Characterization of dense bovine cancellous bone tissue microstructure by ultrasonic backscattering using weak scattering models

Conical shell X-ray beam tomosynthesis and micro-computed tomography for microarchitectural characterisation

Bone quality is commonly used to diagnose bone diseases such as osteoporosis, with many studies focusing on microarchitecture for fracture prediction. In this study a bovine distal femur was imaged using both micro-computed tomography (µCT) and tomosynthesis using focal construct geometry (FCG) for comparison of microarchitectural parameters. Six regions of interest (ROIs) were compared between the two imaging modalities, with both global and adaptive methods used to binarize the images. FCG images were downsampled to the same pixel size as the µCT images. Bone morphometrics were determined using BoneJ, for each imaging modality, binarization technique and ROI. Bone area/total area was found to have few significant differences between FCG and µCT (p < 0.05 for two of six ROIs). Fractal Dimension had only one significant difference (p < 0.05 for one of six ROIs) between µCT and downsampled FCG (where pixel size was equalized). Trabecular thickness and trabecular spacing were observed to follow trends as observed for the corresponding µCT images, although many absolute values were significantly different (p < 0.05 for between one and six ROIs depending on image types used). This study demonstrates the utility of tomosynthesis for measurement of microarchitectural morphometrics.

Three-dimensional-printed replica models of bone for experimentally decoupling trabecular bone properties contribution to ultrasound propagation parameters

A detailed investigation of the relationship between ultrasonic (US) properties and trabecular bone microstructure is difficult because of the great variability in the bone loss process. The aim of this work was twofold. First, to verify by compressive tests that the three-dimensional (3D)-printer is able to produce precisely and repeatedly "bone replica models" of different size and density. Following, replicas of the original specimens with two different polymers and thinned trabeculae models were used to investigate US properties (speed of sound, SOS, and backscatter coefficient), aiming to deconvolute the influence of material properties on ultrasound characteristics. The results revealed that matrix material properties influence only the magnitude of the backscatter coefficient, whereas the characteristic undulated patterns are related to the trabecular structure. Simulation of perforation and thinning of cancellous bone, associated with bone loss, showed that SOS and mechanical properties were reduced perfectly linearly with apparent density when structure deteriorated. The 3D-printed bone replicas have the potential to enable systematic investigations of the influence of structure on both acoustical and mechanical properties and evaluate changes caused by bone loss. The development of replicas from materials with properties close to those of bone will permit quantitative conclusions for 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 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.

Acoustoelasticity in cancellous bone

Strain-dependence of ultrasound speed in cancellous bone was determined by applying a range of uniaxial compressive strains in the elasticity region, in a single direction, parallel or perpendicular to the propagating wave. Compressive strain modulated the ultrasound speed significantly. The decrease of ultrasound speed was found to change linearly as a function of strain. The changes of broadband ultrasound attenuation were also determined for the two dilatational waves (parallel or perpendicular to the strain). They do not follow linear relation or constant sign of change with strain for the examined specimens. Considerable possibilities open up for using developments in acoustoelasticity for nondestructive ultrasonic techniques.

Ultrasonic backscatter from cancellous bone: the apparent backscatter transfer function

Ultrasonic backscatter techniques are being developed to detect changes in cancellous bone caused by osteoporosis. Many techniques are based on measurements of the apparent backscatter transfer function (ABTF), which represents the backscattered power from bone corrected for the frequency response of the measurement system. The ABTF is determined from a portion of the backscatter signal selected by an analysis gate of width τw delayed by an amount τd from the start of the signal. The goal of this study was to characterize the ABTF for a wide range of gate delays (1 μs ≤ τd ≤ 6 μs) and gate widths (1 μs ≤ τw ≤ 6 μs). Measurements were performed on 29 specimens of human cancellous bone in the frequency range 1.5 to 6.0 MHz using a broadband 5-MHz transducer. The ABTF was found to be an approximately linear function of frequency for most choices of τd and τw. Changes in τd and τw caused the frequency-averaged ABTF [quantified by apparent integrated backscatter (AIB)] and the frequency dependence of the ABTF [quantified by frequency slope of apparent backscatter (FSAB)] to change by as much as 24.6 dB and 6.7 dB/MHz, respectively. τd strongly influenced the measured values of AIB and FSAB and the correlation of AIB with bone density (-0.95 ≤ R ≤ +0.68). The correlation of FSAB with bone density was influenced less strongly by τd (-0.97 ≤ R ≤ -0.87). τw had a weaker influence than τd on the measured values of AIB and FSAB and the correlation of these parameters with bone density.

Effect of intervening tissues on ultrasonic backscatter measurements of bone: An in vitro study

Ultrasonic backscatter techniques are being developed to diagnose osteoporosis. Tissues that lie between the transducer and the ultrasonically interrogated region of bone may produce errors in backscatter measurements. The goal of this study is to investigate the effects of intervening tissues on ultrasonic backscatter measurements of bone. Measurements were performed on 24 cube shaped specimens of human cancellous bone using a 5 MHz transducer. Measurements were repeated after adding a 1 mm thick plate of cortical bone to simulate the bone cortex and a 3 cm thick phantom to simulate soft tissue at the hip. Signals were analyzed to determine three apparent backscatter parameters (apparent integrated backscatter, frequency slope of apparent backscatter, and frequency intercept of apparent backscatter) and three backscatter difference parameters [normalized mean backscatter difference (nMBD), normalized slope of the backscatter difference, and normalized intercept of the backscatter difference]. The apparent backscatter parameters were impacted significantly by the presence of intervening tissues. In contrast, the backscatter difference parameters were not affected by intervening tissues. However, only one backscatter difference parameter, nMBD, demonstrated a strong correlation with bone mineral density. Thus, among the six parameters tested, nMBD may be the best choice for in vivo backscatter measurements of bone when intervening tissues are present.

Computed radiographic and ultrasonic evaluation of bone regeneration during tibial distraction osteogenesis in rabbits

Computed radiography (CR) and a combined ultrasound (US) approach involving two-dimensional (2-D) and three-dimensional (3-D) ultrasonography with ultrasonometry were employed to evaluate their respective efficacies in monitoring bone regeneration during rabbit tibial distraction osteogenesis (DO). Results demonstrated that 2-D and 3-D ultrasonography depicted bone callus growth changes during distraction while CR could not. Evaluation of callus speed of sound, acoustic reflection and attenuation showed significant linear changes over time during early DO stage (p < 0.05). However, surrogate measure of callus density by CR only showed such significant linear changes during consolidation (p < 0.05). Also, callus speed of sound and acoustic reflection during early DO stage showed strong predictions to the bone mineral density and microstructural properties (adjusted-R(2) = 0.43-0.67) of consolidated bone callus measured at the treatment end-point by microcomputed tomography. Findings of the present study indicated a preferred use of the combined US approach over CR in the early monitoring of bone regeneration during DO treatment.

Frequency-dependent attenuation and backscatter coefficients in bovine trabecular bone from 0.2 to 1.2 MHz

The frequency-dependent attenuation and backscatter coefficients were measured in 25 bovine femoral trabecular bone samples from 0.2 to 1.2 MHz. When the average attenuation coefficient was fitted to a nonlinear power law α(f)=α(0)+α(1)f(n), the exponent n was found to be 1.65. In contrast, the average backscatter coefficient was fitted to a power law η(f)=η(1)f(n) and the exponent n was measured as 3.25. The apparent bone density was significantly correlated with the parameter α(1) (0.2-0.7 MHz: r = 0.852, 0.6-1.2 MHz: r = 0.832) as well as the backscatter coefficient (0.5 MHz: r = 0.751, 1.0 MHz: r = 0.808).

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.

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.

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.