Measurements of phase velocity and group velocity in human calcaneus

Review of the Low-Temperature Acoustic Properties of Water, Aqueous Solutions, Lipids, and Soft Biological Tissues

Existing data on the acoustic properties of low-temperature biological materials is limited and widely dispersed across fields. This makes it difficult to employ this information in the development of ultrasound applications in the medical field, such as cryosurgery and rewarming of cryopreserved tissues. In this review, the low-temperature acoustic properties of biological materials, and the measurement methods used to acquire them were collected from a range of scientific fields. The measurements were reviewed from the acoustic setup to thermal methodologies for samples preparation, temperature monitoring, and system insulation. The collected data contain the longitudinal and shear velocity, and attenuation coefficient of biological soft tissues and biologically relevant substances-water, aqueous solutions, and lipids-in the temperature range down to -50 °C and in the frequency range from 108 kHz to 25 MHz. The multiple reflection method (MRM) was found to be the preferred method for low-temperature samples, with a buffer rod inserted between the transducer and sample to avoid direct contact. Longitudinal velocity changes are observed through the phase transition zone, which is sharp in pure water, and occurs more slowly and at lower temperatures with added solutes. Lipids show longer transition zones with smaller sound velocity changes; with the longitudinal velocity changes observed during phase transition in tissues lying between these two extremes. More general conclusions on the shear velocity and attenuation coefficient at low-temperatures are restricted by the limited data. This review enhance knowledge guiding for further development of ultrasound applications in low-temperature biomedical fields, and may help to increase the precision and standardization of low-temperature acoustic property measurements.

Ultrasound Characterization of Cortical Bone Using Shannon Entropy

OBJECTIVE

Ultrasound backscattered signals encompass information on the microstructure of heterogeneous media such as cortical bone, in which pores act as scatterers and result in the scattering and multiple scattering of ultrasound waves. The objective of this study was to investigate whether Shannon entropy can be exploited to characterize cortical porosity.

METHODS

In the study described here, to demonstrate proof of concept, Shannon entropy was used as a quantitative ultrasound parameter to experimentally evaluate microstructural changes in samples with controlled scatterer concentrations made of a highly absorbing polydimethylsiloxane matrix (PDMS). Similar assessment was then performed using numerical simulations on cortical bone structures with varying average pore diameter (Ct.Po.Dm.), density (Ct.Po.Dn.) and porosity (Ct.Po.).

RESULTS

The results suggest that an increase in pore diameter and porosity lead to an increase in entropy, indicating increased levels of randomness in the signals as a result of increased scattering. The entropy-versus-scatterer volume fraction in PDMS samples indicates an initial increasing trend that slows down as the scatterer concentration increases. High levels of attenuation cause the signal amplitudes and corresponding entropy values to decrease drastically. The same trend is observed when porosity of the bone samples is increased above 15%.

CONCLUSION

Sensitivity of entropy to microstructural changes in highly scattering and absorbing media can potentially be exploited to diagnose and monitor osteoporosis.

Spatio-Spectral Ultrasound Characterization of Reflection and Transmission Through Bone With Temperature Dependence

Transcranial focused ultrasound (tFUS) is a promising approach for the treatment of neurological disorders. It has proven useful in several clinical applications, with promising outcomes reported in the recent literature. Furthermore, it is currently being investigated in a range of neuromodulation (NM) and ablative applications, including epilepsy. In this application, tFUS access through the temporal window is the key to optimizing the treatment safety and efficacy. Traditional approaches have utilized transducers with low operating frequencies for tFUS applications. Modern array transducers and driving systems allow for more intelligent use of the temporal window by exploiting the spatio-spectral transmission bandwidth to a specified target or targets within the brain. To demonstrate the feasibility of this approach, we have investigated the ultrasound reflection and transmission characteristics for different access points within the temporal window of human skull samples ex vivo. Different transmit-receive (Rx) configurations are used for characterization of the spatio-spectral variability in reflection and transmission through the temporal window. In this article, we show results from a dual-piston transducer set up in the frequency range of 2-7 MHz. Broadband pulses as well as synthesized orthogonal frequency division multiplexed (OFDM) waveforms were used. The latter was used to improve the magnitude and phase measurements in 100-kHz subbands within the 2-7 MHz spectral window. A temperature-controlled water bath was used to characterize the change in reflection and transmission characteristics with temperature in the 25°C-43°C range. The measured values of the complex reflection and transmission coefficients exhibited significant variations with space, frequency, and temperature. On the other hand, the measured transmission phase varied more with location and frequency, with smaller sensitivity to temperature. A measurement-based hybrid angular spectrum (HAS) simulation through the human temporal bone was used to demonstrate the dependence of focusing gain on the skull profile and spatial distribution of change of speed of sound (SOS) at different skull temperatures.

Tissue-mimicking phantoms for performance evaluation of photoacoustic microscopy systems

Phantom-based performance test methods are critically needed to support development and clinical translation of emerging photoacoustic microscopy (PAM) devices. While phantoms have been recently developed for macroscopic photoacoustic imaging systems, there is an unmet need for well-characterized tissue-mimicking materials (TMMs) and phantoms suitable for evaluating PAM systems. Our objective was to develop and characterize a suitable dermis-mimicking TMM based on polyacrylamide hydrogels and demonstrate its utility for constructing image quality phantoms. TMM formulations were optically characterized over 400-1100 nm using integrating sphere spectrophotometry and acoustically characterized using a pulse through-transmission method over 8-24 MHz with highly confident extrapolation throughout the usable band of the PAM system. This TMM was used to construct a spatial resolution phantom containing gold nanoparticle point targets and a penetration depth phantom containing slanted tungsten filaments and blood-filled tubes. These phantoms were used to characterize performance of a custom-built PAM system. The TMM was found to be broadly tunable and specific formulations were identified to mimic human dermis at an optical wavelength of 570 nm and acoustic frequencies of 10-50 MHz. Imaging results showed that tungsten filaments yielded 1.1-4.2 times greater apparent maximum imaging depth than blood-filled tubes, which may overestimate real-world performance for vascular imaging applications. Nanoparticles were detectable only to depths of 120-200 µm, which may be due to the relatively weaker absorption of single nanoparticles vs. larger targets containing high concentration of hemoglobin. The developed TMMs and phantoms are useful tools to support PAM device characterization and optimization, streamline regulatory decision-making, and accelerate clinical translation.

Polyacrylamide hydrogel phantoms for performance evaluation of multispectral photoacoustic imaging systems

As photoacoustic imaging (PAI) begins to mature and undergo clinical translation, there is a need for well-validated, standardized performance test methods to support device development, quality control, and regulatory evaluation. Despite recent progress, current PAI phantoms may not adequately replicate tissue light and sound transport over the full range of optical wavelengths and acoustic frequencies employed by reported PAI devices. Here we introduce polyacrylamide (PAA) hydrogel as a candidate material for fabricating stable phantoms with well-characterized optical and acoustic properties that are biologically relevant over a broad range of system design parameters. We evaluated suitability of PAA phantoms for conducting image quality assessment of three PAI systems with substantially different operating parameters including two commercial systems and a custom system. Imaging results indicated that appropriately tuned PAA phantoms are useful tools for assessing and comparing PAI system image quality. These phantoms may also facilitate future standardization of performance test methodology.

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.

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.

Biologically relevant photoacoustic imaging phantoms with tunable optical and acoustic properties

Established medical imaging technologies such as magnetic resonance imaging and computed tomography rely on well-validated tissue-simulating phantoms for standardized testing of device image quality. The availability of high-quality phantoms for optical-acoustic diagnostics such as photoacoustic tomography (PAT) will facilitate standardization and clinical translation of these emerging approaches. Materials used in prior PAT phantoms do not provide a suitable combination of long-term stability and realistic acoustic and optical properties. Therefore, we have investigated the use of custom polyvinyl chloride plastisol (PVCP) formulations for imaging phantoms and identified a dual-plasticizer approach that provides biologically relevant ranges of relevant properties. Speed of sound and acoustic attenuation were determined over a frequency range of 4 to 9 MHz and optical absorption and scattering over a wavelength range of 400 to 1100 nm. We present characterization of several PVCP formulations, including one designed to mimic breast tissue. This material is used to construct a phantom comprised of an array of cylindrical, hemoglobin-filled inclusions for evaluation of penetration depth. Measurements with a custom near-infrared PAT imager provide quantitative and qualitative comparisons of phantom and tissue images. Results indicate that our PVCP material is uniquely suitable for PAT system image quality evaluation and may provide a practical tool for device validation and intercomparison.

Effect of alumina composition and surface integrity in alumina/epoxy composites on the ultrasonic attenuation properties

We report a method of fabricating backing blocks for ultrasonic imaging transducers, using alumina/epoxy composites. Backing blocks contain scatterers such as alumina particles interspersed in the epoxy matrix for the effective scattering and attenuation of ultrasound. Here, the surface integrity can be an issue, where the composite material may be damaged during machining because of differences in strength, hardness and brittleness of the hard alumina particles and the soft epoxy matrix. Poor surface integrity results in the formation of air cavities between the backing block and the piezoelectric element upon assembly, hence the increased reflection off the backing block and the eventual degradation in image quality. Furthermore, with an issue of poor surface integrity due to machining, it is difficult to increase alumina as scatterers more than a specific mass fraction ratio. In this study, we increased the portion of alumina within epoxy matrix by obtaining an enhanced surface integrity using a net shape fabrication method, and verified that this method could allow us to achieve higher ultrasonic attenuation. Backing blocks were net-shaped with various mass fractions of alumina to characterize the formability and the mechanical properties, including hardness, surface roughness and the internal micro-structure, which were compared with those of machined backing blocks. The ultrasonic attenuation property of the backing blocks was also measured.

Mechanical and thermal properties of γ-Mg2SiO4 under high temperature and high pressure conditions such as in mantle: A first principles study

γ-Mg2SiO4 is an important mineral in mantle, and our knowledge on its mechanical and thermal properties is critical for many areas of geological sciences. In this work, the crystal structure of γ-Mg2SiO4 under high temperature and high pressure conditions is optimized by using the GOMASC method, and the total energy, thermal expansion coefficients, and elastic constants at different temperature and pressure conditions are obtained. On the basis of phonon spectrum, group velocity, phase velocity, Grüneisen parameter, and thermal conductivity are calculated for γ-Mg2SiO4 under high temperature and high pressure conditions. These calculated results can provide an important reference for geological research.

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.

Dependences of ultrasonic properties on frequency and trabecular spacing in trabecular-bone-mimicking phantoms

The dependences of ultrasonic properties on the frequency and the trabecular spacing were investigated in 20 trabecular-bone-mimicking phantoms consisting of cellular copper foams. The strong slow waves were consistently observed in the signals transmitted through all of the phantoms. The frequency-dependent phase velocity and attenuation coefficient of the slow wave were measured at frequencies from 0.7 to 1.3 MHz. The phase velocity decreased approximately linearly with increasing frequency while the attenuation coefficients increased with increasing frequency. The phase velocity increased monotonically with increasing trabecular spacing from 1337 to 2931 μm while the attenuation coefficient decreased with increasing spacing.

Fast and slow wave detection in bovine cancellous bone in vitro using bandlimited deconvolution and Prony's method

Fast and slow waves were detected in a bovine cancellous bone sample for thicknesses ranging from 7 to 12 mm using bandlimited deconvolution and the modified least-squares Prony's method with curve fitting (MLSP + CF). Bandlimited deconvolution consistently isolated two waves with linear-with-frequency attenuation coefficients as evidenced by high correlation coefficients between attenuation coefficient and frequency: 0.997 ± 0.002 (fast wave) and 0.986 ± 0.013 (slow wave) (mean ± standard deviation). Average root-mean-squared (RMS) differences between the two algorithms for phase velocities were 5 m/s (fast wave, 350 kHz) and 13 m/s (slow wave, 750 kHz). Average RMS differences for signal loss were 1.6 dB (fast wave, 350 kHz) and 0.4 dB (slow wave, 750 kHz). Phase velocities for thickness = 10 mm were 1726 m/s (fast wave, 350 kHz) and 1455 m/s (slow wave, 750 kHz). Results show support for the model of two waves with linear-with frequency attenuation, successful isolation of fast and slow waves, good agreement between bandlimited deconvolution and MLSP + CF as well as with a Bayesian algorithm, and potential variations of fast and/or slow wave properties with bone sample thickness.

Time-domain separation of interfering waves in cancellous bone using bandlimited deconvolution: simulation and phantom study

In through-transmission interrogation of cancellous bone, two longitudinal pulses ("fast" and "slow" waves) may be generated. Fast and slow wave properties convey information about material and micro-architectural characteristics of bone. However, these properties can be difficult to assess when fast and slow wave pulses overlap in time and frequency domains. In this paper, two methods are applied to decompose signals into fast and slow waves: bandlimited deconvolution and modified least-squares Prony's method with curve-fitting (MLSP + CF). The methods were tested in plastic and Zerdine(®) samples that provided fast and slow wave velocities commensurate with velocities for cancellous bone. Phase velocity estimates were accurate to within 6 m/s (0.4%) (slow wave with both methods and fast wave with MLSP + CF) and 26 m/s (1.2%) (fast wave with bandlimited deconvolution). Midband signal loss estimates were accurate to within 0.2 dB (1.7%) (fast wave with both methods), and 1.0 dB (3.7%) (slow wave with both methods). Similar accuracies were found for simulations based on fast and slow wave parameter values published for cancellous bone. These methods provide sufficient accuracy and precision for many applications in cancellous bone such that experimental error is likely to be a greater limiting factor than estimation error.

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.

Estimation of fast and slow wave properties in cancellous bone using Prony's method and curve fitting

The presence of two longitudinal waves in poroelastic media is predicted by Biot's theory and has been confirmed experimentally in through-transmission measurements in cancellous bone. Estimation of attenuation coefficients and velocities of the two waves is challenging when the two waves overlap in time. The modified least squares Prony's (MLSP) method in conjuction with curve-fitting (MLSP + CF) is tested using simulations based on published values for fast and slow wave attenuation coefficients and velocities in cancellous bone from several studies in bovine femur, human femur, and human calcaneus. The search algorithm is accelerated by exploiting correlations among search parameters. The performance of the algorithm is evaluated as a function of signal-to-noise ratio (SNR). For a typical experimental SNR (40 dB), the root-mean-square errors (RMSEs) for one example (human femur) with fast and slow waves separated by approximately half of a pulse duration were 1 m/s (slow wave velocity), 4 m/s (fast wave velocity), 0.4 dB/cm MHz (slow wave attenuation slope), and 1.7 dB/cm MHz (fast wave attenuation slope). The MLSP + CF method is fast (requiring less than 2 s at SNR = 40 dB on a consumer-grade notebook computer) and is flexible with respect to the functional form of the parametric model for the transmission coefficient. The MLSP + CF method provides sufficient accuracy and precision for many applications such that experimental error is a greater limiting factor than estimation error.

Clinical assessment of the 1/3 radius using a new desktop ultrasonic bone densitometer

The objectives of this study were to evaluate the capability of a novel ultrasound device to clinically estimate bone mineral density (BMD) at the 1/3 radius. The device rests on a desktop and is portable, and permits real-time evaluation of the radial BMD. The device measures two net time delay (NTD) parameters, NTD(DW) and NTD(CW). NTD(DW) is defined as the difference between the transit time of an ultrasound pulse to travel through soft-tissue, cortex and medullary cavity, and the transit time through soft tissue only of equal overall distance. NTD(CW) is defined as the difference between the transit time of an ultrasound pulse to travel through soft-tissue and cortex only, and the transit time through soft tissue only again of equal overall distance. The square root of the product of these two parameters is a measure of the radial BMD at the 1/3 location as measured by dual-energy X-ray absorptiometry (DXA). A clinical IRB-approved study measured ultrasonically 60 adults at the 1/3 radius. BMD was also measured at the same anatomic site and time using DXA. A linear regression using NTD produced a linear correlation coefficient of 0.93 (p < 0.001). These results are consistent with previously reported simulation and in vitro studies. In conclusion, although X-ray methods are effective in bone mass assessment, osteoporosis remains one of the largest undiagnosed and under-diagnosed diseases in the world today. The research described here should enable significant expansion of diagnosis and monitoring of osteoporosis through a desktop device that ultrasonically assesses bone mass at the 1/3 radius.

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.

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.

Correlations of group velocity, phase velocity, and dispersion with bone density in bovine trabecular bone

The present study investigated the correlations of the group velocity, the phase velocity, and the velocity dispersion with the apparent bone density in bovine trabecular bone in vitro. The phase velocity exhibited the negative dispersion, consistent with the behavior in human trabecular bone. The group and the phase velocities were found to increase with increasing apparent bone density, respectively, exhibiting similar high correlations of r=0.94 and 0.96. The negative dispersion rate exhibited a decreasing dependence on the apparent bone density, with a significant correlation of r=-0.86.

Determining attenuation properties of interfering fast and slow ultrasonic waves in cancellous bone

Previous studies have shown that interference between fast waves and slow waves can lead to observed negative dispersion in cancellous bone. In this study, the effects of overlapping fast and slow waves on measurements of the apparent attenuation as a function of propagation distance are investigated along with methods of analysis used to determine the attenuation properties. Two methods are applied to simulated data that were generated based on experimentally acquired signals taken from a bovine specimen. The first method uses a time-domain approach that was dictated by constraints imposed by the partial overlap of fast and slow waves. The second method uses a frequency-domain log-spectral subtraction technique on the separated fast and slow waves. Applying the time-domain analysis to the broadband data yields apparent attenuation behavior that is larger in the early stages of propagation and decreases as the wave travels deeper. In contrast, performing frequency-domain analysis on the separated fast waves and slow waves results in attenuation coefficients that are independent of propagation distance. Results suggest that features arising from the analysis of overlapping two-mode data may represent an alternate explanation for the previously reported apparent dependence on propagation distance of the attenuation coefficient of cancellous bone.

Statistics of the envelope of ultrasonic backscatter from human trabecular bone

The paper describes the investigations intended to compare the results of experimental measurements of backscattering properties of the trabecular bone with the results of computer simulations. Ultrasonic RF echoes were collected using two bone scanners operating at 0.58 and 1.3 MHz. The simulations of the backscattered RF echoes were performed using the scattering model of the trabecular bone that consisted of cylindrical and spherical elements uniformly distributed in water-like medium. For each measured or simulated RF backscatter the statistical properties of the signal envelope were determined. Experimental results suggest deviations of the backscattering properties from the Rayleigh distribution. The results of simulation suggest that deviation from Rayleigh distribution depends on the variation of trabeculae diameters and the number of thin trabeculae. Experimentally determined deviations corresponded well to the deviations calculated from simulated echoes assuming trabeculae thickness variation equaled to the earlier published histomorphometric study results.

Velocity dispersion and attenuation in granular marine sediments: comparison of measurements with predictions using acoustic models

The large velocity dispersion recently reported could be explained by a gap stiffness model incorporated into the Biot model (the BIMGS model) proposed by the author. However, at high frequencies, some measured results have been reported for negative velocity dispersion and attenuation proportional to the first to fourth power of frequency. In this study, first, it is shown that the results of velocity dispersion and attenuation calculated using the BIMGS model are consistent with the results measured in two kinds of water-saturated sands with different grain sizes, except in the high-frequency range. Then, the velocity dispersion and attenuation in six kinds of water-saturated glass beads and four kinds of water-saturated silica sands with different grain sizes are measured in the frequency ranges of 80-140 and 300-700 kHz. The measured results are compared with those calculated using the BIMGS model plus some acoustic models. It is shown that the velocity dispersion and attenuation are well predicted by using the BIMGS model in the range of kd ≤ 0.5 (k: wavenumber in water, d: grain diameter) and by using the BIMGS model plus multiple scattering effects in the range of kd ≥ 0.5 in which negative velocity dispersion appears.

Multi-frequency characterization of the speed of sound and attenuation coefficient for longitudinal transmission of freshly excised human skulls

For medical applications of ultrasound inside the brain, it is necessary to understand the relationship between the apparent density of skull bone and its corresponding speed of sound and attenuation coefficient. Although there have been previous studies exploring this phenomenon, there is still a need to extend the measurements to cover more of the clinically relevant frequency range. The results of measurements of the longitudinal speed of sound and attenuation coefficient are presented for specimens of human calvaria. The study was performed for the frequencies of 0.27, 0.836, 1.402, 1.965 and 2.525 MHz. Specimens were obtained from fresh cadavers through a protocol with the Division of Anatomy of the University of Toronto. The protocol was approved by the Research Ethics Board of Sunnybrook Health Sciences Centre. The specimens were mounted in polycarbonate supports that were marked for stereoscopic positioning. Computer tomography (CT) scans of the skulls mounted on their supports were performed, and a three-dimensional skull surface was reconstructed. This surface was used to guide a positioning system to ensure the normal sound incidence of an acoustic signal. This signal was produced by a focused device with a diameter of 5 cm and a focal length of 10 cm. Measurements of delay in time of flight were carried out using a needle hydrophone. Measurements of effective transmitted energy were carried out using a radiation force method with a 10 µg resolution scale. Preliminary functions of speed of sound and attenuation coefficient, both of which are related to apparent density, were established using a multi-layer propagation model that takes into account speed of sound, density and thickness of the layer. An optimization process was executed from a large set of random functions and the best functions were chosen for those ones that closest reproduced the experimental observations. The final functions were obtained after a second pass of the optimization process was executed, but this time using a finite-difference time-difference solution of the Westervelt equation, which is more precise than the multi-layer model but much more time consuming for computation. For six of seven specimens, measurements were carried out on five locations on the calvaria, and for the other specimen three measurements were made. In total, measurements were carried out on 33 locations. Results indicated the presence of dispersion effects and that these effects are different according to the type of bone in the skull (cortical and trabecular). Additionally, both the speed of sound and attenuation showed dependence on the skull density that varied with the frequency. Using the optimal functions and the information of density from the CT scans, the average values (±s.d.) of the speed of sound for cortical bone were estimated to be 2384(± 130), 2471(± 90), 2504(± 120), 2327(± 90) and 2053(± 40) m s(-1) for the frequencies of 270, 836, 1402, 1965 and 2526 kHz, respectively. For trabecular bone, and in the same order of frequency values, the speeds of sound were 2140(± 130), 2300(± 100), 2219(± 200), 2133(± 130) and 1937(± 40) m s(-1), respectively. The average values of the attenuation coefficient for cortical bone were 33(± 9), 240(± 9) and 307(± 30) Np m(-1) for the frequencies of 270, 836, and 1402, respectively. For trabecular bone, and in the same order of frequency values, the average values of the attenuation coefficient were 34(± 13), 216(± 16) and 375(± 30) Np m(-1), respectively. For frequencies of 1.965 and 2.525 MHz, no measurable radiation force was detected with the setup used.

Inverse problems in cancellous bone: estimation of the ultrasonic properties of fast and slow waves using Bayesian probability theory

Quantitative ultrasonic characterization of cancellous bone can be complicated by artifacts introduced by analyzing acquired data consisting of two propagating waves (a fast wave and a slow wave) as if only one wave were present. Recovering the ultrasonic properties of overlapping fast and slow waves could therefore lead to enhancement of bone quality assessment. The current study uses Bayesian probability theory to estimate phase velocity and normalized broadband ultrasonic attenuation (nBUA) parameters in a model of fast and slow wave propagation. Calculations are carried out using Markov chain Monte Carlo with simulated annealing to approximate the marginal posterior probability densities for parameters in the model. The technique is applied to simulated data, to data acquired on two phantoms capable of generating two waves in acquired signals, and to data acquired on a human femur condyle specimen. The models are in good agreement with both the simulated and experimental data, and the values of the estimated ultrasonic parameters fall within expected ranges.

Cancellous bone analysis with modified least squares Prony's method and chirp filter: phantom experiments and simulation

The presence of two longitudinal waves in porous media is predicted by Biot's theory and has been confirmed experimentally in cancellous bone. When cancellous bone samples are interrogated in through-transmission, these two waves can overlap in time. Previously, the Modified Least-Squares Prony's (MLSP) method was validated for estimation of amplitudes, attenuation coefficients, and phase velocities of fast and slow waves, but tended to overestimate phase velocities by up to about 5%. In the present paper, a pre-processing chirp filter to mitigate the phase velocity bias is derived. The MLSP/chirp filter (MLSPCF) method was tested for decomposition of a 500 kHz-center-frequency signal containing two overlapping components: one passing through a low-density-polyethylene plate (fast wave) and another passing through a cancellous-bone-mimicking phantom material (slow wave). The chirp filter reduced phase velocity bias from 100 m/s (5.1%) to 69 m/s (3.5%) (fast wave) and from 29 m/s (1.9%) to 10 m/s (0.7%) (slow wave). Similar improvements were found for 1) measurements in polycarbonate (fast wave) and a cancellous-bone-mimicking phantom (slow wave), and 2) a simulation based on parameters mimicking bovine cancellous bone. The MLSPCF method did not offer consistent improvement in estimates of attenuation coefficient or amplitude.

Decomposition of two-component ultrasound pulses in cancellous bone using modified least squares prony method--phantom experiment and simulation

Porous media such as cancellous bone often support the simultaneous propagation of two compressional waves. When small bone samples are interrogated in through-transmission with broadband sources, these two waves often overlap in time. The modified least-squares Prony's (MLSP) method was tested for decomposing a 500 kHz-center-frequency signal containing two overlapping components: one passing through a polycarbonate plate (to produce the "fast" wave) and another passing through a cancellous-bone-mimicking phantom (to produce the "slow" wave). The MLSP method yielded estimates of attenuation slopes accurate to within 7% (polycarbonate plate) and 2% (cancellous bone phantom). The MLSP method yielded estimates of phase velocities accurate to within 1.5% (both media). The MLSP method was also tested on simulated data generated using attenuation slopes and phase velocities corresponding to bovine cancellous bone. Throughout broad ranges of signal-to-noise ratio (SNR), the MLSP method yielded estimates of attenuation slope that were accurate to within 1.0% and estimates of phase velocity that were accurate to within 4.3% (fast wave) and 1.3% (slow wave).

Frequency dependence of average phase shift from human calcaneus in vitro

If dispersion in a medium is weak and approximately linear with frequency (over the experimental band of frequencies), then it can be shown that the constant term in a polynomial representation of phase shift as a function of frequency can produce errors in measurements of phase-velocity differences in through-transmission, substitution experiments. A method for suppressing the effects of the constant phase shift in the context of the single-wave-model was tested on measurements from 30 cancellous human calcaneus samples in vitro. Without adjustment for constant phase shifts, the estimated phase velocity at 500 kHz was 1516+/-6 m/s (mean+/-standard error), and the estimated dispersion was -24+/-4 m/s MHz (mean+/-standard error). With adjustment for constant phase shifts, the estimated mean velocity decreased by 4-9 m/s, and the estimated magnitude of mean dispersion decreased by 50%-100%. The average correlation coefficient between the measured attenuation coefficient and frequency was 0.997+/-0.0026 (mean+/-standard deviation), suggesting that the signal for each sample was dominated by one wave. A single-wave, linearly dispersive model conformed to measured complex transfer functions from the 30 cancellous-bone samples with an average root-mean-square error of 1.9%+/-1.0%.

Influence of the filling fluid on frequency-dependent velocity and attenuation in cancellous bones between 0.35 and 2.5 MHz

The paper is focused on experiments on human cancellous bones filled with different fluids with the goal of evaluating their contribution to velocity dispersion, absorption, and scattering mechanisms. The specimens were measured first filled with marrow and subsequently, after marrow removal, with water and alcohol. No significant influence of the fluids was evidenced on the attenuation coefficient. Given the absence of impact of viscosity of the saturating fluid, the authors hypothesized that the source of attenuation is associated with viscoelastic absorption in the solid trabeculae and with scattering. Alteration of scattering obtained by changing the acoustic impedance mismatch between the fluid (alcohol vs water) and the trabeculae was reflected neither in the attenuation nor in its slope. This led the authors to suggest that longitudinal-to-shear scattering together with absorption in the solid phase are candidates as main sources for the attenuation. The differences in velocity values indicate that the elastic properties of the fluid are main determinants of the phase velocity. This finding is particularly significant in the context of /in vivo/ measurements, because it demonstrates that the subject-dependent properties of marrow may partly explain the inter-subject variability of speed of sound values.

The dependencies of phase velocity and dispersion on volume fraction in cancellous-bone-mimicking phantoms

Frequency-dependent phase velocity was measured in eight cancellous-bone-mimicking phantoms consisting of suspensions of randomly oriented nylon filaments (simulating trabeculae) in a soft-tissue-mimicking medium (simulating marrow). Trabecular thicknesses ranged from 152 to 356 mum. Volume fractions of nylon filament material ranged from 0% to 10%. Phase velocity varied approximately linearly with frequency over the range from 300 to 700 kHz. The increase in phase velocity (compared with phase velocity in a phantom containing no filaments) at 500 kHz was approximately proportional to volume fraction occupied by nylon filaments. The derivative of phase velocity with respect to frequency was negative and exhibited nonlinear, monotonically decreasing dependence on volume fraction. The dependencies of phase velocity and its derivative on volume fraction in these phantoms were similar to those reported in previous studies on (1) human cancellous bone and (2) phantoms consisting of parallel nylon wires immersed in water.

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.

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.

The application of quantitative ultrasound (QUS) on study of aging effects of achilles tendons

Recently, the quantitative ultrasound (QUS) technique has been widely applied for the characterization of tissues. For example, it can be used for the quantization of Achilles tendons based on the broadband ultrasound attenuation (BUA) and speed of sound (SOS) when the ultrasound wave passes through the tissues. The main purpose of this study is to develop an integrated system to investigate the correlations between the measurements of Achilles tendons using QUS (UBIS 5000) and 2D ultrasound instrument (HDI 5000). Subjects including young (32 females and 17 males; mean age: 23.7+/-2.0) and middle-age groups (8 female and 8 males; mean age: 47.3+/-8.5 s) were recruited and tested for this study. All the subjects were ensured to have no habit of regular exercise and no record of tendon injury. The results show that BUA is significantly higher for the young group (45.2+/-1.6 dB/MHz) than the middle-age group (40.5+/-1.9 dB/MHz), while SOS is significantly lower for the young (1601.9+/-11.2m/s) than the middle-age (1624.1+/-8.7m/s). The thickness of Achilles tendons for both groups (young: 4.31+/-0.23mm; middle age: 4.24+/-0.23mm) are very similar. The noninvasive ultrasonic assessment of Achilles tendons might be helpful in clinical diagnosis and in evaluation of a therapeutic regimen. In the future, further animal studies should be made by measuring the BUA and SOS invasively to evaluate the accuracy of the parameters measured using QUS parametric images.

Interference between wave modes may contribute to the apparent negative dispersion observed in cancellous bone

Previous work has shown that ultrasonic waves propagating through cancellous bone often exhibit a linear-with-frequency attenuation coefficient, but a decrease in phase velocity with frequency (negative dispersion) that is inconsistent with the causality-imposed Kramers-Kronig relations. In the current study, interfering wave modes similar to those observed in bone are shown to potentially contribute to the observed negative dispersion. Biot theory, the modified Biot-Attenborogh model, and experimental results are used to aid in simulating multiple-mode wave propagation through cancellous bone. Simulations entail constructing individual wave modes exhibiting a positive dispersion using plausible velocities and amplitudes, and then summing the individual modes to create mixed-mode output wave forms. Results of the simulations indicate that mixed-mode wave forms can exhibit negative dispersion when analyzed conventionally under the assumption that only one wave is present, even when the individual interfering waves exhibit positive dispersions in accordance with the Kramers-Kronig relations. Furthermore, negative dispersion is observed when little or no visual evidence of interference exists in the time-domain data. Understanding the mechanisms responsible for the observed negative dispersion could aid in determining the true material properties of cancellous bone, as opposed to the apparent properties measured using conventional data analysis techniques.

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.

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.

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.

Negative dispersion in bone: the role of interference in measurements of the apparent phase velocity of two temporally overlapping signals

In this study the attenuation coefficient and dispersion (frequency dependence of phase velocity) are measured using a phase sensitive (piezoelectric) receiver in a phantom in which two temporally overlapping signals are detected, analogous to the fast and slow waves typically found in measurements of cancellous bone. The phantom consisted of a flat and parallel Plexiglas plate into which a step discontinuity was milled. The phase velocity and attenuation coefficient of the plate were measured using both broadband and narrowband data and were calculated using standard magnitude and phase spectroscopy techniques. The observed frequency dependence of the phase velocity and attenuation coefficient exhibit significant changes in their frequency dependences as the interrogating ultrasonic field is translated across the step discontinuity of the plate. Negative dispersion is observed at specific spatial locations of the plate at which the attenuation coefficient rises linearly with frequency, a behavior analogous to that of bone measurements reported in the literature. For all sites investigated, broadband and narrowband data (3-7 MHz) demonstrate excellent consistency. Evidence suggests that the interference between the two signals simultaneously reaching the phase sensitive piezoelectric receiver is responsible for this negative dispersion.

Fast wave ultrasonic propagation in trabecular bone: numerical study of the influence of porosity and structural anisotropy

Our goal is to assess the potential of computational methods as an alternative to analytical models to predict the two longitudinal wave modes observed in cancellous bone and predicted by the Biot theory. A three-dimensional (3D) finite-difference time-domain method is coupled with 34 human femoral trabecular microstructures measured using microcomputed tomography. The main trabecular alignment (MTA) and the degree of anisotropy (DA) were assessed for all samples. DA values were comprised between 1.02 and 1.9. The influence of bone volume fraction (BV/TV) between 5% and 25% on the properties of the fast and slow waves was studied using a dedicated image processing algorithm to modify the initial 3D microstructures. A heuristic method was devised to determine when both wave modes are time separated. The simulations (performed in three perpendicular directions) predicted that both waves generally overlap in time for a direction of propagation perpendicular to the MTA. When these directions are parallel, both waves are separated in time for samples with high DA and BV/TV values. A relationship was found between the least bone volume fraction required for the observation of nonoverlapping waves and the degree of anisotropy: The higher the DA, the lower the least BV/TV.

Prediction of negative dispersion by a nonlocal poroelastic theory

The objective of this work is to show that the negative dispersion of ultrasonic waves propagating in cancellous bone can be explained by a nonlocal version of Biot's theory of poroelasticity. The nonlocal poroelastic formulation is presented in this work and the exact solutions for one- and two-dimensional systems are obtained by the method of Fourier transform. The nonlocal phase speeds for solid- and fluid-borne waves show the desired negative dispersion where the magnitude of dispersion is strongly dependent on the nonlocal parameters and porosity. Dependence of the phase speed and attenuation is studied for both porosity and frequency variation. It is shown that the nonlocal parameter can be easily estimated by comparing the theoretical dispersion rate with experimental observations. It is also shown that the modes of Lamb waves show similar negative dispersion when predicted by the nonlocal poroelastic theory.

Bone surface topology mapping and its role in trabecular bone quality assessment using scanning confocal ultrasound

INTRODUCTION

Quantitative ultrasound (QUS) has been used to assess non-invasively bone quality, in which ultrasound velocity (UV) is a primary acoustic property.

METHODS

While UV calculation requires the tissue thickness in the ultrasound path, a bone surface topology mapping (STM) method was developed in this study for enhancing the accuracy of the UV measurement. STM accuracy was verified by both aluminum and a QUS heel phantom, indicating that the STM can determine the phantom thickness within 0.02 mm thickness error and the aluminum calibration step within 0.1 mm thickness error. STM performance was further evaluated using 25 cadaveric human calcanei samples.

RESULTS

The UV calculations using STM had a significant better correlation to bone mineral density (BMD) (r = 0.75, p < 0.05), volume fraction (r = 0.72, p < 0.05) and modulus (r = 0.69, p < 0.05) than the UV with fixed thickness. The later correlation coefficients were r = 0.64 for BMD, r = 0.65 for volume fraction, and r = 0.58 for modulus. The nBUA value determined using STM was also highly correlated to BMD (r(2) = 0.74) and modulus (r(2) = 0.62). This was comparable to the correlation result for BUA (BMD: r(2) = 0.76; Modulus: r(2) = 0.64).

CONCLUSION

These results suggested that STM technique in scanning ultrasound is capable of determining calcaneus bone thickness and hence enhancing the accuracy of UV measurement.

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

Time-domain speed-of-sound (SOS) measurements in calcaneus are effective predictors of osteoporotic fracture risk. High attenuation and dispersion in bone, however, produce severe distortion of transmitted pulses that leads to ambiguity of time-domain SOS measurements. An equation to predict the effects of system parameters (center frequency and bandwidth), algorithm parameters (pulse arrival-time marker), and bone properties (attenuation coefficient and thickness) on time-domain SOS estimates is derived for media with attenuation that varies linearly with frequency. The equation is validated using data from a bone-mimicking phantom and from 30 human calcaneus samples in vitro. The data suggest that the effects of dispersion are small compared with the effects of frequency-dependent attenuation. The equation can be used to retroactively compensate data. System-related variations in SOS are shown to decrease as the pulse-arrival-time marker is moved toward the pulse center. Therefore, compared with other time-domain measures of SOS, group velocity exhibits the minimum system dependence.

Wavelet-based signal processing of in vitro ultrasonic measurements at the proximal femur

To estimate osteoporotic fracture risk, several techniques for quantitative ultrasound (QUS) measurements at peripheral sites have been developed. As these techniques are limited in the prediction of fracture risk of the central skeleton, such as the hip, we are developing a QUS device for direct measurements at the femur. In doing so, we noticed the necessity to improve the conventional signal processing because it failed in a considerable number of measurements due to multipath transmission. Two sets of excised human femurs (n = 6 + 34) were scanned in transmission mode. Instead of using the conventional methods, the radio-frequency signals were processed with the continuous wavelet transform to detect their time-of-flights for the calculation of speed-of-sound (SOS) in bone. The SOS-values were averaged over a region similar to the total hip region of dual X-ray absorptiometry (DXA) measurements and compared with bone mineral density (BMD) measured with DXA. Testing six standard wavelets, this algorithm failed for only 0% to 6% of scan in test set 1 compared with 29% when using conventional algorithms. For test set 2, it failed for 2% to 12% compared with approximately 40%. SOS and BMD correlated significantly in both test sets (test set 1: r2 = 0.87 to 0.92, p < 0.007; test set 2: r2 = 0.68 to 0.79, p < 0.0001). The correlations are comparable with correlations recently reported. However, the number of evaluable signals could be substantially increased, which improves the perspectives of the in vivo measurements.

Phase velocity and normalized broadband ultrasonic attenuation in Polyacetal cuboid bone-mimicking phantoms

The variations of phase velocity and normalized broadband ultrasonic attenuation (nBUA) with porosity were investigated in Polyacetal cuboid bone-mimicking phantoms with circular cylindrical pores running normal to the surface along the three orthogonal axes. The frequency-dependent phase velocity and attenuation coefficient in the phantoms with porosities from 0% to 65.9% were measured from 0.65 to 1.10 MHz. The results showed that the phase velocity at 880 kHz decreased linearly with porosity, whereas the nBUA increased linearly with porosity. This study provides a useful insight into the relationships between ultrasonic properties and porosity in bone at porosities lower than 70%.

Frequency dependencies of phase velocity and attenuation coefficient in a water-saturated sandy sediment from 0.3 to 1.0 MHz

The frequency-dependent phase velocity and attenuation coefficient for the fast longitudinal wave in a water-saturated sandy sediment were measured over the frequency range from 0.3 to 1.0 MHz. The experimental data of phase velocity exhibited the significant negative dispersion, with the mean rate of decline of 120 +/- 20 m/s/MHz. The Biot model predicted the approximately nondispersive phase velocity and the grain-shearing (GS) model exhibited the slightly positive dispersion. In contrast, the predictions of the multiple scattering models for the negative dispersion in the glass-grain composite were in general agreement with the experimental data for the water-saturated sandy sediment measured here. The experimental data of attenuation coefficient was found to increase nonlinearly with frequency from 0.3 to 1.0 MHz. However, both the Biot and the GS models yielded the attenuation coefficient increasing almost linearly with frequency. The total attenuation coefficient given by the algebraic sum of absorption and scattering components showed a reasonable agreement with the experimental data for overall frequencies. This study suggests that the scattering is the principal mechanism responsible for the variations of phase velocity and attenuation coefficient with frequency in water-saturated sandy sediments at high frequencies.

Ultrasonic speed of sound dispersion imaging

The feasibility for speed of sound dispersion (SOSD) imaging was investigated here. A through transmission new method for measuring the SOSD was utilized. With this method a long pulse comprising of two frequencies one being the double of the other is transmitted through the object and detected on its other side. SOSD projection images were obtained by scanning objects immersed in water using a raster mode utilizing a computerized scanning system. Using this approach SOSD projection images were obtained for solids and fluids as well as for a tissue mimicking breast phantom and an in vitro soft tissues phantom. The results obtained here, have clearly demonstrated the feasibility of SOSD projection imaging. SOSD may serve as a new contrast source and potentially may aid in breast diagnosis.