenuation are considerable, and the effects of dispersion are negligible.

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.

Acoustic and ultrasonic tissue characterization--assessment of osteoporosis

Osteoporosis, often termed the 'silent epidemic', has been defined as 'a decrease in bone mass and architectural deterioration of bone tissue, leading to enhanced bone fragility and consequent increase in fracture risk'. In the United Kingdom alone, the annual health costs are in excess of 750 million Pounds, with 60,000 patients suffering a hip fracture each year. A quarter of these will die within 12 months of their fracture, half of the remainder will never regain independent living. The established procedure for assessing the risk of osteoporotic fracture is via bone mineral density (BMD) assessment using dual-energy X-ray absorptiometry (DXA). However, DXA is an expensive technique and is not widely available. Within the past 15 years, ultrasound assessment of bone has rapidly advanced in scientific understanding, technical development and clinical utility. Measurements of cancellous bone (particularly at the calcaneus) are generally performed in preference to those of cortical bone (tibial cortex). There are currently 15 commercial systems available and over 3500 systems are in use world-wide. The low cost and portability offered by ultrasound systems should enable an integrated community-based screening programme to be established in the near future. Ultrasound measurements of bone are generally obtained using transmission rather than pulse-echo techniques owing to its highly attenuating nature. Ultrasound velocity and attenuation measurements are utilized. For velocity, there are well-defined fundamental relationships describing the dependence upon the elasticity and density of bone.