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

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.

Diagnosis of Bone Mineral Density Based on Backscattering Resonance Phenomenon Using Coregistered Functional Laser Photoacoustic and Ultrasonic Probes

Dual-energy X-ray absorptiometry (DXA) machines based on bone mineral density (BMD) represent the gold standard for osteoporosis diagnosis and assessment of fracture risk, but bone strength and toughness are strongly correlated with bone collagen content (CC). Early detection of osteoporosis combined with BMD and CC will provide improved predictability for avoiding fracture risk. The backscattering resonance (BR) phenomenon is present in both ultrasound (US) and photoacoustic (PA) signal transmissions through bone, and the peak frequencies of BR can be changed with BM and CC. This phenomenon can be explained by the formation of standing waves within the pores. Simulations were then conducted for the same bone µCT images and the resulting resonance frequencies were found to match those predicted using the standing wave hypothesis. Experiments were performed on the same bone sample using an 808 nm wavelength laser as the PA source and 3.5 MHz ultrasonic transducer as the US source. The backscattering resonance effect was observed in the transmitted waves. These results verify our hypothesis that the backscattering resonance phenomenon is present in both US and PA signal transmissions and can be explained using the standing waves model, which will provide a suitable method for the early detection of osteoporosis.

Acoustical properties of 3D printed thermoplastics

With focused ultrasound (FUS) gaining popularity as a therapeutic modality for brain diseases, the need for skull phantoms that are suitable for evaluating FUS protocols is increasing. In the current study, the acoustical properties of several three-dimensional (3D) printed thermoplastic samples were evaluated to assess their suitability to mimic human skull and bone accurately. Samples were 3D printed using eight commercially available thermoplastic materials. The acoustic properties of the printed samples, including attenuation coefficient, speed of sound, and acoustic impedance, were investigated using transmission-through and pulse-echo techniques. The ultrasonic attenuation, estimated at a frequency of 1.1 MHz, varied from approximately 7 to 32 dB/cm. The frequency dependence of attenuation was described by a power law in the frequency range of 0.2-3.5 MHz, and the exponential index of frequency was found to vary from 1.30 to 2.24. The longitudinal velocity of 2.7 MHz sound waves was in the range of 1700-3050 m/s. The results demonstrate that thermoplastics could potentially be used for the 3D construction of high-quality skull phantoms.

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.

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.

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.

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.

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.

Nonlinear attenuation and dispersion in human calcaneus in vitro: statistical validation and relationships to microarchitecture

Through-transmission measurements were performed on 30 human calcaneus samples in vitro. Nonlinear attenuation and dispersion measurements were investigated by estimating 95% confidence intervals of coefficients of polynomial expansions of log magnitude and phase of transmission coefficients. Bone mineral density (BMD) was measured with dual x-ray absorptiometry. Microarchitecture was measured with microcomputed tomography. Statistically significant nonlinear attenuation and nonzero dispersion were confirmed for a clinical bandwidth of 300-750 kHz in 40%-43% of bone samples. The mean linear coefficient for attenuation was 10.3 dB/cm MHz [95% confidence interval (CI): 9.0-11.6 dB/cm MHz]. The mean quadratic coefficient for attenuation was 1.6 dB/cm MHz(2) (95% CI: 0.4-2.8 dB/cm MHz(2)). Nonlinear attenuation provided little information regarding BMD or microarchitecture. The quadratic coefficient for phase (which is related to dispersion) showed moderate correlations with BMD (r = -0.65; 95% CI: -0.82 to -0.36), bone surface-to-volume ratio (r = 0.47; 95% CI: 0.12-0.72) and trabecular thickness (r = -0.40; 95% CI: -0.67 to -0.03). Dispersion was proportional to bone volume fraction raised to an exponent of 2.1 ± 0.2, which is similar to the value for parallel nylon-wire phantoms (2.4 ± 0.2) and supports a multiple-scattering model for dispersion.

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.

Propagation of time-reversed Lamb waves in bovine cortical bone in vitro

The present study aims to investigate the propagation of time-reversed Lamb waves in bovine cortical bone in vitro. The time-reversed Lamb waves were successfully launched at 200 kHz in 18 bovine tibiae through a time reversal process of Lamb waves. The group velocities of the time-reversed Lamb waves in the bovine tibiae were measured using the axial transmission technique. They showed a significant correlation with the cortical thickness and tended to follow the theoretical group velocity of the lowest order antisymmetrical Lamb wave fairly well, consistent with the behavior of the slow guided wave in long cortical bones.

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.

Correlations of linear and nonlinear ultrasound parameters with density and microarchitectural parameters in trabecular bone

In the present study, correlations of linear and nonlinear ultrasound parameters (speed of sound, normalized broadband ultrasound attenuation, and nonlinear parameter B/A) with bone mineral density and microarchitectural parameters were investigated in 28 bovine femoral trabecular bone samples in vitro. All three ultrasound parameters exhibited relatively high correlation coefficients with the indexes of bone quantity (bone mineral density and bone volume fraction) and lower correlation coefficients with the remaining microarchitectural parameters. These results suggest that B/A, in addition to speed of sound and attenuation, may have potential as an index for the assessment of bone status and osteoporosis.