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

Relationships of the ultrasonic backscatter measurements with the bone mineral density and the microarchitectural parameters in bovine trabecular bone in vitro

Relationships of the backscatter coefficient (BC), the apparent integrated backscatter (AIB), and the integrated reflection coefficient (IRC) with the bone mineral density (BMD) and the microarchitectural parameters were investigated in 28 bovine femoral trabecular bone samples. The BC was highly correlated with the BMD and the microarchitectural parameters (R = -0.66 to 0.71). In contrast, the AIB and the IRC exhibited high correlations with the BMD and the bone volume fraction (R = -0.68 to 0.77) and relatively lower correlations with the remaining microarchitectural parameters (R = -0.62 to 0.60). The multiple regression models yielded the adjusted squared correlation coefficients of 0.54-0.76.

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.

Poromicromechanics reveals that physiological bone strains induce osteocyte-stimulating lacunar pressure

Mechanical loads which are macroscopically acting onto bony organs, are known to influence the activities of biological cells located in the pore spaces of bone, in particular so the signaling and production processes mediated by osteocytes. The exact mechanisms by which osteocytes are actually able to “feel” the mechanical loading and changes thereof, has been the subject of numerous studies, and, while several hypotheses have been brought forth over time, this topic has remained a matter of debate. Relaxation times reported in a recent experimental study of Gardinier et al. (Bone 46(4):1075–1081, 2010) strongly suggest that the lacunar pores are likely to experience, during typical physiological load cycles, not only fluid transport, but also undrained conditions. The latter entail the buildup of lacunar pore pressures, which we here quantify by means of a thorough multiscale modeling approach. In particular, the proposed model is based on classical poroelasticity theory, and able to account for multiple pore spaces. First, the model reveals distinct nonlinear dependencies of the resulting lacunar (and vascular) pore pressures on the underlying bone composition, highlighting the importance of a rigorous multiscale approach for appropriate computation of the aforementioned pore pressures. Then, the derived equations are evaluated for macroscopic (uniaxial as well as hydrostatic) mechanical loading of physiological magnitude. The resulting model-predicted pore pressures agree very well with the pressures that have been revealed, by means of in vitro studies, to be of adequate magnitude for modulating the responses of biological cells, including osteocytes. This underlines that osteocytes may respond to many types of loading stimuli at the same time, in particular so to fluid flow and hydrostatic pressure.

Poro-Micromechanics of Bone: Impact Loading and Wave Propagation

Based on ‘universal’ mechanical building blocks inherent to all different bones, this paper shows the integration of two classically separated fields of bone biomechanics, namely bone micromechanics[1] on the one hand, and bone poromechanics[2] on the other. Indeed, despite the complex hierarchical organization of bone, it was recently possible to identify such elementary components at the micro and nanolevel of the material for the explanation of the diversity of macroscopic (poro-)elastic properties of different bones. The mechanical properties (i.e. elasticity) of these elementary components are (within limits of experimental scatter) the same for all bones; they are ‘universal’, i.e. independent of tissue type, species, and anatomical location. The mechanical interaction between these elementary components (mechanical morphology) and the dosages of these components in different tissues determine the macroscopic material properties.

Continuum micromechanics has turned out as well-suited theoretical tool to derive tissue-dependent elastic properties at different length scales from upscaling the elasticity of ‘universal’ building blocks from the nanometer scale. Once respective micromechanics models are developed and validated, poro-micromechanics allows for the quantification of poroelastic properties such as the Biot and Skempton coefficients, as functions of the volume fractions of mineral, collagen, and the micropore space (Haversian and Volkmann canals, and the inter-trabecular space). Skempton coefficients, related to undrained conditions, allow for quantification of the marrow pressure rise due to impact loading, as can be shown by model predictions of non-destructive impact experiments. Moreover, the aforementioned poroelastic properties enter the governing equations for wave propagation in anisotropic porous media. They allow for the prediction of undrained, fast and slow waves, as is verified by comparison of model results with experimental findings.

Ultrasonic attenuation estimation of the pregnant cervix: a preliminary report

OBJECTIVE

Estimates of ultrasonic attenuation (the loss of energy as an ultrasonic wave propagates through tissue) have been used to evaluate the structure and function of tissues in health and disease. The purpose of this research was to develop a method to estimate ultrasonic cervical attenuation during human pregnancy using a clinical ultrasound system.

METHODS

Forty women underwent a cervical scan once during pregnancy with the Zonare z.one clinical ultrasound system using a 4-9-MHz endovaginal transducer. This ultrasound system provides access to radiofrequency (RF) image data for processing and analysis. In addition, a scan of a tissue-mimicking phantom with a known attenuation coefficient was acquired and used as a reference. The same settings and transducer used in the clinical scan were used in the reference scan. Digital data of the beam-formed image were saved in Digital Imaging and Communications in Medicine (DICOM) format on a flash drive and converted to RF data on a personal computer using a Matlab program supplied by Zonare. Attenuation estimates were obtained using an algorithm that was independently validated using tissue-mimicking ultrasonic phantoms.

RESULTS

RF data were acquired and analyzed to estimate attenuation of the human pregnant cervix. Regression analysis revealed that attenuation was: a predictor of the interval from ultrasound examination to delivery (beta = 0.43, P = 0.01); not a predictor of gestational age at time of examination (beta = - 0.23, P = 0.15); and not a predictor of cervical length (beta = 0.077, P = 0.65).

CONCLUSIONS

Ultrasonic attenuation estimates have the potential to be an early and objective non-invasive method to detect interval between examination and delivery. We hypothesize that a larger sample size and a longitudinal study design will be needed to detect gestational age-associated changes in cervical attenuation.

Measurement of human trabecular bone by novel ultrasonic bone densitometry based on fast and slow waves

SUMMARY

Two longitudinal transmitted waves, fast and slow waves, were observed by employing a new quantitative ultrasound (QUS) method. The trabecular bone measurements generated by this method reflect three-dimensional structural information, and the new QUS parameters were able to identify vertebral fractures.

INTRODUCTION

The aims were to identify new quantitative ultrasound (QUS) parameters that based on new QUS method reflecting not only bone volume but also the microstructures of trabecular bone ex vivo and to observe how much they predict fracture risk in vivo.

METHODS

Ex vivo measurement: Three human femoral heads were used for the experiment. Attenuation of the slow wave, attenuation of the fast wave, speed of the slow wave, speed of the fast wave (SOFW), bone mass density of trabecular bone, and elastic modulus of the trabecular bone (EMTb) of each specimen were obtained using a new QUS method and compared with three-dimensional structural parameters measured by micro-computed tomography. In vivo measurement: Eighty-nine volunteers were enrolled, and the bone status in the distal radius was measured using a new QUS method. These parameters were compared with data evaluated by peripheral quantitative computed tomography and dual X-ray absorptiometry.

RESULTS

Ex vivo measurement: SOFW and EMTb showed correlations with the parameter of trabecular anisotropy. In vivo measurement: The new QUS parameters were able to identify vertebral fractures.

CONCLUSION

The newly developed QUS technique reflects the three-dimensional structure and is a promising method to evaluate fracture risk.

Nonlinear parameter estimation in water-saturated sandy sediment with difference frequency acoustic wave

Difference frequency acoustic wave from nonlinear interaction of two primary acoustic waves at frequencies of 76 and 114 kHz was utilized with a parametric acoustic array theory to estimate the nonlinearity parameter of water-saturated sandy sediment. Such nonlinearity parameter can be used as background information for the nonlinear acoustic investigation of bottom or sub-bottom profiling in the ocean sandy sediments. Because of its lower attenuation the difference frequency acoustic wave method can be usefully applied to estimate the nonlinearity parameter of ocean sediment in the ocean as well as under laboratory conditions. The nonlinearity parameter beta for the water-saturated sandy sediment used as a reference in this study was estimated as beta=80.5+/-5.1 at the difference frequency of 38 kHz. It was agreed very well with that estimated at the difference frequency of 67 kHz, when two primary frequencies were 137 and 204 kHz. The estimated nonlinearity parameter of water-saturated sandy sediment in this study was also compared and analyzed with those estimated in previously published literatures. It was suggested that the difference frequency wave method used to estimate the nonlinearity parameter of water-saturated sandy sediment can be employed as a good method to estimate the nonlinearity parameters of fluid-like granular media.

Ultrasonic attenuation in parallel-nylon-wire cancellous-bone-mimicking phantoms

Attenuation coefficients between 1.5 and 3.5 MHz were measured on four parallel-nylon-wire arrays (simulating cancellous bone) with four different wire diameters (150, 200, 250, and 300 microm). Interwire spacing was 800 microm for all four parallel-nylon-wire arrays. The measured frequency dependencies of attenuation were consistent with theoretical predications based on Faran's theory, which considers the component of attenuation due to scattering of longitudinal waves.

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.

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.

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.

Influence of microarchitecture alterations on ultrasonic backscattering in an experimental simulation of bovine cancellous bone aging

An experimental model which can simulate physical changes that occur during aging was developed in order to evaluate the effects of change of mineral content and microstructure on ultrasonic properties of bovine cancellous bone. Timed immersion in hydrochloric acid was used to selectively alter the mineral content. Scanning electron microscopy and histological staining of the acid-treated trabeculae demonstrated a heterogeneous structure consisting of a mineralized core and a demineralized layer. The presence of organic matrix contributed very little to normalized broadband ultrasound attenuation (nBUA) and speed of sound. All three ultrasonic parameters, speed of sound, nBUA and backscatter coefficient, were sensitive to changes in apparent density of bovine cancellous bone. A two-component model utilizing a combination of two autocorrelation functions (a densely populated model and a spherical distribution) was used to approximate the backscatter coefficient. The predicted attenuation due to scattering constituted a significant part of the measured total attenuation (due to both scattering and absorption mechanisms) for bovine cancellous bone. Linear regression, performed between trabecular thickness values and estimated from the model correlation lengths, showed significant linear correlation, with R(2)=0.81 before and R(2)=0.80 after demineralization. The accuracy of estimation was found to increase with trabecular thickness.

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.

Effects of frequency-dependent attenuation and velocity dispersion on in vitro ultrasound velocity measurements in intact human femur specimens

Numerous studies have shown that ultrasonic velocity measured in bone provides a good assessment of osteoporotic fracture risk. However, a lack of standardization of signal processing techniques used to compute the speed of sound (SOS) complicates the comparison between data obtained with different commercial devices. In this study, 38 intact femurs were tested using a through-transmission technique and SOS determined using different techniques. The resulting difference in measured SOS was determined as functions of the attenuation and the velocity dispersion. A numerical simulation was used to explain how attenuation and dispersion impact two different SOS measurements (group velocity, velocity based on the first zero crossing of the signal). A new method aimed at compensating for attenuation was devised and led to a significant reduction in the difference between SOS obtained with both signal processing techniques. A comparison between SOS and X-ray density measurements indicated that the best correlation was reached for SOS based on the first zero crossing apparently because it used a marker located in the early part of the signal and was less sensitive to multipath interference. The conclusion is that first zero crossing velocity may be preferred to group velocity for ultrasonic assessment at this potential fracture site.

In vitro speed of sound measurement at intact human femur specimens

Quantitative ultrasound has been recognized as a useful tool for fracture risk prediction. Current measurement techniques are limited to peripheral skeletal sites. Our objective was to demonstrate the in vitro feasibility of ultrasonic velocity measurements on human proximal femur and to investigate the relationship between velocity and bone mineral density (BMD). Sound velocity images were computed from 2-D scans performed on 38 excised human femurs in transmission at 0.5 MHz. Different regions-of-interest were investigated. Dual x-ray absorptiometry scans have been achieved for BMD measurements in site-matched regions. Our study demonstrates the feasibility of ultrasonic velocity measurements at the hip with reasonable precision (coefficient of variation of 0.3%). The best prediction of BMD was reached in the intertrochanter region (r(2) = 0.91, p < 10(-4)), with a residual error of 0.06 g/cm(2) (10%). Because BMD measured at the femur is the best predictor of hip fracture risk, the highly significant correlation and small residual error found in this study suggest that speed of sound measurement at the femur might be a good candidate for hip fracture risk prediction.

Prediction of density and mechanical properties of human trabecular bone in vitro by using ultrasound transmission and backscattering measurements at 0.2-6.7 MHz frequency range

The ultrasound (US) backscattering method has been introduced as an alternative for the through-transmission measurement of sound attenuation and speed in diagnosis of osteoporosis. Both attenuation and backscattering depend strongly on the US frequency. In this study, 20 human trabecular bone samples were measured in transmission and pulse-echo geometry in vitro. The aim of the study was to find the most sensitive frequency range for the quantitative ultrasound (QUS) analyses. Normalized broadband US attenuation (nBUA), speed of sound (SOS), broadband US backscatter (BUB) and integrated reflection coefficient (IRC) were determined for each sample. The samples were spatially scanned with five pairs of US transducers covering a frequency range of 0.2-6.7 MHz. Furthermore, mechanical properties and density of the same samples were determined. At all frequencies, SOS, BUB and IRC showed statistically significant linear correlations with the mechanical properties or density of human trabecular bone (0.51 < r < 0.82, 0.54 < r < 0.81 and 0.70 < r < 0.85, respectively). In contrast to SOS, IRC and BUB, nBUA showed statistically significant correlations with mechanical parameters or density at the centre frequency of 1 MHz only. Our results suggest that frequencies up to 5 MHz can be useful in QUS analyses for the prediction of bone mechanical properties and density. Since the use of higher frequencies provides better axial and spatial resolution, improved structural analyses may be possible. While extensive attenuation of high frequencies in trabecular bone limits the clinically feasible frequency range, selection of optimal frequency range for in vivo QUS application should be carefully considered.

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.