The influence of porosity and pore size on the ultrasonic properties of bone investigated using a phantom material

Genetic and environmental determinants of bone quality: a cross-sectional analysis of the Hungarian Twin Registry

There is abundant evidence that bone mineral content is highly heritable, while the heritability of bone quality (i.e. trabecular bone score [TBS] and quantitative ultrasound index [QUI]) is rarely investigated. We aimed to disentangle the role of genetic, shared and unique environmental factors on TBS and QUI among Hungarian twins. Our study includes 82 twin (48 monozygotic, 33 same-sex dizygotic) pairs from the Hungarian Twin Registry. TBS was determined by DXA, QUI by calcaneal bone ultrasound. To estimate the genetic and environmental effects, we utilized ACE-variance decomposition. For the unadjusted model of TBS, an AE model provided the best fit with > 80% additive genetic heritability. Adjustment for age, sex, BMI and smoking status improved model fit with 48.0% of total variance explained by independent variables. Furthermore, there was a strong dominant genetic effect (73.7%). In contrast, unadjusted and adjusted models for QUI showed an AE structure. Adjustments improved model fit and 25.7% of the total variance was explained by independent variables. Altogether 70-90% of the variance in QUI was related to additive genetic influences. We found a strong genetic heritability of bone quality in unadjusted models. Half of the variance of TBS was explained by age, sex and BMI. Furthermore, the adjusted model suggested that the genetic component of TBS could be dominant or an epistasis could be present. In contrast, independent variables explained only a quarter of the variance of QUI and the additive heritability explained more than half of all the variance.

Measurement of Ultrasound Parameters of Bovine Cancellous Bone as a Function of Frequency for a Range of Porosities via Through-Transmission Ultrasonic Spectroscopy

The relationship between ultrasonic parameters (attenuation coefficients and velocity) and bone porosity in bovine cancellous bone is explored to understand the possibility of fracture risk diagnosis associated with osteoporosis by applying ultrasound. In vitro measurements of ultrasonic parameters on twenty-one bovine cancellous bone samples from tibia were conducted, using ultrasonic spectroscopy in the through-transmission mode. Transducers of three different center frequencies were used to cover a wide diagnostic frequency range between 1.0–7.8 MHz. The nonlinear relationship of porosity and normalized attenuation coefficient (nATTN) and normalized broadband attenuation coefficient (nBUA) were well described by a third-order polynomial fit, whereas porosity and the phase velocity (UV) were found to be negatively correlated with the linear correlation coefficients of −0.93, −0.89 and −0.83 at 2.25, 5.00 and 7.50 MHz, respectively. The results imply that the ultrasound parameters attain maximum values for the bone sample with the lowest porosity, and then decrease for samples with greater porosity for the range of porosities in our samples for all frequencies. Spatial variation in the ultrasound parameters was found to be caused by non-uniform pore size distribution, which was examined at five different locations within the same bone specimen. However, it did not affect the relationship of ultrasound parameters and porosity at these frequencies.

Effects of scattering on ultrasound wave transmission through bioinspired scaffolds

Enhancing tissue growth in scaffolds using ultrasound waves while maintaining the structural integrity of the scaffolds is a challenging problem. Previous studies have primarily focused on the effect of ultrasound waves directly on the tissue, but how the ultrasound wave interacts with the scaffold needs to be further understood, which will have a significant effect on the response of tissue to mechanical stimulation. In this study we investigate how ultrasound wave transmission differs between scaffolds with uniform pore shapes (triangle, square, rectangle, hexagon) and a bioinspired scaffold with higher structural integrity that is inspired from the atomic structure of hydroxyapatite which is a primary component of bone. We use finite element method and ultrasound experiments on 3D-printed scaffolds composed of Acrylonitrile butadiene styrene (ABS) with constant porosity to predict the effect of pore shape and wave signal frequency in the range of 1-20 MHz on acoustic wave scattering and transmission. We find that the pore shape of the scaffold affects the magnitude of ultrasound transmission even when porosity is constant, and that the bioinspired scaffolds can allow as much as 67% more wave transmission compared to scaffolds with rectangular or square pore shapes at 1 MHz frequency. Triangular and hexagonal pores are also found to produce more nonuniform transmitted wavefronts compared to the square and rectangular pores. Peak density is defined as the number of local extrema of the transmitted wave frequency power spectrum and measures the uniformity of the transmitted wave. We find that a higher peak density value for the bioinspired scaffold due to its nonsymmetric structure further produces more nonuniform wave scattering. The results of this study are important for designing bioinspired tissue scaffold geometries to control ultrasound wave penetration and to enhance mechanical stimulation for tissue growth and will also aid in the ultrasonic characterization of porous structures based on changes in pore geometry.

Investigation of the Effect of the Skull in Transcranial Photoacoustic Imaging: A Preliminary Ex Vivo Study

Although transcranial photoacoustic imaging (TCPAI) has been used in small animal brain imaging, in animals with thicker skull bones or in humans both light illumination and ultrasound propagation paths are affected. Hence, the PA image is largely degraded and in some cases completely distorted. This study aims to investigate and determine the maximum thickness of the skull through which photoacoustic imaging is feasible in terms of retaining the imaging target structure without incorporating any post processing. We identify the effect of the skull on both the illumination path and acoustic propagation path separately and combined. In the experimental phase, the distorting effect of ex vivo sheep skull bones with thicknesses in the range of 0.7~1.3 mm are explored. We believe that the findings in this study facilitate the clinical translation of TCPAI.

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.

A rapid beam simulation framework for transcranial focused ultrasound

Transcranial focused ultrasound is a non-invasive therapeutic modality that can be used to treat essential tremor. Beams of energy are focused into a small spot in the thalamus, resulting in tissue heating and ablation. Here, we report on a rapid 3D numeric simulation framework that can be used to predict focal spot characteristics prior to the application of ultrasound. By comparing with magnetic resonance proton resonance frequency shift thermometry (MR thermometry) data acquired during treatments of essential tremor, we verified that our simulation framework can be used to predict focal spot position, and with patient-specific calibration, predict focal spot temperature rise. Preliminary data suggests that lateral smearing of the focal spot can be simulated. The framework may also be relevant for other therapeutic ultrasound applications such as blood brain barrier opening and neuromodulation.

The effect of pore size and density on ultrasonic attenuation in porous structures with mono-disperse random pore distribution: A two-dimensional in-silico study

This work proposes a power law model to describe the attenuation of ultrasonic waves in non-absorbing heterogeneous media with randomly distributed scatterers, mimicking a simplified structure of cortical bone. This paper models the propagation in heterogeneous structures with controlled porosity using a two-dimensional finite-difference time domain numerical simulation in order to measure the frequency dependent attenuation. The paper then fits a phenomenological model to the simulated frequency dependent attenuation by optimizing parameters under an ordinary least squares framework. Local sensitivity analysis is then performed on the resulting parameter estimates in order to determine to which estimates the model is most sensitive. This paper finds that the sensitivity of the model to various parameter estimates depends on the micro-architectural parameters, pore diameter (ϕ) and pore density (ρ). In order to get a sense for how confidently model parameters are able to be estimated, 95% confidence intervals for these estimates are calculated. In doing so, the ability to estimate model-sensitive parameters with a high degree of confidence is established. In the future, being able to accurately estimate model parameters from which micro-architectural ones could be inferred will allow pore density and diameter to be estimated via an inverse problem given real or simulated ultrasonic data to be determined.

Characterization of a polymer, open-cell rigid foam that simulates the ultrasonic properties of cancellous bone

Materials that simulate the ultrasonic properties of tissues are used widely for clinical and research purposes. However, relatively few materials are known to simulate the ultrasonic properties of cancellous bone. The goal of the present study was to investigate the suitability of using a polymer, open-cell rigid foam (OCRF) produced by Sawbones^®. Measurements were performed on OCRF specimens with four different densities. Ultrasonic speed of sound and normalized broadband ultrasonic attenuation were measured with a 0.5 MHz transducer. Three backscatter parameters were measured with a 5 MHz transducer: apparent integrated backscatter, frequency slope of apparent backscatter, and normalized mean of the backscatter difference. X-ray micro-computed tomography was used to measure the microstructural characteristics of the OCRF specimens. The trabecular thickness and relative bone volume of the OCRF specimens were similar to those of human cancellous bone, but the trabecular separation was greater. In most cases, the ultrasonic properties of the OCRF specimens were similar to values reported in the literature for cancellous bone, including dependence on density. In addition, the OCRF specimens exhibited an ultrasonic anisotropy similar to that reported for cancellous bone.

Towards assessing cortical bone porosity using low-frequency quantitative acoustics: A phantom-based study

PURPOSE

Cortical porosity is a key characteristic governing the structural properties and mechanical behaviour of bone, and its quantification is therefore critical for understanding and monitoring the development of various bone pathologies such as osteoporosis. Axial transmission quantitative acoustics has shown to be a promising technique for assessing bone health in a fast, non-invasive, and radiation-free manner. One major hurdle in bringing this approach to clinical application is the entanglement of the effects of individual characteristics (e.g. geometry, porosity, anisotropy etc.) on the measured wave propagation. In order to address this entanglement problem, we therefore propose a systematic bottom-up approach, in which only one bone property is varied, before addressing interaction effects. This work therefore investigated the sensitivity of low-frequency quantitative acoustics to changes in porosity as well as individual pore characteristics using specifically designed cortical bone phantoms.

MATERIALS AND METHODS

14 bone phantoms were designed with varying pore size, axial-, and radial pore number, resulting in porosities (bone volume fraction) between 0% and 15%, similar to porosity values found in human cortical bone. All phantoms were manufactured using laser sintering, measured using axial-transmission acoustics and analysed using a full-wave approach. Experimental results were compared to theoretical predictions based on a modified Timoshenko theory.

RESULTS

A clear dependence of phase velocity on frequency and porosity produced by increasing pore size or radial pore number was demonstrated, with the velocity decreasing by between 2-5 m/s per percent of additional porosity, which corresponds to -0.5% to -1.0% of wave speed. While the change in phase velocity due to axial pore number was consistent with the results due to pore size and radial pore number, the relative uncertainties for the estimates were too high to draw any conclusions for this parameter.

CONCLUSIONS

This work has shown the capability of low-frequency quantitative acoustics to reflect changes in porosity and individual pore characteristics and demonstrated that additive manufacturing is an appropriate method that allows the influence of individual bone properties on the wave propagation to be systematically assessed. The results of this work opens perspectives for the efficient development of a multi-frequency, multi-mode approach to screen, diagnose, and monitor bone pathologies in individuals.

Predicting variation in subject thermal response during transcranial magnetic resonance guided focused ultrasound surgery: Comparison in seventeen subject datasets

PURPOSE

In transcranial magnetic resonance-guided focused ultrasound (tcMRgFUS) treatments, the acoustic and spatial heterogeneity of the skull cause reflection, absorption, and scattering of the acoustic beams. These effects depend on skull-specific parameters and can lead to patient-specific thermal responses to the same transducer power. In this work, the authors develop a simulation tool to help predict these different experimental responses using 3D heterogeneous tissue models based on the subject CT images. The authors then validate and compare the predicted skull efficiencies to an experimental metric based on the subject thermal responses during tcMRgFUS treatments in a dataset of seventeen human subjects.

METHODS

Seventeen human head CT scans were used to create tissue acoustic models, simulating the effects of reflection, absorption, and scattering of the acoustic beam as it propagates through a heterogeneous skull. The hybrid angular spectrum technique was used to model the acoustic beam propagation of the InSightec ExAblate 4000 head transducer for each subject, yielding maps of the specific absorption rate (SAR). The simulation assumed the transducer was geometrically focused to the thalamus of each subject, and the focal SAR at the target was used as a measure of the simulated skull efficiency. Experimental skull efficiency for each subject was calculated using the thermal temperature maps from the tcMRgFUS treatments. Axial temperature images (with no artifacts) were reconstructed with a single baseline, corrected using a referenceless algorithm. The experimental skull efficiency was calculated by dividing the reconstructed temperature rise 8.8 s after sonication by the applied acoustic power.

RESULTS

The simulated skull efficiency using individual-specific heterogeneous models predicts well (R(2) = 0.84) the experimental energy efficiency.

CONCLUSIONS

This paper presents a simulation model to predict the variation in thermal responses measured in clinical ctMRGFYS treatments while being computationally feasible.

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.

Prediction of trabecular bone qualitative properties using scanning quantitative ultrasound

Microgravity induced bone loss represents a critical health problem in astronauts, particularly occurred in weight-supporting skeleton, which leads to osteopenia and increase of fracture risk. Lack of suitable evaluation modality makes it difficult for monitoring skeletal status in long term space mission and increases potential risk of complication. Such disuse osteopenia and osteoporosis compromise trabecular bone density, and architectural and mechanical properties. While X-ray based imaging would not be practical in space, quantitative ultrasound may provide advantages to characterize bone density and strength through wave propagation in complex trabecular structure. This study used a scanning confocal acoustic diagnostic and navigation system (SCAN) to evaluate trabecular bone quality in 60 cubic trabecular samples harvested from adult sheep. Ultrasound image based SCAN measurements in structural and strength properties were validated by μCT and compressive mechanical testing. This result indicated a moderately strong negative correlations observed between broadband ultrasonic attenuation (BUA) and μCT-determined bone volume fraction (BV/TV, R²=0.53). Strong correlations were observed between ultrasound velocity (UV) and bone's mechanical strength and structural parameters, i.e., bulk Young's modulus (R²=0.67) and BV/TV (R²=0.85). The predictions for bone density and mechanical strength were significantly improved by using a linear combination of both BUA and UV, yielding R²=0.92 for BV/TV and R²=0.71 for bulk Young's modulus. These results imply that quantitative ultrasound can characterize trabecular structural and mechanical properties through measurements of particular ultrasound parameters, and potentially provide an excellent estimation for bone's structural integrity.

Modeling and prediction of density distribution and microstructure in particleboards from acoustic properties by correlation of non-contact high-resolution pulsed air-coupled ultrasound and X-ray images

Non-destructive density and microstructure quality control testing in particleboards (PBs) is necessary in production lines. A pulsed air-coupled ultrasound (ACU) high-resolution normal transmission system, together with a first wave tracking algorithm, were developed to image amplitude transmission G(p) and velocity c(p) distributions at 120kHz for PBs of specific nominal densities and five particle geometries, which were then correlated to X-ray in-plane density images ρ(s). Test PBs with a homogeneous vertical density profile were manufactured in a laboratory environment and conditioned in a standard climate (T=20°C, RH=65%) before the measurements. Continuous trends (R(2)>0.97) were obtained by matching the lateral resolution of X-ray images with the ACU sound field radius (σ(w)(o)=21mm) and by clustering the scatter plots. ρ(s)↦c(p) was described with a three-parameter non-linear model for each particle geometry, allowing for ACU density prediction with 3% uncertainty and PB testing according to EN312. ρ(s)↦G(p) was modeled by calculating ACU coupling gain and by fitting inverse power laws with offset of ρ(s) and c(p) to material attenuation, which scaled with particle volume. G(p) and c(p) variations with the frequency were examined, showing thickness resonances and scattering attenuation. The combination of ACU and X-ray data enabled successful particle geometry classification. The observed trends were interpreted in terms of multi-scale porosity and grain scattering with finite-difference time-domain simulations, which modeled arbitrarily complex stiffness and density distributions. The proposed method allows for non-contact determination of relations between acoustic properties and in-plane density distribution in plate materials. In future work, commercial PBs with non-uniform vertical density profiles should be investigated.

Phase velocity and attenuation predictions of waves in cancellous bone using an iterative effective medium approximation

The quantitative determination of wave dispersion and attenuation in bone is an open research area as the factors responsible for ultrasound absorption and scattering in composite biological tissues have not been completely explained. In this study, we use the iterative effective medium approximation (IEMA) proposed in [1] so as to calculate phase velocity and attenuation in media with properties similar to those of cancellous bones. Calculations are performed for a frequency range of 0.4-0.8 MHz and for different inclusions' volume concentrations and sizes. Our numerical results are compared with previous experimental findings so as to assess the effectiveness of IEMA. It was made clear that attenuation and phase velocity estimations could provide supplementary information for cancellous bone characterization.

Measurements of ultrasonic phase velocities and attenuation of slow waves in cellular aluminum foams as cancellous bone-mimicking phantoms

The water-saturated aluminum foams with an open network of interconnected ligaments were investigated by ultrasonic transmission technique for the suitability as cancellous bone-mimicking phantoms. The phase velocities and attenuation of nine samples covering three pores per inch (5, 10, and 20 PPI) and three aluminum volume fractions (5, 8, and 12% AVF) were measured over a frequency range of 0.7-1.3 MHz. The ligament thickness and pore sizes of the phantoms and low-density human cancellous bones are similar. A strong slow wave and a weak fast wave are observed for all samples while the latter is not visible without significant amplification (100x). This study reports the characteristics of slow wave, whose speeds are less than the sound speed of the saturating water and decrease mildly with AVF and PPI with an average 1469 m/s. Seven out of nine samples show positive dispersion and the rest show minor negative dispersion. Attenuation increases with AVF, PPI, and frequency except for the 20 PPI samples, which exhibit non-increasing attenuation level with fluctuations due to scattering. The phase velocities agree with Biot's porous medium theory. The RMSE is 16.0 m/s (1%) at n = 1.5. Below and above this value, the RMSE decreases mildly and rises sharply, respectively.

The 25th Anniversary of BUA for the Assessment of Osteoporosis: Time for a New Paradigm?

The measurement of broadband ultrasonic attenuation (BUA) in cancellous bone at the calcaneus for the assessment of osteoporosis was first described within this journal 25 years ago. It was recognized in 2006 by Universities UK as being one of the ‘100 discoveries and developments in UK Universities that have changed the world’ over the past 50 years. In 2008, the UK's Department of Health also recognized BUA assessment of osteoporosis in a publication highlighting 11 projects that have contributed to ‘60 years of NHS research benefiting patients’. The BUA technique has been extensively clinically validated and is utilized worldwide, with at least seven commercial systems currently providing calcaneal BUA measurement. However, there is still no fundamental understanding of the dependence of BUA upon the material and structural properties of cancellous bone. This review aims to provide an ‘engineering in medicine’ perspective and proposes a new paradigm based upon phase cancellation due to variation in propagation transit time across the receive transducer face to explain the non-linear relationship between BUA and bone volume fraction in cancellous bone.

Ultrasonic wave propagation in stereo-lithographical bone replicas

Predictions of a modified anisotropic Biot-Allard theory are compared with measurements of pulses centered on 100 kHz and 1 MHz transmitted through water-saturated stereo-lithographical bone replicas. The replicas are 13 times larger than the original bone samples. Despite the expected effects of scattering, which is neglected in the theory, at 100 kHz the predicted and measured transmitted waveforms are similar. However, the magnitude of the leading negative edge of the waveform is overpredicted, and the trailing parts of the waveforms are not predicted well. At 1 MHz, although there are differences in amplitudes, the theory predicts that the transmitted waveform is almost a scaled version of that incident in conformity with the data.

Measurement of tortuosity in aluminum foams using airborne ultrasound

The slow compressional wave in air-saturated aluminum foams was studied by means of ultrasonic transverse transmission method over a frequency range from 0.2 MHz to 0.8 MHz. The samples investigated have three different cell sizes or pores per inch (5, 10 and 20 ppi) and each size has three aluminum volume fractions (5%, 8% and 12% AVF). Phase velocities show minor dispersion at low frequencies but remain constant after 0.7 MHz. Pulse broadening and amplitude attenuation are obvious and increase with increasing ppi. Attenuation increases considerably with AVF for 20 ppi foams. Tortuosity ranges from 1.003 to 1.032 and increases with AVF and ppi. However, the increase of tortuosity with AVF is very small for 10 and 20 ppi samples.

Bone morphogenetic protein-2 activity is regulated by secreted phosphoprotein-24 kd, an extracellular pseudoreceptor, the gene for which maps to a region of the human genome important for bone quality

The material properties of bone are the sum of the complex and interrelated anabolic and catabolic processes that modulate formation and turnover. The 2q33-37 region of the human genome contains quantitative trait loci important in determining the broadband ultrasound attenuation (an index of trabecular microarchitecture, bone elasticity, and susceptibility to fracture) of the calcaneus, but no genes of significance to bone metabolism have been identified in this domain. Secreted phosphoprotein-24 kd (SPP24 or SPP2) is a novel and relatively poorly characterized growth hormone-regulated gene that maps to 2q37. The purpose of this review is to summarize the status of research related to spp24 and how it regulates bone morphogenetic protein (BMP) bioactivity in bone. SPP24 codes for an extracellular matrix protein that contains a high-affinity BMP-2-binding transforming growth factor-beta receptor II homology 1 loop similar to those identified in fetuin and the receptor itself. SPP24 is transcribed primarily in the liver and bone. High levels of spp24 (a hydroxyapatite-binding protein) are found in bone, and small amounts are found in fetuin-mineral complexes. Full-length secretory spp24 inhibits ectopic bone formation, and overexpression of spp24 reduces murine bone mass and density. Spp24 is extremely labile to proteolysis, a process that regulates its bioactivity in vivo. For example, an 18.5-kd degradation product of spp24, designated spp18.5, is pro-osteogenic. A synthetic cyclized Cys(1)-to-Cys(19) disulfide-bonded peptide (BMP binding peptide) corresponding to the transforming growth factor-beta receptor II homology 1 domain of spp24 and spp18.5 binds BMP-2 and increases the rate and magnitude of BMP-2-mediated ectopic bone formation. Thus, the mechanism of action of spp18.5 and spp24 may be to regulate the local bioavailability of BMP cytokines. SPP24 is regulated by growth hormone and 3 major families of transcription factors (nuclear factor of activated T cells, CCAAT/enhancer-binding protein, Cut/Cux/CCAAT displacement protein) that regulate mesenchymal cell proliferation, embryonic patterning, and terminal differentiation. The gene contains at least 2 single nucleotide polymorphisms. Given its mechanism of action and sequence variability, SPP24 may be an interesting candidate for future studies of the genetic regulation of bone mass, particularly during periods of BMP-mediated endochondral bone growth, development, and fracture healing.

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.

The measurement of broadband ultrasonic attenuation in cancellous bone--a review of the science and technology

The measurement of broadband ultrasonic attenuation (BUA) in cancellous bone at the calcaneus was first described in 1984. The assessment of osteoporosis by BUA has recently been recognized by Universities UK, within its EurekaUK book, as being one of the "100 discoveries and developments in UK Universities that have changed the world" over the past 50 years, covering the whole academic spectrum from the arts and humanities to science and technology. Indeed, BUA technique has been clinically validated and is utilized worldwide, with at least seven commercial systems providing calcaneal BUA measurement. However, a fundamental understanding of the dependence of BUA upon the material and structural properties of cancellous bone is still lacking. This review aims to provide a science- and technology-orientated perspective on the application of BUA to the medical disease of osteoporosis.

Relationships of trabecular bone structure with quantitative ultrasound parameters: in vitro study on human proximal femur using transmission and backscatter measurements

The present study was designed to assess the relationships between QUS parameters and bone density or microarchitecture on samples of human femoral trabecular bone. The normalized slope of the frequency-dependent attenuation (nBUA), the speed of sound (SOS) and the broadband ultrasound backscatter coefficient (BUB) were measured on 37 specimens of pure trabecular bones removed from upper parts of fresh human femurs. Bone mineral density (BMD) was assessed using a clinical scanner. Finally, 8 mm diameter cylindrical cores were extracted from the specimens and their microarchitecture was reconstructed after synchrotron radiation microtomography experiments (isotropic resolution of 10 microm). A large number of microarchitectural parameters were computed, describing morphology, connectivity and geometry of the specimens. BMD correlated with all the microarchitectural parameters and the number of significant correlations was found among the architectural parameters themselves. All QUS parameters were significantly correlated to BMD (R=0.83 for nBUA, R=0.81 for SOS and R=0.69 for BUB) and to microarchitectural parameters (R=-0.79 between nBUA and Tb.Sp, R=-0.81 between SOS and Tb.Sp, R=-0.65 between BUB and BS/BV). Using multivariate model, it was found that microstructural parameters adds 10%, 19%, and 4% to the respective BMD alone contribution for the three variables BUA, SOS and BUB. Moreover, the RMSE was reduced by up to 50% for SOS, by up to 21% for nBUA and up to 11% when adding structural variables to BMD in explaining QUS results. Given the sample, which is not osteoporosis-enriched, the added contribution is quite substantial. The variability of SOS was indeed completely explained by a multivariate model including BMD and independent structural parameters (R(2)=0.94). The inverse problem on the data presented here has been addressed using simple and multiple linear regressions. It was shown that the predictions (in terms of R(2) or RMSE) of microarchitectural parameters was not enhanced when combining 2 or 3 QUS in multiple linear regressions compared to the prediction obtained with one QUS parameter alone. The best model was found for the prediction of Tb.Th() from BUA (R(2)=0.58, RMSE=17 microm). Given the high values of RMSE, these linear models appear of limited clinical value, suggesting that appropriate models have to be derived in order to solve the inverse problem. In this regard, a very interesting multivariate model was found for nBUA and BUB with Tb.Th and Tb.N, in agreement with single scattering theories by random medium. However, the source of residual variability of nBUA and BUB (15% and 45% respectively) remained unexplained.

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.

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

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

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%.

Group velocity, phase velocity, and dispersion in human calcaneus in vivo

Commercial bone sonometers measure broadband ultrasonic attenuation and/or speed of sound (SOS) in order to assess bone status. Phase velocity, which is usually measured in frequency domain, is a fundamental material property of bone that is related to SOS, which is usually measured in time domain. Four previous in vitro studies indicate that phase velocity in human cancellous bone decreases with frequency (i.e., negative dispersion). In order to investigate frequency-dependent phase velocity in vivo, through-transmission measurements were performed in 73 women using a GE Lunar Achilles Insight commercial bone sonometer. Average phase velocity at 500 kHz was 1489 +/- 55 m/s (mean +/- standard deviation). Average dispersion rate was -59 +/- 52 m/sMHz. Group velocity was usually lower than phase velocity, as is expected for negatively dispersive media. Using a stratified model to represent cancellous bone, the reductions in phase velocity and dispersion rate in vivo as opposed to in vitro can be explained by (1) the presence of marrow instead of water as a fluid filler, and (2) the decreased porosity of bones of living (compared with deceased) subjects.

Quantitative ultrasound variables of the heel in Finnish men aged 18-20 yr: predictors, relationship to bone mineral content, and changes during military service

INTRODUCTION

Determinants of BUA and SOS and their changes during military service-associated physical training were studied in 196 army recruits and 50 control men, aged 18-20 years.

METHODS

Heel ultrasound measurement, DXA, muscle strength test, Cooper's running test and genetic analyses were performed. Lifestyle factors were recorded. Sex steroids and bone turnover markers were determined. Heel ultrasound was repeated after six months.

RESULTS

Exercise was the most significant determinant of both BUA (p<0.0001) and SOS (p<0.0001). There were 10% and 1.3% differences in BUA (p=0.006) and SOS (p=0.0001), respectively, between men belonging to the lowest and highest quartiles of exercise index. Weight associated with BUA (p=0.005) and height with SOS (p=0.03). BUA and SOS correlated with BMC and BMD (p<0.0001) but explained only up to 21% of their variance. Over six months SOS increased more in recruits than in control men (p=0.0043), the increase being higher, the lower muscle strength at baseline (r =-0.27, p=0.0028).

CONCLUSION

Exercise is the most important determinant of ultrasonographic variables in men, aged 18-20 years. Physical loading during military training increases SOS.

The dependencies of phase velocity and dispersion on trabecular thickness and spacing in trabecular bone-mimicking phantoms

Frequency-dependent phase velocity was measured in trabecular-bone-mimicking phantoms consisting of two-dimensional arrays of parallel nylon wires (simulating trabeculae) with thicknesses ranging from 152 to 305 microm and spacings ranging from 700 to 1000 microm. Phase velocity varied approximately linearly with frequency over the range from 400 to 750 kHz. Dispersion was characterized by the slope of a linear least-squares regression fit to phase velocity versus frequency data. The increase in phase velocity (compared with that in water) at 500 kHz was approximately proportional to the (1) square of trabecular thickness, (2) inverse square of trabecular spacing, and (3) volume fraction occupied by nylon wires. The first derivative of phase velocity with respect to frequency was negative and exhibited nonlinear, monotonically decreasing dependencies on trabecular thickness and volume fraction. The dependencies of phase velocity and its first derivative on volume fraction in the phantoms were consistent with those reported in trabecular bone.

Use of multiple acoustic wave modes for assessment of long bones: model study

Multiple acoustic wave mode method has been proposed as a new modality in axial bone QUS. The new method is based on measurement of ultrasound velocity at different ratio of wavelength to the bone thickness, and taking into account both bulk and guided waves. It allows assessment of changes in both the material properties related to porosity and mineralization as well as the cortical thickness influenced by resorption from inner layers, which are equally important in diagnostics of osteoporosis and other bone osteopenia. Developed method was validated in model studies using a dual-frequency (100 and 500 kHz) ultrasound device. Three types of bone phantoms for long bones were developed and tested: (1) tubular specimens from polymer materials to model combined changes of material stiffness and cortical wall thickness; (2) layered specimens to model porosity in compact bone progressing from endosteum towards periosteum; (3) animal bone specimens with both cortical and trabecular components. Observed changes of the ultrasound velocity of guided waves at 100 kHz followed gradual changes in the thickness of the intact cortical layer. On the other hand, the bulk velocity at 500 kHz remained nearly constant at the different cortical layer thickness but was affected by the material stiffness. Similar trends were observed in phantoms and in fragments of animal bones.

Recent developments in trabecular bone characterization using ultrasound

Currently available quantitative ultrasound technologies to assess cancellous bone are based on the measurements in transmission of speed of sound or slope of frequency-dependent attenuation (so called broadband ultrasonic attenuation). These two parameters are now considered as surrogate markers of site-matched bone mineral density. The ability of ultrasound techniques to provide non-bone mineral density-related bone properties (eg, microstructure) has not been clearly demonstrated yet. This is mainly because of two factors: a lack of understanding of ultrasound propagation with clear identification of the different underlying physical interactions; and the difficulty of performing experiments because of the limited sample size, the large number of statistical relationships to be tested with multiple variables, and the usual strong covariance observed between bone quantity and microarchitecture. The aim of this paper is to review the most recent development in the field of ultrasound characterization of trabecular bone. We present research work on ultrasound backscatter and how it could be used to estimate microarchitectural properties independently of bone quantity, and the first promising results obtained for the estimation of trabecular thickness. We then introduce numeric simulations of wave propagation through trabecular microarchitecture and show how it could contribute to elucidate and better characterize the physical underlying physics and result in more predictive models. These innovative acquisition schemes and the possibility of virtual experiments should altogether contribute to rapid advancement of ultrasonic bone characterization.

Effect of temperature on the longitudinal variability of quantitative ultrasound variables

It is unclear whether longitudinal change in phantom measurements bears any relation to the long-term in vivo instrument performance of quantitative ultrasound devices. Longitudinal quantitative ultrasound phantom data were obtained by measuring the manufacturer-provided phantom at ambient temperature and two different sets of Leeds phantoms at either ambient temperature or following a phantom temperature-control protocol. Measurements were performed using the Achilles Plus bone densitometer. Changes in longitudinal phantom data were compared to in vivo quantitative ultrasound data obtained from seven healthy, young volunteers. A cosinor model with linear trend and Hotelling's T2-test were used to quantify seasonal rhythms and long-term drift in quantitative ultrasound variables. Temperature effects and marked seasonal rhythms on quantitative ultrasound phantom measurements were evident but were far less apparent in vivo. Longitudinal precision of quantitative ultrasound variables was poorer for the manufacturer-provided phantom than for phantoms that were subjected to a temperature-control protocol or for healthy volunteers. This study has shown that longitudinal precision and longitudinal change differs between in vivo and phantom data. Longitudinal quantitative ultrasound measurements for monitoring change in skeletal status cannot, as yet, be properly controlled.

Heritability of calcaneal quantitative ultrasound measures in healthy adults from the Fels Longitudinal Study

Quantitative ultrasound (QUS) measurements of bone have been reported to predict osteoporotic fracture risk in postmenopausal women and older men. Although many studies have examined the heritability of bone mineral density (BMD), few studies have estimated the heritability of calcaneal QUS phenotypes. In the present study, we examined the genetic regulation of calcaneal QUS parameters in individuals from nuclear and extended families. The study population includes 260 men and 295 women aged 18-91 years (mean+/-SD: 46+/-16 years) who belong to 111 pedigrees in the Fels Longitudinal Study. Three measures of calcaneal structure were collected from both the right and left heel using the Sahara bone sonometer. These measures included broadband ultrasound attenuation (BUA), speed of sound (SOS), and the quantitative ultrasound index (QUI). We used a variance components based maximum likelihood method to estimate the heritability of QUS parameters while simultaneously adjusting for covariate effects. Additionally, we used bivariate extensions of these methods to calculate additive genetic and random environmental correlations among QUS measures. All phenotypes demonstrated statistically significant heritabilities (P<0.0000001). Heritabilities in the right heel (h2+/-SE) were h2=0.59+/-0.10 for BUA, h2=0.73+/-0.09 for SOS, and h2=0.72+/-0.09 for QUI. Similarly, heritabilities for the left heel were h2=0.52+/-0.10, h2=0.75+/-0.10, and h2=0.70+/0.10, respectively. There was evidence for significant genetic and environmental correlations among these six QUS measures. Combinations of QUS measures in the right and left heel demonstrated genetic correlations of 0.94-0.99 and all were significantly different from one indicating at least a partially unique genetic architecture for each of these measures. This study demonstrates that QUS measures of the calcaneus among healthy men and women are heritable, and there are large shared additive genetic effects among all of the traits examined.

Association of five quantitative ultrasound devices and bone densitometry with osteoporotic vertebral fractures in a population-based sample: the OPUS Study

We compared the performance of five QUS devices with DXA in a population-based sample of 2837 women. All QUS approaches discriminated women with and without osteoporotic vertebral fractures. QUS of the calcaneus performed as well as central DXA.

INTRODUCTION

Quantitative ultrasound (QUS) methods have found widespread use for the assessment of bone status in osteoporosis, but their optimal use remains to be established. To determine QUS performance for current devices in direct comparison with central DXA, we initiated a large population-based investigation, the Osteoporosis and Ultrasound Study (OPUS).

MATERIALS AND METHODS

A total of 463 women 20-39 years of age and 2374 women 55-79 years of age were measured on five different QUS devices along with DXA of the spine and the proximal femur. Their vertebral fracture status was evaluated radiographically. The association of QUS and DXA with vertebral fracture status was evaluated using logistic regression.

RESULTS

All QUS approaches tested discriminated women with and without osteoporotic vertebral fractures (20% height reduction), with age-adjusted standardized odds ratios ranging 1.2-1.3 for amplitude-dependent speed of sound (AD-SOS) at the finger phalanges, 1.2-1.4 for broadband ultrasound attenuation (BUA) at the calcaneus, and 1.4-1.5 for speed of sound (SOS) at the calcaneus, 1.4-1.6 for DXA of the total femur, and 1.5-1.6 for DXA at the spine. For more severe fractures (40% height reduction), age-adjusted standardized odds ratios increased to up to 1.9 for DXA of the spine and 2.3 for SOS of the calcaneus.

CONCLUSIONS

In conclusion, all five QUS devices tested showed significant age-adjusted differences between subjects with and without vertebral fracture. When selecting the strongest variable, QUS of the calcaneus worked as well as central DXA for identification of women at high risk for prevalent osteoporotic vertebral fractures. QUS-based case-finding strategies would allow halving the number of radiographs in high-risk populations, and this strategy works increasingly well for women with more severe vertebral fractures. It is likely that the good performance of QUS was in part achieved by rigorous quality assurance measures that should also be used in clinical practice.

Acoustic wave propagation in bovine cancellous bone: application of the Modified Biot-Attenborough model

Acoustic wave propagation in bovine cancellous bone is experimentally and theoretically investigated in the frequency range of 0.5-1 MHz. The phase velocity, attenuation coefficient, and broadband ultrasonic attenuation (BUA) of bovine cancellous bone are measured as functions of frequency and porosity. For theoretical estimation, the Modified Biot-Attenborough (MBA) model is employed with three new phenomenological parameters: the boundary condition, phase velocity, and impedance parameters. The MBA model is based on the idealization of cancellous bone as a nonrigid porous medium with circular cylindrical pores oriented normal to the surface. It is experimentally observed that the phase velocity is approximately nondispersive and the attenuation coefficient linearly increases with frequency. The MBA model predicts a slightly negative dispersion of phase velocity linearly with frequency and the nonlinear relationships of attenuation and BUA with porosity. The experimental results are in good agreement with the theoretical results estimated with the MBA model. It is expected that the MBA model can be usefully employed in the field of clinical bone assessment for the diagnosis of osteoporosis.

Correlations between acoustic properties and bone density in bovine cancellous bone from 0.5 to 2 MHz

Correlations between acoustic properties and bone density were investigated in the 12 defatted bovine cancellous bone specimens in vitro. Speed of sound (SOS) and broadband ultrasonic attenuation (BUA) were measured in three different frequency bandwidths from 0.5 to 2 MHz using three matched pairs of transducers with the center frequencies of 1, 2.25, and 3.5 MHz. The relative orientation between ultrasonic beam and bone specimen was the mediolateral (ML) direction of the bovine tibia. SOS shows significant linear positive correlation with apparent density for all three pairs of transducers. However, BUA shows relatively weak correlation with apparent density. SOS and BUA are only weakly correlated with each other. The linear combination of SOS and BUA in a multiple regression model leads to a significant improvement in predicting apparent density. The correlations among SOS, BUA, and bone density can be effectively and clearly represented in the three-dimensional space by the multiple regression model. These results suggest that the frequency range up to 1.5 MHz and the multiple regression model in the three-dimensional space can be useful in the osteoporosis diagnosis.

Bone mineral density, ultrasound velocity, and broadband attenuation predict mechanical properties of trabecular bone differently

Measurement of areal bone mineral density (BMD(areal)), broadband ultrasound (US) attenuation (BUA), and speed-of-sound (SOS) are widely used ways to perform clinical assessment of bone quality. In this study, bovine (n = 37) and human (n = 32) trabecular bone was investigated in vitro and in vivo to reveal relationships between mechanical properties, mineral density, and US parameters BUA and SOS. To fulfill these aims, clinical US and dual-energy X-ray absorptiometry (DXA) techniques, as well as dynamic and destructive mechanical testing, were utilized. BUA correlated positively and linearly with BMD(areal) only in human calcaneus of low or moderate density (r = 0.849, n = 32, p < 0.01). When calcaneal areas with high BMD(areal) were included in the analysis, however, the in vivo study revealed that the BUA-BMD(areal) relationship could be described by a second-order polynomial fit (r(2) = 0.618, n = 408). In high-density human or bovine bone, the BUA-bone density relationship was negative. In the in vitro assessment, BUA correlated linearly and negatively with volumetric BMD (BMD(vol)) (r = -0.540, n = 29, p < 0.01) and with storage modulus, as measured at 1 Hz (r = -0.505, n = 28, p < 0.01). A weak positive correlation was found between BUA and mechanical loss tangent (r = 0.322, n = 28, p < 0.1). SOS correlated strongly positively with BMD(vol) (r = 0.888, n = 29, p < 0.01), as well with storage modulus (r = 0.649, n = 28, p < 0.01). In contrast, SOS correlated negatively with loss tangent (r = -0.417, n = 28, p < 0.05). When tested dynamically in the frequency range of 0.01-22.7 Hz, bovine trabecular bone was only slightly viscoelastic. In summary, the most accurate parameters for measuring storage modulus and strength of bovine trabecular bone were SOS and BMD(vol), respectively. BUA failed to predict the mechanical properties of high-density trabecular bone. In vivo mapping of the calcaneus revealed the importance of standardized and reproducible localization of the measurement site for the validity of BUA values.

Quantitative ultrasound and trabecular architecture in the human calcaneus

Relationships between quantitative ultrasound (QUS), density (bone volume density [BV/TV]), and trabecular architecture were investigated in 69 calcaneal cancellous bone cubes. Ultrasound signal velocity, phase velocity, attenuation, and broadband ultrasonic attenuation (BUA) measurements were made along the mediolateral axis. Density and architectural parameters were measured using microcomputed tomography (microCT). Density yielded the best correlations with QUS (r2 = 73-77%). Of the individual architectural parameters, correlations with QUS were highest for the Structure Model Index (SMI), a parameter quantifying the relative proportion of rods and plates (r2 = 57-63%). After adjustment for density, significant associations with QUS remained for SMI, trabecular spacing (Tb.Sp), and trabecular number (Tb.N), although the variance in QUS attributable uniquely to individual architectural parameters was at best 4%. In multivariate regression models, combinations of density and architectural parameters explained 76-82% of the variance in QUS, representing an r2 increase of, at most, 8% compared with using density alone. However, multivariate models using combinations of architectural parameters alone (i.e., density excluded) also had a good predictive ability for QUS (r2 = 73-81%). Thus, although these data show modest but significant density-independent relationships between QUS and trabecular architecture in the human calcaneus for the first time, the causal relationships behind the variation in acoustic properties remain obscure. Given the relative weakness and complexity of the emerging associations between QUS and architecture, it is prudent to regard QUS measurements in calcaneal bone primarily as an indicator of bone density.

Quantitative ultrasound in postmenopausal osteoporosis

Ultrasound has been proposed as a low-cost, radiation-free method for osteoporosis assessment in postmenopausal women. Large prospective studies have shown that ultrasound parameters can be used for fracture risk estimate in this population, providing that adequate quality control is performed. The places of both ultrasound and the current gold standard method for bone assessment, dual energy x-ray absorptiometry, are still to be determined. Further studies are needed on the diagnosis of osteoporosis using ultrasound, because current diagnostic thresholds, designed by the World Health Organization, do not apply to this-new technology. Monitoring of skeletal changes and treatment effects by ultrasound cannot be recommended.

Scattering of ultrasound in cancellous bone: predictions from a theoretical model

An understanding of the interaction between acoustic waves and cancellous bone is needed in order to realize the full clinical potential of ultrasonic bone measurements. Scattering is likely to be of central importance but has received little attention to date. In this study, we adopted a theoretical model from the literature in which scattering was assumed to be proportional to the mean fluctuation in sound speed, and bone was considered to be a random continuum containing identical scatterers. The model required knowledge only of sound speeds in bone and marrow, porosity, and scatter size. Predicted attenuation, broadband ultrasonic attenuation (BUA) and backscatter coefficient were obtained for a range of porosities and scatterer sizes, and were found to be comparable to published values for cancellous bone. Trends in predicted BUA with porosity agreed with previous experimental observations. All three predicted acoustic parameters showed a non-linear dependence on scatterer size which was independent of porosity. These data confirm the value of the scattering approach and provide the first quantitative predictions of the independent influence of structure and porosity on bone acoustic properties.

Bone properties as estimated by mineral density, ultrasound attenuation, and velocity

Quantitative ultrasound (QUS) analysis of bone has been suggested to have a level of performance equal to dual-energy X-ray absorptiometry (DXA) for the assessment of fracture risk. In this study, QUS and DXA measurements were conducted on bovine trabecular bone in vitro using commercially available clinical instruments. The samples were then mechanically tested to obtain Young's modulus and ultimate strength. In addition, QUS and DXA parameters of the human calcaneus (n = 34) were measured in vivo. The measurements revealed a significant effect of bovine bone size on broadband ultrasound attenuation (BUA) and speed of sound (SOS) in vitro. By normalizing the DXA and QUS results with bone thickness we could systematically improve their ability to predict bone strength. However, in bovine trabecular bone, BUA showed no significant linear correlation with either bone mineral density (BMD), Young's modulus, or ultimate strength. This finding may be typical of only high-density and low-porosity bovine bone. We significantly improved prediction of ultimate strength by combining density and ultrasound velocity results as compared with assessments of volumetric BMDvol (p < 0.05) or SOS (p < 0.001) alone. However, the improvement was not significant if BMDvol, instead of wet density, was used. Altogether, 88% of the variation in the ultimate strength of bovine bone could be explained by combined density and ultrasound velocity. In vivo, SOS showed a weak negative correlation with heel width (r = -1.350). The in vivo measurements also showed a close correlation for BUA with BMD in the human calcaneus. This suggests that BUA is more suitable for quantitative analysis of low-density trabecular bone.

A model for ultrasonic scattering in cancellous bone based on velocity fluctuations in a binary mixture

A scattering model based on velocity fluctuations in a binary mixture (marrow fat and cortical matrix) was used to estimate the ultrasonic attenuation in cancellous bone as a function of volume fraction. The calculation of velocity fluctuations alone seems to be suitable for the qualitative estimation of attenuation. The predicted values of the attenuation were of the same order of magnitude as experimentally determined values from the literature. This agreement was achieved with only a small number of variables (the velocities of the two components and the scatterer size) in the model, representing a major advantage compared with other theories. Hence the suggested approach appears to be a good starting point for further theoretical investigations using scattering theories. However, this has to be accompanied by accurate ultrasonic and microstructural measurements.