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

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.

Estimation of multipath transmission parameters for quantitative ultrasound measurements of bone

When applying quantitative ultrasound (QUS) measurements to bone for predicting osteoporotic fracture risk, the multipath transmission of sound waves frequently occurs. In the last 10 years, the interest in separating multipath QUS signals for their analysis awoke, and led to the introduction of several approaches. Here, we compare the performances of the two fastest algorithms proposed for QUS measurements of bone: the modified least-squares Prony method (MLSP), and the space alternating generalized expectation maximization algorithm (SAGE) applied in the frequency domain. In both approaches, the parameters of the transfer functions of the sound propagation paths are estimated. To provide an objective measure, we also analytically derive the Cramér-Rao lower bound of variances for any estimator and arbitrary transmit signals. In comparison with results of Monte Carlo simulations, this measure is used to evaluate both approaches regarding their accuracy and precision. Additionally, with simulations using typical QUS measurement settings, we illustrate the limitations of separating two superimposed waves for varying parameters with focus on their temporal separation. It is shown that for good SNRs around 100 dB, MLSP yields better results when two waves are very close. Additionally, the parameters of the smaller wave are more reliably estimated. If the SNR decreases, the parameter estimation with MLSP becomes biased and inefficient. Then, the robustness to noise of the SAGE clearly prevails. Because a clear influence of the interrelation between the wavelength of the ultrasound signals and their temporal separation is observable on the results, these findings can be transferred to QUS measurements at other sites. The choice of the suitable algorithm thus depends on the measurement conditions.

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.

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.

Velocity dispersion in trabecular bone: influence of multiple scattering and of absorption

Speed of sound measurements are widely used clinically to assess bone strength. Trabecular bone is an attenuating composite material in which negative values of velocity dispersion have been measured, this behavior remaining poorly explained physically. The aim of this work is to describe the ultrasonic propagation in trabecular bone modeled by infinite cylinders immersed in a saturating matrix, and to derive the physical determinants of velocity dispersion. A homogenization model accounting for the coupling of multiple scattering and absorption phenomena allows the computation of phase velocity and of dispersion while varying bone properties. The present model is adapted from the generalized self-consistent method developed in the work of Yang and Mal [(1994). "Multiple-scattering of elastic waves in a fiber-reinforced composite," J. Mech. Phys. Solids 42, 1945-1968]. It predicts negative values of velocity dispersion, in agreement with experimental results obtained in phantoms mimicking trabecular bone. In trabecular bone, mostly negative and also positive values of velocity dispersion are predicted by the model, which span within the range of values measured experimentally. Scattering effects are responsible for the negative values of dispersion, whereas the frequency dependence of the absorption coefficient in bone marrow and/or in the trabeculae results in an increase in dispersion, which may then become positive.

Ultrasonic velocity dispersion in bovine cortical bone: an experimental study

Cortical bone quality is determinant in bone fragility and its ultrasonic evaluation has become possible in clinical practice. However, the interaction between a broadband ultrasonic pulse and this complex multiscale medium remains poorly understood. The frequency dependence of phase velocity, which may impact clinical measurements, has been sparsely investigated. Our objective is to evaluate the determinants of the frequency dependence of phase velocity in bovine femoral cortical bone samples using an in vitro ultrasonic transmission device. The apparent phase velocity varies quasilinearly on a 1 MHz restricted bandwidth around 4 MHz. After compensating for diffraction effects, significant differences in velocity dispersion are obtained according to the anatomical location. The microstructure of each sample is determined using an optical microscope, which allows assessing the dependence of dispersion on the type of bone microstructure. Mostly positive but also negative values of dispersion are measured. Negative dispersion is mainly obtained in samples constituted of mixed microstructure, which may be explained by phase cancellation effects due to the presence of different microstructures within the same sample. Dispersion is shown to be related to broadband ultrasonic attenuation values, especially in the radial direction. Results are compared with the local Kramers-Kronig relationships.

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

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