The dependence of ultrasonic properties on orientation in human vertebral bone

Associations between physical physique/fitness in children and bone development during puberty: a 4-year longitudinal study

Bone growth is most remarkable during puberty. This study aimed to clarify the effects of physique and physical strength on bone mineral density and bone metabolism markers during puberty to help improve bone growth during puberty and prevent future osteoporosis. There were 277 pubertal participants (125 boys and 152 girls) in this survey from 2009 to 2015, all aged 10/11 and 14/15 years. The measures included physical fitness/physique indices (such as muscle ratio etc.), grip strength, bone density (osteo sono-assessment index, OSI), and bone metabolism markers (bone-type alkaline phosphatase and type I collagen cross-linked N-telopeptide). At 10/11-years-old for girls, a positive correlation was found between body size/grip strength and OSI. At 14/15-year-old for boys, all body size factors/grip strength were positively correlated with OSI. The change in body muscle ratio was positively correlated with change in OSI for both sexes. The height, body muscle ratio and grip strength at 10/11-year-old were significantly associated with OSI (positively) and bone metabolism markers (negatively) at 14/15-year-old for both sexes. Adequate physique building after 10/11 years for boys and before 10/11 years for girls may be effective in increasing peak bone mass.

Establishing density-dependent longitudinal sound speed in the vertebral lamina

Focused ultrasound treatments of the spinal cord may be facilitated using a phased array transducer and beamforming to correct spine-induced focal aberrations. Simulations can non-invasively calculate aberration corrections using x-ray computed tomography (CT) data that are correlated to density (ρ) and longitudinal sound speed (c_L). We aimed to optimize vertebral lamina-specific c_L(ρ) functions at a physiological temperature (37 °C) to maximize time domain simulation accuracy. Odd-numbered ex vivo human thoracic vertebrae were imaged with a clinical CT-scanner (0.511 × 0.511 × 0.5 mm), then sonicated with a transducer (514 kHz) focused on the canal via the vertebral lamina. Vertebra-induced signal time shifts were extracted from pressure waveforms recorded within the canals. Measurements were repeated 5× per vertebra, with 2.5 mm vertical vertebra shifts between measurements. Linear functions relating c_L with CT-derived density were optimized. The optimized function was c_L(ρ)=0.35(ρ-ρ_w)+ c_L,w m/s, where w denotes water, giving the tested laminae a mean bulk density of 1600 ± 30 kg/m³ and a mean bulk c_L of 1670 ± 60 m/s. The optimized lamina c_L(ρ) function was accurate to λ/16 when implemented in a multi-layered ray acoustics model. This modelling accuracy will improve trans-spine ultrasound beamforming.

Ultrasonic Bone Assessment: Ability of Apparent Backscatter Techniques to Detect Changes in the Microstructure of Human Cancellous Bone

Ultrasonic backscatter techniques may offer a useful approach for detecting changes in bone caused by osteoporosis. The goal of this study was to investigate how bone mineral density (BMD) and the microstructure of human cancellous bone affect three ultrasonic backscatter parameters that have been identified as potentially useful for ultrasonic bone assessment purposes: the apparent integrated backscatter (AIB), the frequency slope of apparent backscatter (FSAB), and the frequency intercept of apparent backscatter (FIAB). Ultrasonic measurements were performed with a 3.5-MHz broadband transducer on 54 specimens of human cancellous bone prepared from the proximal femur. Microstructural parameters and BMD were measured using X-ray microcomputed tomography (micro-CT). Relationships between AIB, FSAB, FIAB, and the micro-CT parameters were investigated using univariate and multivariate statistical analysis techniques. Moderate-to-strong univariate correlations were observed between the backscatter parameters and microstructure and BMD in many cases. The partial correlation analysis indicated that the backscatter parameters are dependent on microstructure independently of BMD in some cases. Multiple stepwise linear regression analysis used to generate multivariate models found that microstructure was a significant predictor of the backscatter parameters in most cases.

In silico feasibility assessment of extracorporeal delivery of low-intensity pulsed ultrasound to intervertebral discs within the lumbar spine

Low intensity pulsed ultrasound (LIPUS) may have utility for non-invasive treatment of discogenic lower back pain through stimulating, remodeling and accelerating healing of injured or degenerated intervertebral disc (IVD) tissues. This study investigates the feasibility of delivering LIPUS to lumbar IVDs between L2 and S1 spine vertebra using a planar extracorporeal phased array (8 × 8 cm, 1024 elements, 500 kHz). Three 3D anatomical models with heterogenous tissues were generated from patient CT image sets and used in the simulation-based analysis. Time-reversal acoustic modeling techniques were applied to optimize posterior-lateral placement of the array with respect to the body to facilitate energy deposition in discrete target regions spanning the annulus fibrosus and central nucleus of each IVD. Forward acoustic and biothermal simulations were performed with time-reversal optimized array placements and driving amplitude/phase settings to predict LIPUS intensity distributions at target sites and to investigate off-target energy deposition and heating potential. Simulation results demonstrate focal intensity gain of 5-168 across all IVD targets and anatomical models, with greater average intensity gain (>50) and energy localization in posterior, posterolateral, and lateral target sites of IVDs. Localized LIPUS delivery was enhanced in thinner patient anatomies and in the high lumbar levels (L2-L3 and L3-L4). Multiple amplitude/phasing illumination patterns could be sequenced at a fixed array position for larger regional energy coverage in the IVD. Biothermal simulations demonstrated that LIPUS-appropriate exposures of 100 mW cm^-2 I_SPTA to the target disc region would result in <1 °C global peak temperature elevation for all cases. Hence, simulations suggest that spatially-precise extracorporeal delivery of therapeutically relevant LIPUS doses to discrete regions of lumbar IVDs is feasible and may be useful in clinical management of discogenic back pain.

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.

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

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

Analysis of Multifrequency and Phase Keying Strategies for Focusing Ultrasound to the Human Vertebral Canal

Focused ultrasound has been shown to increase the permeability of the blood-brain barrier and its feasibility for opening the blood-spinal cord barrier has also been demonstrated in small animal models, with great potential to impact the treatment of spinal cord (SC) disorders. For clinical translation, challenges to transvertebral focusing of ultrasound energy on the human spinal canal, such as a focal depth of field and standing-wave formation, must be addressed. A dual-aperture approach using multifrequency and phase-shift keying (PSK) strategies for achieving a controlled focus in human thoracic vertebrae was investigated through numerical simulations and benchtop experiments in ex vivo human vertebrae. An ~85% reduction in the focal depth of field was achieved compared to a single-aperture approach at 564 kHz. Short-burst (two-cycle) excitations in combination with PSK were found to suppress the formation of standing waves in ex vivo human thoracic vertebrae when focusing through the vertebral laminae. The results make an important contribution toward the development of a clinical-scale approach for targeting ultrasound therapy to the SC.

Simulating transvertebral ultrasound propagation with a multi-layered ray acoustics model

The simulation accuracy of transvertebral ultrasound propagation using a multi-layered ray acoustics model based on CT-derived vertebral geometry was investigated through comparison with experimental measurements of pressure fields in ex vivo human vertebral foramen. A spherically focused transducer (5 cm diameter, f-number 1.2, 514 kHz) was geometrically focused to the centre of individual thoracic vertebral foramen, through the posterior bony elements. Transducer propagation paths through the laminae and the spinous processes were tested. Simulation transducer-vertebra configurations were registered to experiment transducer-vertebra configurations, and simulation accuracy of the simulation model was evaluated for predicting maximum transmitted pressure to the canal, voxel pressure in the canal, and focal distortion. Accuracy in predicting maximum transmitted pressure was calculated by vertebra, and it is shown that simulation predicts maximum pressure with a greater degree of accuracy than a vertebra-specific insertion loss. Simulation error in voxel pressure was evaluated using root-mean-square error and cross-correlation, and found to be similar to the water-only case. Simulation accuracy in predicting focal distortion was evaluated by comparing experiment and simulation maximum pressure location and weighted  >50% focal volume location. Average simulation error across all measurements and simulations in maximum pressure location and weighted  >50% focal volume location were 2.3 mm and 1.5 mm, respectively. These errors are small relative to the dimensions of the transducer focus (4.9 mm full width half maximum), the spinal cord (10 mm diameter), and vertebral canal diameter (15-20 mm diameter). These results suggest that ray acoustics can be applied to simulating transvertebral ultrasound propagation.

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.

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

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

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

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

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.

Attenuated Fractional Wave Equations With Anisotropy

This paper develops new fractional calculus models for wave propagation. These models permit a different attenuation index in each coordinate to fully capture the anisotropic nature of wave propagation in complex media. Analytical expressions that describe power law attenuation and anomalous dispersion in each direction are derived for these fractional calculus models.

Frequency specific ultrasound attenuation is sensitive to trabecular bone structure

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

Prediction of trabecular bone principal structural orientation using quantitative ultrasound scanning

Bone has the ability to adapt its structure in response to the mechanical environment as defined as Wolff's Law. The alignment of trabecular structure is intended to adapt to the particular mechanical milieu applied to it. Due to the absence of normal mechanical loading, it will be extremely important to assess the anisotropic deterioration of bone during the extreme conditions, i.e., long term space mission and disease orientated disuse, to predict risk of fractures. The propagation of ultrasound wave in trabecular bone is substantially influenced by the anisotropy of the trabecular structure. Previous studies have shown that both ultrasound velocity and amplitude is dependent on the incident angle of the ultrasound signal into the bone sample. In this work, seven bovine trabecular bone balls were used for rotational ultrasound measurement around three anatomical axes to elucidate the ability of ultrasound to identify trabecular orientation. Both ultrasound attenuation (ATT) and fast wave velocity (UV) were used to calculate the principal orientation of the trabecular bone. By comparing to the mean intercept length (MIL) tensor obtained from μCT, the angle difference of the prediction by UV was 4.45°, while it resulted in 11.67° angle difference between direction predicted by μCT and the prediction by ATT. This result demonstrates the ability of ultrasound as a non-invasive measurement tool for the principal structural orientation of the trabecular bone.

Quantitative ultrasound and vertebral fractures in patients with type 2 diabetes

Patients with type 2 diabetes (T2DM) are known to have increased risks of femoral neck and vertebral fractures, although their bone mineral density (BMD) is normal or even slightly increased compared to non-DM controls. This observation suggests that bone fragility not reflected by BMD, possibly deterioration of bone quality, may participate in their fracture risks. Quantitative ultrasound (QUS), unlike BMD, could possibly evaluate bone quality, especially the microarchitecture, and therefore may be useful for assessing fracture risk in T2DM. To test this hypothesis, we measured calcaneal QUS as well as BMD at the lumbar spine, femoral neck, and 1/3 radius in 96 women (mean age 66.6 years old) and 99 men (64.7 years old) with T2DM, and examined their associations with prevalent vertebral fractures (VFs). Calcaneal QUS was performed by CM-200 (Elk Corp., Osaka, Japan), and speed of sound (SOS) values were obtained. BMD was measured by QDR4500 (Hologic, Waltham, MA). In T2DM patients, VFs were found in 33 and 45 subjects in women and men, respectively. When compared between subjects with and without VFs, there were no significant differences in values of SOS or BMD at any site between the groups in either gender. The distribution of SOS as a function of age showed that those with VFs were scattered widely, and there were no SOS thresholds for VFs in either gender. Logistic regression analysis adjusted for age and BMI showed that either SOS or BMD was not significantly associated with the presence of VFs in either gender. These results show that QUS as well as BMD are unable to discriminate T2DM patients with prevalent VFs from those without VFs. It seems necessary to seek other imaging modalities or biochemical markers evaluating bone fragility and fracture risk in T2DM.

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

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

Influence of cancellous bone microstructure on two ultrasonic wave propagations in bovine femur: an in vitro study

The influence of cancellous bone microstructure on the ultrasonic wave propagation of fast and slow waves was experimentally investigated. Four spherical cancellous bone specimens extracted from two bovine femora were prepared for the estimation of acoustical and structural anisotropies of cancellous bone. In vitro measurements were performed using a PVDF transducer (excited by a single sinusoidal wave at 1 MHz) by rotating the spherical specimens. In addition, the mean intercept length (MIL) and bone volume fraction (BV/TV) were estimated by X-ray micro-computed tomography. Separation of the fast and slow waves was clearly observed in two specimens. The fast wave speed was strongly dependent on the wave propagation direction, with the maximum speed along the main trabecular direction. The fast wave speed increased with the MIL. The slow wave speed, however, was almost constant. The fast wave speeds were statistically higher, and their amplitudes were statistically lower in the case of wave separation than in that of wave overlap.

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.

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

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

Measurement of tortuosity in aluminum foams using airborne ultrasound

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

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.

Propagation of two longitudinal waves in human cancellous bone: an in vitro study

The ultrasonic wave propagation of fast and slow waves was investigated in vitro in 35 cubic cancellous bone specimens extracted from human femoral heads. Measurements were performed in three orthogonal directions using home-made PVDF transducers excited by a single sinusoidal wave at 1 MHz. The apparent density of the specimens was measured. Two separated fast and slow waves were clearly observed in 16 specimens, mainly in the main load direction. The waveforms and the sound speeds of fast and slow waves were similar to the reported data in bovine bone. The group of specimens in which the two waves were observed did not exhibit statistically higher apparent density than the rest of the specimens, but did exhibit statistically higher acoustic anisotropy ratio. The speeds in the main load direction were higher than those in the other direction. The fast and slow wave speeds were in good agreement with Biot's model, showing an increase with bone volume fraction (BV/TV). The ratio of peak amplitudes of the fast and slow waves nonlinearly increased as a function of BV/TV. These results open interesting perspective for acoustic assessment of cancellous bone micro-architecture and especially anisotropy that might lead to an improved assessment of bone strength.

Velocity dispersion in trabecular bone: influence of multiple scattering and of absorption

Speed of sound measurements are widely used clinically to assess bone strength. Trabecular bone is an attenuating composite material in which negative values of velocity dispersion have been measured, this behavior remaining poorly explained physically. The aim of this work is to describe the ultrasonic propagation in trabecular bone modeled by infinite cylinders immersed in a saturating matrix, and to derive the physical determinants of velocity dispersion. A homogenization model accounting for the coupling of multiple scattering and absorption phenomena allows the computation of phase velocity and of dispersion while varying bone properties. The present model is adapted from the generalized self-consistent method developed in the work of Yang and Mal [(1994). "Multiple-scattering of elastic waves in a fiber-reinforced composite," J. Mech. Phys. Solids 42, 1945-1968]. It predicts negative values of velocity dispersion, in agreement with experimental results obtained in phantoms mimicking trabecular bone. In trabecular bone, mostly negative and also positive values of velocity dispersion are predicted by the model, which span within the range of values measured experimentally. Scattering effects are responsible for the negative values of dispersion, whereas the frequency dependence of the absorption coefficient in bone marrow and/or in the trabeculae results in an increase in dispersion, which may then become positive.

Ultrasound and the biomechanical competence of bone

Ultrasound is a mechanical wave and consequently has a unique potential to characterize the mechanical properties of bone. In some applications, such as determination of the anisotropic elastic constants of cortical bone specimens, this potential has been realized. In other applications, including the hugely important field of clinical measurements, current ultrasonic techniques struggle to provide information directly relating to mechanical properties. This article reviews the successes and shortcomings of ultrasound as a tool for determination of bone mechanical properties and highlights those new developments likely to bring progress in the future.

Effects of structural anisotropy of cancellous bone on speed of ultrasonic fast waves in the bovine femur

Ultrasonic waves in cancellous bone change dramatically depending on its structural complexity. One good example is the separation of an ultrasonic longitudinal wave into fast and slow waves during propagation. In this study, we examined fast wave propagation in cancellous bone obtained from the head of the bovine femur, taking the bone structure into consideration. We investigated the wave propagation perpendicular to the bone axis and found the two-wave phenomenon. By rotating the cylindrical cancellous bone specimen, changes in the fast wave speed due to the rotation angle then were observed. In addition to the ultrasonic evaluation, the structural anisotropy of each specimen was measured by X-ray micro-computed tomography (CT). From the CT images, we obtained the mean intercept length (MIL), degree of anisotropy (DA), and angle of insonification relative to the trabecular orientation. The ultrasonic and CT results showed that the fast wave speed was dependent on the structural anisotropy, especially on the trabecular orientation and length. The fast wave speeds always were higher for propagation parallel to the trabecular orientation. In addition, there was a strong correlation between the DA and the ratio between maximum and minimum speeds (V(max)/V(min)) (R(2) = 0.63).

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

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

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

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

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

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

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.

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

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

Problems with ultrasonic measurements of shear modules of structured media

The elastic constants of linearly elastic, isotropic or anisotropic bone material are required for many numerical simulations. These constants are often measured ultrasonically, but this can lead to mistakes, especially if shear modules of spongiosa are considered. The reason is that spongiosa is a structure composed of trabeculae, each of which acts as a kind of beam which allows longitudinal, shear and also bending waves to propagate; the bending waves are as fast as the longitudinal waves and are indistinguishable from the shear waves. Furthermore, mistakes in measuring Young's modulus cannot be avoided in every case. Several numerical simulations of wave propagations in homogeneous media, and especially in periodically and irregularly structured media, were carried out via the application of explicit finite element codes. Results showing the above-mentioned effects are presented and discussed. These can help to explain in detail why mistakes may occur during ultrasonic measurements.

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.

Phase velocity and normalized broadband ultrasonic attenuation in Polyacetal cuboid bone-mimicking phantoms

The variations of phase velocity and normalized broadband ultrasonic attenuation (nBUA) with porosity were investigated in Polyacetal cuboid bone-mimicking phantoms with circular cylindrical pores running normal to the surface along the three orthogonal axes. The frequency-dependent phase velocity and attenuation coefficient in the phantoms with porosities from 0% to 65.9% were measured from 0.65 to 1.10 MHz. The results showed that the phase velocity at 880 kHz decreased linearly with porosity, whereas the nBUA increased linearly with porosity. This study provides a useful insight into the relationships between ultrasonic properties and porosity in bone at porosities lower than 70%.

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.

Numerical simulation of the dependence of quantitative ultrasonic parameters on trabecular bone microarchitecture and elastic constants

Finite-difference numerical simulation of ultrasound propagation in complex media such as cancellous bone represents a fertile alternative to analytical approaches because it can manage the complex 3D bone structure by coupling the numerical computation with 3D numerical models of bone microarchitecture obtained from high-resolution imaging modalities. The objective of this work was to assess in silico the sensitivity of ultrasound parameters to controlled changes of microarchitecture and variation of elastic constants. The simulation software uses a finite-difference approach based on the Virieux numerical scheme. An incident plane wave was propagated through a volume of bone of approximately 5 x 5 x 8 mm(3). The volumes were reconstructed from high-resolution micro-computed tomography data. An iterative numerical scenario of "virtual osteoporosis" was implemented using a dedicated image processing algorithm in order to modify the initial 3D microstructures. Numerical computations of wave propagation were performed at each step of the process. The sensitivity to bone material properties was also tested by changing the elastic constants of bone tissue. Our results suggest that ultrasonic variables (slope of the frequency-dependent attenuation coefficient and speed of sound) are mostly influenced by bone volume fraction. However, material properties and structure also appear to play a role. The impact of modifications of the stiffness coefficients remained lower than the variability caused by structural variations. This study emphasizes the potential of numerical computations tools coupled to realistic 3D structures to elucidate the physical mechanisms of interaction between ultrasound and bone structure and to assess the sensitivity of ultrasound variables to different bone properties.

Experimental evaluation of bone quality measuring speed of sound in cadaver mandibles

OBJECTIVES

To demonstrate in vitro the feasibility of speed of sound (SOS) measurements through the mandible and to investigate the relationships between mandibular SOS, local bone mineral density (BMD), and the ratio between trabecular and cortical thicknesses (Tb.Th/Cort.Th). The long-term goal is to find a safe, simple test for bone quality in sites for dental implant placement.

METHODS

Excised human mandibles (N = 23) were used for the measurement of sound transmission with two 1.6 MHz transducers. Three regions of interest (ROIs) were selected in each of the specimens, namely incisor, premolar, and molar regions. To determine short-term precision, 10 measurements (with repositioning between measures) were performed for each ROI. Local BMD and mandibular cross-sectional morphological characteristics were determined by dual x-ray absorptiometry (DXA) and computed tomography (CT).

RESULTS

The coefficient of variation for SOS was found to be 1%. SOS measurements at different sites were significantly different. A significant linear relationship was found between SOS and BMD (r2 = 0.62; P < .0001), whereas a nonlinear relationship was found between SOS and Tb.Th/Cort.Th (r2 = 0.53; P < .0001).

CONCLUSION

This in vitro study demonstrated the feasibility of SOS measurement through the mandible. Mandibular SOS reflects local BMD and Tb.Th/Cort.Th. In vivo studies are now required to confirm the predictive power of SOS measurement for bone quality assessment and its potential usefulness as a clinical diagnostic technique.

Cross-sectional reference data for phalangeal quantitative ultrasound from early childhood to young-adulthood according to gender, age, skeletal growth, and pubertal development

Bone mineral status by phalangeal quantitative ultrasound (QUS, DBM Sonic, IGEA, Carpi, Modena, Italy) was examined in 3044 (1513 males and 1531 females) healthy subjects, aged 2-21 years. The aim of the study was to provide a reference database for phalangeal QUS parameters, amplitude-dependent speed of sound (AD-SoS) and bone transmission time (BTT), both expressed as centiles and Z score, according to gender, age, height, weight, body mass index (BMI), and pubertal stage to be used for estimating bone mineral status in patients with disorders of growth or of bone and mineral metabolism. In both sexes, AD-SoS and BTT increased significantly (P<0.0001) according to all the anthropometric variables. Females showed higher values than males in the age groups 9-14 for AD-SoS (P<0.04-P<0.0001) and in the age groups 11-13 for BTT (P<0.02). Males had higher BTT values than females in the age groups 6-8 and 15-21 (P<0.04-P<0.0001). AD-SoS was higher (P<0.02-P<0.0001) in females than in males at pubertal stages 2, 3, and 4, but it was higher (P=0.001) in males compared with females at pubertal stage 5. BTT was higher in males than females at pubertal stages 1 (P<0.0001), 2 (P<0.01), and 5 (P<0.0001). In both sexes, AD-SoS and BTT were significantly correlated between them (r=0.92, P<0.0001) and with all the anthropometric variables (r=0.53-r=0.85, P<0.0001). Age, weight, BMI, and pubertal stage were independent predictors of AD-SoS in males; age and pubertal stage were independent predictors of AD-SoS in females. In both sexes, height and pubertal stage, and also age only in females, were independent predictors of BTT. In conclusion, our data show that gender, age, height, and timing of sexual maturation are main determinants of bone structure and geometry, and that both these two processes may be captured by phalangeal QUS. It may be a useful tool to assess bone mineral status from early childhood to young-adulthood with a very small confounding effect related to bone sizes and without exposing the subjects to a source of radiation.

Determination of ultrasound phase velocity in trabecular bone using time dependent phase tracking technique

Ultrasound velocity is one of the key acoustic parameters for noninvasive diagnosis of osteoporosis. Ultrasound phase velocity can be uniquely measured from the phase of the ultrasound signal at a specified frequency. Many previous studies used fast Fourier transform (FFT) to determine the phase velocity, which may cause errors due to the limitations of FFT. The new phase tracking technique applied an adaptive tracking algorithm to detect the time dependent phase and amplitude of the ultrasound signal at a specified frequency. This overcame the disadvantages of FFT to ensure the accuracy of the ultrasound phase velocity. As a result, the new method exhibited high accuracy in the measurement of ultrasound phase velocity of two phantom blocks with the error less than 0.4%. 41 cubic trabecular samples from sheep femoral condyles were used in the study. The phase velocity of the samples using the new method had significantly high correlation to the bulk stiffness of the samples (r = 0.84) compared to the phase velocity measured using fast Fourier transform FFT (r = 0.14). In conclusion, the new method provided an accurate measurement of the ultrasound phase velocity in bone.

Quantitative heel ultrasound in a population-based study in Italy and its relationship with fracture history: the ESOPO study

We assessed the clinical usefulness of quantitative ultrasound (QUS) in defining the prevalence rates of osteoporosis and osteopenia and their association with fractures of the forearm, vertebrae, and hip. The ESOPO study was conducted in 2001 and assessed a random sample of 11,011 women and 4,981 men, in 83 centers spread all over Italy. A large array of risk factors was investigated, and self-reported history of fractures was collected in a questionnaire. After the patient had undergone interview and a brief physical examination, QUS of the heel was performed, using the Achilles apparatus (GE-Lunar, Madison, USA). The prevalence rate of osteoporosis in women 40-79 years old was approximately 18.5%, while the rate of osteopenia was about 44.7%; in men 60-79 years of age the rates were 10% and 36%, respectively. A strong association with fractures was found for osteoporosis and osteopenia in both men and women, independently of all traditional risk factors, including age. These results confirm the suitability of US measurements as a tool for detecting individuals at risk of fractures.

Kramers-Kronig analysis of attenuation and dispersion in trabecular bone

A restricted-bandwidth form of the Kramers-Kronig dispersion relations is applied to in vitro measurements of ultrasonic attenuation and dispersion properties of trabecular bone specimens from bovine tibia. The Kramers-Kronig analysis utilizes only experimentally measured properties and avoids extrapolation of ultrasonic properties beyond the known bandwidth. Compensation for the portions of the Kramers-Kronig integrals over the unknown bandwidth is partially achieved by the method of subtractions, where a subtraction frequency acts as an adjustable parameter. Good agreement is found between experimentally measured and Kramers-Kronig reconstructed dispersions. The restricted-bandwidth approach improves upon other forms of the Kramers-Kronig relations and may provide further insight into how ultrasound interacts with trabecular bone.

Recent developments in trabecular bone characterization using ultrasound

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