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.     

Singular spectrum analysis applied to backscattered ultrasound signals from in vitro human cancellous bone specimens

Mean scatterer spacing (MSS) holds particular promise for the detection of changes in quasiperiodic tissue microstructures such as may occur during development of disease in the liver, spleen, or bones. Many techniques that may be applied for MSS estimation (temporal and spectral autocorrelation, power spectrum and cepstrum, higher order statistics, and quadratic transformation) characterize signals that contain a mixture of periodic and nonperiodic contributions. In contrast, singular spectrum analysis (SSA), a method usually applied in nonlinear dynamics, first identifies components of signals corresponding to periodic structures and, second, identifies dominant periodicity. Thus, SSA may better separate periodic structures from nonperiodic structures and noise. Using an ultrasound echo simulation model, we previously demonstrated SSA's potential to identify MSS of structures in quasiperiodic scattering media. The current work aims to observe the behavior of MSS estimation by SSA using ultrasound measurements in phantom materials (two parallel, nylon-line phantoms and four foam phantoms of different densities). The SSA was able to estimate not only the nylon-line distances but also nylon-line thickness. The method also was sensitive to the average pore-size differences of the four sponges. The algorithms then were applied to characterize human cancellous bone microarchitectures. Using 1-MHz center-frequency, radio-frequency ultrasound signals, MSS was measured in 24 in vitro bone samples and ranged from 1.0 to 1.7 mm. The SSA MSS estimates correlate significantly to MSS measured independently from synchrotron microtomography, r2 = 0.68. Thus, application of SSA to backscattered ultrasound signals seems to be useful for providing information linked to tissue microarchitecture that is not evident from clinical images.     

Correlation of cancellous bone microarchitectural parameters from microCT to CT number and bone mechanical properties

Cancellous bone density alone is not a sufficient predictor of bone mechanical stiffness and strength. Microarchitectural parameters of bone may improve the accuracy of prediction. It is well established that bone density can be inferred from the intensities of clinical CT image datasets, however it is unknown if microarchitectural parameters manifest any relationship to the image intensities. Thirty-eight porcine cancellous bone cubes were subjected to clinical CT and microCT imaging to obtain the CT number and microarchitectural parameters respectively. They were subsequently compressed to failure to obtain the mechanical properties. Linear regression analyses were carried out for the three testing modalities to determine any possible correlations. Significant correlations (R² ≥ 0.5) were obtained between Hounsfield units and (1) volume fraction (BV/TV), (2) bone trabecular pattern (Tb.Pf), (3) trabeculae spacing (Tb.Sp), (4) structure model index (SMI) and (5) trabeculae number (Tb.N). Significant correlations were also discerned for microarchitectural parameters and mechanical properties. In conclusion, we established linear regression models between image-measured density in terms of Hounsfield units (HU) and microarchitectural parameters as well as models between cancellous bone microarchitectural parameters and mechanical properties. It should be noted that both density and microarchitectural parameters important to bone research could be inferred from clinical CT images.     

Ultrasonic assessment of cortical bone thickness in vitro and in vivo

In osteoporosis, total bone mass decreases and the thickness of the cortical layer diminishes in the shafts of the long bones. In this study, a simple ultrasonic in vivo method for determining the thickness of the cortical bone layer was applied, and the suitability of two different signal analysis techniques, i.e., envelope and cepstral methods, for measuring cortical thickness was compared. The values of cortical thickness, as determined with both techniques, showed high linear correlations (r ges 0.95) with the thickness values obtained from in vitro measurements with a caliper or in vivo measurements by peripheral quantitative CT (pQCT). No systematic errors that could be related to the cortical thickness were found. The in vivo accuracy of the measurements was 6.6% and 7.0% for the envelope and cepstral methods, respectively. Further, the in vivo precision for the envelope and cepstral methods was 0.26 mm and 0.28 mm, respectively. Although the results are similar for both of the techniques, the simplicity of the envelope method makes it more attractive for clinical applications. In conclusion, a simple ultrasound measurement provides an accurate estimate of the cortical bone thickness. The techniques investigated may have clinical potential for osteoporosis screening and therefore warrant more extensive clinical investigations with healthy and osteoporotic individuals.     

Ultrasonic phased-array scanner with digital echo synthesis for Doppler echocardiography

For the purpose of the quantitative assessment of subtle disease processes in the cardiovascular system an electronically steered sector scanner that combines echographic imaging and Doppler blood velocity measurements has been developed. The integrated operation of a fast Fourier transform (FFT) Doppler signal processor for the simultaneous blood velocity evaluation of 64 individual gates is among the specific design goals. The instrument incorporates an unusually high degree of digital signal processing, which allows for high integration density, easy manufacturing and high reliability in future designs. The complex Doppler spectra are determined for each of the 64 Doppler gates in real time, and the subsequent computation of the first moment provides a reliable estimate of the mean blood flow velocities at the respective locations. The instantaneous velocity profile along the Doppler beam is displayed together with the calculated volume flow rate and a range-selected complete frequency spectrum. Results of both in vitro and in vivo tests indicate that in the future, a higher degree of digital signal processing could be implemented in complex ultrasonic systems.     

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.     

Velocity dispersion of acoustic waves in cancellous bone

Measurement of ultrasonic attenuation and velocity in cancellous bone are being applied to aid diagnosis of women with high fracture risk due to osteoporosis. However, velocity dispersion in cancellous bone has received little attention up to now. The overall goal of this research was to characterize the velocity dispersion of human cancellous bone based on a spectral analysis of ultrasound transmitted through the bone specimens. We have followed a systematic approach, beginning with the investigation of a test material, moving on to the investigation of bone specimens. Particular attention is given to diffraction effect, a potential source of artifacts. Parametric images of phase velocity (measured at the center frequency of the pulse spectrum), slope of attenuation coefficient (dB/cm/MHz) and velocity dispersion were obtained by scanning 15 bone specimens. We have demonstrated that the diffraction effect is negligible in the useful frequency bandwidth, and that the ultrasonic parameters reflect intrinsic acoustic properties of bone tissue. The measured attenuation showed approximately linear behavior over the frequency range 200 to 600 kHz. Velocity dispersion of cancellous bone in the frequency range 200 to 600 kHz was unexpectedly found to be either negative or positive and not correlated with the slope of attenuation coefficient. There was a highly significant correlation between the slope of attenuation coefficient and phase velocity at the center frequency of the spectrum. This behavior contrasts with other biological or nonbiological materials where the local form of the Kramers-Kronig relationship provides accurate prediction of velocity dispersion from the experimental frequency dependent-attenuation for unbounded waves.     

Young's modulus,density and material properties in cancellous bone over a large density range

Data on the compressive properties of cancellous bone cubes with a large range of densities (relative densities compared with compact bone of 0.04–0.60) show that the exponent relating the Young's modulus to the density is close to quadratic and that it is improbable that the material Young's modulus of our specimens was less than 8 GPa, and was probably considerably higher.     

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。     

Ultrasonic on-machine measurement for internal topographies

The integration of metrology into the manufacturing process is becoming increasingly important for production technology. The measurement directly on machine tools is especially improving manufacturing strategies. So far, optical or tactile measuring systems are the state-of-the-art for dimensional measurements in process metrology. However, the wall thickness of structures with inner cavities cannot be measured with these systems. Owing to these deficits, an ultrasonic system was integrated into the peripheral equipment of a machine tool. Both the extensive signal processing of the acoustic echoes and the developed software tool ' w -sonic' are discussed. The aim is to show the potential of the ultrasonic in-line measurement. A practical application for the individual machining of gas cylinders and initial results are also presented.     

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.     

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.     

Ultrasound research scanner for real-time synthetic aperture data acquisition

Conventional ultrasound systems acquire ultrasound data sequentially one image line at a time. The architecture of these systems is therefore also sequential in nature and processes most of the data in a sequential pipeline. This often makes it difficult to implement radically different imaging strategies on the platforms and makes the scanners less accessible for research purposes. A system designed for imaging research flexibility is the prime concern. The possibility of sending out arbitrary signals and the storage of data from all transducer elements for 5 to 10 seconds allows clinical evaluation of synthetic aperture and 3D imaging. This paper describes a real-time system specifically designed for research purposes. The system can acquire multichannel data in real-time from multi-element ultrasound transducers, and can perform some real-time processing on the acquired data. The system is capable of performing real-time beamforming for conventional imaging methods using linear, phased, and convex arrays. Image acquisition modes can be intermixed, and this makes it possible to perform initial trials in a clinical environment with new imaging modalities for synthetic aperture imaging, 2D and 3D B-mode, and velocity imaging using advanced coded emissions. The system can be used with 128-element transducers and can excite 128 transducer elements and receive and sample data from 64 channels simultaneously at 40 MHz with 12-bit precision. Two-to-one multiplexing in receive can be used to cover 128 receive channels. Data can be beamformed in real time using the system's 80 signal processing units, or it can be stored directly in RAM. The system has 16 Gbytes RAM and can, thus, store more than 3.4 seconds of multichannel data. It is fully software programmable and its signal processing units can also be reconfigured under software control. The control of the system is done over a 100-Mbits/s Ethernet using C and Matlab. Programs for doing, e.g., B-mode imaging can be written directly in Matlab and executed on the system over the net from any workstation running Matlab. The overall system concept is presented along with its implementation and examples of B-mode and in vivo synthetic aperture flow imaging.     

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.     

An improved method for the measurement of mechanical properties of bone by nanoindentation

Nanoindentation is widely used to measure the mechanical properties of bio-tissues. However, viscoelastic effects during the nanoindentation are seldom considered rigorously, although they are in general very significant in bio-tissues. In this study, a recently developed method for correcting the viscoelastic effects during nanoindentation is applied to mice bone samples. This method is found to yield reliable elastic modulus and hardness results from forelimb and femur cortical bone samples of C57 BL/6N and ICR mice. The creep properties of the samples are also characterized by a novel procedure using nanoindentation. The measured mechanical properties correlate well with the calcium content of the bone samples.     

Ultrasonic guided waves in bone

Recent progress in quantitative ultrasound (QUS) has shown increasing interest toward measuring long bones by ultrasonic guided waves. This technology is widely used in the field of nondestructive testing and evaluation of different waveguide structures. Cortical bone provides such an elastic waveguide and its ability to sustain loading and resist fractures is known to be related to its mechanical properties at different length scales. Because guided waves could yield diverse characterizations of the bone's mechanical properties at the macroscopic level, the method of guided waves has a strong potential over the standardized bone densitometry as a tool for bone assessment. Despite this, development of guided wave methods is challenging, e.g., due to interferences and rnultiparametric inversion problems. This paper discusses the promises and challenges related to bone characterization by ultrasonic guided waves.     

Recovery of parameters of cancellous bone by acoustic interrogation

The parameter recovery problem for cancellous bone by acoustic interrogation is investigated numerically. Biot’s equations coupled with boundary integral equations are used to model ultrasound propagation through a bone sample immersed in a water tank. The mathematical formulation for two-dimensional orthotropic bone is presented, but numerical results are only discussed in the isotropic case. The inversion procedure consists in minimizing some error on the pressure at measurement points located outside the bone sample. For this purpose, two different minimization algorithms are considered. A number of numerical tests are performed for a range of frequencies, which demonstrate the model’s ability to recover some bone parameters with satisfactory accuracy.     

Fast-Fourier-domain delay line for in vivo optical coherence tomography with a polygonal scanner

We demonstrate in vivo optical coherence tomography using a Fourier-domain optical delay line constructed with a commercially available polygonal scanner. The 20-faceted polygonal mirror array, capable of scanning at rates up to 15 kHz, is implemented at 4 kHz to acquire 500 x 500 pixel images at 8 frames/s with a signal-to-noise ratio of 80 dB. Features of this delay line include scalability to high repetition rates, 98.6% linearity in group delay over 2 mm, and bandwidth support exceeding 150 nm. Images are obtained in an animal model (Xenopus laevis), and limitations due to phase-delay nonlinearity and polygon asymmetry are discussed.