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

The Protocol of Ultrasonic Backscatter Measurements of Musculoskeletal Properties

This study aims to introduce the protocol for ultrasonic backscatter measurements of musculoskeletal properties based on a novel ultrasonic backscatter bone diagnostic (UBBD) instrument. Dual-energy X-ray absorptiometry (DXA) can be adopted to measure bone mineral density (BMD) in the hip, spine, legs and the whole body. The muscle and fat mass in the legs and the whole body can be also calculated by DXA body composition analysis. Based on the proposed protocol for backscatter measurements by UBBD, ultrasonic backscatter signals can be measured in vivo, deriving three backscatter parameters [apparent integral backscatter (AIB), backscatter signal peak amplitude (BSPA) and the corresponding arrival time (BSPT)]. AIB may provide important diagnostic information about bone properties. BSPA and BSPT may be important indicators of muscle and fat properties. The standardized backscatter measurement protocol of the UBBD instrument may have the potential to evaluate musculoskeletal characteristics, providing help for promoting the application of the backscatter technique in the clinical diagnosis of musculoskeletal disorders (MSDs), such as osteoporosis and muscular atrophy.

Ultrasonic Backscatter Measurements of Human Cortical and Trabecular Bone Densities in a Head-Down Bed-Rest Study

This study aims to investigate the feasibility of quantitative ultrasonic backscatter in evaluating human cortical and trabecular bone densities in vivo based on a head-down-tilt bed rest study, with 36 participants tested through 90 d of bed rest and 180 d of recovery. Backscatter measurements were performed using an ultrasonic backscatter bone diagnostic instrument. Backscatter parameters were calculated with a dynamic signal-of-interest method, which was proposed to ensure the same ultrasonic interrogated volume in cortical and trabecular bones. The backscatter parameters exhibited significant correlations with site-matched bone densities provided by high-resolution peripheral quantitative computed tomography (0.33 < |R| < 0.72, p < 0.05). Some bone densities and backscatter parameters exhibited significant changes after the 90-d bed rest. The proposed method can be used to characterize bone densities, and the portable ultrasonic backscatter bone diagnostic device might be used to non-invasively reveal mean bone loss (across a group of people) after long-term bed rest and microgravity conditions of spaceflight missions.

Three-dimensional-printed replica models of bone for experimentally decoupling trabecular bone properties contribution to ultrasound propagation parameters

A detailed investigation of the relationship between ultrasonic (US) properties and trabecular bone microstructure is difficult because of the great variability in the bone loss process. The aim of this work was twofold. First, to verify by compressive tests that the three-dimensional (3D)-printer is able to produce precisely and repeatedly "bone replica models" of different size and density. Following, replicas of the original specimens with two different polymers and thinned trabeculae models were used to investigate US properties (speed of sound, SOS, and backscatter coefficient), aiming to deconvolute the influence of material properties on ultrasound characteristics. The results revealed that matrix material properties influence only the magnitude of the backscatter coefficient, whereas the characteristic undulated patterns are related to the trabecular structure. Simulation of perforation and thinning of cancellous bone, associated with bone loss, showed that SOS and mechanical properties were reduced perfectly linearly with apparent density when structure deteriorated. The 3D-printed bone replicas have the potential to enable systematic investigations of the influence of structure on both acoustical and mechanical properties and evaluate changes caused by bone loss. The development of replicas from materials with properties close to those of bone will permit quantitative conclusions for trabecular bone.

Relationships of the ultrasonic backscatter measurements with the bone mineral density and the microarchitectural parameters in bovine trabecular bone in vitro

Relationships of the backscatter coefficient (BC), the apparent integrated backscatter (AIB), and the integrated reflection coefficient (IRC) with the bone mineral density (BMD) and the microarchitectural parameters were investigated in 28 bovine femoral trabecular bone samples. The BC was highly correlated with the BMD and the microarchitectural parameters (R = -0.66 to 0.71). In contrast, the AIB and the IRC exhibited high correlations with the BMD and the bone volume fraction (R = -0.68 to 0.77) and relatively lower correlations with the remaining microarchitectural parameters (R = -0.62 to 0.60). The multiple regression models yielded the adjusted squared correlation coefficients of 0.54-0.76.

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.

Ultrasonic Backscatter Difference Measurement of Bone Health in Preterm and Term Newborns

Metabolic bone disease of prematurity remains a significant problem for preterm infants. Quantitative ultrasound (QUS) has potential as a non-invasive tool for assessing bone health of newborns. The aim of this study was to assess bone health in preterm and term newborns using ultrasonic backscatter difference measurement. This study analyzed a total of 493 neonates, including 239 full-term infants (gestational age [GA] >37 wk), 201 preterm I infants (GA: 32-37 wk) and 53 extreme preterm II infants (GA <32 wk). Ultrasonic backscatter measurements were performed on the calcaneus of infants at birth, and the normalized mean of the backscatter difference spectrum (nMBD) was calculated as an ultrasonic index of neonatal bone status. Simple and multiple linear regressions were performed to determine the association of ultrasonic nMBD with GA, anthropometric characteristics and biochemical markers. Statistically significant differences in GA, anthropometric characteristics (birth weight, birth length [BL], birth head circumference and body mass index [BMI]) and biochemical markers (alkaline phosphatase, serum calcium and serum phosphate) were observed among preterm and term infants. The nMBD for term infants (median = 3.72 dB/μs, interquartile range [IR] = 1.95 dB/μs) was significantly higher than that for preterm I infants (median = 1.95 dB/μs, IR = 3.12 dB/μs), which was, in turn, significantly higher than that for preterm II infants (median = 0.19 dB/μs, IR = 3.50 dB/μs). The nMBD yielded moderate correlations (ρ = 0.57-0.62, p < 0.001) with GA and anthropometric characteristics and weak correlations (|ρ| = 0.08-0.21, p < 0.001 or not significant) with biochemical markers. Multivariate regressions revealed that only BL (p = 0.002) and BMI (p = 0.032) yielded significantly independent contributions to the nMBD measurement, and combinations of BL and BMI could explain up to 42% of the variation of nMBD in newborn infants. This study found that ultrasonic backscatter difference measurement might be helpful in bone health evaluation in preterm and term newborns. The utility of ultrasonic backscatter measurement in diagnosis of metabolic bone disease in infants should be investigated further.

Relationships of Ultrasonic Backscatter With Bone Densities and Microstructure in Bovine Cancellous Bone

This study was designed to investigate the associations among ultrasonic backscatter, bone densities, and microstructure in bovine cancellous bone. Ultrasonic backscatter measurements were performed on 33 bovine cancellous bone specimens with a 2.25-MHz transducer. Ultrasonic apparent backscatter parameters ("apparent" means not compensating for ultrasonic attenuation and diffraction) were calculated with optimal signals of interest. The results showed that ultrasonic backscatter was significantly related to bone densities and microstructure ( R² = 0.17 -0.88 and ). After adjusting the correlations by bone mineral density (BMD), the bone apparent density (BAD) and some trabecular structural features still contributed significantly to the adjusted correlations, with moderate additional variance explained ( ∆R² = 9.7 % at best). Multiple linear regressions revealed that both BAD and trabecular structure contributed significantly and independently to the prediction of ultrasound backscatter (adjusted R² = 0.75 -0.89 and ), explaining an additional 14% of the variance at most, compared with that of BMD measurements alone. The results proved that ultrasonic backscatter was primarily determined by BAD, not BMD, but the combination of bone structure and densities could achieve encouragingly better performances (89% of the variance explained at best) in predicting backscatter properties. This study demonstrated that ultrasonic apparent backscatter might provide additional density and structural features unrelated to current BMD measurement. Therefore, we suggest that ultrasonic backscatter measurement could play a more important role in cancellous bone evaluation.

Ultrasonic backscatter difference measurements of cancellous bone from the human femur: Relation to bone mineral density and microstructure

Ultrasonic backscatter techniques are being developed to detect changes in cancellous bone caused by osteoporosis. One technique, called the backscatter difference technique, measures the power difference between two portions of a backscatter signal. The goal of the present study is to investigate how bone mineral density (BMD) and the microstructure of human cancellous bone influence four backscatter difference parameters: the normalized mean of the backscatter difference (nMBD) spectrum, the normalized slope of the backscatter difference spectrum, the normalized intercept of the backscatter difference spectrum, and the normalized backscatter amplitude ratio (nBAR). Ultrasonic measurements were performed with a 3.5 MHz broadband transducer on 54 specimens of human cancellous bone from the proximal femur. Volumetric BMD and the microstructural characteristics of the specimens were measured using x-ray micro-computed tomography. Of the four ultrasonic parameters studied, nMBD and nBAR demonstrated the strongest univariate correlations with density and microstructure. Multivariate analyses indicated that nMBD and nBAR depended on trabecular separation and possibly other microstructural characteristics of the specimens independently of BMD. These findings suggest that nMBD and nBAR may be sensitive to changes in the density and microstructure of bone caused by osteoporosis.

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.

Three-dimensional Simulation of Quantitative Ultrasound in Cancellous Bone Using the Echographic Response of a Metallic Pin

Degenerative discopathy is a common pathology that may require spine surgery. A metallic cylindrical pin is inserted into the vertebral body to maintain soft tissues and may be used as a reflector of ultrasonic wave to estimate bone density. The first aim of this paper is to validate a three-dimensional (3-D) model to simulate the ultrasonic propagation in a trabecular bone sample in which a metallic pin has been inserted. We also aim at determining the effect of changes of bone volume fraction (BV/TV) and of positioning errors on the quantitative ultrasound (QUS) parameters in this specific configuration. The approach consists in coupling finite-difference time-domain simulation with X-ray microcomputed tomography. The correlation coefficient between experimental and simulated speed of sound (SOS)-respectively, broadband ultrasonic attenuation (BUA)-was equal to 0.90 (respectively, 0.55). The results show a significant correlation of SOS with BV/TV ( R = 0.82), while BUA values exhibit a nonlinear behavior versus BV/TV. The orientation of the pin should be controlled with an accuracy of around 1° to obtain accurate results. The results indicate that using the ultrasonic wave reflected by a pin has a potential to estimate the bone density. SOS is more reliable than BUA due to its lower sensitivity to the tilt angle.

Ultrasonic backscatter from cancellous bone: the apparent backscatter transfer function

Ultrasonic backscatter techniques are being developed to detect changes in cancellous bone caused by osteoporosis. Many techniques are based on measurements of the apparent backscatter transfer function (ABTF), which represents the backscattered power from bone corrected for the frequency response of the measurement system. The ABTF is determined from a portion of the backscatter signal selected by an analysis gate of width τw delayed by an amount τd from the start of the signal. The goal of this study was to characterize the ABTF for a wide range of gate delays (1 μs ≤ τd ≤ 6 μs) and gate widths (1 μs ≤ τw ≤ 6 μs). Measurements were performed on 29 specimens of human cancellous bone in the frequency range 1.5 to 6.0 MHz using a broadband 5-MHz transducer. The ABTF was found to be an approximately linear function of frequency for most choices of τd and τw. Changes in τd and τw caused the frequency-averaged ABTF [quantified by apparent integrated backscatter (AIB)] and the frequency dependence of the ABTF [quantified by frequency slope of apparent backscatter (FSAB)] to change by as much as 24.6 dB and 6.7 dB/MHz, respectively. τd strongly influenced the measured values of AIB and FSAB and the correlation of AIB with bone density (-0.95 ≤ R ≤ +0.68). The correlation of FSAB with bone density was influenced less strongly by τd (-0.97 ≤ R ≤ -0.87). τw had a weaker influence than τd on the measured values of AIB and FSAB and the correlation of these parameters with bone density.

Effect of intervening tissues on ultrasonic backscatter measurements of bone: An in vitro study

Ultrasonic backscatter techniques are being developed to diagnose osteoporosis. Tissues that lie between the transducer and the ultrasonically interrogated region of bone may produce errors in backscatter measurements. The goal of this study is to investigate the effects of intervening tissues on ultrasonic backscatter measurements of bone. Measurements were performed on 24 cube shaped specimens of human cancellous bone using a 5 MHz transducer. Measurements were repeated after adding a 1 mm thick plate of cortical bone to simulate the bone cortex and a 3 cm thick phantom to simulate soft tissue at the hip. Signals were analyzed to determine three apparent backscatter parameters (apparent integrated backscatter, frequency slope of apparent backscatter, and frequency intercept of apparent backscatter) and three backscatter difference parameters [normalized mean backscatter difference (nMBD), normalized slope of the backscatter difference, and normalized intercept of the backscatter difference]. The apparent backscatter parameters were impacted significantly by the presence of intervening tissues. In contrast, the backscatter difference parameters were not affected by intervening tissues. However, only one backscatter difference parameter, nMBD, demonstrated a strong correlation with bone mineral density. Thus, among the six parameters tested, nMBD may be the best choice for in vivo backscatter measurements of bone when intervening tissues are present.

Ultrasound backscatter measurements of intact human proximal femurs--relationships of ultrasound parameters with tissue structure and mineral density

Ultrasound reflection and backscatter parameters are related to the mechanical and structural properties of bone in vitro. However, the potential of ultrasound reflection and backscatter measurements has not been tested with intact human proximal femurs ex vivo. We hypothesize that ultrasound backscatter can be measured from intact femurs and that the measured backscattered signal is associated with cadaver age, bone mineral density (BMD) and trabecular bone microstructure. In this study, human femoral bones of 16 male cadavers (47.0±16.1 years, range: 21-77 years) were investigated using pulse-echo ultrasound measurements at the femoral neck in the antero-posterior direction and at the trochanter major in the anteroposterior and lateromedial directions. Recently introduced ultrasound backscatter parameters, independent of cortical thickness, e.g., time slope of apparent integrated backscatter (TSAB) and mean of the backscatter difference technique (MBD) were obtained and compared with the structural properties of trabecular bone samples, extracted from the locations of ultrasound measurements. Moreover, more conventional backscatter parameters, e.g., apparent integrated backscatter (AIB) and frequency slope of apparent integrated backscatter (FSAB) were analyzed. Bone mineral density of the intact femurs was evaluated using dual energy X-ray absorptiometry (DXA). AIB and MDB measured from the femoral neck correlated significantly (p<0.01) with the neck BMD (R2=0.44 and 0.45), cadaver age (R2=0.61 and 0.41) and several structural parameters, e.g., bone volume fraction (R2=0.33 and 0.39, p<0.05 and p<0.01), respectively. To conclude, ultrasound backscatter parameters, measured from intact proximal femurs, are significantly related (p<0.05) to structural properties and mineral density of trabecular bone.

Ultrasound to assess bone quality

Bone quality is determined by a variety of compositional, micro- and ultrastructural properties of the mineralized tissue matrix. In contrast to X-ray-based methods, the interaction of acoustic waves with bone tissue carries information about elastic and structural properties of the tissue. Quantitative ultrasound (QUS) methods represent powerful alternatives to ionizing x-ray based assessment of fracture risk. New in vivo applicable methods permit measurements of fracture-relevant properties, [eg, cortical thickness and stiffness at fragile anatomic regions (eg, the distal radius and the proximal femur)]. Experimentally, resonance ultrasound spectroscopy and acoustic microscopy can be used to assess the mesoscale stiffness tensor and elastic maps of the tissue matrix at microscale resolution, respectively. QUS methods, thus, currently represent the most promising approach for noninvasive assessment of components of fragility beyond bone mass and bone microstructure providing prospects for improved assessment of fracture risk.

Feasibility of bone assessment with ultrasonic backscatter signals in neonates

The objective of this study was to assess the value of ultrasonic backscatter signals and the backscatter coefficient (BSC) in the analysis of bone status in neonates and to analyze the relationships between the BSC and gestational age, birth weight, length, head circumference and gender. A total of 122 neonates participated in the study, including 83 premature infants and 39 full-term infants. Their BSCs were measured by ultrasound after birth. The results revealed a significant correlation between the BSC and gestational age (R = 0.47, p < 0.001), birth weight (R = 0.47, p < 0.0001) and length at birth (R = 0.43, p < 0.001) at a frequency of 5.0 MHz. This study suggests that the use of ultrasonic backscattering and the BSC is feasible for assessment of the bone status of neonates.

Estimation of fast and slow wave properties in cancellous bone using Prony's method and curve fitting

The presence of two longitudinal waves in poroelastic media is predicted by Biot's theory and has been confirmed experimentally in through-transmission measurements in cancellous bone. Estimation of attenuation coefficients and velocities of the two waves is challenging when the two waves overlap in time. The modified least squares Prony's (MLSP) method in conjuction with curve-fitting (MLSP + CF) is tested using simulations based on published values for fast and slow wave attenuation coefficients and velocities in cancellous bone from several studies in bovine femur, human femur, and human calcaneus. The search algorithm is accelerated by exploiting correlations among search parameters. The performance of the algorithm is evaluated as a function of signal-to-noise ratio (SNR). For a typical experimental SNR (40 dB), the root-mean-square errors (RMSEs) for one example (human femur) with fast and slow waves separated by approximately half of a pulse duration were 1 m/s (slow wave velocity), 4 m/s (fast wave velocity), 0.4 dB/cm MHz (slow wave attenuation slope), and 1.7 dB/cm MHz (fast wave attenuation slope). The MLSP + CF method is fast (requiring less than 2 s at SNR = 40 dB on a consumer-grade notebook computer) and is flexible with respect to the functional form of the parametric model for the transmission coefficient. The MLSP + CF method provides sufficient accuracy and precision for many applications such that experimental error is a greater limiting factor than estimation error.

Ultrasonic evaluation of bone quality in cadaver ilia

Several imaging modalities have traditionally been utilized to assess bone health. However, none of these standards is capable of providing a clear rendition or display of the damaged bone layers caused, for instance, by osteoporosis. This study examines the use of ultrasound for non-invasive monitoring of bone quality in bone samples with various degrees of porosity. A user-defined region of interest (ROI) in the iliac portion of extracted human cadaver coxal bones is monitored and quantified. Raster C-scan images of the ROI were acquired and compared to basic physical measurements, and to bone scans using dual energy X-ray absorptiometry (DXA). A quantitative measure of the superficial sub-surface composite matrix (ScM) content was analyzed using linear regression with all physical and DXA measures. The trend in the degree of percent bone loss (PBL) measured by ultrasound (US) was found to be closely paralleled with that measured by DXA (R(2) = 0.82, p < .0005). Also, the trend in which PBL (US) correlated with bone mineral density (BMD) (R(2) = 0.62, p < .01) was found to exhibit a similar behavior when the latter was compared to dry mass density (DmD) of the bone samples (R(2) = 0.63, p < .01). However, when PBL (DXA) was compared to DmD, it did reveal a better linearity (R(2) = 0.69, p < .005) than the one obtained when PBL (US) was compared with the same DmD (R(2) = 0.45, p < .05). A similar outcome was observed when PBL (US) was compared with percent porosity (R(2) = 0.51, p < .05), as opposed to the better linearity exhibited between PBL (DXA) and porosity (R(2) = 0.86, p < .0005). Despite these slight variations, further analyses on the statistical significance between these correlations suggest that ultrasound can be an effective imaging technique in assessing the degree of bone damage, and can be used to assess the structural integrity of bones.

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.

Acoustic backscattering enhancements resulting from the interaction of an obliquely incident plane wave with an infinite cylinder

BACKGROUND AND OBJECTIVE

The analysis of the acoustic backscattering enhancements from tilted cylinders is of particular importance in determining some of the (visco)elastic properties of the cylinder, and/or its surrounding fluid in ultrasonic non-destructive evaluation (NDE) and imaging (NDI) applications. Previous related investigations on an aluminum cylinder limited to incidence angles varying from 0 degrees to 40 degrees , revealed the existence of an anomalous "pseudo-Rayleigh" mode (above the critical Rayleigh angle) identified as the rigid-body translational dipole (n=1) mode. The objective here is to provide a complete investigation on the backscattering enhancements for incidence angles larger than 40 degrees for various elastic and viscoelastic cylinder materials.

METHOD

Using the partial-wave series solution for the linear scattering by an infinite circular cylinder, the acoustic backscattering from isotropic elastic and viscoelastic (polymer-type) cylinders excited by an obliquely incident plane acoustic wave is investigated. Total and resonance backscattering form functions are calculated for several elastic and viscoelastic cylinder materials immersed in water versus the angle of incidence 0 degrees alpha < 90 degrees . The "pure" resonance peaks are isolated by subtracting a rigid background from the total form function, so the associated resonance modes are properly identified.

RESULTS AND CONCLUSION

The plots of the partial-wave series reveal acoustic backscattering enhancements (not shown in previous investigations) generally occurring at ka less, similar 0.1 at a critical angle alpha(c) bounded by the longitudinal and shear waves coupling angles theta(L)=sin(-1)(c/c(L)) and theta(S)=sin(-1)(c/c(S)) such that theta(L) < alpha(c) < theta(S) (where c(L) and c(S) are the phase velocities of the longitudinal and shear waves inside the elastic cylinder, and c is the speed of sound in the surrounding medium). It is shown here that the backscattering enhancements with a critical angle theta(L) < alpha(c) < theta(S) result from the excitation of the monopole (n=0) resonance mode. Moreover, additional acoustic backscattering enhancements still occur in the range 1 less, similar ka less similar 6 even though the angle of tilt is greater than the Rayleigh wave coupling angle theta(R)=sin(-1)(c/c(R)) (where c(R) is the Rayleigh wave velocity in an elastic half-space). The resonance scattering theory shows that such additional enhancements are associated with the excitation of a dipole (n=1) resonance mode which may result from the interference of meridional and/or helical waves propagating along the cylinder's surface. It is therefore essential to consider tilt angles ranging from normal to end-on incidence for a complete analysis of the backscattering by elastic and viscoelastic cylinders.

Ultrasound backscatter imaging provides frequency-dependent information on structure, composition and mechanical properties of human trabecular bone

The strength as well as the acoustic properties of trabecular bone are determined by its structure and composition. Consequently, tissue structure and compositional properties also affect the ultrasound propagation in bone. The diagnostic potential of ultrasound has not been fully exploited in clinical quantitative ultrasound devices. The aim of this study was to investigate the ability of quantitative ultrasound pulse-echo imaging, conducted over a broad range of frequencies (1 to 5 MHz), to predict the mechanics, composition and microstructure of trabecular bone. Ultrasound reflection and backscatter parameters correlated significantly with the ultimate strength of the trabecular bone and the bone volume fraction (r=0.76-0.90, n=20, p<0.01). Ultrasound backscatter associated significantly (independently of bone structure or mineral content) with the collagen content of the bone matrix (r=0.75, r(adjusted)=0.66, p<0.01). Interestingly, the applied ultrasound frequency seemed to relate the sensitivity of ultrasound backscatter to different properties of trabecular bone. At frequencies ranging from 1 to 3.5 MHz, the ultrasound backscatter associated significantly with the tissue mechanical and structural parameters. At 5MHz, the composition of the bone matrix was a more significant determinant of the measured backscatter. This study provides useful information for optimizing the use of pulse-echo measurements, and thereby further emphasizes the diagnostic potential of the ultrasound backscatter measurements of trabecular bone.

Characterization of the trabecular bone structure using frequency modulated ultrasound pulse

The objective of this study was to investigate the efficacy of modulated ultrasound signals in the measurement of bone properties as an early indicator of osteoporosis. Twenty-one trabecular bone cubes were harvested from sheep femoral condyles and the cube axes corresponded to the anatomic superior-inferior (SI), antero-posterior (AP), and medio-lateral (ML) orientations. Micro-CT measurements were made on those samples to obtain bone volume fraction (BV/TV), trabecular thickness (Tb.Th), and trabecular separation (Tb.Sp). Ultrasound tests were performed in the three orthogonal orientations using pulse and frequency modulated ultrasound. The comparison of the frequency modulated attenuation (FMA) with the broadband ultrasound attenuation (BUA) was made within the frequency band between 300 and 700 kHz. Results showed that FMA demonstrated higher correlations to the trabecular structure properties in the SI orientation (R(2)=0.84 for BV/TV, R(2)=0.77 for Tb.Th, R(2)=0.7 for Tb.Sp) than BUA (R(2)=0.30 for BV/TV, R(2)=0.27 for Tb.Th, R(2)=0.33 for Tb.Sp). In the AP orientation, FMA had higher correlation to Tr.Sp (R(2)=0.64) than BUA (R(2)=0.48), and relatively lower correlation to BV/TV (R(2)=0.48) and Tb.Th (R(2)=0.31) than BUA (R(2)=0.64 for BV/TV and R(2)=0.58 for Tb.Th). The results suggested that FMA could be a new ultrasound index for bone properties assessment.

Analysis of frequency dependence of ultrasonic backscatter coefficient in cancellous bone

The ultrasonic scattering mechanism in cancellous bone is investigated theoretically and a model describing the frequency dependence of ultrasonic scattering from cancellous bone is presented. The ultrasonic backscatter coefficient (BSC) of bovine tibiae, human calcanei in vitro and in vivo, were measured and discussed. The data of BSC were also fitted by polynomial. The results demonstrate that BSC is a nonlinear function of frequency and increases with frequency. A good agreement was obtained between BSC values from theory and experiment. Also, the high correlation coefficient between BSC and bone mineral density was obtained, r=0.85+/-0.07 (mean+/-SD) (n=15, p<0.001). Based on the values of BSC, the status of cancellous bone and the degree of osteoporotic fracture risk may be assessed.

Ultrasonic attenuation in parallel-nylon-wire cancellous-bone-mimicking phantoms

Attenuation coefficients between 1.5 and 3.5 MHz were measured on four parallel-nylon-wire arrays (simulating cancellous bone) with four different wire diameters (150, 200, 250, and 300 microm). Interwire spacing was 800 microm for all four parallel-nylon-wire arrays. The measured frequency dependencies of attenuation were consistent with theoretical predications based on Faran's theory, which considers the component of attenuation due to scattering of longitudinal waves.

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.

Frequency dependence of backscatter from thin, oblique, finite-length cylinders measured with a focused transducer-with applications in cancellous bone

A model is presented for the echo from a thin, oblique, finite-length cylinder. The echo is calculated from the line integral of the transducer directivity pattern along the cylinder axis. The model was validated with broadband pulse-echo measurements from (1) a perpendicular (to the ultrasound beam) nylon wire as a function of lateral displacement from the beam center, (2) a tilted nylon wire as a function of the angle of inclination relative to the ultrasound beam, and (3) a quasi-parallel-nylon-wire phantom, which mimicked the scattering properties of cancellous bone. The transducer directivity pattern (as a function of position and frequency) was measured with a membrane hydrophone. The model predicts an approximately cubic frequency dependence of backscatter coefficient from the phantom, as has been observed experimentally in cancellous bone. The model also predicts the relationship between the cylinder length and the exponent of a power law fit to backscatter coefficient versus frequency, which is 4 for very short (compared to a wavelength) cylinders and asymptotically approaches 3 for very long cylinders.

Relationship between ultrasonic attenuation, size and axial strain parameters for ex vivo atherosclerotic carotid plaque

Many ultrasonic parameters, primarily related to attenuation and scatterer size, have been used to characterize the composition of atherosclerotic plaque tissue. In this study, we combine elastographic (axial strain ratio) and ultrasonic tissue characterization parameters, namely the attenuation coefficient and a scattering parameter associated with an "equivalent" scatterer size to delineate between fibrous, calcified, and lipidic plaque tissue. We present results obtained from 44 ex vivo atherosclerotic plaque specimens obtained after carotid endarterectomy on human patients. Our results in the frequency range 2.5 - 7.5 MHz indicate that softer plaques (with higher values of the strain ratio) are usually associated with larger equivalent scatterer size estimates (200 - 500 microm) and lower values of the attenuation coefficient slope (<1 dB/cm/MHz). On the other hand, stiffer plaques (with lower strain ratio values) are associated with smaller equivalent scatterer size estimates (100 - 200 microm) and higher values of the attenuation coefficient slope (1 - 3 dB/cm/MHz). These results indicate that ultrasonic tissue characterization and strain parameters have the potential to differentiate between different plaque types. These parameters can be estimated from radio-frequency data acquired under in vivo conditions and may help the clinician decide on appropriate interventional techniques.

Comparison of the Faran Cylinder Model and the Weak Scattering Model for predicting the frequency dependence of backscatter from human cancellous femur in vitro

This letter presents the first side-by-side comparison of the Faran Cylinder Model and the Weak Scattering Model for predicting backscatter from human femur. Both models are applied to the same dataset of frequency-dependent backscatter coefficients from 26 human femur cancellous bone samples in vitro. The Faran Cylinder Model predicts a slightly slower rate of increase of backscatter with frequency than the Weak Scattering Model, but both models are in reasonable agreement with the data and with each other, given the uncertainty in the measurements.

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.

Effects of structural anisotropy of cancellous bone on speed of ultrasonic fast waves in the bovine femur

Ultrasonic waves in cancellous bone change dramatically depending on its structural complexity. One good example is the separation of an ultrasonic longitudinal wave into fast and slow waves during propagation. In this study, we examined fast wave propagation in cancellous bone obtained from the head of the bovine femur, taking the bone structure into consideration. We investigated the wave propagation perpendicular to the bone axis and found the two-wave phenomenon. By rotating the cylindrical cancellous bone specimen, changes in the fast wave speed due to the rotation angle then were observed. In addition to the ultrasonic evaluation, the structural anisotropy of each specimen was measured by X-ray micro-computed tomography (CT). From the CT images, we obtained the mean intercept length (MIL), degree of anisotropy (DA), and angle of insonification relative to the trabecular orientation. The ultrasonic and CT results showed that the fast wave speed was dependent on the structural anisotropy, especially on the trabecular orientation and length. The fast wave speeds always were higher for propagation parallel to the trabecular orientation. In addition, there was a strong correlation between the DA and the ratio between maximum and minimum speeds (V(max)/V(min)) (R(2) = 0.63).

Ultrasonic characterization of human cancellous bone in vitro using three different apparent backscatter parameters in the frequency range 0.6-15.0 mhz

Ultrasonic techniques based on measurements of apparent backscatter may provide a useful means for diagnosing bone diseases such as osteoporosis. The term "apparent" means that the backscattered signals are not compensated for the frequency-dependent effects of attenuation and diffraction. We performed in vitro apparent backscatter measurements on 23 specimens of human cancellous bone prepared from the left and right femoral heads of seven donors. A mechanical scanning system was used to obtain backscattered signals from each specimen at several sites. Scans were performed using five different ultrasonic transducers with center frequencies of 1, 2.25, 5, 7.5, and 10 MHz. The -6 dB bandwidths of these transducers covered a frequency range of 0.6-15.0 MHz. The backscattered signals were analyzed to determine three ultrasonic parameters: apparent integrated backscatter (AIB), frequency slope of apparent backscatter (FSAB), and time slope of apparent backscatter (TSAB). Linear regression analysis was used to examine the correlation of these ultrasonic parameters with five measured physical characteristics of the specimens: mass density, X-ray bone mineral density, Young's modulus, yield strength, and ultimate strength. A total of 75 such correlations were examined (3 ultrasonic parameters x 5 specimen characteristics x 5 transducers). Good correlations were observed for AIB using the 5 MHz (r = 0.70 - 0.89) and 7.5 MHz (r = 0.75-0.93) transducers; for FSAB using the 2.25 MHz (r = 0.70 - 0.88), 5 MHz (r = 0.79 - 0.94), and 7.5 MHz (r = 0.80 - 0.92) transducers; and for TSAB using the 5 MHz (r = 0.68 - 0.89), 7.5 MHz (r = 0.75 - 0.89), and 10 MHz (r = 0.75 - 0.92) transducers.

The effect of phase cancellation on estimates of broadband ultrasound attenuation and backscatter coefficient in human calcaneus in vitro

Broadband ultrasound attenuation (BUA) is a clinically proven indicator of osteoporotic fracture risk. BUA measurements are typically performed in throughtransmission with single-element phase sensitive (PS) receivers and therefore can be compromised by phase cancellation artifact. Phase-insensitive (PI) receivers suppress phase cancellation artifact. To study the effect of phase cancellation on BUA measurements, through-transmission measurements were performed on 16 human calcaneus samples in vitro using a two-dimensional receiver array that enabled PS and PI BUA estimation. The means plus or minus standard deviations for BUA measurements were 22.1 +/- 15.8 dB/MHz (PS) and 17.6 +/- 7.2 dB/MHz (PI), suggesting that, on the average, approximately 20% of PS BUA values in vitro can be attributed to phase cancellation artifact. Therefore, although cortical plates are often regarded as the primary source of phase cancellation artifact, the heterogeneity of cancellous bone in the calcaneal interior may also be a significant source. Backscatter coefficient estimates in human calcaneus that are based on PS attenuation compensation overestimate 1) average magnitude of backscatter coefficient at 500 kHz by a factor of about 1.6 +/- 0.3 and 2) average exponent (n) of frequency dependence by about 0.34 +/- 0.12 (where backscatter coefficient is fit to a power law form proportional to frequency to the nth power).

Influence of microarchitecture alterations on ultrasonic backscattering in an experimental simulation of bovine cancellous bone aging

An experimental model which can simulate physical changes that occur during aging was developed in order to evaluate the effects of change of mineral content and microstructure on ultrasonic properties of bovine cancellous bone. Timed immersion in hydrochloric acid was used to selectively alter the mineral content. Scanning electron microscopy and histological staining of the acid-treated trabeculae demonstrated a heterogeneous structure consisting of a mineralized core and a demineralized layer. The presence of organic matrix contributed very little to normalized broadband ultrasound attenuation (nBUA) and speed of sound. All three ultrasonic parameters, speed of sound, nBUA and backscatter coefficient, were sensitive to changes in apparent density of bovine cancellous bone. A two-component model utilizing a combination of two autocorrelation functions (a densely populated model and a spherical distribution) was used to approximate the backscatter coefficient. The predicted attenuation due to scattering constituted a significant part of the measured total attenuation (due to both scattering and absorption mechanisms) for bovine cancellous bone. Linear regression, performed between trabecular thickness values and estimated from the model correlation lengths, showed significant linear correlation, with R(2)=0.81 before and R(2)=0.80 after demineralization. The accuracy of estimation was found to increase with trabecular thickness.

Acoustic properties of trabecular bone--relationships to tissue composition

In osteoporosis, changes in tissue composition and structure reduce bone strength and expose it to fractures. The current primary diagnostic technique, i.e., dual energy X-ray absorptiometry, measures areal bone mineral density (BMD) but provides no direct information on trabecular structure or organic composition. Although still poorly characterized, ultrasound techniques may bring about information on bone composition and structure. In this study, relationships of 2.25-MHz ultrasound speed, attenuation, reflection and backscattering with composition of human trabecular bone (n=26) were characterized experimentally, as well as by using numerical analyses. We also determined composition of the trabecular sample (fat and water content, bone volume fraction) and that of the calcified matrix (mineral, proteoglycan and collagen content of trabeculae). In experimental analyses, bone volume fraction and mineral content of the calcified matrix were the only determinants of BMD. Further, bone volume fraction served as the strongest determinant of ultrasound parameters (r=0.51-0.87). In numerical simulations, density and mechanical properties of the calcified matrix systematically affected ultrasound speed, attenuation, reflection and backscattering. However, partial correlation coefficients revealed only low associations(|r|<or=0.4) between the composition of calcified matrix and ultrasound parameters in experimental measurements. To conclude, the content and structure of calcified matrix, rather than its composition, affect more significantly acoustic properties of healthy trabecular bone.

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.

Wavelet-based signal processing of in vitro ultrasonic measurements at the proximal femur

To estimate osteoporotic fracture risk, several techniques for quantitative ultrasound (QUS) measurements at peripheral sites have been developed. As these techniques are limited in the prediction of fracture risk of the central skeleton, such as the hip, we are developing a QUS device for direct measurements at the femur. In doing so, we noticed the necessity to improve the conventional signal processing because it failed in a considerable number of measurements due to multipath transmission. Two sets of excised human femurs (n = 6 + 34) were scanned in transmission mode. Instead of using the conventional methods, the radio-frequency signals were processed with the continuous wavelet transform to detect their time-of-flights for the calculation of speed-of-sound (SOS) in bone. The SOS-values were averaged over a region similar to the total hip region of dual X-ray absorptiometry (DXA) measurements and compared with bone mineral density (BMD) measured with DXA. Testing six standard wavelets, this algorithm failed for only 0% to 6% of scan in test set 1 compared with 29% when using conventional algorithms. For test set 2, it failed for 2% to 12% compared with approximately 40%. SOS and BMD correlated significantly in both test sets (test set 1: r2 = 0.87 to 0.92, p < 0.007; test set 2: r2 = 0.68 to 0.79, p < 0.0001). The correlations are comparable with correlations recently reported. However, the number of evaluable signals could be substantially increased, which improves the perspectives of the in vivo measurements.

Influence of the precision of spectral backscatter measurements on the estimation of scatterers size in cancellous bone

The goal of this study is to propose a model for the ultrasonic frequency-dependent backscatter coefficient in femoral cancellous bone. This model has been developed with success to predict backscatter in human calcaneal bone [Jenson, Ultr. Med. Biol. 2003]. A weak scattering model is used and the backscatter coefficient is expressed in terms of a Gaussian autocorrelation function of the medium. The backscatter coefficient is computed and comparison is made with experimental data for 37 specimens and for frequency ranging from 0.4 to 1.2 MHz. An excellent agreement between experimental data and predictions is found for both the magnitude and the frequency-dependence of the backscatter coefficient. Then, a nonlinear regression is performed for each specimen, and the mean trabecular thickness is estimated. Experimental data and theoretical predictions are averaged over the 37 specimens. We also find a close agreement between theoretical predictions obtained using the Gaussian autocorrelation function (scatterer size=134+/-15 microm) and the mean trabecular thickness (Tb.Th=132+/-12 microm) derived from the analysis of bone 3-D micro-architecture using high-resolution micro-tomography. However, the correlation between individual experimental and estimated Tb.Th values is moderate (R(2)=0.44). The performance of the estimator are limited mainly by two factors: interference noise due to random positioning of the scatterers and attenuation. We show that the fundamental limitation of our estimator due to the speckle noise is around 5 microm for trabecular thickness estimation. This limitation is lower than the observed biological variability which is around 30 microm and should not be a limiting factor for individual prediction. A second limitation is the tremendous attenuation encountered in highly scattering media such as cancellous bone, which results in highly damped backscatter signals. The compensation for attenuation is difficult to perform, and it may be a critical point that limits the precision of the estimator.

Estimation of trabecular thickness using ultrasonic backcatter

We present a method to estimate trabecular thickness (Tb.Th) in trabecular bones from ultrasound backscatter measurements. The estimation scheme is based on a nonlinear adjustment of predictions from a model to experimental data. The model assumes weak scattering from bone, where scattering is assumed to arise from the elastic solid trabeculae. The fluctuations of acoustical properties between bone tissue and the saturating fluid are assumed to be random and are described by the 3-D spatial autocorrelation function of the medium. In this paper, a Gaussian autocorrelation function is used. The inversion procedure is applied to a set of data measured on 33 femoral bone specimens. Results show that the model can predict both the magnitude and the frequency-dependence of the backscatter coefficient (root mean square error RMSE = 1 dB). The estimated trabecular thickness values are compared to the true trabecular thickness measured on high resolution microcomputed tomography 3-D reconstruction of bones microarchitecture. A close agreement is obtained on average over the group of specimens between predictions and the reference values: true Tb.Th is 132 +/- 12 microm and estimated Tb.Th is 134 +/- 15 microm. However, a moderate correlation between actual and estimated Tb.Th values is found (R2 = 0.44, p<10(-4), RMSE = 8.7 microm) suggesting a modest predictability at the individual level. Sources for the variability of the estimator are studied. Using synthetic rf signals, we demonstrate that the fundamental limitation of the estimator due to speckle noise is approximately 5 microm. Taking into account the measurement errors, the total uncertainty on Tb.Th estimates is of the order of 7 microm. The influence of the attenuation compensation function used to derive the backscatter coefficient is studied. In particular, we demonstrate the necessity of compensating for the effect of the gating time window. The results are discussed with respect to their meaningful clinical value. The requirements to be fulfilled by the performance of the technique change with regard to the question being posed. Two different strategies are examined: 1. characterize trabecular thickness without consideration of bone quantity (or bone mineral density) and 2. estimate trabecular thickness after adjustment for BMD. Considering the first strategy, a comparison between the precision of our estimator and the biological variability leads us to the conclusion that our estimator should only permit to distinguish between micro-architectures characterized by extreme values of trabecular thickness (i.e., very thin or very thick trabecular thickness). In this respect, it would be interesting to test whether the estimator is able to discriminate between rod-like (thin) and plate-like (thick) structures that are known to influence differently bone strength. The second strategy is more demanding in terms of technique performance and our estimator is not able yet to catch small differences in Tb.Th values expected after adjustment to bone density. Progress in the field will require a significant reduction in speckle noise and measurement errors and/or the development of other and more efficient microstructural estimators.

In vitro ultrasonic characterization of human cancellous femoral bone using transmission and backscatter measurements: relationships to bone mineral density

Thirty-eight slices of pure trabecular bone 1-cm thickness were extracted from human proximal femurs. A pair of 1-MHz central frequency transducers was used to measure quantitative ultrasound (QUS) parameters in transmission [normalized broadband ultrasound attenuation (nBUA), speed of sound (SOS)] and in backscatter [broadband ultrasound backscatter (BUB)]. Bone mineral density (BMD) was measured using clinical x-ray quantitative computed tomography. Site-matched identical region of interest (ROIs) of 7 x 7 mm2 were positioned on QUS and QCT images. This procedure resulted in 605 ROIs for all the specimens data pooled together. The short-term precision of the technique expressed in terms of CV was found to be 2.3% for nBUA, 0.3% for SOS and 4.5% for BUB. Significant linear correlation between QUS and BMD were found for all the 605 ROIs pooled, with r2 values of 0.73, 0.77, and 0.58 for nBUA, SOS, and BUB, respectively (all p < 0.05). For the BUB, the best regression was obtained with a polynomial fit of second order (r2 = 0.63). An analysis of measurements errors was developed. It showed that the residual variability of SOS is almost completely predicted by measurements errors, which is not the case for BUA and BUB, suggesting a role for micro-architecture in the determination of BUA and BUB.