Ultrasound simulation in the distal radius using clinical high-resolution peripheral-CT images

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.

Two-wave behavior under various conditions of transition area from cancellous bone to cortical bone

The two-wave phenomenon, the wave separation of a single ultrasonic pulse in cancellous bone, is expected to be a useful tool for the diagnosis of osteoporosis. However, because actual bone has a complicated structure, precise studies on the effect of transition conditions between cortical and cancellous parts are required. This study investigated how the transition condition influenced the two-wave generation using three-dimensional X-ray CT images of an equine radius and a three-dimensional simulation technique. As a result, any changes in the boundary between cortical part and trabecular part, which gives the actual complex structure of bone, did not eliminate the generation of either the primary wave or the secondary wave at least in the condition of clear trabecular alignment. The results led us to the possibility of using the two-wave phenomenon in a diagnostic system for osteoporosis in cases of a complex boundary.

Clinical assessment of the 1/3 radius using a new desktop ultrasonic bone densitometer

The objectives of this study were to evaluate the capability of a novel ultrasound device to clinically estimate bone mineral density (BMD) at the 1/3 radius. The device rests on a desktop and is portable, and permits real-time evaluation of the radial BMD. The device measures two net time delay (NTD) parameters, NTD(DW) and NTD(CW). NTD(DW) is defined as the difference between the transit time of an ultrasound pulse to travel through soft-tissue, cortex and medullary cavity, and the transit time through soft tissue only of equal overall distance. NTD(CW) is defined as the difference between the transit time of an ultrasound pulse to travel through soft-tissue and cortex only, and the transit time through soft tissue only again of equal overall distance. The square root of the product of these two parameters is a measure of the radial BMD at the 1/3 location as measured by dual-energy X-ray absorptiometry (DXA). A clinical IRB-approved study measured ultrasonically 60 adults at the 1/3 radius. BMD was also measured at the same anatomic site and time using DXA. A linear regression using NTD produced a linear correlation coefficient of 0.93 (p < 0.001). These results are consistent with previously reported simulation and in vitro studies. In conclusion, although X-ray methods are effective in bone mass assessment, osteoporosis remains one of the largest undiagnosed and under-diagnosed diseases in the world today. The research described here should enable significant expansion of diagnosis and monitoring of osteoporosis through a desktop device that ultrasonically assesses bone mass at the 1/3 radius.

Microarchitecture and bone quality in the human calcaneus: local variations of fabric anisotropy

The local variability of microarchitecture of human trabecular calcaneus bone is investigated using high-resolution micro-computed tomography (µCT) scanning. The fabric tensor is employed as the measure of the microarchitecture of the pore structure of a porous medium. It is hypothesized that a fabric tensor-dependent poroelastic ultrasound approach will more effectively predict the data variance than will porosity alone. The specific aims of the present study are as follows: (1) to quantify the morphology and local anisotropy of the calcaneus microarchitecture with respect to anatomical directions; (2) to determine the interdependence, or lack thereof, of microarchitecture parameters, fabric, and volumetric bone mineral density (vBMD); and (3) to determine the relative ability of vBMD and fabric measurements in evaluating the variance in ultrasound wave velocity measurements along orthogonal directions in the human calcaneus. Our results show that the microarchitecture in the analyzed regions of human calcanei is anisotropic, with a preferred alignment along the posterior-anterior direction. Strong correlation was found between most scalar architectural parameters and vBMD. However, no statistical correlation was found between vBMD and the fabric components, the measures of the pore microstructure orientation. Therefore, among the parameters usually considered for cancellous bone (ie, classic histomorphometric parameters such as porosity, trabecular thickness, number and separation), only fabric components explain the data variance that cannot be explained by vBMD, a global mass measurement, which lacks the sensitivity and selectivity to distinguish osteoporotic from healthy subjects because it is insensitive to directional changes in bone architecture. This study demonstrates that a multidirectional, fabric-dependent poroelastic ultrasound approach has the capability of characterizing anisotropic bone properties (bone quality) beyond bone mass, and could help to better understand anisotropic changes in bone architecture using ultrasound.

Cancellous bone analysis with modified least squares Prony's method and chirp filter: phantom experiments and simulation

The presence of two longitudinal waves in porous media is predicted by Biot's theory and has been confirmed experimentally in cancellous bone. When cancellous bone samples are interrogated in through-transmission, these two waves can overlap in time. Previously, the Modified Least-Squares Prony's (MLSP) method was validated for estimation of amplitudes, attenuation coefficients, and phase velocities of fast and slow waves, but tended to overestimate phase velocities by up to about 5%. In the present paper, a pre-processing chirp filter to mitigate the phase velocity bias is derived. The MLSP/chirp filter (MLSPCF) method was tested for decomposition of a 500 kHz-center-frequency signal containing two overlapping components: one passing through a low-density-polyethylene plate (fast wave) and another passing through a cancellous-bone-mimicking phantom material (slow wave). The chirp filter reduced phase velocity bias from 100 m/s (5.1%) to 69 m/s (3.5%) (fast wave) and from 29 m/s (1.9%) to 10 m/s (0.7%) (slow wave). Similar improvements were found for 1) measurements in polycarbonate (fast wave) and a cancellous-bone-mimicking phantom (slow wave), and 2) a simulation based on parameters mimicking bovine cancellous bone. The MLSPCF method did not offer consistent improvement in estimates of attenuation coefficient or amplitude.

Potential of first arriving signal to assess cortical bone geometry at the Hip with QUS: a model based study

There is evidence that quantitative ultrasound (QUS) at the proximal femur involves waves propagating circumferentially in the cortical shell. These waves, in theory, convey information on bone geometrical and material characteristics and thus have the potential to improve fracture risk prediction. In this work, the time-of-flight (TOF) of the first arriving signal (FAS) that corresponds to waves propagating circumferentially is considered. The relationships between the TOF of the FAS and geometrical features of the femoral neck are investigated. Five neck cross-sections from 11 human femurs from females (>65y) were extracted from 3-D X-ray quantitative computed tomography (XR-QCT) datasets. Geometrical parameters including cross-sectional area (CSA), minimum moment of inertia (I(min)) and section modulus (Z) were computed from femoral neck cross-section images. Two-dimensional numerical simulation of US propagation through femoral neck was performed and TOF of the FAS was estimated. TOF was best correlated with I(min): R(2)=0.82 (p=10(-4); RMSE=1390mm(4) [13%]) in the region between proximal and mid-femoral neck and with Z: R(2)=0.55 (p<10(-2); RMSE=480mm(3) [17%]) and CSA: R(2)=0.62 (p<5.10(-3); RMSE=22mm(2) [7%]) in the mid-femoral neck. The results suggest that QUS has the potential to assess proximal femur strength based on estimates of geometrical properties of the cortical shell.

Decomposition of two-component ultrasound pulses in cancellous bone using modified least squares prony method--phantom experiment and simulation

Porous media such as cancellous bone often support the simultaneous propagation of two compressional waves. When small bone samples are interrogated in through-transmission with broadband sources, these two waves often overlap in time. The modified least-squares Prony's (MLSP) method was tested for decomposing a 500 kHz-center-frequency signal containing two overlapping components: one passing through a polycarbonate plate (to produce the "fast" wave) and another passing through a cancellous-bone-mimicking phantom (to produce the "slow" wave). The MLSP method yielded estimates of attenuation slopes accurate to within 7% (polycarbonate plate) and 2% (cancellous bone phantom). The MLSP method yielded estimates of phase velocities accurate to within 1.5% (both media). The MLSP method was also tested on simulated data generated using attenuation slopes and phase velocities corresponding to bovine cancellous bone. Throughout broad ranges of signal-to-noise ratio (SNR), the MLSP method yielded estimates of attenuation slope that were accurate to within 1.0% and estimates of phase velocity that were accurate to within 4.3% (fast wave) and 1.3% (slow wave).

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%.

Finite element simulation of ultrasound propagation in bone for quantitative ultrasound toward the diagnosis of osteoporosis

Osteoporosis is a serious bone disease which leads to the increased risk of bone fractures. For prevention and therapy, early detection of osteoporosis is critical. In general, for diagnosis of osteoporosis, dual-energy X-ray absoptiometry (DXA) or densitometry is most commonly used. However DXA exhibits some disadvantages such as ionizing radiation, relatively expensive cost, and limited information on mineralization and geometry of the bone. As an alternative method of DXA, quantitative ultrasound (QUS) is being investigated. In contrast to DXA, QUS is non-ionizing and relatively inexpensive. It can also provide some bone-related parameters (e.g., quantitative measurements including speed of sound and frequency-dependent attenuation). However the estimation of these parameters is difficult and few analytical solutions exist due to the complex behavior of ultrasound propagation in bone. As an alternative to the analytical methods, in most attempts, finite difference time domain (FDTD) method is used for simulation of ultrasound propagation in bone with a limited capability of modeling complex geometries of the bone. Finite element method (FEM) is a better solution since it can handle the complex geometry, but has been rarely applied due to its computational complexity. In this work, we propose an approach of FEM-based simulation of ultrasound propagation in bone. To validate our approach, we have tested simulated and real bone models from micro-CT using the index of speed-of-sound. Our results achieve an average of 97.54% in the computational accuracy.

Ultrasonic assessment of the radius in vitro

The overall objective of this research is to develop an ultrasonic system for noninvasive assessment of the distal radius. The specific objective of this study was to examine the relationship between geometrical features of cortical bone and ultrasound measurements in vitro. Nineteen radii were measured in through transmission in a water bath. A 3.5 MHz rectangular (1 cm x 4.8 cm) single element transducer served as the source and a 3.5 MHz rectangular (1 cm x 4.8 cm) linear array transducer served as the receiver. The linear array consisted of 64 elements with a pitch of 0.75 mm. Ultrasound measurements were carried out at a location that was 1/3rdrd of the length from the distal end of each radius and two net time delay parameters, tau(NetDW) and tau(NetCW), associated with a direct wave (DW) and a circumferential wave (CW), respectively, were evaluated. The cortical thickness (CT), medullar thickness (MT) and cross-sectional area (CSA) of each radius was also evaluated based on a digital image of the cross-section at the 1/3rd location. The linear correlations between CT and tau(NetDW) was r = 0.91 (p < 0.001) and between MT and tau(NetCW) - tau(NetDW) was r = 0.63 (p < 0.05). The linear correlation between CSA and a nonlinear combination of the two net time delays, tau(NetDW) and tau(NetCW), was r = 0.95 (p < 0.001). The study shows that ultrasound measurements can be used to noninvasively assess cortical bone geometrical features in vitro as represented by cortical thickness, medullar thickness and cross-sectional area.