Do quantitative ultrasound measurements reflect structure independently of density in human vertebral cancellous bone?

Ultrasonic Through-Transmission Measurements of Human Musculoskeletal and Fat Properties

The study described here was aimed at investigating the feasibility of using the ultrasonic through-transmission technique to estimate human musculoskeletal and fat properties. Five hundred eighty-two volunteers were assessed by dual-energy X-ray absorptiometry (DXA) and ultrasonic transmission techniques. Bone mineral density (BMD), muscle and fat mass were measured for both legs and the whole body. Hip BMD and spine BMD were also measured. Ultrasonic transmission measurements were performed on the heel, and the measured parameters were broadband ultrasound attenuation (BUA), speed of sound (SOS), ultrasonic stiffness index (SI), T-score and Z-score, which were significantly correlated with all measured BMDs. The optimal correlation was observed between SI and left-leg BMD (p < 0.001) before and after adjustment for age, sex and body mass index (BMI). The linear and partial correlation analyses revealed that BUA and SOS were closely associated with muscle and fat mass, respectively. Multiple regressions revealed that muscle and fat mass significantly contributed to the prediction of transmission parameters, explaining up to 17.83% (p < 0.001) variance independently of BMD. The results suggest that the ultrasonic through-transmission technique could help in the clinical diagnosis of skeletal and muscular system diseases.

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.

Anisotropic Longitudinal Wave Propagation in Swine Skull

To understand the in-plane elastic character of ultrasonic waves in the skull, longitudinal wave velocities were studied in the MHz range using a conventional pulse technique. Taking advantage of the thickness of swine skulls, anisotropic in-plane wave velocity changes in the outer and diploe layers were experimentally investigated using structural information measured by X-ray computer tomography (CT). The velocities in the thin inner layer were difficult to measure. The main trabecular alignment (MTA) in the thick swine diploe layer was almost perpendicular to the thickness direction and changed with position inside the skull. The degree of anisotropy of in-plane longitudinal wave velocity ranged 1.07-1.33 in both outer and diploe layers, depending on position and swine sample. The angle of the fastest velocity in the outer layer was different from that in most parts of the diploe layer. Anisotropic character in the diploe layer gradually changed with position in the thickness direction.

Evaluation of Structural Anisotropy in a Porous Titanium Medium Mimicking Trabecular Bone Structure Using Mode-Converted Ultrasonic Scattering

The mode-converted (longitudinal to transverse, L-T) ultrasonic scattering method was utilized to characterize the structural anisotropy of a phantom mimicking the structural properties of trabecular bone. The sample was fabricated using metal additive manufacturing from high-resolution computed tomography (CT) images of a sample of trabecular horse bone with strong anisotropy. Two focused transducers were used to perform the L-T ultrasonic measurements. A normal incidence transducer was used to transmit longitudinal ultrasonic waves into the sample, while the scattered transverse signals were received by an oblique incidence transducer. At multiple locations on the sample, four L-T measurements were performed by collecting ultrasonic scattering from four directions. The amplitude of the root mean square (rms) of the collected ultrasonic scattering signals was calculated for each L-T measurement. The ratios of rms amplitudes for L-T measurements in different directions were calculated to characterize the anisotropy of sample. The results show that the amplitude of L-T converted scattering is highly dependent on the direction of microstructural anisotropy. A strong anisotropy of the microstructure was observed, which coincides with simulation results previously published on the same structure as well as with the anisotropy estimated from the CT images. These results suggest the potential of mode-converted ultrasonic scattering methods to assess the anisotropy of materials with porous, complex structures, including trabecular bone.

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.

Ultrasonic Backscatter Difference Measurement of Bone Health in Preterm and Term Newborns

Metabolic bone disease of prematurity remains a significant problem for preterm infants. Quantitative ultrasound (QUS) has potential as a non-invasive tool for assessing bone health of newborns. The aim of this study was to assess bone health in preterm and term newborns using ultrasonic backscatter difference measurement. This study analyzed a total of 493 neonates, including 239 full-term infants (gestational age [GA] >37 wk), 201 preterm I infants (GA: 32-37 wk) and 53 extreme preterm II infants (GA <32 wk). Ultrasonic backscatter measurements were performed on the calcaneus of infants at birth, and the normalized mean of the backscatter difference spectrum (nMBD) was calculated as an ultrasonic index of neonatal bone status. Simple and multiple linear regressions were performed to determine the association of ultrasonic nMBD with GA, anthropometric characteristics and biochemical markers. Statistically significant differences in GA, anthropometric characteristics (birth weight, birth length [BL], birth head circumference and body mass index [BMI]) and biochemical markers (alkaline phosphatase, serum calcium and serum phosphate) were observed among preterm and term infants. The nMBD for term infants (median = 3.72 dB/μs, interquartile range [IR] = 1.95 dB/μs) was significantly higher than that for preterm I infants (median = 1.95 dB/μs, IR = 3.12 dB/μs), which was, in turn, significantly higher than that for preterm II infants (median = 0.19 dB/μs, IR = 3.50 dB/μs). The nMBD yielded moderate correlations (ρ = 0.57-0.62, p < 0.001) with GA and anthropometric characteristics and weak correlations (|ρ| = 0.08-0.21, p < 0.001 or not significant) with biochemical markers. Multivariate regressions revealed that only BL (p = 0.002) and BMI (p = 0.032) yielded significantly independent contributions to the nMBD measurement, and combinations of BL and BMI could explain up to 42% of the variation of nMBD in newborn infants. This study found that ultrasonic backscatter difference measurement might be helpful in bone health evaluation in preterm and term newborns. The utility of ultrasonic backscatter measurement in diagnosis of metabolic bone disease in infants should be investigated further.

Are we crying Wolff? 3D printed replicas of trabecular bone structure demonstrate higher stiffness and strength during off-axis loading

Roux's principle of bone functional adaptation postulates that bone tissue, and particularly trabecular bone tissue, responds to mechanical stimuli by adjusting (modeling) its architecture accordingly. Hence, it predicts that the new modeled trabecular structure is mechanically improved (stiffer and stronger) in line with the habitual in vivo loading direction. While previous studies found indirect evidence to support this theory, direct support was so far unattainable. This is attributed to the fact that each trabecular bone is unique, and that trabecular bone tissue tends to be damaged during mechanical testing. Consequently, a unique modeled trabecular structure can be mechanically tested only along one direction and a comparison to other directions for that specific structure is impossible. To address this issue, we have 3D printed 10 replicas of a trabecular structure from a sheep talus cropped along the 3 principal axes of the bone and in line with the principal direction of loading (denoted on-axis model). Next, we have rotated the same cropped trabecular structure in increments of 10° up to 90° to the bone principal direction of loading (denoted off-axis models) and printed 10 replicas of each off-axis model. Finally, all on-axis and off-axis 3D printed replicas were loaded in compression until failure and trabecular structure stiffness and strength were calculated. Contrary to our prediction, and conflicting with Roux's principle of bone functional adaptation, we found that a trabecular structure loaded off-axis tended to have higher stiffness and strength values when compared to the same trabecular structure loaded on-axis. These unexpected results may not disprove Roux's principle of bone functional adaptation, but they do imply that trabecular bone adaptation may serve additional purposes than simply optimizing bone structure to one principal loading scenario and this suggests that we still don't fully understand bone modeling in its entirety.

The Ability of Ultrasonic Backscatter Parametric Imaging to Characterize Bovine Trabecular Bone

The ultrasonic backscatter technique holds the promise of characterizing bone density and microstructure. This paper conducts ultrasonic backscatter parametric imaging based on measurements of apparent integrated backscatter (AIB), spectral centroid shift (SCS), frequency slope of apparent backscatter (FSAB), and frequency intercept of apparent backscatter (FIAB) for representing trabecular bone mass and microstructure. We scanned 33 bovine trabecular bone samples using a 7.5 MHz focused transducer in a 20 mm × 20 mm region of interest (ROI) with a step interval of 0.05 mm. Images based on the ultrasonic backscatter parameters (i.e., AIB, SCS, FSAB, and FIAB) were constructed to compare with photographic images of the specimens as well as two-dimensional (2D) μ-CT images from approximately the same depth and location of the specimen. Similar structures and trabecular alignments can be observed among these images. Statistical analyses demonstrated that the means and standard deviations of the ultrasonic backscatter parameters exhibited significant correlations with bone density (|R| = 0.45-0.78, p < 0.01) and bone microstructure (|R| = 0.44-0.87, p < 0.001). Some bovine trabecular bone microstructure parameters were independently associated with the ultrasonic backscatter parameters (ΔR² = 4.18%-44.45%, p < 0.05) after adjustment for bone apparent density (BAD). The results show that ultrasonic backscatter parametric imaging can provide a direct view of the trabecular microstructure and can reflect information about the density and microstructure of trabecular bone.

Assessment of osteoporotic fracture risk in urban Indian population using quantitative ultrasonography & FRAX tool

Background & objectives

There have been studies around the world on the prevalence of osteoporosis and its related risk factors, but there have been limited studies on risk factors and osteoporosis in the Indian population. In this study, the incidence of osteoporosis and the associated clinical risk factors (CRFs) were studied in the urban Indian population.

Methods

Bone mineral density of 445 individuals >38 yr of age using qualitative ultrasound (QUS) was assessed. The patients were also questioned regarding the presence of the various CRFs as per the FRAX tool. The patients were categorized into normal, osteopenia and osteoporosis groups on the basis of T-score from QUS.

Results

There were 223 males and 222 females in this study. Sex was significantly associated with T-score (P<0.001). Forty (8.99%) patients were osteoporotic, 265 (59.55%) were osteopenic and the remaining 140 (31.46%) were normal. A significant association of T-score was found with parent history of fracture (P<0.05), rheumatoid arthritis (P<0.05) and secondary osteoporosis (P<0.05). Previous history of fracture's association was not found to be significant. Smoking, alcohol intake and steroid intake were not found to be significantly associated with T-scores.

Interpretation & conclusions

The incidence of osteoporosis was found to be high in the urban Indian population. More care and attention should be targeted towards elderly, especially the ones with the risk factors to prevent osteoporosis in future.

Ultrasonic backscatter difference measurements of cancellous bone from the human femur: Relation to bone mineral density and microstructure

Ultrasonic backscatter techniques are being developed to detect changes in cancellous bone caused by osteoporosis. One technique, called the backscatter difference technique, measures the power difference between two portions of a backscatter signal. The goal of the present study is to investigate how bone mineral density (BMD) and the microstructure of human cancellous bone influence four backscatter difference parameters: the normalized mean of the backscatter difference (nMBD) spectrum, the normalized slope of the backscatter difference spectrum, the normalized intercept of the backscatter difference spectrum, and the normalized backscatter amplitude ratio (nBAR). Ultrasonic measurements were performed with a 3.5 MHz broadband transducer on 54 specimens of human cancellous bone from the proximal femur. Volumetric BMD and the microstructural characteristics of the specimens were measured using x-ray micro-computed tomography. Of the four ultrasonic parameters studied, nMBD and nBAR demonstrated the strongest univariate correlations with density and microstructure. Multivariate analyses indicated that nMBD and nBAR depended on trabecular separation and possibly other microstructural characteristics of the specimens independently of BMD. These findings suggest that nMBD and nBAR may be sensitive to changes in the density and microstructure of bone caused by osteoporosis.

Quantitative Ultrasound of the Mandible as a Novel Screening Approach for Osteoporosis

This study used an axial transmission quantitative ultrasound (QUS) device to assess mandibular bone strength. The aim of the study was first to establish the precision and repeatability of the axial transmission QUS measurement for a range of mandibular anatomic sites, and second to investigate the ability of the modality to differentiate between osteoporotic subjects and a control group. Three groups of adult Caucasian women were recruited: (1) healthy premenopausal women (n = 26), (2) healthy postmenopausal women (n = 48), and (3) women with osteoporosis (n = 53). Subjects were excluded from groups 1 and 2 if they had any pre-existing bone conditions. Speed of sound (SOS) measurements were taken from the mandible using an OmniSense multisite QUS device. Group 3 had dual-energy X-ray absorptiometry scans of the lumbar spine and femur. The most suitable site on the mandible was determined by repeat SOS measurements in 10 healthy premenopausal subjects, at 5 different sites. The parasymphysis site had the lowest root mean squared coefficient of variation at 0.74%, and was chosen as the most suitable site for mandibular SOS measurements. Group 1 and group 2 had significantly higher mean SOS measurements than the osteoporotic subjects (group 3), with means of 3683 m/s (210), 3514 m/s (221), and 3312 m/s (264), respectively. A 1-way analysis of variance confirmed a statistically significant difference between mean SOS measurements from the 3 groups (p < 0.0001). Axial transmission QUS of the mandible can differentiate between subjects with osteoporosis and a healthy control group, and shows potential for use as a screening tool for osteoporosis.

Attempt at standardization of bone quantitative ultrasound in Japan

Dual X-ray absorptiometry (DXA) is used to diagnose osteoporosis. On the other hand, quantitative ultrasound (QUS) is widely used to assess bone density as part of medical screening as it is relatively inexpensive and easy to perform. Current QUS devices do not share precise ultrasound-related parameters, such as frequency, waveform, beam pattern, transient response, definition of propagation time, definition of degree of attenuation, and precise measurement site, resulting in different measurements across models. The Japan Osteoporosis Society established a QUS Standardization Committee in 2007 to investigate standardization of speed of sound (SOS) and broadband ultrasonic attenuation (BUA) measurements to resolve this issue. The committee came up with a formula to convert SOS and BUA values yielded by each model available in Japan. This has made it possible to convert QUS measurements from different models into standardized values, greatly improving the effectiveness of QUS measurements.

A μCT-based investigation of the influence of tissue modulus variation, anisotropy and inhomogeneity on ultrasound propagation in trabecular bone

Ultrasound propagation is widely used in the diagnosis of osteoporosis by providing information on bone mechanical quality. When it loses calcium, the tissue properties will first decrease. However, limited research about the influence of tissue properties on ultrasound propagation have been done due to the cumbersome experiment. The goal of this study was to explore the relationships between tissue modulus (Es) and speed of sound (SOS) through numerical simulations, and to study the influence of Es on the acoustical behavior in characterizing the local structural anisotropy and inhomogeneity. In this work, three-dimensional finite element (FE) simulations were performed on a cubic high-resolution (15μm) bovine trabecular bone sample (4×4×4mm(3), BV/TV=0.18) mapped from micro-computed tomography. Ultrasound excitations of 50kHz, 500kHz and 2MHz were applied in three orthogonal axes and the first arriving signal (FAS) was collected to quantify wave velocity. In this study, a strong power law relationship between Es and SOS was measured with estimated exponential index β=2.08-3.44 for proximal-distal (PD), anterior-posterior (AP) and medial-lateral (ML), respectively (all R(2)>0.95). For various Es, a positive dispersion of sound speed with respect to sound frequency was observed and the velocity dispersion magnitude (VDM) was measured. Also, with Es=15GPa in three orientations, the SOS in PD axis is 2009±120m/s, faster than that of AP (1762±106m/s) and ML (1798±132m/s) (f=2MHz) directions. Besides, the standard deviation of SOS increases with the sound frequency and the Es in all directions except for that at 50kHz. For the mechanical properties, the apparent modulus with certain Es was highest in the longitudinal direction compared with the transverse directions. It indicates that the tissue modulus combining with anisotropy and inhomogeneity has great influence on ultrasound propagation. Simulation results agree well with theoretical and experimental results.

Solid volume fraction estimation of bone:marrow replica models using ultrasound transit time spectroscopy

The acceptance of broadband ultrasound attenuation (BUA) for the assessment of osteoporosis suffers from a limited understanding of both ultrasound wave propagation through cancellous bone and its exact dependence upon the material and structural properties. It has recently been proposed that ultrasound wave propagation in cancellous bone may be described by a concept of parallel sonic rays; the transit time of each ray defined by the proportion of bone and marrow propagated. A Transit Time Spectrum (TTS) describes the proportion of sonic rays having a particular transit time, effectively describing the lateral inhomogeneity of transit times over the surface aperture of the receive ultrasound transducer. The aim of this study was to test the hypothesis that the solid volume fraction (SVF) of simplified bone:marrow replica models may be reliably estimated from the corresponding ultrasound transit time spectrum. Transit time spectra were derived via digital deconvolution of the experimentally measured input and output ultrasonic signals, and compared to predicted TTS based on the parallel sonic ray concept, demonstrating agreement in both position and amplitude of spectral peaks. Solid volume fraction was calculated from the TTS; agreement between true (geometric calculation) with predicted (computer simulation) and experimentally-derived values were R(2)=99.9% and R(2)=97.3% respectively. It is therefore envisaged that ultrasound transit time spectroscopy (UTTS) offers the potential to reliably estimate bone mineral density and hence the established T-score parameter for clinical osteoporosis assessment.

Enhanced correlation between quantitative ultrasound and structural and mechanical properties of bone using combined transmission-reflection measurement

Quantitative ultrasound (QUS) is capable of predicting the principal structural orientation of trabecular bone; this orientation is highly correlated with the mechanical strength of trabecular bone. Irregular shape of bone, however, would increase variation in such a prediction, especially under human in vivo measurement. This study was designed to combine transmission and reflection modes of QUS measurement to improve the prediction for the structural and mechanical properties of trabecular bone. QUS, mechanical testing, and micro computed tomography (μCT) scanning were performed on 24 trabecular bone cubes harvested from a bovine distal femur to obtain the mechanical and structural parameters. Transmission and reflection modes of QUS measurement in the transverse and frontal planes were performed in a confined 60° angle range with 5° increment. The QUS parameters, attenuation (ATT) and velocity (UV), obtained from transmission mode, were normalized to the specimen thickness acquired from reflection mode. Analysis of covariance showed that the combined transmission-reflection modes improved prediction for the structural and Young's modulus of bone in comparison to the traditional QUS measurement performed only in the medial-lateral orientation. In the transverse plane, significant improvement between QUS and μCT was found in ATT vs bone surface density (BS/BV) (p < 0.05), ATT vs trabecular thickness (Tb.Th) (p < 0.01), ATT vs degree of anisotropy (DA) (p < 0.05), UV vs trabecular bone number (Tb.N) (p < 0.05), and UV vs Tb.Th (p < 0.001). In the frontal plane, significant improvement was found in ATT vs structural model index (SMI) (p < 0.01), ATT vs bone volume fraction (BV/TV) (p < 0.01), ATT vs BS/BV (p < 0.001), ATT vs Tb.Th (p < 0.001), ATT vs DA (p < 0.001), and ATT vs modulus (p < 0.001), UV vs SMI (p < 0.01), UV vs BV/TV (p < 0.05), UV vs BS/BV (p < 0.05), UV vs Tb.Th (p < 0.01), UV vs trabecular spacing (p < 0.05), and UV vs modulus (p < 0.01). These data suggested that the combined transmission-reflection QUS method is capable of providing information more relevant to the structural and mechanical properties of trabecular bone.

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.

Quantitative ultrasound measurements at the heel: improvement of short- and mid-term speed of sound precision

Calcaneal quantitative ultrasound can be used to predict osteoporotic fracture risk, but its ability to monitor therapy is unclear possibly because of its limited precision. We developed a quantitative ultrasound device (foot ultrasound scanner) that measures the speed of sound at the heel with the aim of minimizing common error sources like the position and penetration angle of the ultrasound beam, as well as the soft tissue temperature. To achieve these objectives, we used a receiver array, mechanics to adjust the beam direction and a foot temperature sensor. In a group of 60 volunteers, short-term precision was evaluated for the foot ultrasound scanner and a commercial device (Achilles Insight, GE Medical, Fairfield, CT, USA‎). In a subgroup of 20 subjects, mid-term precision (1-mo follow-up) was obtained. Compared with measurement of the speed of sound with the Achilles Insight, measurement with the foot ultrasound scanner reduced precision errors by half (p < 0.05). The study indicates that improvement of the precision of calcaneal quantitative ultrasound measurements is feasible.

Correlations of linear and nonlinear ultrasound parameters with density and microarchitectural parameters in trabecular bone

In the present study, correlations of linear and nonlinear ultrasound parameters (speed of sound, normalized broadband ultrasound attenuation, and nonlinear parameter B/A) with bone mineral density and microarchitectural parameters were investigated in 28 bovine femoral trabecular bone samples in vitro. All three ultrasound parameters exhibited relatively high correlation coefficients with the indexes of bone quantity (bone mineral density and bone volume fraction) and lower correlation coefficients with the remaining microarchitectural parameters. These results suggest that B/A, in addition to speed of sound and attenuation, may have potential as an index for the assessment of bone status and osteoporosis.

Estimation of multipath transmission parameters for quantitative ultrasound measurements of bone

When applying quantitative ultrasound (QUS) measurements to bone for predicting osteoporotic fracture risk, the multipath transmission of sound waves frequently occurs. In the last 10 years, the interest in separating multipath QUS signals for their analysis awoke, and led to the introduction of several approaches. Here, we compare the performances of the two fastest algorithms proposed for QUS measurements of bone: the modified least-squares Prony method (MLSP), and the space alternating generalized expectation maximization algorithm (SAGE) applied in the frequency domain. In both approaches, the parameters of the transfer functions of the sound propagation paths are estimated. To provide an objective measure, we also analytically derive the Cramér-Rao lower bound of variances for any estimator and arbitrary transmit signals. In comparison with results of Monte Carlo simulations, this measure is used to evaluate both approaches regarding their accuracy and precision. Additionally, with simulations using typical QUS measurement settings, we illustrate the limitations of separating two superimposed waves for varying parameters with focus on their temporal separation. It is shown that for good SNRs around 100 dB, MLSP yields better results when two waves are very close. Additionally, the parameters of the smaller wave are more reliably estimated. If the SNR decreases, the parameter estimation with MLSP becomes biased and inefficient. Then, the robustness to noise of the SAGE clearly prevails. Because a clear influence of the interrelation between the wavelength of the ultrasound signals and their temporal separation is observable on the results, these findings can be transferred to QUS measurements at other sites. The choice of the suitable algorithm thus depends on the measurement conditions.

NUMERICAL SIMULATIONS OF CHANGE IN TRABECULAR STRUCTURE DUE TO BONE REMODELING UNDER ULTRASOUND PROPAGATION

Bone remodeling is defined as the coupling of bone formation and resorption on the bone surface. Numerical simulations of the remodeling in cancellous bone were performed to reproduce the change in the trabecular structure. Assuming that the formation/resorption in cancellous bone could be generated on the trabecular surface, where the local stress under the mechanical load was larger/smaller than the averaged stress on the surrounding surface, voxel trabecular elements in a numerical model of bovine cancellous bone were added/removed. An ultrasound continuous wave in the frequency range 0.1–1.0 MHz was applied as the mechanical load, and then, the local stress was analyzed using a finite-difference time-domain (FDTD) method. Using the remodeling simulations, both changes in the trabecular structure could be reproduced with decreasing and increasing porosity. In changes, the trabecular elements and the pore spaces became strongly oriented in the direction of ultrasound propagation. In addition, the remodeling simulations indicated that both bone formation and resorption lessened as the frequency increased.

Simulations of ultrasound propagation in random arrangements of elliptic scatterers: occurrence of two longitudinal waves

Ultrasound propagation in clusters of elliptic (two-dimensional) or ellipsoidal (three-dimensional) scatterers randomly distributed in a fluid is investigated numerically. The essential motivation for the present work is to gain a better understanding of ultrasound propagation in trabecular bone. Bone microstructure exhibits structural anisotropy and multiple wave scattering. Some phenomena remain partially unexplained, such as the propagation of two longitudinal waves. The objective of this study was to shed more light on the occurrence of these two waves, using finite-difference simulations on a model medium simpler than bone. Slabs of anisotropic, scattering media were randomly generated. The coherent wave was obtained through spatial and ensemble-averaging of the transmitted wavefields. When varying relevant medium parameters, four of them appeared to play a significant role for the observation of two waves: (i) the solid fraction, (ii) the direction of propagation relatively to the scatterers orientation, (iii) the ability of scatterers to support shear waves, and (iv) a continuity of the solid matrix along the propagation. These observations are consistent with the hypothesis that fast waves are guided by the locally plate/bar-like solid matrix. If confirmed, this interpretation could significantly help developing approaches for a better understanding of trabecular bone micro-architecture using ultrasound.

Frequency specific ultrasound attenuation is sensitive to trabecular bone structure

This study investigated the efficacy of frequency modulated ultrasound attenuation in the assessment of the trabecular structural properties. Four frequency modulated signals were created to represent four frequency bands centered at 500 kHz, 900 kHz, 1.3 MHz and 1.7 MHz with the bandwidth of 400 kHz. Five 1-cm trabecular cubes were harvested from fresh bovine distal femur. The cubes underwent four steps of demineralization process to expand the sample size to 25 with the greater variations of the structural properties for the better correlation study. Pearson correlation study was performed between the ultrasound attenuation in four frequency bands and the trabecular structural properties. The results showed that correlations of frequency modulated ultrasound attenuation to the trabecular structural properties are dependent on frequency bands. The attenuation in proximal-distal orientation had the highest correlation to BV/TV (R(2) = 0.73, p < 0.001) and trabecular thickness (R(2) = 0.50, p < 0.001) at the frequency band centered at 1.7 MHz. It was equivalent in the four frequency bands in correlation to the trabecular number (average R(2) = 0.80, p < 0.001) and to the trabecular separation (average R(2) = 0.83, p < 0.001). The attenuation in anterio-posterial orientation had the highest correlation to BV/TV (R(2) = 0.80, p < 0.001) and trabecular thickness (R(2) = 0.71, p < 0.001) at the frequency band centered at 1.3 MHz. The attenuation in the first frequency band was the most sensitive to the trabecular number (R(2) = 0.71, p < 0.001) and trabecular separation (R(2) = 0.80, p < 0.001). No significant correlation was observed for the attenuation in medial-lateral orientation across the four frequency bands.

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.

IN VITROACOUSTIC WAVE PROPAGATION IN HUMAN AND BOVINE CANCELLOUS BONE AS PREDICTED BY BIOT'S THEORY

Recent in vitro studies have provided evidence of the propagation of two different longitudinal wave modes at ultrasonic frequencies in cancellous bone. The genesis of these two plane waves in fluid-saturated porous media is predicted by the poroelastic approach to wave propagation originally developed by Biot. However, wave velocity is usually analyzed as a function of bone mass density only; therefore, the influence of the cancellous bone microstructure over the wave velocity is not taken into account. In the present study, a descriptor of the microstructure is considered in Biot's theory. This model is used to evaluate the large experimental variability of both fast and slow wave velocities measured on randomly oriented human and bovine cancellous bone samples. The role of the anisotropic solid structure and fluid in the behavior of fast and slow wave velocities is examined. Experimental and theoretically predicted velocities are found in close agreement when analyzed as a function of both porosity and structural index. This model has the potential to be used to determine an acoustically derived structural index in cancellous bone.

Numerical investigation of ultrasound refraction caused by oblique orientation of trabecular network in cancellous bone

Ultrasound propagation through cancellous bone can be greatly affected by the trabecular structure. In the present study, the ultrasound propagation for the oblique orientation of the trabecular network was numerically investigated using 3-D finite-difference time-domain (FDTD) simulations. The models of cancellous bone were reconstructed from X-ray microcomputed tomographic (μCT) images of a bovine bone. Cancellous bone models with various orientations of the trabecular network were realized by cutting the μCT images rotated from 0 to 90°. Ultrasound waveforms propagating through these cancellous bone models were simulated while changing the receiving position. The refraction of the ultrasound wave for the oblique angle of the main orientation was investigated on the basis of the variation in the arrival time and peak amplitude. As the propagation direction approached the direction parallel to the main orientation, the arrival time of the first peak became less and the peak amplitude became smaller. This means that the wave of the first peak, which corresponded to a fast wave, propagated in the direction perpendicular to the main orientation. In addition, a strong correlation between the first-peak amplitude and the arrival time was observed in the porosity range of 0.68 to 0.85, in which the slope of the amplitude with respect to time increased linearly with porosity.

Fabric dependence of wave propagation in anisotropic porous media

Current diagnosis of bone loss and osteoporosis is based on the measurement of the bone mineral density (BMD) or the apparent mass density. Unfortunately, in most clinical ultrasound densitometers: 1) measurements are often performed in a single anatomical direction, 2) only the first wave arriving to the ultrasound probe is characterized, and 3) the analysis of bone status is based on empirical relationships between measurable quantities such as speed of sound (SOS) and broadband ultrasound attenuation (BUA) and the density of the porous medium. However, the existence of a second wave in cancellous bone has been reported, which is an unequivocal signature of poroelastic media, as predicted by Biot's poroelastic wave propagation theory. In this paper, the governing equations for wave motion in the linear theory of anisotropic poroelastic materials are developed and extended to include the dependence of the constitutive relations upon fabric-a quantitative stereological measure of the degree of structural anisotropy in the pore architecture of a porous medium. This fabric-dependent anisotropic poroelastic approach is a theoretical framework to describe the microarchitectural-dependent relationship between measurable wave properties and the elastic constants of trabecular bone, and thus represents an alternative for bone quality assessment beyond BMD alone.

Cortical thickness and medullary canal dimensions of the bone phalanx are predicted by quantitative ultrasound parameters

The aim of the study was to investigate the relationship between quantitative ultrasound (QUS) parameters extracted from the analysis of the ultrasound (US) signal and the geometric properties of the bones. One hundred and one subjects in the age range of 20-7 4yr (mean: 52+/-12 yr) have been measured by QUS at the phalanges for the evaluation of amplitude-dependent speed of sound (AD-SoS), bone transmission time (BTT), US peak amplitude (UPA), signal dynamic (SDY), slope, energy, and fast wave amplitude (FWA). Hand radiograph, lumbar spine dual-energy X-ray absorptiometry (DXA) and quantitative computed tomography (QCT), and femoral neck DXA forearm peripheral QCT were performed on all patients. BTT is related to cortical thickness (CTh) (r=0.62, p<0.0001), and FWA is related to medullary canal thickness (r=-0.64, p<0.0001). Other parameters are related to both medullary canal thickness (AD-SoS: r=-0.21; UPA: r=-0.53; SDY: r=-0.56; slope: r=-0.64; energy: r=-0.44, p<0.05) and CTh (AD-SoS: r=0.54, p<0.0001; UPA: r=0.51; SDY: r=0.38; slope: r=0.32; energy: r=0.56, p<0.001). Linear multivariate models indicate that BTT, UPA, and energy measured at the phalanges carry independent information on CTh of the bone, whereas FWA, SDY, and slope are related only to medullary canal thickness.

Analysis of quantitative ultrasound graphic trace and derived variables assessed at proximal phalanges of the hand in healthy subjects and in patients with cerebral palsy or juvenile idiopathic arthritis. A pilot study

Amplitude-dependent speed of sound (AD-SoS) and bone transmission time (BTT) are the quantitative ultrasound (QUS) variables usually assessed at proximal phalanges of the hand to estimate bone mineral status. The aim of the study was to provide a reference database for some additional QUS variables reflecting morphology of the ultrasound graphic trace according to gender, age, height, weight, and body mass index (BMI), and to assess their clinical usefulness. Fifty-two patients (age 3.1-20.9 years) affected by cerebral palsy with spastic tetraplegia (CPST, n=38) or polyarticular active juvenile idiopathic arthritis (JIA, n=14) were examined. In addition to AD-SoS and BTT, two QUS variables derived from the morphological analysis of ultrasound graphic trace, such as energy, extrapolated from the area under the ultrasound signal received, and weighted-slope (W-slope), derived from the angular coefficient of the regression line fitting the top point of the peaks of the ultrasound signal, were measured by phalangeal QUS (DBM Sonic, IGEA). The values of all the QUS variables measured in the patients were compared with our own sex- and age-reference values (n=1083, 587 males and 496 females, aged 3-21 years). The mean values of AD-SoS, BTT, energy, and W-slope were reduced (P<0.0001) in patients as a whole compared with normative data (-2.4+/-1.2, -2.7+/-1.5, -2.5+/-1.1, -2.5+/-1.1 Z-score, respectively). Fractured patients showed lower (P<0.001-P<0.0001) values of the QUS variables than fracture-free patients (AD-SoS, -3.3+/-1.2 and -1.8+/-0.9; BTT, -3.9+/-1.7 and -1.8+/-1.1; energy, -3.2+/-1.2 and -2.2+/-0.7; W-slope, -3.4+/-1.4 and -2.2+/-0.9 Z-score, respectively). There was no difference (P=NS) between patients with CPST and those with JIA. Age and height were positively correlated with all the QUS variables (r=0.55-0.79, P<0.01-P<0.0001). QUS variables were positively correlated among them (r=0.74-0.94, P<0.0001). Age and number of fractures were independent predictors of the QUS variables (coefficients: AD-SoS, 11.466 and -17.642; BTT, 0.049 and -0.045; energy, 1.072 and -1.303; W-slope, 0.046 and -0.067; respectively). In conclusion, measurement of QUS variables derived from the morphological analysis of the ultrasound signal could give additional information in estimating bone mineral status in children and adolescents, probably reflecting some aspect related to bone structure.

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.

Hierarchical microimaging of bone structure and function

With recent advances in molecular medicine and disease treatment in osteoporosis, quantitative image processing of three-dimensional bone structures is critical in the context of bone quality assessment. Biomedical imaging technology such as MRI or CT is readily available, but few attempts have been made to expand the capabilities of these systems by integrating quantitative analysis tools and by exploring structure-function relationships in a hierarchical fashion. Nevertheless, such quantitative end points are an important factor for success in basic research and in the development of novel therapeutic strategies. CT is key to these developments, as it images and quantifies bone in three dimensions and provides multiscale biological imaging capabilities with isotropic resolutions of a few millimeters (clinical CT), a few tens of micrometers (microCT) and even as high as 100 nanometers (nanoCT). The technology enables the assessment of the relationship between microstructural and ultrastructural measures of bone quality and certain diseases or therapies. This Review focuses on presenting strategies for three-dimensional approaches to hierarchical biomechanical imaging in the study of microstructural and ultrastructural bone failure. From this Review, it can be concluded that biomechanical imaging is extremely valuable for the study of bone failure mechanisms at different hierarchical levels.

Relationship between ultrasonic parameters and apparent trabecular bone elastic modulus: a numerical approach

The physical principles underlying quantitative ultrasound (QUS) measurements in trabecular bone are not fully understood. The translation of QUS results into bone strength remains elusive. However, ultrasound being mechanical waves, it is likely to assess apparent bone elasticity. The aim of this study is to derive the sensitivity of QUS parameters to variations of apparent bone elasticity, a surrogate for strength. The geometry of 34 human trabecular bone samples cut in the great trochanter was reconstructed using 3-D synchrotron micro-computed tomography. Finite-difference time-domain simulations coupled to 3-D micro-structural models were performed in the three perpendicular directions for each sample and each direction. A voxel-based micro-finite element linear analysis was employed to compute the apparent Young's modulus (E) of each sample for each direction. For the antero-posterior direction, the predictive power of speed of sound and normalized broadband ultrasonic attenuation to assess E was equal to 0.9 and 0.87, respectively, which is better than what is obtained using bone density alone or coupled with micro-architectural parameters and of the same order of what can be achieved with the fabric tensor approach. When the direction of testing is parallel to the main trabecular orientation, the predictive power of QUS parameters decreases and the fabric tensor approach always gives the best results. This decrease can be explained by the presence of two longitudinal wave modes. Our results, which were obtained using two distinct simulation tools applied on the same set of samples, highlight the potential of QUS techniques to assess bone strength.

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.

Bone sonometry: reducing phase aberration to improve estimates of broadband ultrasonic attenuation

Previous studies suggest that phase cancellation at the receiving transducer can result in the overestimation of the frequency dependent ultrasonic attenuation of bone, a quantity that has been shown to correlate with bone mineral density and ultimately with osteoporotic fracture risk. Evidence supporting this interpretation is provided by phase insensitive processing of the data, which appear to reduce the apparent overestimates of attenuation. The present study was designed to clarify the components underlying phase aberration artifacts in such through-transmission measurements by conducting systematic studies of the simplest possible test objects capable of introducing phase aberration. Experimental results are presented for a Lexan phantom over the frequency range 300-700 kHz and a Plexiglas phantom over the 3-7 MHz range. Both phantoms were flat and parallel plates featuring a step discontinuity milled into one of their initially flat sides. The through-transmitted signals were received by a 0.6 mm diameter membrane hydrophone that was raster scanned over a grid coaxial with the transmitting transducer. Signals received by the pseudoarray were processed offline to emulate phase sensitive and phase insensitive receivers with different aperture diameters. The data processed phase sensitively were focused to demonstrate the results of planar, geometrical, and correlation-based aberration correction methods. Results are presented illustrating the relative roles of interference in the ultrasonic field and phase cancellation at the receiving transducer in producing phase aberration artifacts. It was found that artifacts due to phase cancellation or interference can only be minimized with phase insensitive summation techniques by choosing an appropriately large receiving aperture. Data also suggest the potentially confounding role of time-and frequency-domain artifacts on ultrasonic measurements and illustrate the advantages of two-dimensional receiving arrays in determining the slope of attenuation (nBUA) for the clinical assessment of osteoporosis.

Analysis of frequency dependence of ultrasonic backscatter coefficient in cancellous bone

The ultrasonic scattering mechanism in cancellous bone is investigated theoretically and a model describing the frequency dependence of ultrasonic scattering from cancellous bone is presented. The ultrasonic backscatter coefficient (BSC) of bovine tibiae, human calcanei in vitro and in vivo, were measured and discussed. The data of BSC were also fitted by polynomial. The results demonstrate that BSC is a nonlinear function of frequency and increases with frequency. A good agreement was obtained between BSC values from theory and experiment. Also, the high correlation coefficient between BSC and bone mineral density was obtained, r=0.85+/-0.07 (mean+/-SD) (n=15, p<0.001). Based on the values of BSC, the status of cancellous bone and the degree of osteoporotic fracture risk may be assessed.

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.

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.

Influence of density, elasticity, and structure on ultrasound transmission through trabecular bone cylinders

The aim of this in vitro study is to evaluate the potentiality of quantitative ultrasound (QUS) to separate information on density, elasticity, and structure on specimens of trabecular bone. Fifteen cylinders of spongy bone extracted from equine vertebrae were progressively demineralized and subjected to QUS, micro computed tomography (muCT), Dual energy X-ray absorptiometry (DXA) at various mineralization levels. Eventually all cylinders underwent a compression test to calculate the Young's modulus. Correlation analysis shows that speed of sound (SOS) is strictly associated to bone mineral density (BMD), Young's modulus, and all muCT parameters except for degree of anisotropy (DA). Fast wave amplitude (FWA) is directly correlated with bone surface and total volume ratio (BS/TV) and trabecular separation (Tb Sp), and inversely correlated with trabecular number (Tb N). Because muCT parameters were strictly correlated to BMD and Young's modulus data, partial correlation analysis was performed between SOS, FWA, and structural and elastic data in order to eliminate the effect of density. SOS was significantly correlated to bone volume and total volume ratio (BV/TV), BS/TV, and Young's modulus, and FWA was significantly correlated to Tb Sp only. These results show that SOS is strongly influenced by volumetric mineral bone density and elastic modulus of the specimen, and FWA is mainly affected by trabecular separation independently on density. Therefore, SOS and FWA are able to provide different and complementary information, at least on trabecular bone samples.

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.

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.

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.

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

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

The correlation between the SOS in trabecular bone and stiffness and density studied by finite-element analysis

For the clinical assessment of osteoporosis (i.e., a degenerative bone disease associated with increased fracture risk), ultrasound has been proposed as an alternative or supplement to the dual-energy X-ray absorptiometry (DEXA) technique. However, the interaction of ultrasound waves with (trabecular) bone remains relatively poorly understood. The present study aimed to improve this understanding by simulating ultrasound wave propagation in 15 trabecular bone samples from the human lumbar spine, using microcomputed tomography-based finite-element modeling. The model included only the solid bone, without the bone marrow. Two structural parameters were calculated: the bone volume fraction (BV/TV) and the structural (apparent) elastic modulus (E(s)), and the ultrasound propagation parameter speed of sound (SOS). Relations between BV/TV and E(s) were similar to published experimental relations. At 1 MHz, correlations between SOS and the structural parameters BV/TV and Es were rather weak, but the results can be explained from the specific features of the trabecular structure and the intrinsic material elastic modulus E(i). In particular, the systematic differences between the three main directions provide information on the trabecular structure. In addition, at 1 MHz the correlation found between the simulated SOS values and those calculated from the simple bar equation was poor when the three directions are considered separately. Hence, under these conditions, the homogenization approach-including the bar equation-is not valid. However, at lower frequencies (50-300 kHz) this correlation significantly improved. It is concluded that detailed analysis of ultrasound wave propagation through the solid structure in various directions and with various frequencies, can yield much information on the structural and mechanical properties of trabecular bone.

Model-based estimation of quantitative ultrasound variables at the proximal femur

To improve the prediction of the osteoporotic fracture risk at the proximal femur we are developing a scanner for quantitative ultrasound (QUS) measurements at this site. Due to multipath transmission in this complex shaped bone, conventional signal processing techniques developed for QUS measurements at peripheral sites frequently fail. Therefore, we propose a model-based estimation of the QUS variables and analyze the performance of the new algorithm. Applying the proposed method to QUS scans of excised proximal femurs increased the fraction of evaluable signals from approx. 60% (using conventional algorithms) to 97%. The correlation of the standard QUS variables broadband ultrasound attenuation (BUA) and speed of sound (SOS) with the established variable bone mineral density (BMD) reported in previous studies is maintained (BUA/BMD: r(2) = 0.69; SOS/BMD: r(2) = 0.71; SOS+BUA/BMD: r(2) = 0.88). Additionally, different wave types could be clearly detected and characterized in the trochanteric region. The ability to separate superimposed signals with this approach opens up further diagnostic potential for evaluating waves of different sound paths and wave types through bone tissue.

Development of a method for ultrasound-guided placement of pedicle screws

Abstract-Many forms of spinal fusion involve the placement of long screws through the pedicles into the vertebral body. During the procedure, there is substantial risk of damage to vital neural and vascular structures due to the limited visibility of anatomic landmarks and high anatomic variability. As an alternative to current guidance systems, we have investigated the feasibility of performing ultrasound imaging through cancellous bone for the purpose of pedicle screw guidance. Quantitative ultrasonic characterization and A-mode imaging of seven defatted vertebral cancellous bone specimens was performed along the craniocaudal axis in water with unfocused, 1-MHz and 3.5- MHz broadband transducers. The center frequency attenuation increased considerably from 10.5 +/- 4.6 dB/cm at 1 MHz to 24.1 +/- 7.2 dB/cm at 3.5 MHz, while the speed of sound exhibited moderate positive dispersion, increasing from 1489 +/- 4.7 m/s at 1 MHz to 1494 +/- 4.2 m/s at 3.5 MHz. Despite the high attenuation and large specimen thickness (1.0-1.9 cm), A-mode imaging through cancellous bone to detect an aluminum reflector was possible in 83.2% and 70.1% of the cases at 1 MHz and 3.5 MHz, respectively. Specimen boundaries were identifiable with clinically sufficient average accuracy of 1.1 mm and 0.9 mm in the 1 MHz and 3.5 MHz A-mode images, respectively.

Spatial variation of acoustic properties is related with mechanical properties of trabecular bone

In clinical applications, ultrasound parameters are measured as an average value over a region of interest (ROI) or as a value at a single measurement point. Due to natural adaptation to loading conditions, trabecular bone is structurally, compositionally and mechanically heterogeneous and anisotropic. Thus, spatial variation of ultrasound parameters within ROI may contain valuable information on the mechanical integrity of trabecular bone. However, this issue has not been thoroughly investigated. In the present study, we aimed at investigating the significance of the spatial variation of ultrasound parameters for the prediction of mechanical properties of human trabecular bone. For this aim, parametric maps of apparent integrated backscattering (AIB), integrated reflection coefficient (IRC), speed of sound (SOS), average attenuation (AA) and normalized broadband ultrasound attenuation (nBUA) were calculated for femoral and tibial bone cylinders (n = 19-20). Further, the effect of time window length on the AIB, variation of AIB within ROI and association between AIB and bone mechanical properties were characterized. Based on linear correlation analysis, spatial variation of AIB, assessed as standard deviation of measurements within ROI, was a strong predictor of bone ultimate strength (r = -0.82, n = 19, p < 0.01). Further, the time window length affected absolute values of AIB and strength of correlation between AIB and bone ultimate strength. Interestingly, linear combination of mean IRC and spatial variation of AIB within ROI was the strongest predictor of bone ultimate strength (r = 0.92, n = 19, p < 0.01). In conclusion, our findings suggest that the measurement of two-dimensional parametric maps of ultrasound parameters could yield information on bone status not extractable from single point measurements. This highlights the potential of parametric imaging in osteoporosis diagnostics.

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.

Quantitative ultrasound predicts bone mineral density and failure load in human lumbar vertebrae

BACKGROUND

Quantitative ultrasound is in widespread clinical use for assessment of bone quality at peripheral skeletal sites, but has not yet been applied to those sites in the axial skeleton, such as the spine and hip, where osteoporotic fractures are common.

METHODS

Ultrasound measurements were made in 11 cadaveric vertebrae and relationships with bone mineral density and failure load were investigated. An ultrasonic imaging system was used to measure speed of sound, broadband ultrasonic attenuation, and attenuation at a single frequency, through the vertebral body in the sagittal plane. Ultrasonic measurements were averaged over a region of interest centrally within the vertebral body, and were calculated with and without normalization for bone size. Vertebral bone mineral density was measured in antero-posterior and lateral projections using dual energy X-ray absorptiometry. Compressive mechanical testing was performed to determine vertebral failure load.

FINDINGS

Bone mineral density correlated with failure load (r=0.74-0.78, all P<0.01), and with quantitative ultrasound (r=0.63-0.82, P=0.038-0.004), in line with previous studies. Of the ultrasonic measurements, those parameters not normalized for bone size gave the highest correlations with failure load, ranging from r=0.71 (P=0.021) for speed of sound to r=0.93 (P<0.001) for attenuation. When ultrasonic measurements were normalized for bone size, the correlations with both failure load and bone mineral density were lower.

INTERPRETATION

These results confirm the feasibility of vertebral quantitative ultrasound in vitro, and indicate that ultrasound does provide information on both bone mineral density and failure load. The predictive performance of ultrasonic measurements for failure load was comparable to or greater than that of bone mineral density, suggesting that ultrasound has the potential to be at least as useful as mineral density in the assessment of vertebral bone. Normalizing ultrasonic measurements for bone size reduced the strength of correlations because both bone mineral density and bone strength reflect bone size to a certain extent.