Ultrasonic scattering from cancellous bone: a review

Backscatter measurement of cancellous bone using the ultrasound transit time spectroscopy

Recently, ultrasound transit time spectroscopy (UTTS) was proposed as a promising method for bone quantitative ultrasound measurement. Studies have showed that UTTS could estimate the bone volume fraction and other trabecular bone structure in ultrasonic through-transmission measurements. The goal of this study was to explore the feasibility of UTTS to be adapted in ultrasonic backscatter measurement and further evaluate the performance of backscattered ultrasound transit time spectrum (BS-UTTS) in the measurement of cancellous bone density and structure. First, taking ultrasonic attenuation into account, the concept of BS-UTTS was verified on ultrasonic backscatter signals simulated from a set of scatterers with different positions and intensities. Then, in vitro backscatter measurements were performed on 26 bovine cancellous bone specimens. After a logarithmic compression of the BS-UTTS, a linear fitting of the log-compressed BS-UTTS versus ultrasonic propagated distance was performed and the slope and intercept of the fitted line for BS-UTTS were determined. The associations between BS-UTTS parameters and cancellous bone features were analyzed using simple linear regression. The results showed that the BS-UTTS could make an accurate deconvolution of the backscatter signal and predict the position and intensity of the simulated scatterers eliminating phase interference, even the simulated backscatter signal was with a relatively low signal-to-noise ratio. With varied positions and intensities of the scatterers, the slope of the fitted line for the log-compressed BS-UTTS versus ultrasonic propagated distance (i.e., slope of BS-UTTS for short) yield a high agreement (r2 = 99.84%-99.96%) with ultrasonic attenuation in simulated backscatter signal. Compared with the high-density cancellous bone, the low-density specimen showed more abundant backscatter impulse response in the BS-UTTS. The slope of BS-UTTS yield a significant correlation with bone mineral density (r = 0.87; p < 0.001), BV/TV (r = 0.87; p < 0.001), and cancellous bone microstructures (r up to 0.87; p < 0.05). The intercept of BS-UTTS was also significantly correlated with bone densities (r = -0.87; p < 0.001) and trabecular structures (|r|=0.43-0.80; p < 0.05). However, the slope of the BS-UTTS underestimated attenuation when measurements were performed experimentally. In addition, a significant non-linear relationship was observed between the measured attenuation and the attenuation estimated by the slope of the BS-UTTS. This study demonstrated that the UTTS method could be adapted to ultrasonic backscatter measurement of cancellous bone. The derived slope and intercept of BS-UTTS could be used in the measurement of bone density and microstructure. The backscattered ultrasound transit time spectroscopy might have potential in the diagnosis of osteoporosis in the clinic.

Factors influencing magnetic resonance imaging changes associated with pelvic bone injury after high-intensity focused ultrasound ablation of uterine fibroids: a retrospective case-control study

Background

The application of high-intensity focused ultrasound (HIFU) in the treatment of uterine fibroids is becoming increasingly widespread, and postoperative collateral thermal damage to adjacent tissue has become a prominent subject of discussion. However, there is limited research related to bone injury. Therefore, the aim of this study was to investigate the potential factors influencing unintentional pelvic bone injury after HIFU ablation of uterine fibroids with magnetic resonance imaging (MRI).

Methods

A total of 635 patients with fibroids treated with HIFU in the First Affiliated Hospital of Chongqing Medical University were enrolled. All patients underwent contrast-enhanced MRI (CE-MRI) pre- and post-HIFU. Based on the post-treatment MRI, the patients were divided into two groups: pelvic bone injury group and non-injury group, while the specific site of pelvic bone injury of each patient was recorded. The univariate and multivariate analyses were used to assess the correlations between the factors of fibroid features and treatment parameters and pelvic bone injury, and to further analyze the factors influencing the site of injury.

Results

Signal changes in the pelvis were observed on CE-MRI in 51% (324/635) of patients after HIFU. Among them, 269 (42.4%) patients developed sacral injuries and 135 (21.3%) had pubic bone injuries. Multivariate analyses showed that patients with higher age [P=0.003; odds ratio (OR), 1.692; 95% confidence interval (CI): 1.191-2.404], large anterior side-to-skin distance of fibroid (P<0.001; OR, 2.297; 95% CI: 1.567-3.365), posterior wall fibroid (P=0.006; OR, 1.897; 95% CI: 1.204-2.989), hyperintensity on T2-weighted imaging (T2WI, P=0.003; OR, 2.125; 95% CI: 1.283-3.518), and large therapeutic dose (TD, P<0.001; OR, 3.007; 95% CI: 2.093-4.319) were at higher risk of postoperative pelvic bone injury. Further analysis of the factors influencing the site of the pelvic bone injury showed that some of the fibroid features and treatment parameters were associated with it. Moreover, some postoperative pain-related adverse events were associated with the pelvic bone injury.

Conclusions

Post-HIFU treatment, patients may experience pelvic injuries to the sacrum, pubis, or a combination of both, and some of them experienced adverse events. Some fibroid features and treatment parameters are associated with the injury. Taking its influencing factors into full consideration preoperatively, slowing down treatment, and prolonging intraoperative cooling phase can help optimize treatment decisions for HIFU.

In Vivo Comparison of Backscatter Techniques for Ultrasonic Bone Assessment at the Femoral Neck

Ultrasonic techniques are being developed to detect changes in cancellous bone caused by osteoporosis. The goal of this study was to test the relative in vivo performance of eight backscatter parameters developed over the last several years for ultrasonic bone assessment: apparent integrated backscatter (AIB), frequency slope of apparent backscatter (FSAB), frequency intercept of apparent backscatter (FIAB), normalized mean of the backscatter difference (nMBD), normalized slope of the backscatter difference (nSBD), normalized intercept of the backscatter difference (nIBD), normalized backscatter amplitude ratio (nBAR) and backscatter amplitude decay constant (BADC). Backscatter measurements were performed on the left and right femoral necks of 80 adult volunteers (age = 25 ± 11 y) using an imaging system equipped with a convex array transducer. For comparison, additional ultrasonic measurements were performed at the left and right heel using a commercially available heel-bone ultrasonometer that measured the stiffness index. Six of the eight backscatter parameters (all but nSBD and nIBD) exhibited similar and highly significant (p < 0.000001) left-right correlations (0.51 ≤ R ≤ 0.68), indicating sensitivity to naturally occurring variations in bone tissue. Left-right correlations for the stiffness index measured at the heel (R = 0.75) were not significantly better than those produced by AIB, FSAB and FIAB. The short-term precisions of AIB, nMBD, nBAR and BADC (7.8%-11.7%) were comparable to that of the stiffness index measured with the heel-bone ultrasonometer (7.5%).

Quantitative Sound Speed Imaging of Cortical Bone and Soft Tissue: Results From Observational Data Sets

This work presents the first quantitative ultrasonic sound speed images of ex vivo limb cross-sections containing both soft tissue and bone using Full Waveform Inversion (FWI) with level set (LS) and travel time regularization. The estimated bulk sound speed of bone and soft tissue are within 10% and 1%, respectively, of ground truth estimates. The sound speed imagery shows muscle, connective tissue and bone features. Typically, ultrasound tomography (UST) using FWI is applied to imaging breast tissue properties (e.g. sound speed and density) that correlate with cancer. With further development, UST systems have the potential to deliver volumetric operator independent tissue property images of limbs with non-ionizing and portable hardware platforms. This work addresses the algorithmic challenges of imaging the sound speed of bone and soft tissue by combining FWI with LS regularization and travel time methods to recover soft tissue and bone sound speed with improved accuracy and reduced soft tissue artifacts when compared to conventional FWI. The value of leveraging LS and travel time methods is realized by evidence of improved bone geometry estimates as well as promising convergence properties and reduced risk of final model errors due to un-modeled shear wave propagation. Ex vivo bulk measurements of sound speed and MRI cross-sections validates the final inversion results.

Ultrasonic Bone Assessment: Ability of Apparent Backscatter Techniques to Detect Changes in the Microstructure of Human Cancellous Bone

Ultrasonic backscatter techniques may offer a useful approach for detecting changes in bone caused by osteoporosis. The goal of this study was to investigate how bone mineral density (BMD) and the microstructure of human cancellous bone affect three ultrasonic backscatter parameters that have been identified as potentially useful for ultrasonic bone assessment purposes: the apparent integrated backscatter (AIB), the frequency slope of apparent backscatter (FSAB), and the frequency intercept of apparent backscatter (FIAB). Ultrasonic measurements were performed with a 3.5-MHz broadband transducer on 54 specimens of human cancellous bone prepared from the proximal femur. Microstructural parameters and BMD were measured using X-ray microcomputed tomography (micro-CT). Relationships between AIB, FSAB, FIAB, and the micro-CT parameters were investigated using univariate and multivariate statistical analysis techniques. Moderate-to-strong univariate correlations were observed between the backscatter parameters and microstructure and BMD in many cases. The partial correlation analysis indicated that the backscatter parameters are dependent on microstructure independently of BMD in some cases. Multiple stepwise linear regression analysis used to generate multivariate models found that microstructure was a significant predictor of the backscatter parameters in most cases.

A novel quantitative and reference-free ultrasound analysis to discriminate different concentrations of bone mineral content

Bone fracture is a continuous process, during which bone mineral matrix evolves leading to an increase in hydroxyapatite and calcium carbonate content. Currently, no gold standard methods are available for a quantitative assessment of bone fracture healing. Moreover, the available tools do not provide information on bone composition. Whereby, there is a need for objective and non-invasive methods to monitor the evolution of bone mineral content. In general, ultrasound can guarantee a quantitative characterization of tissues. However, previous studies required measurements on reference samples. In this paper we propose a novel and reference-free parameter, based on the entropy of the phase signal calculated from the backscattered data in combination with amplitude information, to also consider absorption and scattering phenomena. The proposed metric was effective in discriminating different hydroxyapatite (from 10 to 50% w/v) and calcium carbonate (from 2 to 6% w/v) concentrations in bone-mimicking phantoms without the need for reference measurements, paving the way to their translational use for the diagnosis of tissue healing. To the best of our knowledge this is the first time that the phase entropy of the backscattered ultrasound signals is exploited for monitoring changes in the mineral content of bone-like materials.

Inferring pore radius and density from ultrasonic attenuation using physics-based modeling

This work proposes the use of two physics-based models for wave attenuation to infer the microstructure of cortical bone-like structures. One model for ultrasound attenuation in porous media is based on the independent scattering approximation (ISA) and the other model is based on the Waterman Truell (WT) approximation. The microstructural parameters of interest are pore radius and pore density. Attenuation data are simulated for three-dimensional structures mimicking cortical bone using the finite-difference time domain package SimSonic. These simulated structures have fixed sized pores (monodisperse), allowing fine-tuned control of the microstructural parameters. Structures with pore radii ranging from 50 to 100  μm and densities ranging from 20 to 50 pores/mm3 are generated in which only the attenuation due to scattering is considered. From here, an inverse problem is formulated and solved, calibrating the models to the simulated data and producing estimates of pore radius and density. The estimated microstructural parameters closely match the values used to simulate the data, validating the use of both the ISA and WT approximations to model ultrasonic wave attenuation in heterogeneous structures mimicking cortical bone. Furthermore, this illustrates the effectiveness of both models in inferring pore radius and density solely from ultrasonic attenuation data.

Ultrasonic Bone Assessment Using the Backscatter Amplitude Decay Constant

Ultrasonic backscatter techniques are being developed to detect changes in bone caused by osteoporosis. The present study introduces a new technique that measures the exponential decay in the amplitude of the backscatter signal quantified by a parameter called the backscatter amplitude decay constant (BADC). Measurements were performed on 54 specimens of cancellous bone from 14 human femurs using a 3.5-MHz transducer. Six methods were tested to determine BADC. The recommended method measures the time slope of the natural log of the rectified signal. Measured values of BADC ranged from approximately 0.1 μs^-1 to 0.6 μs^-1. Moderate to strong correlations (Spearman's ρ >0.7) were found between BADC and the density and microstructural characteristics of the specimens determined using X-ray microcomputed tomography. The results of this study suggest that BADC may be able to detect changes in the density and microstructure of cancellous bone caused by osteoporosis and other diseases.

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.

The Ability of Ultrasonic Backscatter Parametric Imaging to Characterize Bovine Trabecular Bone

The ultrasonic backscatter technique holds the promise of characterizing bone density and microstructure. This paper conducts ultrasonic backscatter parametric imaging based on measurements of apparent integrated backscatter (AIB), spectral centroid shift (SCS), frequency slope of apparent backscatter (FSAB), and frequency intercept of apparent backscatter (FIAB) for representing trabecular bone mass and microstructure. We scanned 33 bovine trabecular bone samples using a 7.5 MHz focused transducer in a 20 mm × 20 mm region of interest (ROI) with a step interval of 0.05 mm. Images based on the ultrasonic backscatter parameters (i.e., AIB, SCS, FSAB, and FIAB) were constructed to compare with photographic images of the specimens as well as two-dimensional (2D) μ-CT images from approximately the same depth and location of the specimen. Similar structures and trabecular alignments can be observed among these images. Statistical analyses demonstrated that the means and standard deviations of the ultrasonic backscatter parameters exhibited significant correlations with bone density (|R| = 0.45-0.78, p < 0.01) and bone microstructure (|R| = 0.44-0.87, p < 0.001). Some bovine trabecular bone microstructure parameters were independently associated with the ultrasonic backscatter parameters (ΔR² = 4.18%-44.45%, p < 0.05) after adjustment for bone apparent density (BAD). The results show that ultrasonic backscatter parametric imaging can provide a direct view of the trabecular microstructure and can reflect information about the density and microstructure of trabecular bone.

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

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

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.

Velocity dispersion and backscatter in marrow-filled and water-filled trabecular bone samples in vitro

The phase velocity and the backscatter coefficient were measured in 28 bovine femoral trabecular bone samples filled with marrow and water in vitro from 0.2 to 0.6 MHz. The phase velocities decreased approximately linearly with increasing frequency and the average dispersion rate of -34 ms^-1MHz^-1 in the marrow-filled samples was higher than that of -42 ms^-1MHz^-1 in the water-filled samples. The backscatter coefficients exhibited nonlinear, monotonically increasing dependences on the frequency and the average value of the exponent n = 2.92 (frequency dependence) in the marrow-filled samples was higher than the value of n = 2.79 in the water-filled samples.

The effect of pore size and density on ultrasonic attenuation in porous structures with mono-disperse random pore distribution: A two-dimensional in-silico study

This work proposes a power law model to describe the attenuation of ultrasonic waves in non-absorbing heterogeneous media with randomly distributed scatterers, mimicking a simplified structure of cortical bone. This paper models the propagation in heterogeneous structures with controlled porosity using a two-dimensional finite-difference time domain numerical simulation in order to measure the frequency dependent attenuation. The paper then fits a phenomenological model to the simulated frequency dependent attenuation by optimizing parameters under an ordinary least squares framework. Local sensitivity analysis is then performed on the resulting parameter estimates in order to determine to which estimates the model is most sensitive. This paper finds that the sensitivity of the model to various parameter estimates depends on the micro-architectural parameters, pore diameter (ϕ) and pore density (ρ). In order to get a sense for how confidently model parameters are able to be estimated, 95% confidence intervals for these estimates are calculated. In doing so, the ability to estimate model-sensitive parameters with a high degree of confidence is established. In the future, being able to accurately estimate model parameters from which micro-architectural ones could be inferred will allow pore density and diameter to be estimated via an inverse problem given real or simulated ultrasonic data to be determined.

Characterization of a polymer, open-cell rigid foam that simulates the ultrasonic properties of cancellous bone

Materials that simulate the ultrasonic properties of tissues are used widely for clinical and research purposes. However, relatively few materials are known to simulate the ultrasonic properties of cancellous bone. The goal of the present study was to investigate the suitability of using a polymer, open-cell rigid foam (OCRF) produced by Sawbones^®. Measurements were performed on OCRF specimens with four different densities. Ultrasonic speed of sound and normalized broadband ultrasonic attenuation were measured with a 0.5 MHz transducer. Three backscatter parameters were measured with a 5 MHz transducer: apparent integrated backscatter, frequency slope of apparent backscatter, and normalized mean of the backscatter difference. X-ray micro-computed tomography was used to measure the microstructural characteristics of the OCRF specimens. The trabecular thickness and relative bone volume of the OCRF specimens were similar to those of human cancellous bone, but the trabecular separation was greater. In most cases, the ultrasonic properties of the OCRF specimens were similar to values reported in the literature for cancellous bone, including dependence on density. In addition, the OCRF specimens exhibited an ultrasonic anisotropy similar to that reported for cancellous bone.

Variability in Ultrasound Backscatter Induced by Trabecular Microstructure Deterioration in Cancellous Bone

To determine the relationship between the ultrasonic backscatter parameters and trabecular microstructural variations in cancellous bone, three erosion procedures were performed to simulate various changes in the cancellous bone microstructure. The finite difference time domain (FDTD) method was used to simulate the backscatter signal in cancellous bone. Ultrasonic backscatter properties were derived as functions of the porosity when the ultrasound incident directions were perpendicular and parallel to the major trabeculae direction (MTD), respectively. The variability in the apparent backscatter coefficient (ABC) and apparent integrated backscatter (AIB) due to the trabecular microstructure was revealed. Significant negative correlations between the backscatter parameters (ABC and AIB) and the porosity of the cancellous bone were observed. The simulations showed that the ABC and AIB were influenced by the direction of the trabecular microstructural variations. The linear regressions between the ultrasonic backscatter parameters (ABC and AIB) and the porosity showed significantly different slopes for three erosion procedures when they are ultrasonically perpendicular (for ABC, −1.22 dB, −0.98 dB, and −0.46 dB; for AIB, −0.74 dB, −0.69 dB, and −0.25 dB) and parallel (for ABC, −1.87 dB, −0.69 dB, and −0.51 dB; for AIB, −0.9 dB, −0.5 dB, and −0.34 dB) to the MTD. This paper investigated the relationship between ultrasonic backscatter and cancellous bone microstructure deterioration and indicated that the ultrasonic backscatter could be affected by cancellous bone microstructure deterioration direction.

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.

Finite-element modelling of elastic wave propagation and scattering within heterogeneous media

The scattering treated here arises when elastic waves propagate within a heterogeneous medium defined by random spatial fluctuation of its elastic properties. Whereas classical analytical studies are based on lower-order scattering assumptions, numerical methods conversely present no such limitations by inherently incorporating multiple scattering. Until now, studies have typically been limited to two or one dimension, however, owing to computational constraints. This article seizes recent advances to realize a finite-element formulation that solves the three-dimensional elastodynamic scattering problem. The developed methodology enables the fundamental behaviour of scattering in terms of attenuation and dispersion to be studied. In particular, the example of elastic waves propagating within polycrystalline materials is adopted, using Voronoi tessellations to randomly generate representative models. The numerically observed scattering is compared against entirely independent but well-established analytical scattering theory. The quantitative agreement is found to be excellent across previously unvisited scattering regimes; it is believed that this is the first quantitative validation of its kind which provides significant support towards the existence of the transitional scattering regime and facilitates future deployment of numerical methods for these problems.

Measurement of the Human Calcaneus In Vivo Using Ultrasonic Backscatter Spectral Centroid Shift

OBJECTIVES

The aim of this study was to determine the relationship between the backscattered spectral centroid shift and the bone mineral density (BMD) in vivo and investigate the feasibility of using the backscattered spectral centroid shift to characterize the cancellous bone status.

METHODS

Ultrasonic backscatter measurements were performed in vivo on 1216 participants at the right calcaneus using an ultrasonic backscattered bone diagnostic system, and the backscattered spectral centroid shift was calculated at central frequencies of 3.5 and 5.0 MHz. The BMD values were measured at the sites of the lumbar spine and left hip by dual energy x-ray absorptiometry.

RESULTS

The study population included 592 male and 624 female participants aged 20 to 89 years. The correlations between the backscattered spectral centroid shift in the calcaneus and the spine and hip BMD were found to be statistically significant in both the male and female groups (P < .0001). Linear regression showed that the spectral centroid shift at 3.5 MHz had negative correlations with the spine BMD (R = -0.65 for male participants; R = -0.67 for female participants) and hip BMD (R = -0.64 for male participants; R = -0.64 for female participants). The spectral centroid shift at 5.0 MHz was also found to be closely related to the spine BMD (R = -0.68 for male participants; R = -0.68 for female participants) and hip BMD (R = -0.66 for male participants; R = -0.64 for female participants).

CONCLUSIONS

The moderate correlations observed between the spectral centroid shift and the spine and hip BMD demonstrate that the ultrasonic backscattered spectral centroid shift may be a useful measurement for assessment of the cancellous bone status.

Backscatter-difference Measurements of Cancellous Bone Using an Ultrasonic Imaging System

Backscatter-difference measurements may be used to detect changes in bone caused by osteoporosis. The backscatter-difference technique measures the power difference between two portions of an ultrasonic backscatter signal. The goal of this study is to evaluate the feasibility of using an ultrasonic imaging system to perform backscatter-difference measurements of bone. Ultrasonic images and backscatter signals were acquired from 24 specimens of human cancellous bone. The signals were analyzed in the frequency domain to determine the normalized mean backscatter-difference (nMBD) and in the time domain to determine the normalized backscatter amplitude ratio (nBAR). The images were analyzed to determine the normalized pixel value difference (nPVD), which measures the difference in average pixel brightness between regions of interest placed at two different depths in the image. All three parameters were found to increase with bone mineral density. The signal-based parameters, nMBD and nBAR, correlated well with bone mineral density, yielding linear correlation coefficients that ranged from 0.74 to 0.87. The image based parameter, nPVD, performed somewhat less well, yielding correlation coefficients that ranged from 0.42 to 0.81. These results suggest that ultrasonic imaging systems may be used to perform backscatter-difference measurements for the purpose of ultrasonic bone assessment.

A μCT-based investigation of the influence of tissue modulus variation, anisotropy and inhomogeneity on ultrasound propagation in trabecular bone

Ultrasound propagation is widely used in the diagnosis of osteoporosis by providing information on bone mechanical quality. When it loses calcium, the tissue properties will first decrease. However, limited research about the influence of tissue properties on ultrasound propagation have been done due to the cumbersome experiment. The goal of this study was to explore the relationships between tissue modulus (Es) and speed of sound (SOS) through numerical simulations, and to study the influence of Es on the acoustical behavior in characterizing the local structural anisotropy and inhomogeneity. In this work, three-dimensional finite element (FE) simulations were performed on a cubic high-resolution (15μm) bovine trabecular bone sample (4×4×4mm(3), BV/TV=0.18) mapped from micro-computed tomography. Ultrasound excitations of 50kHz, 500kHz and 2MHz were applied in three orthogonal axes and the first arriving signal (FAS) was collected to quantify wave velocity. In this study, a strong power law relationship between Es and SOS was measured with estimated exponential index β=2.08-3.44 for proximal-distal (PD), anterior-posterior (AP) and medial-lateral (ML), respectively (all R(2)>0.95). For various Es, a positive dispersion of sound speed with respect to sound frequency was observed and the velocity dispersion magnitude (VDM) was measured. Also, with Es=15GPa in three orientations, the SOS in PD axis is 2009±120m/s, faster than that of AP (1762±106m/s) and ML (1798±132m/s) (f=2MHz) directions. Besides, the standard deviation of SOS increases with the sound frequency and the Es in all directions except for that at 50kHz. For the mechanical properties, the apparent modulus with certain Es was highest in the longitudinal direction compared with the transverse directions. It indicates that the tissue modulus combining with anisotropy and inhomogeneity has great influence on ultrasound propagation. Simulation results agree well with theoretical and experimental results.

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.

Signal of Interest Selection Standard for Ultrasonic Backscatter in Cancellous Bone Evaluation

The aim of this study was to examine the effect of the backscattered signal of interest (SOI) on ultrasonic cancellous bone evaluation. In vitro backscatter measurements were performed using 16 bovine cancellous bone specimens and six different transducers with central frequencies of 0.5, 1, 2.25, 3.5, 5 and 10 MHz. The SOI for signal analysis was selected by a rectangular window. The delay (T1) and duration (T2) of the time window were varied, and the apparent integrated backscatter (AIB) and its correlation to bone volume fraction (BV/TV) were calculated. The results indicate that in addition to affecting the measured value of AIB, the SOI influences the observed correlation between AIB and BV/TV. Strong positive correlations were observed for short T1 (0.5 MHz: ≤6 μs, 1 MHz: ≤3 μs, 2.25 and 3.5 MHz: ≤2 μs, 5 and 10 MHz: ≤1 μs). However, strong negative correlations were observed when T1 was long (0.5 MHz: >9 μs, 1 MHz: >7 μs, 2.25 and 3.5 MHz: >3 μs, 5 and 10 MHz: >2 μs). The T2 value, especially low values (≤3 μs), also influenced the correlation coefficients. Positive correlations were more commonly observed at lower frequencies (i.e., 0.5-1 MHz), whereas negative correlations were more common at higher frequencies (i.e., 2.25-10 MHz). An explicit standard for in vitro SOI selection and cancellous bone assessment was proposed for a broad frequency range (0.5-10 MHz). Current conflicting findings are explained, and constructive suggestions for ultrasonic backscatter cancellous bone evaluation are provided.

Ultrasonic wave properties of human bone marrow in the femur and tibia

Ultrasonic wave properties of human bone marrow obtained in the femur and tibia were measured using an ultrasound pulse technique. The measured frequency range was 4-10 MHz, and the temperature range was 30 °C-40 °C. The sound velocity was 1410 m/s, and the attenuation coefficient was 4.4 dB/cm at 36 °C (10 MHz). These values decreased with temperature. Site dependence and individual differences in elderly human bone marrow were negligible. The slopes of the attenuation coefficient were estimated by a power law. The values of the exponent n were 2.0 (30 °C-38 °C) and 2.3 (40 °C).

Photoacoustic and ultrasound imaging of cancellous bone tissue

We used ultrasound (US) and photoacoustic (PA) imaging modalities to characterize cattle trabecular bones. The PA signals were generated with an 805-nm continuous wave laser used for optimally deep optical penetration depth. The detector for both modalities was a 2.25-MHz US transducer with a lateral resolution of ~1 mm at its focal point. Using a lateral pixel size much larger than the size of the trabeculae, raster scanning generated PA images related to the averaged values of the optical and thermoelastic properties, as well as density measurements in the focal volume. US backscatter yielded images related to mechanical properties and density in the focal volume. The depth of interest was selected by time-gating the signals for both modalities. The raster scanned PA and US images were compared with microcomputed tomography (μCT) images averaged over the same volume to generate similar spatial resolution as US and PA. The comparison revealed correlations between PA and US modalities with the mineral volume fraction of the bone tissue. Various features and properties of these modalities such as detectable depth, resolution, and sensitivity are discussed.

Numerical Analysis of Ultrasound Backscattered Waves in Cancellous Bone Using a Finite-Difference Time-Domain Method: Isolation of the Backscattered Waves From Various Ranges of Bone Depths

Using a finite-difference time-domain method, ultrasound backscattered waves inside cancellous bone were numerically analyzed to investigate the backscatter mechanism. Two bone models with different thicknesses were modeled with artificial absorbing layers positioned at the back surfaces of the model, and an ultrasound pulse wave was transmitted toward the front surface. By calculating the difference between the simulated waveforms obtained using the two bone models, the backscattered waves from a limited range of depths in cancellous bone could be isolated. The results showed that the fast and slow longitudinal waves, which have previously been observed only in the ultrasound waveform transmitted through the bone, could be distinguished in the backscattered waveform from a deeper bone depth when transmitting the ultrasound wave parallel to the main orientation of the trabecular network. The amplitudes of the fast and slow backscattered waves were more closely correlated with the bone porosity [R2 = 0.84 and 0.66 (p < 0.001), respectively] than the amplitude of the whole (nonisolated) backscattered waves [R2 = 0.48 (p < 0.001)]. In conclusion, the nonisolated backscattered waves could be regarded as the superposition of the fast and slow waves reflected from various bone depths, returning at different times.

Basic study for ultrasound-based navigation for pedicle screw insertion using transmission and backscattered methods

The purpose of this study was to understand the acoustic properties of human vertebral cancellous bone and to study the feasibility of ultrasound-based navigation for posterior pedicle screw fixation in spinal fusion surgery. Fourteen human vertebral specimens were disarticulated from seven un-embalmed cadavers (four males, three females, 73.14 ± 9.87 years, two specimens from each cadaver). Seven specimens were used to measure the transmission, including tests of attenuation and phase velocity, while the other seven specimens were used for backscattered measurements to inspect the depth of penetration and A-Mode signals. Five pairs of unfocused broadband ultrasonic transducers were used for the detection, with center frequencies of 0.5 MHz, 1 MHz, 1.5 MHz, 2.25 MHz, and 3.5 MHz. As a result, good and stable results were documented. With increased frequency, the attenuation increased (P<0.05), stability of the speed of sound improved (P<0.05), and penetration distance decreased (P>0.05). At about 0.6 cm away from the cortical bone, warning signals were easily observed from the backscattered measurements. In conclusion, the ultrasonic system proved to be an effective, moveable, and real-time imaging navigation system. However, how ultrasonic navigation will benefit pedicle screw insertion in spinal surgery needs to be determined. Therefore, ultrasound-guided pedicle screw implantation is theoretically effective and promising.

The application of backscattered ultrasound and photoacoustic signals for assessment of bone collagen and mineral contents

BACKGROUND

This study examines the backscattered ultrasound (US) and back-propagating photoacoustic (PA) signals from trabecular bones, and their variations with reduction in bone minerals and collagen content. While the collagen status is directly related to the strength of the bone, diagnosis of its condition using US remains a challenge.

METHODS

For both PA and US methods, coded-excitation signals and matched filtering were utilized to provide high sensitivity of the detected signal. The optical source was a 805-nm CW laser and signals were detected employing a 2.2-MHz ultrasonic transducer. Bone decalcification and decollagenization were induced with mild ethylenediaminetetraacetic acid (EDTA) and sodium hypochlorite solutions, respectively.

RESULTS

The PA and US signals were measured on cattle bones, and apparent integrated backscatter/back-propagating (AIB) parameters were compared before and after demineralization and decollagenization.

CONCLUSIONS

The results show that both PA and US are sensitive to mineral changes. In addition, PA is also sensitive to changes in the collagen content of the bone, but US is not significantly sensitive to these changes.

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

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

Analysis of apparent integrated backscatter coefficient and backscattered spectral centroid shift in Calcaneus in vivo for the ultrasonic evaluation of osteoporosis

The purposes of our study were to evaluate the correlation among apparent integrated backscatter coefficient (AIB), spectral centroid shift (SCS) of ultrasonic backscatter signals and bone mineral density (BMD) and to examine the effectiveness of ultrasound variables as predictors of osteoporosis. A total of 1011 persons aged 21-80 y old were included. All study participants underwent BMD measurements of the lumbar spine (LSBMD) and the femoral neck (FNBMD). The participants also underwent calcaneal measurements to determine AIB and SCS with central frequencies of 3.5 (one transducer) and 5.0 MHz (the other transducer). AIB decreased with age and was positively correlated with BMD, while SCS increased with age and was negatively correlated with BMD. The correlation coefficient of SCS with LSBMD and FNBMD at 3.5 MHz was -0.72 and -0.70, respectively. The correlation coefficient at 5.0 MHz was -0.75 and -0.74, respectively. The correlation coefficient of AIB with LSBMD and FNBMD at 3.5 MHz was 0.65 and 0.63. The correlation coefficient at 5.0 MHz was 0.59 and 0.55, respectively. The correlation between SCS and BMD was significantly better than the correlation between AIB and BMD. Using receiver operating characteristic analysis, a significant difference was found between the areas under the curve for SCS and AIB at 3.5 MHz (0.781 vs. 0.715, respectively, p < 0.05), as well as at 5.0 MHz (0.782 vs. 0.709, respectively, p < 0.05). The optimum T-score threshold for SCS was -1.3 for both transducers. The sensitivity and specificity of SCS at 3.5 MHz and 5.0 MHz for the optimum threshold were 64%, 85%, 63% and 86%, respectively. In conclusion, the correlations among the ultrasound parameters and BMDs are strong. SCS performs better than AIB in differentiating patients with osteoporosis. Ultrasound variables may be taken into consideration as predictors of osteoporosis in the future considering its portability.

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.

Time-domain separation of interfering waves in cancellous bone using bandlimited deconvolution: simulation and phantom study

In through-transmission interrogation of cancellous bone, two longitudinal pulses ("fast" and "slow" waves) may be generated. Fast and slow wave properties convey information about material and micro-architectural characteristics of bone. However, these properties can be difficult to assess when fast and slow wave pulses overlap in time and frequency domains. In this paper, two methods are applied to decompose signals into fast and slow waves: bandlimited deconvolution and modified least-squares Prony's method with curve-fitting (MLSP + CF). The methods were tested in plastic and Zerdine(®) samples that provided fast and slow wave velocities commensurate with velocities for cancellous bone. Phase velocity estimates were accurate to within 6 m/s (0.4%) (slow wave with both methods and fast wave with MLSP + CF) and 26 m/s (1.2%) (fast wave with bandlimited deconvolution). Midband signal loss estimates were accurate to within 0.2 dB (1.7%) (fast wave with both methods), and 1.0 dB (3.7%) (slow wave with both methods). Similar accuracies were found for simulations based on fast and slow wave parameter values published for cancellous bone. These methods provide sufficient accuracy and precision for many applications in cancellous bone such that experimental error is likely to be a greater limiting factor than estimation error.

Dependences of quantitative ultrasound parameters on frequency and porosity in water-saturated nickel foams

The frequency-dependent phase velocity, attenuation coefficient, and backscatter coefficient were measured from 0.8 to 1.2 MHz in 24 water-saturated nickel foams as trabecular-bone-mimicking phantoms. The power law fits to the measurements showed that the phase velocity, the attenuation coefficient, and the backscatter coefficient were proportional to the frequency with exponents n of 0.95, 1.29, and 3.18, respectively. A significant linear correlation was found between the phase velocity at 1.0 MHz and the porosity. In contrast, the best regressions for the normalized broadband ultrasound attenuation and the backscatter coefficient at 1.0 MHz were obtained with the polynomial fits of second order.

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.

Clinical assessment of the 1/3 radius using a new desktop ultrasonic bone densitometer

The objectives of this study were to evaluate the capability of a novel ultrasound device to clinically estimate bone mineral density (BMD) at the 1/3 radius. The device rests on a desktop and is portable, and permits real-time evaluation of the radial BMD. The device measures two net time delay (NTD) parameters, NTD(DW) and NTD(CW). NTD(DW) is defined as the difference between the transit time of an ultrasound pulse to travel through soft-tissue, cortex and medullary cavity, and the transit time through soft tissue only of equal overall distance. NTD(CW) is defined as the difference between the transit time of an ultrasound pulse to travel through soft-tissue and cortex only, and the transit time through soft tissue only again of equal overall distance. The square root of the product of these two parameters is a measure of the radial BMD at the 1/3 location as measured by dual-energy X-ray absorptiometry (DXA). A clinical IRB-approved study measured ultrasonically 60 adults at the 1/3 radius. BMD was also measured at the same anatomic site and time using DXA. A linear regression using NTD produced a linear correlation coefficient of 0.93 (p < 0.001). These results are consistent with previously reported simulation and in vitro studies. In conclusion, although X-ray methods are effective in bone mass assessment, osteoporosis remains one of the largest undiagnosed and under-diagnosed diseases in the world today. The research described here should enable significant expansion of diagnosis and monitoring of osteoporosis through a desktop device that ultrasonically assesses bone mass at the 1/3 radius.

Phase velocity and attenuation predictions of waves in cancellous bone using an iterative effective medium approximation

The quantitative determination of wave dispersion and attenuation in bone is an open research area as the factors responsible for ultrasound absorption and scattering in composite biological tissues have not been completely explained. In this study, we use the iterative effective medium approximation (IEMA) proposed in [1] so as to calculate phase velocity and attenuation in media with properties similar to those of cancellous bones. Calculations are performed for a frequency range of 0.4-0.8 MHz and for different inclusions' volume concentrations and sizes. Our numerical results are compared with previous experimental findings so as to assess the effectiveness of IEMA. It was made clear that attenuation and phase velocity estimations could provide supplementary information for cancellous bone characterization.

Frequency specific ultrasound attenuation is sensitive to trabecular bone structure

This study investigated the efficacy of frequency modulated ultrasound attenuation in the assessment of the trabecular structural properties. Four frequency modulated signals were created to represent four frequency bands centered at 500 kHz, 900 kHz, 1.3 MHz and 1.7 MHz with the bandwidth of 400 kHz. Five 1-cm trabecular cubes were harvested from fresh bovine distal femur. The cubes underwent four steps of demineralization process to expand the sample size to 25 with the greater variations of the structural properties for the better correlation study. Pearson correlation study was performed between the ultrasound attenuation in four frequency bands and the trabecular structural properties. The results showed that correlations of frequency modulated ultrasound attenuation to the trabecular structural properties are dependent on frequency bands. The attenuation in proximal-distal orientation had the highest correlation to BV/TV (R(2) = 0.73, p < 0.001) and trabecular thickness (R(2) = 0.50, p < 0.001) at the frequency band centered at 1.7 MHz. It was equivalent in the four frequency bands in correlation to the trabecular number (average R(2) = 0.80, p < 0.001) and to the trabecular separation (average R(2) = 0.83, p < 0.001). The attenuation in anterio-posterial orientation had the highest correlation to BV/TV (R(2) = 0.80, p < 0.001) and trabecular thickness (R(2) = 0.71, p < 0.001) at the frequency band centered at 1.3 MHz. The attenuation in the first frequency band was the most sensitive to the trabecular number (R(2) = 0.71, p < 0.001) and trabecular separation (R(2) = 0.80, p < 0.001). No significant correlation was observed for the attenuation in medial-lateral orientation across the four frequency bands.

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.

Comparison of phase velocity in trabecular bone mimicking-phantoms by time domain numerical (EFIT) and analytical multiple scattering approaches

The corrected Waterman-Truell model and the Elastodynamic Finite Integration Technique were used to analyze the ultrasonic wave dispersion in trabecular bones mimicking phantoms. A simple two-phase model of the trabecular bone is assumed; the trabeculae structure and the bone marrow. The phase velocity for frequencies within the range from 400kHz to 800kHz were computed for different scatterer arrays varying their dimensions and number. The theoretical and numerical results were compared to experimental published data, obtained from a mimicking phantom composed by a periodic array of nylon shreds (trabeculae array) immersed in a water tank. Our results showed an excellent consistency when compared to experimental data. The negative dispersions of -8.48m/s/MHz and -9.16m/s/MHz were computed by the multiple scattering method and the numerical approach, respectively, where the latter is closer to the experimental dispersion of -12.09m/s/MHz. Similar result has been reported in the literature, where the dispersion predicted by the Generalized Self-Consistent Method [J. Acoust. Soc. Am. 124 (2008) 4047] is -9.96m/s/MHz.

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.

Frequency-dependent attenuation and backscatter coefficients in bovine trabecular bone from 0.2 to 1.2 MHz

The frequency-dependent attenuation and backscatter coefficients were measured in 25 bovine femoral trabecular bone samples from 0.2 to 1.2 MHz. When the average attenuation coefficient was fitted to a nonlinear power law α(f)=α(0)+α(1)f(n), the exponent n was found to be 1.65. In contrast, the average backscatter coefficient was fitted to a power law η(f)=η(1)f(n) and the exponent n was measured as 3.25. The apparent bone density was significantly correlated with the parameter α(1) (0.2-0.7 MHz: r = 0.852, 0.6-1.2 MHz: r = 0.832) as well as the backscatter coefficient (0.5 MHz: r = 0.751, 1.0 MHz: r = 0.808).

Properties of ultrasonic waves in bovine bone marrow

We investigated the properties of ultrasonic waves in bovine bone marrow. Six bone marrow samples were obtained from different parts (proximal, middle and distal) of the shafts of two bovine femora without destruction. The measured frequency range was 3 to 10 MHz, and the temperature range was 15 to 40°C. Both wave velocity and attenuation coefficient in bone marrow always decreased as temperature increased. The velocity ranged from 1400 to 1610 m/s and attenuation coefficient ranged from 4 to 16 dB/cm. Wave velocities in bone marrow were similar to those in water, whereas the temperature dependences were different, and the wave attenuation coefficients were much higher than those in water. The dependence of velocity on temperature changed slightly around 23-24°C, where a transition from soft gel to oily liquid occurred. The transition temperature was confirmed by differential scanning calorimetry (DSC). Below this transition temperature, positive velocity dispersion was observed.

Modeling and analysis of multiple scattering of acoustic waves in complex media: application to the trabecular bone

The integral equations that describe scattering in the media with step-rise changing parameters have been numerically solved for the trabecular bone model. The model consists of several hundred discrete randomly distributed elements. The spectral distribution of scattering coefficients in subsequent orders of scattering has been presented. Calculations were carried on for the ultrasonic frequency ranging from 0.5 to 3 MHz. Evaluation of the contribution of the first, second, and higher scattering orders to total scattering of the ultrasounds in trabecular bone was done. Contrary to the approaches that use the μCT images of trabecular structure to modeling of the ultrasonic wave propagation condition, the 3D numerical model consisting of cylindrical elements mimicking the spatial matrix of trabeculae, was applied. The scattering, due to interconnections between thick trabeculae, usually neglected in trabecular bone models, has been included in calculations when the structure backscatter was evaluated. Influence of the absorption in subsequent orders of scattering is also addressed. Results show that up to 1.5 MHz, the influence of higher scattering orders on the total scattered field characteristic can be neglected while for the higher frequencies, the relatively high amplitude interference peaks in higher scattering orders clearly occur.

Analysis of superimposed ultrasonic guided waves in long bones by the joint approximate diagonalization of eigen-matrices algorithm

The parameters of ultrasonic guided waves (GWs) are very sensitive to mechanical and structural changes in long cortical bones. However, it is a challenge to obtain the group velocity and other parameters of GWs because of the presence of mixed multiple modes. This paper proposes a blind identification algorithm using the joint approximate diagonalization of eigen-matrices (JADE) and applies it to the separation of superimposed GWs in long bones. For the simulation case, the velocity of the single mode was calculated after separation. A strong agreement was obtained between the estimated velocity and the theoretical expectation. For the experiments in bovine long bones, by using the calculated velocity and a theoretical model, the cortical thickness (CTh) was obtained. For comparison with the JADE approach, an adaptive Gaussian chirplet time-frequency (ACGTF) method was also used to estimate the CTh. The results showed that the mean error of the CTh acquired by the JADE approach was 4.3%, which was smaller than that of the ACGTF method (13.6%). This suggested that the JADE algorithm may be used to separate the superimposed GWs and that the JADE algorithm could potentially be used to evaluate long bones.

Statistics of the envelope of ultrasonic backscatter from human trabecular bone

The paper describes the investigations intended to compare the results of experimental measurements of backscattering properties of the trabecular bone with the results of computer simulations. Ultrasonic RF echoes were collected using two bone scanners operating at 0.58 and 1.3 MHz. The simulations of the backscattered RF echoes were performed using the scattering model of the trabecular bone that consisted of cylindrical and spherical elements uniformly distributed in water-like medium. For each measured or simulated RF backscatter the statistical properties of the signal envelope were determined. Experimental results suggest deviations of the backscattering properties from the Rayleigh distribution. The results of simulation suggest that deviation from Rayleigh distribution depends on the variation of trabeculae diameters and the number of thin trabeculae. Experimentally determined deviations corresponded well to the deviations calculated from simulated echoes assuming trabeculae thickness variation equaled to the earlier published histomorphometric study results.