Bone marrow influences quantitative ultrasound measurements in human 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.

Bone Strength of the Calcaneus Is Associated with Dietary Calcium Intake in Older Japanese Men, but Not Women

The relationship between calcium intake and bone strength in older Asian individuals, including Japanese, is controversial; therefore, we herein investigated this relationship in older Japanese populations. We performed a cross-sectional analysis of 314 participants older than 65 years who voluntarily participated in a medical examination and responded to questionnaires. The osteo-sono assessment index (OSI) measured at the right calcaneus using a quantitative ultrasonic device was used as an indicator of bone strength. The daily dietary intake of calcium was assessed using a brief-type self-administered diet history questionnaire. A two-way analysis of covariance revealed a significant interaction between sex and calcium intake on the OSI (p < 0.01). A multiple regression analysis showed a positive correlation between calcium intake and the OSI in males (p < 0.01), but not females (p = 0.27). In females, grip strength divided by body weight positively correlated with the OSI (p = 0.04). The present results suggest that a higher calcium intake contributes to bone strength in older Japanese males. Although a higher grip strength may contribute to bone strength in females, the potential of estrogen as a confounding factor needs to be considered.

Frequency dependence of the ultrasonic power reflected from the water-tissue interface of human cancellous bone in vitro

Numerous studies have performed in vitro ultrasonic measurements of cancellous bone in water to develop techniques for ultrasonic bone assessment. Because cancellous bone is a highly porous medium, ultrasonic reflections at the water-bone interface may be frequency dependent. The goal of this study was to investigate the effect of porosity on the frequency dependence of the reflected power. Ultrasonic measurements were performed in a water tank at room temperature on 15 specimens of cancellous bone prepared from the proximal end of 9 human femurs using single element, broadband transducers with center frequencies of 3.5, 5, 7.5, and 10 MHz. Power spectra of pulses reflected from the water-specimen interface were corrected for the frequency response of the measurement system to obtain the reflected power in decibels R^dB(f). To suppress random phase cancellation effects, R^dB(f) was averaged over multiple sites on multiple specimens. A frequency dependence of R^dB(f) was observed in the 2.6-10 MHz range. The frequency dependence was moderate, with a maximum change of less than 6 dB over the entire frequency range. R^dB(f) was greatest for low porosity specimens. The frequency averaged intensity reflection coefficient ranged from 7.4 × 10^-4 to 7.8 × 10^-3 for high and low porosity specimen groups, respectively.

Ultrasonic Bone Assessment Using the Backscatter Amplitude Decay Constant

Ultrasonic backscatter techniques are being developed to detect changes in bone caused by osteoporosis. The present study introduces a new technique that measures the exponential decay in the amplitude of the backscatter signal quantified by a parameter called the backscatter amplitude decay constant (BADC). Measurements were performed on 54 specimens of cancellous bone from 14 human femurs using a 3.5-MHz transducer. Six methods were tested to determine BADC. The recommended method measures the time slope of the natural log of the rectified signal. Measured values of BADC ranged from approximately 0.1 μs^-1 to 0.6 μs^-1. Moderate to strong correlations (Spearman's ρ >0.7) were found between BADC and the density and microstructural characteristics of the specimens determined using X-ray microcomputed tomography. The results of this study suggest that BADC may be able to detect changes in the density and microstructure of cancellous bone caused by osteoporosis and other diseases.

Mechanisms of Interaction of Ultrasound With Cancellous Bone: A Review

Ultrasound is now a clinically accepted modality in the management of osteoporosis. The most common commercial clinical devices assess fracture risk from measurements of attenuation and sound speed in cancellous bone. This review discusses fundamental mechanisms underlying the interaction between ultrasound and cancellous bone. Because of its two-phase structure (mineralized trabecular network embedded in soft tissue-marrow), its anisotropy, and its inhomogeneity, cancellous bone is more difficult to characterize than most soft tissues. Experimental data for the dependencies of attenuation, sound speed, dispersion, and scattering on ultrasound frequency, bone mineral density, composition, microstructure, and mechanical properties are presented. The relative roles of absorption, scattering, and phase cancellation in determining attenuation measurements in vitro and in vivo are delineated. Common speed of sound metrics, which entail measurements of transit times of pulse leading edges (to avoid multipath interference), are greatly influenced by attenuation, dispersion, and system properties, including center frequency and bandwidth. However, a theoretical model has been shown to be effective for correction for these confounding factors in vitro and in vivo. Theoretical and phantom models are presented to elucidate why cancellous bone exhibits negative dispersion, unlike soft tissue, which exhibits positive dispersion. Signal processing methods are presented for separating "fast" and "slow" waves (predicted by poroelasticity theory and supported in cancellous bone) even when the two waves overlap in time and frequency domains. Models to explain dependencies of scattering on frequency and mean trabecular thickness are presented and compared with measurements. Anisotropy, the effect of the fluid filler medium (marrow in vivo or water in vitro), phantoms, computational modeling of ultrasound propagation, acoustic microscopy, and nonlinear properties in cancellous bone are also discussed.

Velocity dispersion and backscatter in marrow-filled and water-filled trabecular bone samples in vitro

The phase velocity and the backscatter coefficient were measured in 28 bovine femoral trabecular bone samples filled with marrow and water in vitro from 0.2 to 0.6 MHz. The phase velocities decreased approximately linearly with increasing frequency and the average dispersion rate of -34 ms^-1MHz^-1 in the marrow-filled samples was higher than that of -42 ms^-1MHz^-1 in the water-filled samples. The backscatter coefficients exhibited nonlinear, monotonically increasing dependences on the frequency and the average value of the exponent n = 2.92 (frequency dependence) in the marrow-filled samples was higher than the value of n = 2.79 in the water-filled samples.

Relationships among ultrasonic and mechanical properties of cancellous bone in human calcaneus in vitro

Clinical bone sonometers applied at the calcaneus measure broadband ultrasound attenuation and speed of sound. However, the relation of ultrasound measurements to bone strength is not well-characterized. Addressing this issue, we assessed the extent to which ultrasonic measurements convey in vitro mechanical properties in 25 human calcaneal cancellous bone specimens (approximately 2×4×2cm). Normalized broadband ultrasound attenuation, speed of sound, and broadband ultrasound backscatter were measured with 500kHz transducers. To assess mechanical properties, non-linear finite element analysis, based on micro-computed tomography images (34-micron cubic voxel), was used to estimate apparent elastic modulus, overall specimen stiffness, and apparent yield stress, with models typically having approximately 25-30 million elements. We found that ultrasound parameters were correlated with mechanical properties with R=0.70-0.82 (p<0.001). Multiple regression analysis indicated that ultrasound measurements provide additional information regarding mechanical properties beyond that provided by bone quantity alone (p≤0.05). Adding ultrasound variables to linear regression models based on bone quantity improved adjusted squared correlation coefficients from 0.65 to 0.77 (stiffness), 0.76 to 0.81 (apparent modulus), and 0.67 to 0.73 (yield stress). These results indicate that ultrasound can provide complementary (to bone quantity) information regarding mechanical behavior of cancellous bone.

Ultrasonic wave properties of human bone marrow in the femur and tibia

Ultrasonic wave properties of human bone marrow obtained in the femur and tibia were measured using an ultrasound pulse technique. The measured frequency range was 4-10 MHz, and the temperature range was 30 °C-40 °C. The sound velocity was 1410 m/s, and the attenuation coefficient was 4.4 dB/cm at 36 °C (10 MHz). These values decreased with temperature. Site dependence and individual differences in elderly human bone marrow were negligible. The slopes of the attenuation coefficient were estimated by a power law. The values of the exponent n were 2.0 (30 °C-38 °C) and 2.3 (40 °C).

Basic study for ultrasound-based navigation for pedicle screw insertion using transmission and backscattered methods

The purpose of this study was to understand the acoustic properties of human vertebral cancellous bone and to study the feasibility of ultrasound-based navigation for posterior pedicle screw fixation in spinal fusion surgery. Fourteen human vertebral specimens were disarticulated from seven un-embalmed cadavers (four males, three females, 73.14 ± 9.87 years, two specimens from each cadaver). Seven specimens were used to measure the transmission, including tests of attenuation and phase velocity, while the other seven specimens were used for backscattered measurements to inspect the depth of penetration and A-Mode signals. Five pairs of unfocused broadband ultrasonic transducers were used for the detection, with center frequencies of 0.5 MHz, 1 MHz, 1.5 MHz, 2.25 MHz, and 3.5 MHz. As a result, good and stable results were documented. With increased frequency, the attenuation increased (P<0.05), stability of the speed of sound improved (P<0.05), and penetration distance decreased (P>0.05). At about 0.6 cm away from the cortical bone, warning signals were easily observed from the backscattered measurements. In conclusion, the ultrasonic system proved to be an effective, moveable, and real-time imaging navigation system. However, how ultrasonic navigation will benefit pedicle screw insertion in spinal surgery needs to be determined. Therefore, ultrasound-guided pedicle screw implantation is theoretically effective and promising.

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.

Introduction to Through-Transmission Alveolar Ultrasonography (TAU) in Dental Medicine

Through-transmission alveolar ultrasonography (TAU) is a novel imaging modality in dental medicine. A brief introduction to through-transmission ultrasonography (TTU) is followed by a description of the first commercially available TAU device, the Cavitat CAV 4000 (Cavitat Medical Technologies, Inc., Alba, TX). Recent associations between systemic osteoporosis, oral osteoporosis, periodontal diseases, and cardiovascular diseases underline the importance of early detection and treatment of oral cancellous bone pathologies associated with low bone density (LBD), such as regional ischemic osteoporosis, chronic nonsuppurative osteomyelitis, bone marrow edema, and cavitational ischemic osteonecrosis (osteocavitation). While the impact of osteoporosis on maxillofacial bones is acknowledged, there is a lack of reliable prevalence rate, and the National Institutes of Health (NIH) recommend that more attention should be paid to skeletal health, especially in persons with conditions known to be associated with secondary osteoporosis. TAU, a safe and effective imaging modality, can be a valuable tool in research as well as for the clinical assessment of alveolar cancellous bone pathologies associated with LBD and ischemia.

Numerical investigation of ultrasonic attenuation through 2D trabecular bone structures reconstructed from CT scans and random realizations

In this paper, we compare ultrasound interrogations of actual CT-scanned images of trabecular bone with artificial randomly constructed bone. Even though it is known that actual bone does not have randomly distributed trabeculae, we find that the ultrasound attenuations are close enough to cast doubt on any microstructural information, such as trabeculae width and distance between trabeculae, being gleaned from such experiments. More precisely, we perform numerical simulations of ultrasound interrogation on cancellous bone to investigate the phenomenon of ultrasound attenuation as a function of excitation frequency and bone porosity. The theoretical model is based on acoustic propagation equations for a composite fluid-solid material and is solved by a staggered-grid finite-difference scheme in the time domain. Numerical experiments are performed on two-dimensional bone samples reconstructed from CT-scanned images of real human calcaneus and from random distributions of fluid-solid particles generated via the turning bands method. A detailed comparison is performed on various parameters such as the attenuation rate and speed of sound through the bone samples as well as the normalized broadband ultrasound attenuation coefficient. Comparing results from these two types of bone samples allows us to assess the role of bone microstructure in ultrasound attenuation. It is found that the random model provides suitable bone samples for ultrasound interrogation in the transverse direction of the trabecular network.

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.

Ultrasonic properties in marrow-filled and water-filled bovine femoral trabecular bones in vitro

Phase velocity and normalized broadband ultrasound attenuation (nBUA) were measured in 22 marrow-filled and water-filled bovine femoral trabecular bone samples. Replacement of marrow by water led to a significant increase in the mean phase velocity of 47 ± 12 m/s (+3.1%), but a decrease in the mean nBUA of 10.4 ± 2.9 dB/cm/MHz (-38.9%). All the ultrasonic properties in the marrow-filled and water-filled samples exhibited significant negative Pearson's correlation coefficients of r = -0.87 to -0.92 with porosity. High correlations were also observed between pairs of the ultrasonic properties, with r = 0.85 to 0.93.

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.

Properties of ultrasonic waves in bovine bone marrow

We investigated the properties of ultrasonic waves in bovine bone marrow. Six bone marrow samples were obtained from different parts (proximal, middle and distal) of the shafts of two bovine femora without destruction. The measured frequency range was 3 to 10 MHz, and the temperature range was 15 to 40°C. Both wave velocity and attenuation coefficient in bone marrow always decreased as temperature increased. The velocity ranged from 1400 to 1610 m/s and attenuation coefficient ranged from 4 to 16 dB/cm. Wave velocities in bone marrow were similar to those in water, whereas the temperature dependences were different, and the wave attenuation coefficients were much higher than those in water. The dependence of velocity on temperature changed slightly around 23-24°C, where a transition from soft gel to oily liquid occurred. The transition temperature was confirmed by differential scanning calorimetry (DSC). Below this transition temperature, positive velocity dispersion was observed.

A-Mode ultrasound guidance for pedicle screw advancement in ovine vertebral bodies

BACKGROUND CONTEXT

In pedicle screw fixation surgery, rigid instruments are inserted into a vertebral body. When the instruments are misdirected within the pedicle or advanced too far beyond it, perforations of the inner or outer cortex can cause damage to the spinal nerve roots and spinal cord. These complications can occur despite the use of imaging modalities, such as radiographs, fluoroscopy, and computerized axial tomography (CAT) scans. A-Mode ultrasound (US), a nonionizing modality, merits study for its possible use in such a type of surgery.

PURPOSE

The purpose of the study was to determine the utility of A-mode US during pedicle screw placement, to characterize the approach to the marrow-cortex interface, and to obtain the signature profiles of cortex perforations.

STUDY DESIGN

A-Mode data were generated on insertion of a forward-viewing transducer (FVT) and a side-viewing transducer (SVT) to successively greater drilled depths along the insertion pathway. A-Mode broadband US backscatter (BUB) pedicle screw emulation experiments were conducted with transducers inserted into drilled sheep vertebral bodies. BUB amplitude patterns were observed and analyzed. Descriptive statistics were used.

METHODS

In vitro acoustic experiments on vertebral bodies in a water bath were performed with two 1-MHz unfocused transducers to measure sound speed, broadband US attenuation, and backscatter coefficients. Micro-CAT scan three-dimensional (3-D) images of 10 disarticulated vertebral bodies were obtained pre- and postdrilling done in 5-mm depth increments with a flat-bottom drill. BUB patterns were noted of transducers inserted through rostral outer cortex, through the pedicle, and advanced to the ventral marrow-cortex interface. 2.5-MHz FVT and SVT were co-advanced in successive 5-mm increments along the insertion pathway, with BUBs measured at each point and the echoes composited into a single figure. Deliberate perforations of ventral cortex were made.

RESULTS

Evident patterns or measures indicating the proximity of the ventral marrow-cortex interface were: 1) marrow BUB values increasing in amplitude over three distal peaks in most FVT cases (7 out of 10) and SVT cases (9 out of 10); 2) BUB ratio of marrow-cortex interface to the smallest marrow value greater than 2, in all FVT cases (10 out of 10) with FVT mean of 4.00+/-1.82 (2.25-8.33); and 3) a ratio of distal BUB value to starting cortex BUB in the 0. 82 to 1.62 range (mean, 0.98+/-0.30) in 80% of FVT cases. Ventral FVT perforations resulted in a major drop in the BUB value.

CONCLUSIONS

The increase in the BUB amplitudes in the distal insertion pathway suggests that, at least with a 2.5-MHz transducer, an approximate 1.5-cm US window exists in most cases, by which close approach of the ventral marrow-cortex interface could be anticipated. Other ratios may serve as stop criteria to prevent further drilling. A precipitous drop in BUB amplitude may be an indication of a cortex perforation.

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.

Effect of bone marrow on acoustic properties of trabecular bone--3D finite difference modeling study

The composition of bone marrow is influenced by many factors, such as age and diseases. The present numerical study investigates the contribution of marrow on the acoustic measurements of trabecular bone. Cylindrical bone samples (n = 11), extracted from three anatomical sites of human cadaver knees, were imaged with a high-resolution microtomography (microCT). Three-dimensional finite difference time domain (FDTD) models (Wave 3000 Pro 2.2, Cyberlogic Inc., NY, USA) were created using the segmented microCT images of each sample. First, we evaluated the effect of voxel size on the computer resource requirements, morphological parameters and acoustic simulations. Second, the effect of bone marrow on ultrasonic measurements was assessed. The simulations were repeated with two voxel sizes before and after substitution of bone marrow (i.e., fat) with water. The voxel size of the FDTD mesh controlled the fine structure of the modeled calcified matrix and significantly affected the simulation results. However, present simulations showed that the effect of bone marrow on ultrasound parameters can be reliably simulated with the applied voxel sizes of 72 and 90 microm. Ultrasound attenuation and speed were found (p < 0.01) to decrease and increase, respectively, when bone marrow was substituted with water. Moreover, reflection from the surface of the sample increased (p < 0.01) and backscatter from internal structures decreased (p < 0.01) after removal of marrow. The effect of bone marrow on the acoustic properties was stronger in samples with low bone volume fraction. The present results indicate that the amount and quality of bone marrow significantly influence the acoustic properties of trabecular bone. Possible interindividual differences in the composition of bone marrow may increase uncertainty in clinical ultrasound diagnostics of osteoporosis. Importantly, the effect is most significant in osteoporotic low-density bone.

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.

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).

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.

Instrumentation for in vivo ultrasonic characterization of bone strength

Although it has been more than 20 years since the first recorded use of a quantitative ultrasound (QUS) technology to predict bone fragility, the field has not yet reached its maturity. QUS has the potential to predict fracture risk in several clinical circumstances and has the advantages of being nonionizing, inexpensive, portable, highly acceptable to patients, and repeatable. However, the wide dissemination of QUS in clinical practice is still limited and suffering from the absence of clinical consensus on how to integrate QUS technologies in bone densitometry armamentarium. Several critical issues need to be addressed to develop the role of QUS within rheumatology. These include issues of technologies adapted to measure the central skeleton, data acquisition, and signal processing procedures to reveal bone properties beyond bone mineral quantity and elucidation of the complex interaction between ultrasound and bone structure. This article reviews the state-of-the art in technological developments applied to assess bone strength in vivo. We describe generic measurement and signal processing methods implemented in clinical ultrasound devices, the devices and their practical use, and performance measures. The article also points out the present limitations, especially those related to the absence of standardization, and the lack of comprehensive theoretical models. We conclude with suggestions of future lines and trends in technology challenges and research areas such as new acquisition modes, advanced signal processing techniques, and modelization.

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.

Acoustic properties of trabecular bone--relationships to tissue composition

In osteoporosis, changes in tissue composition and structure reduce bone strength and expose it to fractures. The current primary diagnostic technique, i.e., dual energy X-ray absorptiometry, measures areal bone mineral density (BMD) but provides no direct information on trabecular structure or organic composition. Although still poorly characterized, ultrasound techniques may bring about information on bone composition and structure. In this study, relationships of 2.25-MHz ultrasound speed, attenuation, reflection and backscattering with composition of human trabecular bone (n=26) were characterized experimentally, as well as by using numerical analyses. We also determined composition of the trabecular sample (fat and water content, bone volume fraction) and that of the calcified matrix (mineral, proteoglycan and collagen content of trabeculae). In experimental analyses, bone volume fraction and mineral content of the calcified matrix were the only determinants of BMD. Further, bone volume fraction served as the strongest determinant of ultrasound parameters (r=0.51-0.87). In numerical simulations, density and mechanical properties of the calcified matrix systematically affected ultrasound speed, attenuation, reflection and backscattering. However, partial correlation coefficients revealed only low associations(|r|<or=0.4) between the composition of calcified matrix and ultrasound parameters in experimental measurements. To conclude, the content and structure of calcified matrix, rather than its composition, affect more significantly acoustic properties of healthy trabecular bone.

Euler(strut.cavity), a new histomorphometric parameter of connectivity reflects bone strength and speed of sound in trabecular bone from human os calcis

The amount of bone and the trabecular microarchitecture are two determinants of bone strength which can be quantified by bone histomorphometry. Among the parameters of bone microarchitecture, the Euler number developed in our laboratory (E( strut.cavity )) and trabecular bone pattern factor (TBPf) evaluate the connectivity and complexity independently of the bone quantity, and the speed of sound (SOS) measured by quantitative ultrasound (QUS) corroborates E( strut.cavity ). The aim of the present study was to validate E( strut.cavity ), TBPf, and SOS as parameters of bone microarchitecture and their contribution to bone strength. We examined 20 right os calcis taken after necropsy in 11 males and 9 females, aged 52-95 years. At the same anatomic location, we measured SOS and broadband ultrasound attenuation (BUA) using a Hologic Sahara device and bone mineral density (BMD) using a Hologic QDR 1000W. At this site a transcortical cylinder was cut for both apparent density measurement (Ap.Dens) and biomechanical tests (maximum compressive stress (sigma(max)) and Young's modulus (E)), and histomorphometry was performed with an automatic image analyzer (Visiolab, Explora Nova, France). E and sigma(max) were significantly correlated with the parameters of bone quantity, microarchitecture, and QUS. However, after adjustment for the bone quantity, E correlated only with E( strut.cavity ), TBPf, and SOS, and sigma(max) with BUA. In conclusion, the bone connectivity and complexity evaluated by E( strut.cavity ) and TBPf contribute to bone strength, independently of the bone quantity. The bone mechanical properties may be assessed, in os calcis, in the elastic domain by SOS and in the plastic domain by BUA.

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

A weak scattering model was proposed for the ultrasonic frequency-dependent backscatter in dense bovine cancellous bone, using two autocorrelation functions to describe the medium: one with discrete homogeneities (spherical distribution of equal spheres) and another, which considers tissue as an inhomogeneous continuum (densely populated medium). The inverse problem to estimate trabecular thickness of bone tissue has been addressed. A combination of the two autocorrelation functions was required to closely approximate the backscatter from bovine bone with various microarchitecture, given that the shape of trabeculae ranges from a rodlike to a platelike shape. Because of the large variation in trabecular thickness, both at an intraspecimen and an interspecimen level, thickness distributions for individual trabeculae for each bone specimen were obtained, and dominant trabecular sizes were determined. Comparison of backscatter measurements to theoretical predictions indicated that there were more than one dominant trabecular sizes that scatter sound for most specimens. Linear regression, performed between dominant trabecular thickness and estimated correlation length, showed significant linear correlation (R(2)=0.81). Attenuation due to scattering by a continuous distribution of scatterers was predicted to be linear over a frequency range from 0.3 to 0.9 MHz, suggesting a possibility that scattering may be a significant source of attenuation.

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.

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

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

Investigation of an anisotropic tortuosity in a biot model of ultrasonic propagation in cancellous bone

The modeling of ultrasonic propagation in cancellous bone is relevant to the study of clinical bone assessment. Historical experiments revealed the importance of both the viscous effects of bone marrow and the anisotropy of the porous microstructure. Of those propagation models previously applied to cancellous bone, Biot's theory incorporates viscosity, but has only been applied in isotropic form, while Schoenberg's anisotropic model does not include viscosity. In this paper we present an approach that incorporates the merits of both models, by utilizing the tortuosity, a key parameter describing pore architecture. An angle-dependent tortuosity for a layered structure is used in Biot's theory to generate the "Stratified Biot Model" for cancellous bone, which is compared with published bone data. While the Stratified Biot model was inferior to Schoenberg's model for slow wave velocity prediction, the proposed model improved agreement fast wave velocity at high propagation angles, particularly when sorted for porosity. An attempt was made to improve the fast wave agreement at low angles by introducing an angle-dependent Young's Modulus, which, while improving the agreement of predicted fast wave velocity at low angles, degraded agreement at high angles. In this paper the utility of the tortuosity in characterizing the architecture of cancellous bone is highlighted.

Influence of overlying soft tissues on trabecular bone acoustic measurement at various ultrasound frequencies

Ultrasound (US) has been introduced as a promising tool for osteoporosis diagnostics. However, soft tissues overlying the bones affect reliability of the ultrasound (US) techniques. In this in vitro study, the effect of soft tissues on bone US measurements was investigated numerically and experimentally. Particularly, the dependence of the error induced by soft tissues on the applied US frequency (0.3 to 6.7 MHz) was addressed. For these aims, human trabecular bone samples (n = 25) were measured using acoustic, dual energy x-ray absorptiometry (DXA) and mechanical techniques. US attenuation, speed, reflection and backscattering were determined from the through-transmission and pulse-echo measurements. Numerical correction, based on the inclusion of acoustic characteristics of specific soft tissue components, i.e., adipose and lean tissues, was derived for the analysis of experimental measurements. Values of US parameters, interrelationships between the US parameters and mechanical properties, as well as the errors induced by the soft tissues, were significantly dependent on the US frequency. The errors induced by the soft tissues on the US measurement were typically reduced by approximately 50% after introduction of the numerical correction technique. Thereby, the acoustic prediction of mechanical properties of trabecular bone was also improved. We conclude that the numerical correction of the contribution of overlying soft tissues on acoustic measurements can reduce uncertainties related to in vivo US measurements.

The temperature dependence of the speed of sound in bovine bone marrow at 750 kHz

We present values for the speed of sound (SOS) in bovine bone marrow as a function of temperature between 17 degrees C and 44 degrees C. The measurements were made using a time-of-flight approach on a volume of roughly 10 mL, at 750 kHz. The equipment was validated using both distilled water and castor oil. The results show a linear response with SOS changing from 1456.23 ms(-1) at 17 degrees C to 1342.40 ms(-1) at 44 degrees C. The mean value at 37 degrees C was (1371.91 ms(-1)). The temperature coefficient of the SOS was found to be -4.21 +/- 0.19 ms(-1) degrees C(-1). This was well fitted to a least squares model with R2 = 0.88.

Ultrasonic characterization of cancellous bone using apparent integrated backscatter

Apparent integrated backscatter (AIB) is a measure of the frequency-averaged (integrated) backscattered power contained in some portion of a backscattered ultrasonic signal. AIB has been used extensively to study soft tissues, but its usefulness as a tissue characterization technique for cancellous bone has not been demonstrated. To address this, we performed measurements on 17 specimens of cancellous bone over two different frequency ranges using a 1 MHz and 5 MHz broadband ultrasonic transducer. Specimens were obtained from bovine tibiae and prepared in the shape of cubes (15 mm side length) with faces oriented along transverse (anterior, posterior, medial and lateral) and longitudinal (superior and inferior) principal anatomic directions. A mechanical scanning system was used to acquire multiple backscatter signals from each direction for each cube. AIB demonstrated highly significant linear correlations with bone mineral density (BMD) for both the transverse (R2 = 0.817) and longitudinal (R2 = 0.488) directions using the 5 MHz transducer. In contrast, the correlations with density were much weaker for the 1 MHz transducer (R2 = 0.007 transverse, R2 = 0.228 longitudinal). In all cases where a significant correlation was observed, AIB was found to decrease with increasing BMD.

Ultrasonic characterization of human trabecular bone microstructure

New quantitative ultrasound (QUS) techniques involving ultrasound backscattering have been introduced for the assessment of bone quality. QUS parameters are affected by the transducer characteristics, e.g. frequency range, wave and pulse length. Although frequency-dependent backscattering has been studied extensively, understanding of the ultrasound scattering phenomenon in trabecular bone is still limited. In the present study, the relationships between QUS parameters and the microstructure of human trabecular bone were investigated experimentally and by using numerical simulations. Speed of sound (SOS), normalized broadband ultrasound attenuation (nBUA), average attenuation, integrated reflection coefficient (IRC) and broadband ultrasound backscatter (BUB) were measured for 26 human trabecular bone cylinders. Subsequently, a high-resolution microCT system was used to determine the microstructural parameters. Moreover, based on the sample-specific microCT data, a numerical model for ultrasound propagation was developed for the simulation of experimental measurements. Experimentally, significant relationships between the QUS parameters and microstructural parameters were demonstrated. The relationships were dependent on the frequency, and the strongest association (r = 0.88) between SOS and structural parameters was observed at a centre frequency of 5 MHz. nBUA, average attenuation, IRC and BUB showed somewhat lower linear correlations with the structural properties at a centre frequency of 5 MHz, as compared to those determined at lower frequencies. Multiple regression analyses revealed that the variation of acoustic parameters could best be explained by parameters reflecting the amount of mineralized tissue. A principal component analysis demonstrated that the strongest determinants of BUB and IRC were related to the trabecular structure. However, other structural characteristics contributed significantly to the prediction of the acoustic parameters as well. The two-dimensional numerical model introduced in the present study demonstrated good agreement with the experimental measurements. However, further studies with the simulation model are warranted to systematically investigate the relation between the structural parameters and ultrasound scattering.

Evaluation and development of automatic two-dimensional measurements of histomorphometric parameters reflecting trabecular bone connectivity: correlations with dual-energy x-ray absorptiometry and quantitative ultrasound in human calcaneum

In osteoporosis, bone fragility results from both bone loss and changes in trabecular microarchitecture, which can be quantified by bone histomorphometric parameters. Twenty human calcaneum were collected after necropsy. All measurements were performed at the same anatomical location. Bone histomorphometric parameters were measured on histological slides with an automatic image analyzer. The aims of our study were (1) to develop automatic measurements of four additional parameters reflecting trabecular network connectivity and complexity, i.e., trabecular bone pattern factor (TBPf), Euler number/tissue volume (Euler) according to the three definitions previously reported and to a fourth one established in the laboratory (Euler(strut.cavity)), marrow star volume, and interconnectivity index, and to determine their usefulness in microarchitecture characterization; and (2) to validate these parameters by evaluating their relationship with dual-energy X-ray absorptiometry and quantitative ultrasound (QUS) measurements performed on the same samples. The statistical analysis showed that TBPf and Euler(strut.cavity) appeared to be the most significant connectivity parameters, independently of bone quantity (bone mineral density, apparent density, cancellous bone volume). For QUS, after adjustment for bone quantity, only speed of sound (SOS) was significantly and negatively correlated to Euler(strut.cavity). Broadband ultrasound attenuation depends only on bone quantity. In conclusion, TBPf (a strut analysis parameter extrapolable in three dimensions) and Euler(strut.cavity) (the only bone connectivity parameter reflecting SOS) are two valid bone microarchitecture parameters. These new parameters were significantly correlated to the established trabecular structure parameters: trabecular thickness or trabecular spacing, being weakly correlated with SOS.

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

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

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.

Ability of ultrasound backscattering to predict mechanical properties of bovine trabecular bone

Ultrasound (US) backscatter measurements have been proposed for the quantitative evaluation of bone quality. In this study, we explored the ability of broadband US backscatter (BUB) and integrated reflection coefficient (IRC) to predict density and mechanical properties of trabecular bone, as compared to normalized broadband US attenuation (nBUA) and speed of sound (SOS). These acoustic parameters were measured in 41 in vitro samples of bovine trabecular bone and correlated with a number of mechanical parameters and with volumetric bone mineral density (BMDvol). BUB correlated statistically significantly with the volumetric bone mineral density (r = 0.61, p < 0.01), Young's modulus (r = 0.40, p < 0.01) and ultimate strength (r = 0.40, p < 0.01). IRC was even more strongly correlated with BMD(vol) (r = 0.92, p < 0.01) and most of the mechanical parameters (0.81 < r < 0.85). Strong correlations were also found between mechanical parameters and SOS (0.87 < r < 0.90). No significant correlation was found between attenuation (nBUA) and either BMD(vol) or mechanical parameters. Reproducibilities (standardized CV%) of BUB (3.5%) and IRC (1.5%) were comparable to those of nBUA (2.3%) and SOS (0.5%). To conclude, BUB and IRC are promising parameters for the evaluation of density and mechanical properties of trabecular bone. Advantageously, BUB and IRC can be determined with a single transducer, hypothetically enabling measurements at many clinically relevant fracture sites.

In vitro acoustic waves propagation in human and bovine cancellous bone

The acoustic behavior of cancellous bone with regard to its complex poroelastic nature has been investigated. The existence of two longitudinal modes of propagation is demonstrated in both bovine and human cancellous bone. Failure to take into account the presence of these two waves may result in inaccurate material characterization.

INTRODUCTION

Acoustic wave propagation is now a commonly used nondestructive method for cancellous bone characterization. However, wave propagation in this material may be affected by fluid-solid interactions inherent to its poroelastic nature, resulting in two different longitudinal waves. This phenomenon has been demonstrated in previous studies and is in agreement with Biot's theory. The purpose of this paper is to extend these findings to human trabecular bone and to thoroughly investigate these two waves.

MATERIALS AND METHODS

Sixty human and 14 bovine cancellous bone cubic specimens were tested in vitro in three different directions using an immersion acoustic transmission method. Original procedures were developed to quantify both velocity and attenuation characteristics of each wave. In term of attenuation, a modified broadband ultrasound attenuation (BUA), describing the rate of change of the frequency-dependent attenuation, was defined for each wave (FDUA).

RESULTS

Both waves were identified in most of the specimens. The fast wave velocities demonstrated a negative linear correlation with porosity (1500-2300 m/s, R2 = 0.44, p < 10(-3)), whereas the slow wave velocities exhibited two different behaviors: (1) a first set of data clearly dependent on porosity showing a positive linear correlation (1150-1450 m/s, R2 = 0.26, p < 10(-3)) and (2) a second group independent on porosity. The fast wave FDUA (20-140 dB/cmMHz) showed a parabolic behavior and reached a maximum for 75% porosity (second degree relationship R2 = 0.41,p < 10(-3)), whereas a positive linear behavior was observed for the slow wave FDUA (15-40 dB/cmMHz; R2 = 0.15, p < 10(-2)).

CONCLUSIONS

Existence of two wave propagation modes were demonstrated in human cancellous bone. Our data suggest that, in some cases, the amplitude of the slow wave is much larger than the amplitude of the fast wave. For this reason, care should be taken when using measurement systems that incorporate simple threshold detection because the fast wave could remain undetected. Moreover, failure to consider the presence of these two waves could result in an inaccurate quantification of cancellous bone physical properties.

The dependence of ultrasonic backscatter on trabecular thickness in human calcaneus: theoretical and experimental results

Trabecular thickness within cancellous bone is an important determinant of osteoporotic fracture risk. Noninvasive assessment of trabecular thickness potentially could yield useful diagnostic information. Faran's theory of elastic scattering from a cylindrical object immersed in a fluid has been used to predict the dependence of ultrasonic backscatter on trabecular thickness. The theory predicts that, in the range of morphological and material properties expected for trabecular bone, the backscatter coefficient at 500 kHz should be approximately proportional to trabecular thickness to the power of 2.9. Experimental measurements of backscatter coefficient were performed on 43 human calcaneus samples in vitro. Mean trabecular thicknesses on the 43 samples were assessed using micro computed tomography (CT). A power law fit to the data showed that the backscatter coefficient empirically varied as trabecular thickness to the 2.8 power. The 95% confidence interval for this exponent was 1.7 to 3.9. The square of the correlation coefficient for the linear regression to the log transformed data was 0.40. This suggests that 40% of variations in backscatter may be attributed to variations in trabecular thickness. These results reinforce previous studies that offered validation for the Faran cylinder model for prediction of scattering properties of cancellous bone, and provide added evidence for the potential diagnostic utility of the backscatter measurement.

Characterization of trabecular bone using the backscattered spectral centroid shift

Ultrasonic attenuation in bone in vivo is generally measured using a through-transmission method at the calcaneus. Although attenuation in calcaneus has been demonstrated to be a useful predictor for osteoporotic fracture risk, measurements at other clinically important sites, such as hip and spine, could potentially contain additional useful diagnostic information. Through-transmission measurements may not be feasible at these sites due to complex bone shapes and the increased amount of intervening soft tissue. Centroid shift from the backscattered signal is an index of attenuation slope and has been used previously to characterize soft tissues. In this paper, centroid shift from signals backscattered from 30 trabecular bone samples in vitro were measured. Attenuation slope also was measured using a through-transmission method. The correlation coefficient between centroid shift and attenuation slope was -0.71. The 95% confidence interval was (-0.86, -0.47). These results suggest that the backscattered spectral centroid shift may contain useful diagnostic information potentially applicable to hip and spine.

Prediction of backscatter coefficient in trabecular bones using a numerical model of three-dimensional microstructure

A model of ultrasonic backscattering for cancellous bone saturated by water is proposed. This model assumes that scattering is caused by the solid trabeculae and describes the cancellous bone as a weak scattering medium. The backscatter coefficient is related to the spatial Fourier transform of bone microarchitecture and to the density and compressibility fluctuations between the solid trabeculae and the saturating fluid. The computations of the model make use of three-dimensional numerical images of bone microarchitecture, obtained by tomographic reconstructions with a 10 microm spatial resolution. With this model, the predictions of the frequency dependence and of the magnitude of the backscatter coefficient are reasonably accurate. The theoretical predictions are compared to experimental data obtained on 19 specimens. An accuracy error of approximately 1 dB was found (difference between the averaged experimental values and theoretical predictions). One limit of the model may come from inaccurate values of trabecular bone characteristics needed for the computations (density and longitudinal velocity), which are yet to be precisely determined for human trabecular bone. However, the model is only slightly sensitive to variations of bone material properties. It was found that an accuracy error of 2.2 dB at maximum resulted from inaccurate a priori values of bone material properties. A computation of the elastic mean free path in the medium suggests that multiple scattering plays a minor role in the working frequency bandwidth (0.4-1.2 MHz). It follows from these results that a weak scattering medium model may be appropriate to describe scattering from trabecular bone.