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.     

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

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

Finite element modelling—predictor of implant survival?

The cancellous bone stresses surrounding proximal femoral prostheses were investigated using the finite element method and the results correlated with clinical subsidence data for similar implant configurations. The finite element study has shown that press-fit prostheses generate significantly higher cancellous bone stresses than bonded (cemented and HA coated) prostheses. The cancellous bone stresses surrounding press-fit implants are sensitive to the coefficient of friction, with up to a 60% decrease observed when the coefficient of friction was increased from 0 to 0.4. Resecting the femoral neck generally increased the cancellous bone stresses however varying the thickness of the cement mantle had little or no effect. Good correlation was found between the finite element results and the clinically measured subsidence data. Implant configurations generating higher cancellous bone stresses were those which subsided the most. This observation suggests that it may be possible to use the initial cancellous bone stresses to predict the likelihood of migration and hence late aseptic loosening.     

Development of a numerical cancellous bone model for finite-difference time-domain simulations of ultrasound propagation

The trabecular frame in cancellous bone has numerous porous spaces of various sizes and shapes. Their continual arrangement changes with position in the bone. Assuming that the complicated pore space is the aggregation of spherical pores, in this study, the trabecular structure was analyzed using a three-dimensional (3-D) X-ray microcomputed tomography (muCT) image. Analysis involved a 3-D cancellous bone model developed for numerical simulations of ultrasound propagation. In this model, the trabecular structure was simplified by regularly arranging spherical pores in a solid bone. Using a viscoelastic, finite-difference, time-domain (FDTD) method with the simplified cancellous bone model, ultrasound pulse waveforms propagating through cancellous bone were simulated in two cases of the propagations parallel and perpendicular to the main trabecular orientation. The porosity dependences of the propagation properties, attenuation, and propagation speed were derived from the simulated waveforms. Comparisons with simulated results using the realistic cancellous bone model reconstructed from a 3-D muCT image, assisted to further validate this simplified model.     

Propagation of ultrasonic waves through demineralized cancellous bone

Ultrasonic velocity is determined in a number of bovine cancellous (spongy) bone samples by using a double-probe-through-transmission ultrasonic pulse technique. The ultrasonic velocity, total mineral content, bone density, and solid volume fraction of the specimen were determined. The relation between fast velocity and each of the other parameters was examined to explore the best correlation using linear, logarithmic, power, and exponential relationships. There is a strong positive relationship between ultrasonic velocity and each of the other parameters. The exponential model fits the data better than the linear model, logarithmic model, and power model. Biot's theory also is used to predict the velocity of ultrasound in the demineralized bone. It is shown that the transmission of ultrasonic pulses in the cancellous bone samples can be adequately described using Biot's theory. The different parameters occurring in the Biot theory have been measured independently, and the calculation has been compared with measured velocity of water-saturated bone samples. The correlation coefficients for regression analysis between the experimental velocities and those predicted by Biot's theory are greater than 0.86.     

Numerical analysis of variability in ultrasound propagation properties induced by trabecular microstructure in cancellous bone

The manner by which the trabecular microstructure affects the propagation of ultrasound waves through cancellous bone is numerically investigated by finite difference time-domain (FDTD) simulation. Sixteen 3-D numerical models of 6.45times6.45times6.45 mm with a voxel size of 64.5 mum are reconstructed using a 3-D microcomputed tomographic (muCT) image taken from a bovine cancellous bone specimen of approximately 20times20times9 mm. All cancellous bone models have an oriented trabecular structure, and their trabecular elements are gradually eroded to increase the porosity using an image processing technique. Three erosion procedures are presented to realize various changes in the trabecular microstructure with increasing porosity. FDTD simulations of the ultrasound pulse waves propagating through the cancellous bone models at each eroded step are performed in 2 cases of the propagations parallel and perpendicular to the major trabecular orientation. The propagation properties of the wave amplitudes and propagation speeds are derived as a function of the porosity, and their variability due to the trabecular microstructure is revealed. To elucidate an effect of the microstructure, the mean intercept length (MIL), which is a microstructural parameter, is introduced, and the correlations of the propagation properties with the MILs of the trabecular elements and pore spaces are investigated.     

Application of the biot model to ultrasound in bone: direct problem

Ultrasonic wave propagation in human cancellous bone is considered using Biot's theory modified by the Johnson-Koplik-Dashen model for viscous exchange between fluid and structure. The transmission coefficient is derived for a slab of porous material. Experimental results for fast and slow waves transmitted through human cancellous bone samples are given and compared with theoretical predictions.     

The effects of frequency-dependent attenuation and dispersion on sound speed measurements: applications in human trabecular bone

Sound speed may be measured by comparing the transit time of a broadband ultrasonic pulse transmitted through an object with that transmitted through a reference water path. If the speed of sound in water and the thickness of the sample are known, the speed of sound in the object may be computed. To measure the transit time differential, a marker such as a zero-crossing, may be used. A sound speed difference between the object and water shifts all markers backward or forward. Frequency-dependent attenuation and dispersion may alter the spectral characteristics of the waveform, thereby distorting the locations of markers and introducing variations in sound-speed estimates. Theory is derived to correct for this distortion for Gaussian pulses propagating through linearly attenuating, weakly dispersive media. The theory is validated using numerical analysis, measurements on a tissue mimicking phantom, and on 24 human calcaneus samples in vitro. Variations in soft tissue-like media are generally not exceptionally large for most applications but can be substantial, particularly for high bandwidth pulses propagating through media with high attenuation coefficients. At 500 kHz, variations in velocity estimates in bone can be very substantial, on the order of 40 to 50 m/s because of the high attenuation coefficient of bone. In trabecular bone, the effects of frequency-dependent attenuation are considerable, and the effects of dispersion are negligible.     

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.     

Modelling optical properties of soft tissue by fractal distribution of scatterers

Abstract

A knowledge of the local refractive index variations and size distribution of scatterers in biological tissue is required to understand the physical processes involved in light-tissue interaction. This paper describes a method for modelling the complicated soft tissue, based on the fractal approach, permitting numerical evaluation of the phase functions and four optical properties of tissue—scattering coefficient, reduced scattering coefficient, backscatter-ing coefficient, and anisotropy factor—by the use of the Mie scattering theory. A key assumption of the model is that refractive index variations caused by microscopic tissue elements can be treated as particles with size distribution according to the power law. The model parameters, such as refractive index, incident wavelength, and fractal dimension, that are likely to affect the predictions of optical properties are investigated. The results suggest that the fractal dimension used to describe how biological tissue can be approximated by particle distribution is highly dependent on how the continuous distribution is discretized. The optical properties of the tissue significantly depend on the refractive index of tissue, implying that the refractive index of the particles should be carefully chosen in the model in order accurately to predict the optical properties of the tissue concerned.     

Exploration of trabecular bone nonlinear elasticity using time-of-flight modulation

Bone tissue contains microcracks that may affect its mechanical properties as well as the whole trabecular structure. The relationship between crack density and bone strength is nevertheless poorly understood. Linear ultrasound techniques being almost insensitive to the level of damage, we propose a method to measure acoustic non- linearity in trabecular bone using time-of-flight modulation (TOFM) measurements. Ultrasonic short bursts times-of- flight (TOF) are modulated as a result of nonlinear interaction with a low-frequency (LF) wave in the medium. TOF variations are directly related to elastic modulus variations. Classical and nonclassical nonlinear parameters beta, delta, and alpha can be derived from these measurements. The method was validated in materials with classical, quadratic, nonlinear elasticity. In dense trabecular bone region, TOFM related to classical, quadratic, nonlinear elasticity as a function of the LF pressure exhibits tension-compression asymmetry. The TOFM amplitude measured in dense areas of trabecular bone is almost one order of magnitude higher than in a low-density area, but the linear parameters show much smaller variations: 5% for ultrasound propagation velocity and 100% for broadband ultrasonic attenuation (BUA). In high-density trabecular bone regions, beta depends on the LF pressure amplitude and can reach 400 at 50 kPa.     

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.     

Scatter correction of transmission near-infrared spectra by photon migration data: quantitative analysis of solids

The scope of this work is a new methodology to correct conventional near-infrared (NIR) data for scattering effects. The technique aims at measuring the absorption coefficient of the samples rather than the total attenuation measured in conventional NIR spectroscopy. The main advantage of this is that the absorption coefficient is independent of the path length of the light inside the sample and therefore independent of the scattering effects. The method is based on time-resolved spectroscopy and modeling of light transport by diffusion theory. This provides an independent measure of the scattering properties of the samples and therefore of the path length of light. This yields a clear advantage over other preprocessing techniques, where scattering effects are estimated and corrected for by using the shape of the measured spectrum only. Partial least squares (PLS) calibration models show that, by using the proposed evaluation scheme, the predictive ability is improved by 50% as compared to a model based on conventional NIR data alone. The method also makes it possible to predict the concentration of active substance in samples with other physical properties than the samples included in the calibration model.     

Tests of backscatter coefficient measurement using broadband pulses

An adaptation to a data reduction method is outlined for determining backscatter coefficients, eta, when broad-bandwidth pulses are employed. The accuracy of these eta values is assessed with well-characterized phantoms, for which backscatter coefficients based on their physical properties have been independently calculated. One phantom produces Rayleigh-like scattering, where the backscatter coefficient varies smoothly with frequency over the analysis bandwidth. A second phantom exhibits local maxima and minima in the scattering function versus frequency due to the presence of millimeter-sized graphite gel spheres in a gel background. The method was found to produce accurate results using time gate durations as small as 2 mus, although better accuracy is obtained for longer gate durations, particularly when the sample exhibits resonance peaks in backscatter versus frequency. Use of a Hamming window in place of a rectangular window extends the accuracy near the upper and lower limits of the frequency range.     

评价松质骨状况的一种背散射频谱方法

采用超声背散射信号的质心偏移量来评价松质骨,并对牛胫骨和人体跟骨中背散射信号的质心偏移量与松质骨表观密度的关系,以及人体跟骨松质骨中背散射信号频谱质心位置与年龄的关系进行了分析讨论。分析结果表明,随松质骨表观密度的增大,背散射信号频谱的质心向低频方向移动;随年龄的增大,质心位置越接近于发射超声的中心频率。根据超声背散射信号质心偏移量的大小,可用于评价松质骨健康状况。     

Quantitative measurements of apoptotic cell properties using acoustic microscopy

Time-resolved acoustic microscopy was used to measure properties of cells such as the thickness, sound velocity, acoustic impedance, density, bulk modulus, and attenuation, before and after apoptosis. A total of 12 cells were measured, 5 apoptotic and 7 non-apoptotic. Measurements made at 375 MHz showed a statistically significant increase in the cell thickness from 13.6 ± 3.1 μm to 17.3 ± 1.6 μm, and in the attenuation from 1.08 ± 0.21 dB/cm/MHz to 1.74 ± 0.36 dB/cm/MHz. The other parameters, such as the sound velocity, density, acoustic impedance, and bulk modulus remained similar within experimental error. Acoustic images obtained at 1.0 GHz showed increased RF-signal backscatter and a clear delineation of the nucleus and cytoplasm from apoptotic cells compared with non-apoptotic cells. Extensive activity was observed optically and acoustically within apoptotic cells. Acoustic measurements made one minute apart showed variations in the ultrasonic backscatter but not attenuation in the cells, which indicated rapid structural changes were occurring but not changes in bulk composition. The normalized crosscorrelation coefficient was used to quantify the variations in the backscatter RF-signal during apoptosis by comparing the first RF signal measured to each successive RF signal every 10 s. A coefficient of 1 indicates strong correlation, whereas a coefficient of 0 indicates no correlation. An average correlation coefficient of 0.93 ± 0.05 was measured for non-apoptotic cells, compared with 0.68 ± 0.17 for apoptotic cells, indicating that the RF signal as a function of time varied rapidly during apoptosis.     

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

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

Phase function effects on oceanic light fields

Numerical simulations show that underwater radiances, irradiances, and reflectances are sensitive to the shape of the scattering phase function at intermediate and large scattering angles, although the exact shape of the phase function in the backscatter directions (for a given backscatter fraction) is not critical if errors of the order of 10% are acceptable. We present an algorithm for generating depth- and wavelength-dependent Fournier-Forand phase functions having any desired backscatter fraction. Modeling of a comprehensive data set of measured inherent optical properties and radiometric variables shows that use of phase functions with the correct backscatter fraction and overall shape is crucial to achieve model-data closure.     

Ultrasonic scanner for in vivo measurement of cancellous bone properties from backscattered data

A dedicated ultrasonic scanner for acquiring RF echoes backscattered from the trabecular bone was developed. The design of device is based on the goal of minimizing of custom electronics and computations executed solely on the main computer processor and the graphics card. The electronic encoder-digitizer module executing all of the transmission and reception functions is based on a single low-cost field programmable gate array (FPGA). The scanner is equipped with a mechanical sector-scan probe with a concave transducer with 50 mm focal length, center frequency of 1.5 MHz and 60% bandwidth at -6 dB. The example of femoral neck bone examination shows that the scanner can provide ultrasonic data from deeply located bones with the ultrasound penetrating the trabecular bone up to a depth of 20 mm. It is also shown that the RF echo data acquired with the scanner allow for the estimation of attenuation coefficient and frequency dependence of backscattering coefficient of trabecular bone. The values of the calculated parameters are in the range of corresponding in vitro data from the literature but their variation is relatively high.     

Characterization of trabecular bone using the backscattered spectral centroid shift

Ultrasonic attenuation in bone in vivo is generally measured using a through-transmission method at the calcaneus. Although attenuation in calcaneus has been demonstrated to be a useful predictor for osteoporotic fracture risk, measurements at other clinically important sites, such as hip and spine, could potentially contain additional useful diagnostic information. Through-transmission measurements may not be feasible at these sites due to complex bone shapes and the increased amount of intervening soft tissue. Centroid shift from the backscattered signal is an index of attenuation slope and has been used previously to characterize soft tissues. In this paper, centroid shift from signals backscattered from 30 trabecular bone samples in vitro were measured. Attenuation slope also was measured using a through-transmission method. The correlation coefficient between centroid shift and attenuation slope was -0.71. The 95% confidence interval was (-0.86, -0.47). These results suggest that the backscattered spectral centroid shift may contain useful diagnostic information potentially applicable to hip and spine.