The effects of frequency-dependent attenuation and dispersion on sound speed measurements: applications in human trabecular bone

Ultrasound attenuation of cortical bone correlates with biomechanical, microstructural, and compositional properties

BACKGROUND

We investigated the relationship of two commonly used quantitative ultrasound (QUS) parameters, speed of sound (SoS) and attenuation coefficient (α), with water and macromolecular contents of bovine cortical bone strips as measured with ultrashort echo time (UTE) magnetic resonance imaging (MRI).

METHODS

SoS and α were measured in 36 bovine cortical bone strips utilizing a single-element transducer with nominal 5 MHz center frequency based on the time of flight principles after accommodating for reflection losses. Specimens were then scanned using UTE MRI to measure total, bound, and pore water proton density (TWPD, BWPD, and PWPD) as well as macromolecular proton fraction and macromolecular transverse relaxation time (T2-MM). Specimens were also scanned using microcomputed tomography (μCT) at 9-μm isometric voxel size to measure bone mineral density (BMD), porosity, and pore size. The elastic modulus (E) of each specimen was measured using a 4-point bending test.

RESULTS

α demonstrated significant positive Spearman correlations with E (R = 0.69) and BMD (R = 0.44) while showing significant negative correlations with porosity (R = -0.41), T2-MM (R = -0.47), TWPD (R = -0.68), BWPD (R = -0.67), and PWPD (R = -0.45).

CONCLUSIONS

The negative correlation between α and T2-MM is likely indicating the relationship between QUS and collagen matrix organization. The higher correlations of α with BWPD than with PWPD may indicate that water organized in finer structure (bound to matrix) provides lower acoustic impedance than water in larger pores, which is yet to be investigated thoroughly.

RELEVANCE STATEMENT

This study highlights the importance of future investigations exploring the relationship between QUS measures and all major components of the bone, including the collagenous matrix and water. Investigating the full potential of QUS and its validation facilitates a more affordable and accessible tool for bone health monitoring in clinics.

KEY POINTS

• Ultrasound attenuation demonstrated significant positive correlations with bone mechanics and mineral density. • Ultrasound attenuation demonstrated significant negative correlations with porosity and bone water contents. • This study highlights the importance of future investigations exploring the relationship between QUS measures and all major components of the bone.

Bone samples' behavior in sunlight, IR light, and temperature increase with FEM simulation

Biological and environmental factors produce biochemical processes that modify the bone structure. A few studies have attempted to show the adverse biological effects of sun radiation. The bone tissue exposures to infrared and sunlight radiation are analyzed by using focused sound, characterization spectroscopy techniques, and image processing. The study is complemented with a finite element method simulation on temperature behaviors. The crystal morphology on the bone hydroxyapatite and functional groups was characterized by X-ray diffraction and infrared spectroscopy. The infrared spectra confirmed the hydroxyl group of bovine hydroxyapatite, amines, and lipids are also correlated with modifications of the hydroxyapatite. The diffractograms showed the characteristic peaks of hydroxyapatite, with the main intensity at 2θ = 32.02°. Bone samples exposed to sun radiation presented a peak at 2θ = 27.5°, evidencing the possible formation of β-TCP y α-TCP. The analysis with the spectroscopy techniques about the structural changes in the samples suggests interpreting an increase of sound obtained by expanding the exposure time. It is possible to verify that there are some structural changes in the bone samples due to exposure to non-ionizing radiation. These results show an increase in the registered intensity sound correlated with the interpretation of the structural changes of bone. Thanks to the different novel analysis techniques established in the present study, it could establish the changes that experienced the bone structure under different sources of radiation, which will help to better detect scenarios of bone deficiency.

Ultrasound Characterization of Cortical Bone Using Shannon Entropy

OBJECTIVE

Ultrasound backscattered signals encompass information on the microstructure of heterogeneous media such as cortical bone, in which pores act as scatterers and result in the scattering and multiple scattering of ultrasound waves. The objective of this study was to investigate whether Shannon entropy can be exploited to characterize cortical porosity.

METHODS

In the study described here, to demonstrate proof of concept, Shannon entropy was used as a quantitative ultrasound parameter to experimentally evaluate microstructural changes in samples with controlled scatterer concentrations made of a highly absorbing polydimethylsiloxane matrix (PDMS). Similar assessment was then performed using numerical simulations on cortical bone structures with varying average pore diameter (Ct.Po.Dm.), density (Ct.Po.Dn.) and porosity (Ct.Po.).

RESULTS

The results suggest that an increase in pore diameter and porosity lead to an increase in entropy, indicating increased levels of randomness in the signals as a result of increased scattering. The entropy-versus-scatterer volume fraction in PDMS samples indicates an initial increasing trend that slows down as the scatterer concentration increases. High levels of attenuation cause the signal amplitudes and corresponding entropy values to decrease drastically. The same trend is observed when porosity of the bone samples is increased above 15%.

CONCLUSION

Sensitivity of entropy to microstructural changes in highly scattering and absorbing media can potentially be exploited to diagnose and monitor osteoporosis.

Acoustic Attenuation and Dispersion in Fatty Tissues and Tissue Phantoms Influencing Ultrasound Biomedical Imaging

The development of ultrasonic imaging techniques is optimized using artificial tissue phantoms before the practical applications. However, due to the strong attenuation and dispersion, accumulated fatty tissues can significantly impact the resolution and even feasibility of certain ultrasonic imaging modalities. An appropriate characterization of the acoustic properties on fatty phantoms can help the community to overcome the limitations. Some of the existing methods heavily overestimate attenuation coefficients by including the reflection loss and dispersion effects. Hence, in this study, we use numerical simulation-based comparison between two major attenuation measurement configurations. We further pointed out the pulse dispersion in viscoelastic tissue phantoms by simulations, which barely attracted attention in the existing studies. Using the selected attenuation and dispersion testing methods that were selected from the numerical simulation, we experimentally characterized the acoustic properties of common fatty tissue phantoms and compared the acoustic properties with the natural porcine fatty tissue samples. Furthermore, we selected one of the tissue phantoms to construct ultrasound imaging samples with some biomasses. With the known attenuation and dispersion of the tissue phantom, we showed the clarity enhancement of ultrasound imaging by signal post-processing to weaken the attenuation and dispersion effects.

The effects of temperature and frequency dispersion on sound speed in bulk poly (vinyl alcohol) poly (N-isopropylacrylamide) hydrogels caused by the phase transition

Bulk Poly (Vinyl Alcohol) (PVA) Poly (N-isopropyl acrylamide) (PNIPAm) hydrogel, one of the thermally responsive phase transitive hydrogels, is a versatile material due to its sharp volumetric phase transition and anomalous behaviors with facile tunability by thermal stimulation. At the lower critical solution temperature (LCST) of 33 °C, the hydrogels undergo a volumetric phase transition that causes drastic, non-monotonic change in the elastic modulus, viscosity, stiffness, and speed of sound. Here, we report the temperature and frequency dependence of the speed of sound in bulk PVA-PNIPAm hydrogel as measured by means of a planar resonant cavity. The linear response theory is applied for calculation of frequency dependent speed of sound. Comparisons find standard time of flight techniques underestimate the speed of sound by up to 6%, with variation in the frequency dependent speed of sound reaching as high as 200 m/s in the ultrasonic range of 0.2-0.8 MHz. The first characterization of frequency dependent speed of sound in PVA-PNIPAm hydrogel is addressed and delineated into its phase transition behaviors as connected to temperature. The findings can lead to better characterization of mechanical properties using ultrasonic spectroscopy, and higher resolution in ultrasonic imaging applications with dispersive media.

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.

Artificial neural network to estimate micro-architectural properties of cortical bone using ultrasonic attenuation: A 2-D numerical study

The goal of this study is to estimate micro-architectural parameters of cortical porosity such as pore diameter (φ), pore density (ρ) and porosity (ν) of cortical bone from ultrasound frequency dependent attenuation using an artificial neural network (ANN). First, heterogeneous structures with controlled pore diameters and pore densities (mono-disperse) were generated, to mimic simplified structure of cortical bone. Then, more realistic structures were obtained from high resolution CT scans of human cortical bone. 2-D finite-difference time-domain simulations were conducted to calculate the frequency-dependent attenuation in the 1-8 MHz range. An ANN was then trained with the ultrasonic attenuation at different frequencies as the input feature vectors while the output was set as the micro-architectural parameters (pore diameter, pore density and porosity). The ANN is composed of three fully connected dense layers with 24, 12 and 6 neurons, connected to the output layer. The dataset was trained over 6000 epochs with a batch size of 16. The trained ANN exhibits the ability to predict the micro-architectural parameters with high accuracy and low losses. ANN approaches could potentially be used as a tool to help inform physics-based modelling of ultrasound propagation in complex media such as cortical bone. This will lead to the solution of inverse-problems to retrieve bone micro-architectural parameters from ultrasound measurements for the non-invasive diagnosis and monitoring osteoporosis.

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.

Measurements of the Relationship Between CT Hounsfield Units and Acoustic Velocity and How It Changes With Photon Energy and Reconstruction Method

Transcranial magnetic resonance-guided focused ultrasound continues to gain traction as a noninvasive treatment option for a variety of pathologies. Focusing ultrasound through the skull can be accomplished by adding a phase correction to each element of a hemispherical transducer array. The phase corrections are determined with acoustic simulations that rely on speed of sound estimates derived from CT scans. While several studies have investigated the relationship between acoustic velocity and CT Hounsfield units (HUs), these studies have largely ignored the impact of X-ray energy, reconstruction method, and reconstruction kernel on the measured HU, and therefore the estimated velocity, and none have measured the relationship directly. In this paper, 91 ex vivo human skull fragments from two skulls are imaged by 80 CT scans with a variety of energies and reconstruction methods. The average HU from each fragment is found for each scan and correlated with the speed of sound measured using a through transmission technique in that fragment. As measured by the -squared value, the results show that CT is able to account for 23%-53% of the variation in velocity in the human skull. Both the X-ray energy and the reconstruction technique significantly alter the -squared value and the linear relationship between HU and speed of sound in bone. Accounting for these variations will lead to more accurate phase corrections and more efficient transmission of acoustic energy through the skull.

Broadband characterization of plastic and high intensity therapeutic ultrasound phantoms using time delay spectrometry-With validation using Kramers-Kronig relations

Time delay spectrometry (TDS) is extended for broadband characterization of plastics (low-density polyethylene, LDPE) and tissue-mimicking material (TMM). The results suggest that TDS and the conventional broadband pulse method give comparable measurements for frequency-dependent attenuation coefficient and phase velocity near the center frequency, where signal-to-noise ratio is high. However, TDS measurements show enhanced bandwidth for attenuation coefficient of 30%-40% (LDPE) and 89%-100% (TMM) and for phase velocity of 43% (LDPE) and 36% (TMM) for a single transmitter/receiver pair. In addition, TDS provides measurements of dispersion that are consistent with predictions based on the Kramers-Kronig relations to within 5 m/s over the band from 2 to 12 MHz in LDPE and to within 1 m/s in TMM over the band from 0.5 to 29 MHz.

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.

Three-dimensional Simulation of Quantitative Ultrasound in Cancellous Bone Using the Echographic Response of a Metallic Pin

Degenerative discopathy is a common pathology that may require spine surgery. A metallic cylindrical pin is inserted into the vertebral body to maintain soft tissues and may be used as a reflector of ultrasonic wave to estimate bone density. The first aim of this paper is to validate a three-dimensional (3-D) model to simulate the ultrasonic propagation in a trabecular bone sample in which a metallic pin has been inserted. We also aim at determining the effect of changes of bone volume fraction (BV/TV) and of positioning errors on the quantitative ultrasound (QUS) parameters in this specific configuration. The approach consists in coupling finite-difference time-domain simulation with X-ray microcomputed tomography. The correlation coefficient between experimental and simulated speed of sound (SOS)-respectively, broadband ultrasonic attenuation (BUA)-was equal to 0.90 (respectively, 0.55). The results show a significant correlation of SOS with BV/TV ( R = 0.82), while BUA values exhibit a nonlinear behavior versus BV/TV. The orientation of the pin should be controlled with an accuracy of around 1° to obtain accurate results. The results indicate that using the ultrasonic wave reflected by a pin has a potential to estimate the bone density. SOS is more reliable than BUA due to its lower sensitivity to the tilt angle.

Microstructural characterization of trabecular bone using ultrasonic backscattering and diffusion parameters

Finite differences time domain methods were utilized to simulate ultrasound propagation and scattering in anisotropic trabecular bone structures obtained from high resolution Computed Tomography (CT). The backscattered signals were collected and the incoherent contribution was extracted. The diffusion constant was calculated for propagations along and across the main direction of anisotropy, and was used to characterize the anisotropy of the trabecular microstructures. In anisotropic structures, the diffusion constant was significantly different in both directions, and the anisotropy of the diffusion constant was strongly correlated to the structural anisotropy measured on the CT images. These results indicate that metrics based on diffusion can be used to quantify the anisotropy of complex structures such as trabecular bone.

Micro-scale finite element modeling of ultrasound propagation in aluminum trabecular bone-mimicking phantoms: A comparison between numerical simulation and experimental results

The present study investigated the accuracy of micro-scale finite element modeling for simulating broadband ultrasound propagation in water-saturated trabecular bone-mimicking phantoms. To this end, five commercially manufactured aluminum foam samples as trabecular bone-mimicking phantoms were utilized for ultrasonic immersion through-transmission experiments. Based on micro-computed tomography images of the same physical samples, three-dimensional high-resolution computational samples were generated to be implemented in the micro-scale finite element models. The finite element models employed the standard Galerkin finite element method (FEM) in time domain to simulate the ultrasonic experiments. The numerical simulations did not include energy dissipative mechanisms of ultrasonic attenuation; however, they expectedly simulated reflection, refraction, scattering, and wave mode conversion. The accuracy of the finite element simulations were evaluated by comparing the simulated ultrasonic attenuation and velocity with the experimental data. The maximum and the average relative errors between the experimental and simulated attenuation coefficients in the frequency range of 0.6-1.4 MHz were 17% and 6% respectively. Moreover, the simulations closely predicted the time-of-flight based velocities and the phase velocities of ultrasound with maximum relative errors of 20 m/s and 11 m/s respectively. The results of this study strongly suggest that micro-scale finite element modeling can effectively simulate broadband ultrasound propagation in water-saturated trabecular bone-mimicking structures.

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.

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.

Fast and slow wave detection in bovine cancellous bone in vitro using bandlimited deconvolution and Prony's method

Fast and slow waves were detected in a bovine cancellous bone sample for thicknesses ranging from 7 to 12 mm using bandlimited deconvolution and the modified least-squares Prony's method with curve fitting (MLSP + CF). Bandlimited deconvolution consistently isolated two waves with linear-with-frequency attenuation coefficients as evidenced by high correlation coefficients between attenuation coefficient and frequency: 0.997 ± 0.002 (fast wave) and 0.986 ± 0.013 (slow wave) (mean ± standard deviation). Average root-mean-squared (RMS) differences between the two algorithms for phase velocities were 5 m/s (fast wave, 350 kHz) and 13 m/s (slow wave, 750 kHz). Average RMS differences for signal loss were 1.6 dB (fast wave, 350 kHz) and 0.4 dB (slow wave, 750 kHz). Phase velocities for thickness = 10 mm were 1726 m/s (fast wave, 350 kHz) and 1455 m/s (slow wave, 750 kHz). Results show support for the model of two waves with linear-with frequency attenuation, successful isolation of fast and slow waves, good agreement between bandlimited deconvolution and MLSP + CF as well as with a Bayesian algorithm, and potential variations of fast and/or slow wave properties with bone sample thickness.

The finite element method for micro-scale modeling of ultrasound propagation in cancellous bone

Quantitative ultrasound for bone assessment is based on the correlations between ultrasonic parameters and the properties (mechanical and physical) of cancellous bone. To elucidate the correlations, understanding the physics of ultrasound in cancellous bone is demanded. Micro-scale modeling of ultrasound propagation in cancellous bone using the finite-difference time-domain (FDTD) method has been so far utilized as one of the approaches in this regard. However, the FDTD method accompanies two disadvantages: staircase sampling of cancellous bone by finite difference grids leads to generation of wave artifacts at the solid-fluid interface inside the bone; additionally, this method cannot explicitly satisfy the needed perfect-slip conditions at the interface. To overcome these disadvantages, the finite element method (FEM) is proposed in this study. Three-dimensional finite element models of six water-saturated cancellous bone samples with different bone volume were created. The values of speed of sound (SOS) and broadband ultrasound attenuation (BUA) were calculated through the finite element simulations of ultrasound propagation in each sample. Comparing the results with other experimental and simulation studies demonstrated the capabilities of the FEM for micro-scale modeling of ultrasound in water-saturated cancellous bone.

A linear model approach for ultrasonic inverse problems with attenuation and dispersion

Ultrasonic inverse problems such as spike train deconvolution, synthetic aperture focusing, or tomography attempt to reconstruct spatial properties of an object (discontinuities, delaminations, flaws, etc.) from noisy and incomplete measurements. They require an accurate description of the data acquisition process. Dealing with frequency-dependent attenuation and dispersion is therefore crucial because both phenomena modify the wave shape as the travel distance increases. In an inversion context, this paper proposes to exploit a linear model of ultrasonic data taking into account attenuation and dispersion. The propagation distance is discretized to build a finite set of radiation impulse responses. Attenuation is modeled with a frequency power law and then dispersion is computed to yield physically consistent responses. Using experimental data acquired from attenuative materials, this model outperforms the standard attenuation-free model and other models of the literature. Because of model linearity, robust estimation methods can be implemented. When matched filtering is employed for single echo detection, the model that we propose yields precise estimation of the attenuation coefficient and of the sound velocity. A thickness estimation problem is also addressed through spike deconvolution, for which the proposed model also achieves accurate results.

Time-domain separation of interfering waves in cancellous bone using bandlimited deconvolution: simulation and phantom study

In through-transmission interrogation of cancellous bone, two longitudinal pulses ("fast" and "slow" waves) may be generated. Fast and slow wave properties convey information about material and micro-architectural characteristics of bone. However, these properties can be difficult to assess when fast and slow wave pulses overlap in time and frequency domains. In this paper, two methods are applied to decompose signals into fast and slow waves: bandlimited deconvolution and modified least-squares Prony's method with curve-fitting (MLSP + CF). The methods were tested in plastic and Zerdine(®) samples that provided fast and slow wave velocities commensurate with velocities for cancellous bone. Phase velocity estimates were accurate to within 6 m/s (0.4%) (slow wave with both methods and fast wave with MLSP + CF) and 26 m/s (1.2%) (fast wave with bandlimited deconvolution). Midband signal loss estimates were accurate to within 0.2 dB (1.7%) (fast wave with both methods), and 1.0 dB (3.7%) (slow wave with both methods). Similar accuracies were found for simulations based on fast and slow wave parameter values published for cancellous bone. These methods provide sufficient accuracy and precision for many applications in cancellous bone such that experimental error is likely to be a greater limiting factor than estimation error.

Mean scatterer spacing estimation in normal and thermally coagulated ex vivo bovine liver

The liver has been hypothesized to have a unique arrangement of microvasculature that presents as an arrangement of quasiperiodic scatterers to an interrogating ultrasound pulse. The mean scatterer spacing (MSS) of these quasiperiodic scatterers has been proposed as a useful quantitative ultrasound biomarker for characterizing liver tissue. Thermal ablation is an increasingly popular method for treating hepatic tumors, and ultrasonic imaging approaches for delineating the extent of thermal ablation are in high demand. In this work, we examine the distribution of estimated MSS in thermally coagulated bovine liver and normal untreated bovine liver ex vivo. We estimate MSS by detecting local maxima in the spectral coherence function of radio frequency echoes from a clinical transducer, the Siemens VFX 9L4 transducer operating on an S2000 scanner. We find that normal untreated bovine liver was characterized by an MSS of approximately 1.3 mm. We examined regions of interest 12 mm wide laterally, and ranging from 12 mm to 18 mm axially, in 2 mm increments. Over these parameters, the mode of the MSS estimates was between 1.25 and 1.37 mm. On the other hand, estimation of MSS in thermally coagulated liver tissue yields a distribution of MSS estimates whose mode varied between 0.45 and 1.0 mm when examining regions of interest over the same sizes. We demonstrate that the estimated MSS in thermally coagulated liver favors small spacings because the randomly positioned scatterers in this tissue are better modeled as aperiodic scatterers. The submillimeter spacings result from the fact that this was the most probable spacing to be estimated if the discretely sampled spectral coherence function was a uniformly random two-dimensional function.

Estimation of fast and slow wave properties in cancellous bone using Prony's method and curve fitting

The presence of two longitudinal waves in poroelastic media is predicted by Biot's theory and has been confirmed experimentally in through-transmission measurements in cancellous bone. Estimation of attenuation coefficients and velocities of the two waves is challenging when the two waves overlap in time. The modified least squares Prony's (MLSP) method in conjuction with curve-fitting (MLSP + CF) is tested using simulations based on published values for fast and slow wave attenuation coefficients and velocities in cancellous bone from several studies in bovine femur, human femur, and human calcaneus. The search algorithm is accelerated by exploiting correlations among search parameters. The performance of the algorithm is evaluated as a function of signal-to-noise ratio (SNR). For a typical experimental SNR (40 dB), the root-mean-square errors (RMSEs) for one example (human femur) with fast and slow waves separated by approximately half of a pulse duration were 1 m/s (slow wave velocity), 4 m/s (fast wave velocity), 0.4 dB/cm MHz (slow wave attenuation slope), and 1.7 dB/cm MHz (fast wave attenuation slope). The MLSP + CF method is fast (requiring less than 2 s at SNR = 40 dB on a consumer-grade notebook computer) and is flexible with respect to the functional form of the parametric model for the transmission coefficient. The MLSP + CF method provides sufficient accuracy and precision for many applications such that experimental error is a greater limiting factor than estimation error.

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.

A restoration framework for ultrasonic tissue characterization

Ultrasonic tissue characterization has become an area of intensive research. This procedure generally relies on the analysis of the unprocessed echo signal. Because the ultrasound echo is degraded by the non-ideal system point spread function, a deconvolution step could be employed to provide an estimate of the tissue response that could then be exploited for a more accurate characterization. In medical ultrasound, deconvolution is commonly used to increase diagnostic reliability of ultrasound images by improving their contrast and resolution. Most successful algorithms address deconvolution in a maximum a posteriori estimation framework; this typically leads to the solution of l(2)-norm or (1)-norm constrained optimization problems, depending on the choice of the prior distribution. Although these techniques are sufficient to obtain relevant image visual quality improvements, the obtained reflectivity estimates are, however, not appropriate for classification purposes. In this context, we introduce in this paper a maximum a posteriori deconvolution framework expressly derived to improve tissue characterization. The algorithm overcomes limitations associated with standard techniques by using a nonstandard prior model for the tissue response. We present an evaluation of the algorithm performance using both computer simulations and tissue-mimicking phantoms. These studies reveal increased accuracy in the characterization of media with different properties. A comparison with state-of-the-art Wiener and l(1)-norm deconvolution techniques attests to the superiority of the proposed algorithm.

3D ultrasound reconstruction algorithms from analog and digital data

Freehand 3D ultrasound is increasingly being introduced in the clinic for diagnostics and image-assisted interventions. Various algorithms exist for combining 2D images of regular ultrasound probes to 3D volumes, being either voxel-, pixel- or function-based. Previously, the most commonly used input to 3D ultrasound reconstruction has been digitized analog video. However, recent scanners that offer access to digital image frames exist, either as processed or unprocessed data. To our knowledge, no comparison has been performed to determine which data source gives the best reconstruction quality. In the present study we compared both reconstruction algorithms and data sources using novel comparison methods for detecting potential differences in image quality of the reconstructed volumes. The ultrasound scanner used in this study was the Sonix RP from Ultrasonix Medical Corp (Richmond, Canada), a scanner that allow third party access to unprocessed and processed digital data. The ultrasound probe used was the L14-5/38 linear probe. The assessment is based on a number of image criteria: detectability of wire targets, spatial resolution, detectability of small barely visible structures, subjective tissue image quality, and volume geometry. In addition we have also performed the more "traditional" comparison of reconstructed volumes by removing a percentage of the input data. By using these evaluation methods and data from the specific scanner, the results showed that the processed video performed better than the digital scan-line data, digital video being better than analog video. Furthermore, the results showed that the choice of video source was more important than the choice of tested reconstruction algorithms.

Nonlinear propagation delay and pulse distortion resulting from dual frequency band transmit pulse complexes

A method of acoustic imaging is discussed that potentially can improve the diagnostic capabilities of medical ultrasound. The method, given the name second order ultrasound field imaging, is achieved by the processing of the received signals from transmitted dual frequency band pulse complexes with at least partly overlapping high frequency (HF) and low frequency (LF) pulses. The transmitted HF pulses are used for image reconstruction whereas the transmitted LF pulses are used to manipulate the elastic properties of the medium observed by the HF imaging pulses. In the present paper, nonlinear propagation effects observed by a HF imaging pulse due to the presence of a LF manipulation pulse is discussed. When using dual frequency band transmit pulse complexes with a large separation in center frequency (e.g., 1:10), these nonlinear propagation effects are manifested as a nonlinear HF propagation delay and a HF pulse distortion different from conventional harmonic distortion. In addition, with different transmit foci for the HF and LF pulses, nonlinear aberration will occur.

Characterization of bone tissue using microstrip antennas

The use of electromagnetic waves in the characterization of biological tissues has been conducted since the nineteenth century after the confirmation that electric and magnetic fields can interact with biological materials. In this paper, electromagnetic waves are used to characterize tissues with different levels of bone mass. In this way, one antenna array on microstrip lines was used. It can be seen that bones with different mass has different behavior in microwave frequencies.

Broadband reduction of the second harmonic distortion during nonlinear ultrasound wave propagation

Ultrasound contrast harmonic imaging and detection techniques are hampered by the harmonic distortion of the ultrasound wave caused by the nonlinearities of the medium. To increase the discrimination between the tissue and ultrasound contrast agents at higher harmonics, we investigate a tissue harmonic suppression technique. The main attention of the research is the signal that is introduced at the source and is constructed out of several discrete frequency components from the second harmonic band. Therefore, this method was coined as the multiple component second harmonic reduction signal or multiple component SHRS. By adjusting the amplitude and phase of discrete components and simultaneously propagating multiple component SHRS with the imaging signal, the nonlinear distortion of the ultrasound waveform is considerably reduced. Using the numerical simulation, the optimal parameters for multiple component SRHS were deduced. The simulations results were corroborated in the water tank experiments and showed 40 dB reduction with respect to the fundamental, covering up to 75% of the entire second harmonic band. In the other series of experiments with the clinically used contrast agent, the uniform increase in agent-to-tissue ratio of 7.4 dB over a relatively large region of imaging was observed. The use of the proposed method in the everyday clinical practice can improve discrimination between the tissue and the contrast agent in harmonic imaging.

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.

Influence of viscoelastic and viscous absorption on ultrasonic wave propagation in cortical bone: Application to axial transmission

Cortical bone and the surrounding soft tissues are attenuating and heterogeneous media, which might affect the signals measured with axial transmission devices. This work aims at evaluating the effect of the heterogeneous acoustic absorption in bone and in soft tissues on the bone ultrasonic response. Therefore, a two-dimensional finite element time-domain method is derived to model transient wave propagation in a three-layer medium composed of an inhomogeneous transverse isotropic viscoelastic solid layer, sandwiched between two viscous fluid layers. The model couples viscous acoustic propagation in both fluid media with the anisotropic viscoelastic response of the solid. A constant spatial gradient of material properties is considered for two values of bone thicknesses (0.6 and 4 mm). In the studied configuration, absorption in the surrounding fluid tissues does not affect the results, whereas bone viscoelastic properties have a significant effect on the first arriving signal (FAS) velocity. For a thin bone, the FAS velocity is governed by the spatially averaged bone properties. For a thick bone, the FAS velocity may be predicted using a one-dimensional model.

Phase velocity analysis of acoustic propagation in trabecular bone

The trabecular bones are highly dispersive acoustic media composed by randomly shaped trabeculae (considered as scatterers) and surrounded by bone marrow. An acoustic wave generated by an incident ultrasonic pulse with respect to the media under study, shows that its velocity and amplitude are a function of the density size and shaped of the scatterers. Two different methods were used to theoretically study this scattering phenomena: i) a self-consistent model proposed by Sabina and Willis, and ii) the multiple-scattering theory of Waterman-Truell. These methods were able to compute the phase velocity and amplitude as a function of operating frequency, density and size of scatterers. The theoretical results were compared with experimental data already published and the phase veloctiy shows a good agreement for low concentration of scatterers.

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%.

Imaging of gaps in digital joints by measurement of ultrasound transmission using a linear array

In orthodontic dentistry for young subjects, it is important to assess the degree of growth of the jaw bones to determine the optimum time for treatment. The structure of the digital joint changes with age, with such changes correlating to the degree of bone growth (including jaw bones). There are two gaps in the digital joint of a young subject, one of which disappears with aging. In the present study, a method for noninvasive assessment of such change in the structure of a digital joint was examined, in which continuous-wave ultrasound is radiated to a digital joint by a single-element ultrasonic transducer. This continuous ultrasound, which passes through the digital joint, is received by a linear array ultrasonic probe situated opposite the transducer. The probe simultaneously realizes pulse-echo imaging and imaging of transmission ultrasound, which passes through the joint. Using this experimental apparatus, the existence and position of a gap can be detected clearly by imaging the transmission ultrasound on a pulse-echo image. In basic experiments, continuous-wave ultrasound generated by a planar or focused transducer was radiated to a gap between two acrylic bars, which simulated that in a digital joint; transmission ultrasound, which passed through the gap, was measured with a linear array probe. The basic experimental results showed that a gap with a width >0.4 mm is detectable and that the width at half maximum of the amplitude profile of the received transmission ultrasound that passed through the gap correlated with the width of the gap. Furthermore, in the preliminary in vivo experiments, transmission ultrasound that passed through two gaps in the case of a child was clearly imaged by the proposed method, and that which passed through only one gap in the case of an adult was also imaged. These results show the possibility for the use of the proposed method to noninvasively assess the change in the structure of a joint as a result of aging.

The dependencies of phase velocity and dispersion on volume fraction in cancellous-bone-mimicking phantoms

Frequency-dependent phase velocity was measured in eight cancellous-bone-mimicking phantoms consisting of suspensions of randomly oriented nylon filaments (simulating trabeculae) in a soft-tissue-mimicking medium (simulating marrow). Trabecular thicknesses ranged from 152 to 356 mum. Volume fractions of nylon filament material ranged from 0% to 10%. Phase velocity varied approximately linearly with frequency over the range from 300 to 700 kHz. The increase in phase velocity (compared with phase velocity in a phantom containing no filaments) at 500 kHz was approximately proportional to volume fraction occupied by nylon filaments. The derivative of phase velocity with respect to frequency was negative and exhibited nonlinear, monotonically decreasing dependence on volume fraction. The dependencies of phase velocity and its derivative on volume fraction in these phantoms were similar to those reported in previous studies on (1) human cancellous bone and (2) phantoms consisting of parallel nylon wires immersed in water.

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.

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.

Characterization of ultrasound propagation through ex-vivo human temporal bone

Adjuvant therapies that lower the thrombolytic dose or increase its efficacy would represent a significant breakthrough in the treatment of patients with ischemic stroke. The objective of this study was to perform intracranial measurements of the acoustic pressure field generated by 0.12, 1.03 and 2.00-MHz ultrasound transducers to identify optimal ultrasound parameters that would maximize penetration and minimize aberration of the beam. To achieve this goal, in vitro experiments were conducted on five human skull specimens. In a water-filled tank, two unfocused transducers (0.12 and 1.03 MHz) and one focused transducer (2.00 MHz) were consecutively placed near the right temporal bone of each skull. A hydrophone, mounted on a micropositioning system, was moved to an estimated location of the middle cerebral artery (MCA) origin, and measurements of the surrounding acoustic pressure field were performed. For each measurement, the distance from the position of maximum acoustic pressure to the estimated origin of the MCA inside the skulls was quantified. The -3 dB depth-of-field and beamwidth in the skull were also investigated as a function of the three frequencies. Results show that the transducer alignment relative to the skull is a significant determinant of the detailed behavior of the acoustic field inside the skull. For optimal penetration, insonation normal to the temporal bone was needed. The shape of the 0.12-MHz intracranial beam was more distorted than those at 1.03 and 2.00 MHz because of the large aperture and beamwidth. However, lower ultrasound pressure reduction was observed at 0.12 MHz (22.5%). At 1.03 and 2.00 MHz, two skulls had an insufficient temporal bone window and attenuated the beam severely (up to 96.6% pressure reduction). For all frequencies, constructive and destructive interference patterns were seen near the contralateral skull wall at various elevations. The 0.12-MHz ultrasound beam depth-of-field was affected the most when passing through the temporal bone and showed a decrease in size of more than 55% on average. The speed of sound in the temporal bone of each skull was estimated at 1.03 MHz and demonstrated a large range (1752.1 to 3285.3 m/s). Attenuation coefficients at 1.03 and 2.00 MHz were also derived for each of the five skull specimens. This work provides needed information on ultrasound beam shapes inside the human skull, which is a necessary first step for the development of an optimal transcranial ultrasound-enhanced thrombolysis device.

Ultrasonic velocity dispersion in bovine cortical bone: an experimental study

Cortical bone quality is determinant in bone fragility and its ultrasonic evaluation has become possible in clinical practice. However, the interaction between a broadband ultrasonic pulse and this complex multiscale medium remains poorly understood. The frequency dependence of phase velocity, which may impact clinical measurements, has been sparsely investigated. Our objective is to evaluate the determinants of the frequency dependence of phase velocity in bovine femoral cortical bone samples using an in vitro ultrasonic transmission device. The apparent phase velocity varies quasilinearly on a 1 MHz restricted bandwidth around 4 MHz. After compensating for diffraction effects, significant differences in velocity dispersion are obtained according to the anatomical location. The microstructure of each sample is determined using an optical microscope, which allows assessing the dependence of dispersion on the type of bone microstructure. Mostly positive but also negative values of dispersion are measured. Negative dispersion is mainly obtained in samples constituted of mixed microstructure, which may be explained by phase cancellation effects due to the presence of different microstructures within the same sample. Dispersion is shown to be related to broadband ultrasonic attenuation values, especially in the radial direction. Results are compared with the local Kramers-Kronig relationships.

Ultrasonic scattering from cancellous bone: a review

This paper reviews theory, measurements, and computer simulations of scattering from cancellous bone reported by many laboratories. Three theoretical models (binary mixture, Faran cylinder, and weak scattering) for scattering from cancellous bone have demonstrated some consistency with measurements of backscatter. Backscatter is moderately correlated with bone mineral density in human calcaneus in vitro (r(2) = 0.66 - 0.68). Backscatter varies approximately as frequency cubed and trabecular thickness cubed in human calcaneus and femur in vitro. Backscatter from human calcaneus and bovine tibia exhibits substantial anisotropy. So far, backscatter has demonstrated only modest clinical utility. Computer simulation models have helped to elucidate mechanisms underlying scattering from cancellous bones.

A method for improved standardization of in vivo calcaneal time-domain speed-of-sound measurements

Although calcaneal speed of sound (SOS) is an effective predictor of osteoporotic fracture risk, clinical SOS measurements exhibit a high degree of inter-system variability. Calcaneal SOS is usually computed from time-of-flight measurements of broadband ultrasound pulses that propagate through the foot. In order to minimize the effects of multi-path interference, many investigators measure time-of-flight from markers near the leading edge of the pulse. The calcaneus is a highly attenuating, highly inhomogeneous bone that distorts propagating ultrasound pulses via frequency-dependent attenuation, reverberation, dispersion, multiple scattering, and refraction. This pulse distortion can produce errors in leading-edge transit-time marker-based SOS measurements. In this paper, an equation to predict dependence of time-domain SOS measurements on system parameters (center frequency and bandwidth), transit-time marker location, and bone properties (attenuation coefficient and thickness) is validated with through-transmission measurements in a bone-mimicking phantom and in 73 women in vivo, using a clinical bone sonometer. In order to test the utility of the formula for suppressing system dependence of SOS measurements, a wideband laboratory data acquisition system was used to make a second set of through-transmission measurements on the phantom. The compensation formula reduced system-dependent leading-edge transit-time marker-based SOS measurements in the phantom from 41 m/s to 5 m/s and reduced average transit-time marker-related SOS variability in 73 women from 40 m/s to 10 m/s. The compensation formula can be used to improve standardization in bone sonometry.

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.

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.

Blind deconvolution of medical ultrasound images: a parametric inverse filtering approach

The problem of reconstruction of ultrasound images by means of blind deconvolution has long been recognized as one of the central problems in medical ultrasound imaging. In this paper, this problem is addressed via proposing a blind deconvolution method which is innovative in several ways. In particular, the method is based on parametric inverse filtering, whose parameters are optimized using two-stage processing. At the first stage, some partial information on the point spread function is recovered. Subsequently, this information is used to explicitly constrain the spectral shape of the inverse filter. From this perspective, the proposed methodology can be viewed as a "hybridization" of two standard strategies in blind deconvolution, which are based on either concurrent or successive estimation of the point spread function and the image of interest. Moreover, evidence is provided that the "hybrid" approach can outperform the standard ones in a number of important practical cases. Additionally, the present study introduces a different approach to parameterizing the inverse filter. Specifically, we propose to model the inverse transfer function as a member of a principal shift-invariant subspace. It is shown that such a parameterization results in considerably more stable reconstructions as compared to standard parameterization methods. Finally, it is shown how the inverse filters designed in this way can be used to deconvolve the images in a nonblind manner so as to further improve their quality. The usefulness and practicability of all the introduced innovations are proven in a series of both in silico and in vivo experiments. Finally, it is shown that the proposed deconvolutioh algorithms are capable of improving the resolution of ultrasound images by factors of 2.24 or 6.52 (as judged by the autocorrelation criterion) depending on the type of regularization method used.

A portable real-time ultrasonic bone densitometer

The objectives of this study were to develop a novel ultrasound device to estimate bone mineral density (BMD) at the calcaneus. The device is entirely self-contained, portable (<or=1 kg) and handheld and permits real-time evaluation of the BMD by computing a parameter known as net time delay (NTD). The NTD is defined as the difference between the transit time through the heel of an ultrasound signal and the transit time through a hypothetical object of equal thickness (to the heel) but containing soft tissue only. This parameter is sensitive primarily to the total amount (i.e., the average total thickness) of bone contained in the propagation path, and thus is equivalent to the bone mineral content estimated by dual-energy X-ray absorptiometry (DXA) scanners, and to the (areal) BMD when normalized by transducer area. Computer simulations of ultrasound propagation were used to study the relationship between NTD and BMD. The simulations used micro-computed tomography (micro-CT) images of a set of 10 calcaneal bone cores, which were further processed by morphologic image processing to obtain a set of 30 "samples" with BMDs ranging from 0.25 to 1.83 g/cm2. The NTD and BMD were found to be very highly correlated (r=0.99), demonstrating the high sensitivity of NTD to bone mass. A clinical institutional review board-approved study measured 85 adult women at the heel. BMD was measured at the same time using DXA. A linear regression using NTD produced a linear correlation coefficient of 0.86, which represents a significant improvement over present ultrasound bone densitometers, but not nearly as good as the simulation results. Reasons for this have been identified (viz., errors in distance measurement and lack of coincidence between the DXA and ultrasound regions of interest), and a new device and experimental protocol to deal with these sources of error has been developed and is currently under clinical trials. It is expected that this should improve the correlation between NTD and BMD even further (>or=0.9), effectively making the former parameter a proxy for the latter. 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, in conjunction with the fact that the devices are designed to be manufactured at very low cost (approximately $400 USD), should enable the significant expansion of diagnosis and monitoring of osteoporosis.

The dependence of time-domain speed-of-sound measurements on center frequency, bandwidth, and transit-time marker in human calcaneus in vitro

Time-domain speed-of-sound (SOS) measurements in calcaneus are effective predictors of osteoporotic fracture risk. High attenuation and dispersion in bone, however, produce severe distortion of transmitted pulses that leads to ambiguity of time-domain SOS measurements. An equation to predict the effects of system parameters (center frequency and bandwidth), algorithm parameters (pulse arrival-time marker), and bone properties (attenuation coefficient and thickness) on time-domain SOS estimates is derived for media with attenuation that varies linearly with frequency. The equation is validated using data from a bone-mimicking phantom and from 30 human calcaneus samples in vitro. The data suggest that the effects of dispersion are small compared with the effects of frequency-dependent attenuation. The equation can be used to retroactively compensate data. System-related variations in SOS are shown to decrease as the pulse-arrival-time marker is moved toward the pulse center. Therefore, compared with other time-domain measures of SOS, group velocity exhibits the minimum system dependence.

Bayesian estimation of the underlying bone properties from mixed fast and slow mode ultrasonic signals

We recently proposed that the observed apparent negative dispersion in bone can arise from the interference between fast wave and slow wave modes, each exhibiting positive dispersion [Marutyan et al., J. Acoust. Soc. Am. 120, EL55-EL61 (2006)]. In the current study, we applied Bayesian probability theory to solve the inverse problem: extracting the underlying properties of bone. Simulated mixed mode signals were analyzed using Bayesian probability. The calculations were implemented using the Markov chain Monte Carlo with simulated annealing to draw samples from the marginal posterior probability for each parameter.

The frequency dependence of ultrasonic velocity and the anisotropy of dispersion in both freshly excised and formalin-fixed myocardium

The objectives of this study were to measure the frequency dependence of the ultrasonic velocity in myocardium and to quantify the frequency dependence of phase velocity as a function of the insonification angle relative to the predominant direction of the myofibers. Broadband phase spectroscopy data were acquired, spanning a frequency range of 3 to 8 MHz. Measurements were made on 36 tissue specimens cored from 12 freshly excised lamb hearts and were repeated after fixation with formalin. Measured phase velocities were found to be well characterized by a logarithmic fit. For freshly excised myocardium, the dispersion over the 3 to 8 MHz bandwidth was dependent on the direction of insonification, ranging from 1.2 m/s change for perpendicular insonification (across the myofibers) to 3.7 m/s for parallel insonification (along the myofibers). The effects of formalin-fixation resulted in a significant increase in dispersion for perpendicular insonification, but did not appreciably alter the dispersion for parallel insonification.