The effect of trabecular material properties on the frequency dependence of backscatter from cancellous 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).

Liver Steatosis Assessed by Controlled Attenuation Parameter (CAP) Measured with the XL Probe of the FibroScan: A Pilot Study Assessing Diagnostic Accuracy

To assess liver steatosis, the controlled attenuation parameter (CAP; giving an estimate of ultrasound attenuation ∼3.5 MHz) is available with the M probe of the FibroScan. We report on the adaptation of the CAP for the FibroScan XL probe (center frequency 2.5 MHz) without modifying the range of values (100-400 dB/m). CAP validation was successfully performed on Field II simulations and on tissue-mimicking phantoms. In vivo performance was assessed in a cohort of 59 patients spanning the range of steatosis. In vivo reproducibility was good and similar with both probes. The area under receiver operative characteristic curve was equal to 0.83/0.84 and 0.92/0.91 for the M/XL probes to detect >2% and >16% liver fat, respectively, as assessed by magnetic resonance imaging. Patients can now be assessed simultaneously for steatosis and fibrosis using the FibroScan, regardless of their morphology.

Ultrasonic evaluation of bone quality in cadaver ilia

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

Characterization of the trabecular bone structure using frequency modulated ultrasound pulse

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

Mechanisms for attenuation in cancellous-bone-mimicking phantoms

Broadband ultrasound attenuation (BUA) in cancellous bone is useful for prediction of osteoporotic fracture risk, but its causes are not well understood. To investigate attenuation mechanisms, 9 cancellous-bone-mimicking phantoms containing nylon filaments (simulating bone trabeculae) embedded within soft-tissue-mimicking fluid (simulating marrow) were interrogated. The measurements of frequency-dependent attenuation coefficient had 3 separable components: 1) a linear (with frequency) component attributable to absorption in the soft-tissue-mimicking fluid, 2) a quasilinear (with frequency) component, which may include absorption in and longitudinal-shear mode conversion by the nylon filaments, and 3) a nonlinear (with frequency) component, which may be attributable to longitudinal-longitudinal scattering by the nylon filaments. The slope of total linear (with frequency) attenuation coefficient (sum of components #1 and #2) versus frequency was found to increase linearly with volume fraction, consistent with reported measurements on cancellous bone. Backscatter coefficient measurements in the 9 phantoms supported the claim that the nonlinear (with frequency) component of attenuation coefficient (component #3) was closely associated with longitudinal-longitudinal scattering. This work represents the first experimental separation of these 3 components of attenuation in cancellous bone-mimicking phantoms.

Ultrasonic scattering from cancellous bone: a review

This paper reviews theory, measurements, and computer simulations of scattering from cancellous bone reported by many laboratories. Three theoretical models (binary mixture, Faran cylinder, and weak scattering) for scattering from cancellous bone have demonstrated some consistency with measurements of backscatter. Backscatter is moderately correlated with bone mineral density in human calcaneus in vitro (r(2) = 0.66 - 0.68). Backscatter varies approximately as frequency cubed and trabecular thickness cubed in human calcaneus and femur in vitro. Backscatter from human calcaneus and bovine tibia exhibits substantial anisotropy. So far, backscatter has demonstrated only modest clinical utility. Computer simulation models have helped to elucidate mechanisms underlying scattering from cancellous bones.

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

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

Simplified inverse filter tracking algorithm for estimating the mean trabecular bone spacing

Ultrasonic backscatter signals provide useful information relevant to bone tissue characterization. Trabecular bone microstructures have been considered as quasi-periodic tissues with a collection of regular and diffuse scatterers. This paper investigates the potential of a novel technique using a simplified inverse filter tracking (SIFT) algorithm to estimate mean trabecular bone spacing (MTBS) from ultrasonic backscatter signals. In contrast to other frequency-based methods, the SIFT algorithm is a time-based method and utilizes the amplitude and phase information of backscatter echoes, thus retaining the advantages of both the autocorrelation and the cepstral analysis techniques. The SIFT algorithm was applied to backscatter signals from simulations, phantoms, and bovine trabeculae in vitro. The estimated MTBS results were compared with those of the autoregressive (AR) cepstrum and quadratic transformation (QT) . The SIFT estimates are better than the AR cepstrum estimates and are comparable with the QT values. The study demonstrates that the SIFT algorithm has the potential to be a reliable and robust method for the estimation of MTBS in the presence of a small signal-to-noise ratio, a large spacing variation between regular scatterers, and a large scattering strength ratio of diffuse scatterers to regular ones.

Predictions of the modified Biot-Attenborough model for the dependence of phase velocity on porosity in cancellous bone

The modified Biot-Attenborough (MBA) model for acoustic wave propagation in porous media has been found useful to predict wave properties in cancellous bone. The present study is aimed at applying the MBA model to predict the dependence of phase velocity on porosity in cancellous bone. The MBA model predicts a phase velocity that decreases nonlinearly with porosity. The optimum values for input parameters of the MBA model, such as compressional speed c(m) of solid bone and phase velocity parameter s(2), were determined by comparing the predictions with previously published measurements in human calcaneus and bovine cancellous bone. The value of the phase velocity parameter s(2)=1.23 was obtained by curve fitting to the experimental data for 53 human calcaneus samples only, assuming a compressional speed c(m)=2500 m/s of solid bone. The root-mean-square error (RMSE) of the curve fit was 15.3m/s. The optimized value of s(2) for all 75 cancellous bone samples including 22 bovine samples was 1.42 with a value of 55 m/s for the RMSE of the curve fit. The latter fit was obtained by using of a value of c(m)=3200 m/s. Although the MBA model relies on the empirical parameters determined from experimental data, it is expected that the model can be usefully employed as a practical tool in the field of clinical ultrasonic bone assessment.

Empirical angle-dependent Biot and MBA models for acoustic anisotropy in cancellous bone

The Biot and the modified Biot-Attenborough (MBA) models have been found useful to understand ultrasonic wave propagation in cancellous bone. However, neither of the models, as previously applied to cancellous bone, allows for the angular dependence of acoustic properties with direction. The present study aims to account for the acoustic anisotropy in cancellous bone, by introducing empirical angle-dependent input parameters, as defined for a highly oriented structure, into the Biot and the MBA models. The anisotropy of the angle-dependent Biot model is attributed to the variation in the elastic moduli of the skeletal frame with respect to the trabecular alignment. The angle-dependent MBA model employs a simple empirical way of using the parametric fit for the fast and the slow wave speeds. The angle-dependent models were used to predict both the fast and slow wave velocities as a function of propagation angle with respect to the trabecular alignment of cancellous bone. The predictions were compared with those of the Schoenberg model for anisotropy in cancellous bone and in vitro experimental measurements from the literature. The angle-dependent models successfully predicted the angular dependence of phase velocity of the fast wave with direction. The root-mean-square errors of the measured versus predicted fast wave velocities were 79.2 m s(-1) (angle-dependent Biot model) and 36.1 m s(-1) (angle-dependent MBA model). They also predicted the fact that the slow wave is nearly independent of propagation angle for angles about 50 degrees , but consistently underestimated the slow wave velocity with the root-mean-square errors of 187.2 m s(-1) (angle-dependent Biot model) and 240.8 m s(-1) (angle-dependent MBA model). The study indicates that the angle-dependent models reasonably replicate the acoustic anisotropy in cancellous bone.

The frequency dependence of ultrasonic velocity and the anisotropy of dispersion in both freshly excised and formalin-fixed myocardium

The objectives of this study were to measure the frequency dependence of the ultrasonic velocity in myocardium and to quantify the frequency dependence of phase velocity as a function of the insonification angle relative to the predominant direction of the myofibers. Broadband phase spectroscopy data were acquired, spanning a frequency range of 3 to 8 MHz. Measurements were made on 36 tissue specimens cored from 12 freshly excised lamb hearts and were repeated after fixation with formalin. Measured phase velocities were found to be well characterized by a logarithmic fit. For freshly excised myocardium, the dispersion over the 3 to 8 MHz bandwidth was dependent on the direction of insonification, ranging from 1.2 m/s change for perpendicular insonification (across the myofibers) to 3.7 m/s for parallel insonification (along the myofibers). The effects of formalin-fixation resulted in a significant increase in dispersion for perpendicular insonification, but did not appreciably alter the dispersion for parallel insonification.