Considerations for Choosing Sensitive Element Size for Needle and Fiber-Optic Hydrophones-Part II: Experimental Validation of Spatial Averaging Model

Acoustic pressure can be measured with a hydrophone. Hydrophone measurements can underestimate incident acoustic pressure due to spatial averaging effects across the hydrophone sensitive element. The spatial averaging filter for a nonlinear focused beam is a low-pass filter that decreases monotonically from 1 to 0 as frequency increases from 0 to infinity. Experiments were performed to test an analytic model for the spatial averaging filter. Nonlinear pressure tone bursts were generated by three source transducers with driving frequencies ranging from 2.5 to 6 MHz, diameters ranging from 19 to 64 mm, and focal lengths ranging from 38 to 89 mm. The nonlinear pressure fields were measured using four needle hydrophones with nominal geometrical sensitive element diameters of 200, 400, 600, and [Formula: see text]. The average root-mean-square difference between theoretical and experimental spatial averaging filters was 5.8% ± 2.6%.

Directivity and Frequency-Dependent Effective Sensitive Element Size of a Reflectance-Based Fiber-Optic Hydrophone: Predictions From Theoretical Models Compared With Measurements

The goal of this work was to measure the directivity of a reflectance-based fiber-optic hydrophone at multiple frequencies and to compare it to four theoretical models: rigid baffle (RB), rigid piston (RP), unbaffled (UB), and soft baffle (SB). The fiber had a nominal 105- [Formula: see text] diameter core and a 125- [Formula: see text] overall diameter (core + cladding). Directivity measurements were performed at 2.25, 3.5, 5, 7.5, 10, and 15 MHz from ±90° in two orthogonal planes. Effective hydrophone sensitive element radius was estimated by least-squares fitting the four models to the directivity measurements using the sensitive element radius as an adjustable parameter. Over the range from 2.25 to 15 MHz, the average magnitudes of differences between the effective and nominal sensitive element radii were 59% ± 49% (RB), 10% ± 5% (RP), 46% ± 38% (UB), and 71% ± 19% (SB). Therefore, the directivity of a reflectance-based fiber-optic hydrophone may be best estimated by the RP model.

Directivity and Frequency-Dependent Effective Sensitive Element Size of Needle Hydrophones: Predictions From Four Theoretical Forms Compared With Measurements

Directivity is a hydrophone specification that describes response as a function of angle of incidence. The goal of this study was to compare, in the context of needle hydrophones, the commonly used rigid baffle model for hydrophone directivity to three alternative models: soft baffle, unbaffled (UB), and rigid piston (RP). Directivity measurements were performed at 1, 2, 3, 4, 6, 8, and 10 MHz from ±7° in two orthogonal planes for two ceramic and two polymer needle hydrophones with nominal geometrical sensitive element diameters of 200, 400, 600, and 1000 . Effective hydrophone sensitive element radius was estimated by least-squares fitting the four models to directivity measurement data using the sensitive element radius (a) as an adjustable parameter. For > 4 (where and = wavelength), the RP model outperformed the other three models. For , the average error in estimated sensitive element radius was 7% [95% confidence interval (CI): 3%-12%] for the RP model while the lowest average error by the other three models was 46% (95% CI: 38%-54%) for the UB model.

Pressure Pulse Distortion by Needle and Fiber-Optic Hydrophones due to Nonuniform Sensitivity

Needle and fiber-optic hydrophones have frequency-dependent sensitivity, which can result in substantial distortion of nonlinear or broadband pressure pulses. A rigid cylinder model for needle and fiber-optic hydrophones was used to predict this distortion. The model was compared with measurements of complex sensitivity for a fiber-optic hydrophone and three needle hydrophones with sensitive element sizes ( ) of 100, 200, 400, and . Theoretical and experimental sensitivities agreed to within 12 ± 3% [root-mean-square (RMS) normalized magnitude ratio] and 8° ± 3° (RMS phase difference) for the four hydrophones over the range from 1 to 10 MHz. The model predicts that distortions in peak positive pressure can exceed 20% when and spectral index (SI) >7% and can exceed 40% when and SI >14%, where is the wavelength of the fundamental component and SI is the fraction of power spectral density contained in harmonics. The model predicts that distortions in peak negative pressure can exceed 15% when . Measurements of pulse distortion using a 2.25 MHz source and needle hydrophones with , 400, and agreed with the model to within a few percent on the average for SI values up to 14%. This paper 1) identifies conditions for which needle and fiber-optic hydrophones produce substantial distortions in acoustic pressure pulse measurements and 2) offers a practical deconvolution method to suppress these distortions.

Two-layer heterogeneous breast phantom for photoacoustic imaging

Photoacoustic tomography (PAT) is emerging as a potentially important aid for breast cancer detection. Well-validated tissue-simulating phantoms are needed for objective, quantitative, and physically realistic testing for system development. Prior reported PAT phantoms with homogenous structures do not incorporate the irregular layered structure of breast tissue. To assess the impact of this simplification, we design and construct two-layer breast phantoms incorporating vessel-simulating inclusions and realistic undulations at the fat/fibroglandular tissue interface. The phantoms are composed of custom poly(vinyl chloride) plastisol formulations mimicking the acoustic properties of two breast tissue types and tissue-relevant similar optical properties. Resulting PAT images demonstrate that in tissue with acoustic heterogeneity, lateral size of imaging targets is sensitive to the choice of sound speed in image reconstruction. The undulating boundary can further degrade a target's lateral size due to sound speed variation in tissue and refraction of sound waves at the interface. The extent of this degradation is also influenced by the geometric relationship between an absorber and the boundary. Results indicate that homogeneous phantom matrixes may underestimate the degradation of PAT image quality in breast tissue, whereas heterogeneous phantoms can provide more realistic testing through improved reproduction of spatial variations in physical properties.

Variation of High-Intensity Therapeutic Ultrasound (HITU) Pressure Field Characterization: Effects of Hydrophone Choice, Nonlinearity, Spatial Averaging and Complex Deconvolution

Reliable acoustic characterization is fundamental for patient safety and clinical efficacy during high-intensity therapeutic ultrasound (HITU) treatment. Technical challenges, such as measurement variation and signal analysis, still exist for HITU exposimetry using ultrasound hydrophones. In this work, four hydrophones were compared for pressure measurement: a robust needle hydrophone, a small polyvinylidene fluoride capsule hydrophone and two fiberoptic hydrophones. The focal waveform and beam distribution of a single-element HITU transducer (1.05 MHz and 3.3 MHz) were evaluated. Complex deconvolution between the hydrophone voltage signal and frequency-dependent complex sensitivity was performed to obtain pressure waveforms. Compressional pressure (p₊), rarefactional pressure (p_-) and focal beam distribution were compared up to 10.6/-6.0 MPa (p₊/p_-) (1.05 MHz) and 20.65/-7.20 MPa (3.3 MHz). The effects of spatial averaging, local non-linear distortion, complex deconvolution and hydrophone damage thresholds were investigated. This study showed a variation of no better than 10%-15% among hydrophones during HITU pressure characterization.

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.

Phantom-based image quality test methods for photoacoustic imaging systems

As photoacoustic imaging (PAI) technologies advance and applications arise, there is increasing need for standardized approaches to provide objective, quantitative performance assessment at various stages of the product development and clinical translation process. We have developed a set of performance test methods for PAI systems based on breast-mimicking tissue phantoms containing embedded inclusions. Performance standards for mature imaging modalities [magnetic resonance imaging (MRI), computed tomography (CT), and ultrasound] were used to guide selection of critical PAI image quality characteristics and experimental methods. Specifically, the tests were designed to address axial, lateral, and elevational spatial resolution, signal uniformity, penetration depth, sensitivity, spatial measurement accuracy, and PAI-ultrasound coregistration. As an initial demonstration of the utility of these test methods, we characterized the performance of a modular, bimodal PAI-ultrasound system using four clinical ultrasound transducers with varying design specifications. Results helped to inform optimization of acquisition and data processing procedures while providing quantitative elucidation of transducer-dependent differences in image quality. Comparison of solid, tissue-mimicking polymer phantoms with those based on Intralipid indicated the superiority of the former approach in simulating real-world conditions for PAI. This work provides a critical foundation for the establishment of well-validated test methods that will facilitate the maturation of PAI as a medical imaging technology.

Biologically relevant photoacoustic imaging phantoms with tunable optical and acoustic properties

Established medical imaging technologies such as magnetic resonance imaging and computed tomography rely on well-validated tissue-simulating phantoms for standardized testing of device image quality. The availability of high-quality phantoms for optical-acoustic diagnostics such as photoacoustic tomography (PAT) will facilitate standardization and clinical translation of these emerging approaches. Materials used in prior PAT phantoms do not provide a suitable combination of long-term stability and realistic acoustic and optical properties. Therefore, we have investigated the use of custom polyvinyl chloride plastisol (PVCP) formulations for imaging phantoms and identified a dual-plasticizer approach that provides biologically relevant ranges of relevant properties. Speed of sound and acoustic attenuation were determined over a frequency range of 4 to 9 MHz and optical absorption and scattering over a wavelength range of 400 to 1100 nm. We present characterization of several PVCP formulations, including one designed to mimic breast tissue. This material is used to construct a phantom comprised of an array of cylindrical, hemoglobin-filled inclusions for evaluation of penetration depth. Measurements with a custom near-infrared PAT imager provide quantitative and qualitative comparisons of phantom and tissue images. Results indicate that our PVCP material is uniquely suitable for PAT system image quality evaluation and may provide a practical tool for device validation and intercomparison.

Conventional, Bayesian, and Modified Prony's methods for characterizing fast and slow waves in equine cancellous bone

Conventional, Bayesian, and the modified least-squares Prony's plus curve-fitting (MLSP + CF) methods were applied to data acquired using 1 MHz center frequency, broadband transducers on a single equine cancellous bone specimen that was systematically shortened from 11.8 mm down to 0.5 mm for a total of 24 sample thicknesses. Due to overlapping fast and slow waves, conventional analysis methods were restricted to data from sample thicknesses ranging from 11.8 mm to 6.0 mm. In contrast, Bayesian and MLSP + CF methods successfully separated fast and slow waves and provided reliable estimates of the ultrasonic properties of fast and slow waves for sample thicknesses ranging from 11.8 mm down to 3.5 mm. Comparisons of the three methods were carried out for phase velocity at the center frequency and the slope of the attenuation coefficient for the fast and slow waves. Good agreement among the three methods was also observed for average signal loss at the center frequency. The Bayesian and MLSP + CF approaches were able to separate the fast and slow waves and provide good estimates of the fast and slow wave properties even when the two wave modes overlapped in both time and frequency domains making conventional analysis methods unreliable.

Conditionally Increased Acoustic Pressures in Nonfetal Diagnostic Ultrasound Examinations Without Contrast Agents: A Preliminary Assessment

The mechanical index (MI) has been used by the US Food and Drug Administration (FDA) since 1992 for regulatory decisions regarding the acoustic output of diagnostic ultrasound equipment. Its formula is based on predictions of acoustic cavitation under specific conditions. Since its implementation over 2 decades ago, new imaging modes have been developed that employ unique beam sequences exploiting higher-order acoustic phenomena, and, concurrently, studies of the bioeffects of ultrasound under a range of imaging scenarios have been conducted. In 2012, the American Institute of Ultrasound in Medicine Technical Standards Committee convened a working group of its Output Standards Subcommittee to examine and report on the potential risks and benefits of the use of conditionally increased acoustic pressures (CIP) under specific diagnostic imaging scenarios. The term "conditionally" is included to indicate that CIP would be considered on a per-patient basis for the duration required to obtain the necessary diagnostic information. This document is a result of that effort. In summary, a fundamental assumption in the MI calculation is the presence of a preexisting gas body. For tissues not known to contain preexisting gas bodies, based on theoretical predications and experimentally reported cavitation thresholds, we find this assumption to be invalid. We thus conclude that exceeding the recommended maximum MI level given in the FDA guidance could be warranted without concern for increased risk of cavitation in these tissues. However, there is limited literature assessing the potential clinical benefit of exceeding the MI guidelines in these tissues. The report proposes a 3-tiered approach for CIP that follows the model for employing elevated output in magnetic resonance imaging and concludes with summary recommendations to facilitate Institutional Review Board (IRB)-monitored clinical studies investigating CIP in specific tissues.

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.

Correction for frequency-dependent hydrophone response to nonlinear pressure waves using complex deconvolution and rarefactional filtering: application with fiber optic hydrophones

Nonlinear acoustic signals contain significant energy at many harmonic frequencies. For many applications, the sensitivity (frequency response) of a hydrophone will not be uniform over such a broad spectrum. In a continuation of a previous investigation involving deconvolution methodology, deconvolution (implemented in the frequency domain as an inverse filter computed from frequency-dependent hydrophone sensitivity) was investigated for improvement of accuracy and precision of nonlinear acoustic output measurements. Timedelay spectrometry was used to measure complex sensitivities for 6 fiber-optic hydrophones. The hydrophones were then used to measure a pressure wave with rich harmonic content. Spectral asymmetry between compressional and rarefactional segments was exploited to design filters used in conjunction with deconvolution. Complex deconvolution reduced mean bias (for 6 fiber-optic hydrophones) from 163% to 24% for peak compressional pressure (p+), from 113% to 15% for peak rarefactional pressure (p-), and from 126% to 29% for pulse intensity integral (PII). Complex deconvolution reduced mean coefficient of variation (COV) (for 6 fiber optic hydrophones) from 18% to 11% (p+), 53% to 11% (p-), and 20% to 16% (PII). Deconvolution based on sensitivity magnitude or the minimum phase model also resulted in significant reductions in mean bias and COV of acoustic output parameters but was less effective than direct complex deconvolution for p+ and p-. Therefore, deconvolution with appropriate filtering facilitates reliable nonlinear acoustic output measurements using hydrophones with frequency-dependent sensitivity.

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.

Improved measurement of acoustic output using complex deconvolution of hydrophone sensitivity

The traditional method for calculating acoustic pressure amplitude is to divide a hydrophone output voltage measurement by the hydrophone sensitivity at the acoustic working frequency, but this approach neglects frequency dependence of hydrophone sensitivity. Another method is to perform a complex deconvolution between the hydrophone output waveform and the hydrophone impulse response (the inverse Fourier transform of the sensitivity). In this paper, the effects of deconvolution on measurements of peak compressional pressure (p+), peak rarefactional pressure (p_), and pulse intensity integral (PII) are studied. Time-delay spectrometry (TDS) was used to measure complex sensitivities from 1 to 40 MHz for 8 hydrophones used in medical ultrasound exposimetry. These included polyvinylidene fluoride (PVDF) spot-poled membrane, needle, capsule, and fiber-optic designs. Subsequently, the 8 hydrophones were used to measure a 4-cycle, 3 MHz pressure waveform mimicking a pulsed Doppler waveform. Acoustic parameters were measured for the 8 hydrophones using the traditional approach and deconvolution. Average measurements (across all 8 hydrophones) of acoustic parameters from deconvolved waveforms were 4.8 MPa (p+), 2.4 MPa (p_), and 0.21 mJ/cm(2) (PII). Compared with the traditional method, deconvolution reduced the coefficient of variation (ratio of standard deviation to mean across all 8 hydrophones) from 29% to 8% (p+), 39% to 13% (p_), and 58% to 10% (PII).

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.

Time-delay spectrometry measurement of magnitude and phase of hydrophone response

A method based on time-delay spectrometry (TDS) was developed for measuring both magnitude and phase response of a hydrophone. The method was tested on several types of hydrophones used in medical ultrasound exposimetry over the range from 5 to 18 MHz. These included polyvinylidene fluoride (PVDF) spot-poled membrane, needle, and capsule designs. One needle hydrophone was designed for high-intensity focused ultrasound (HIFU) applications. The average reproducibility (after repositioning the hydrophone) of the phase measurement was 2.4°. The minimum-phase model, which implies that the phase response is equal to the inverse Hilbert transform of the natural logarithm of the magnitude response, was tested with TDS hydrophone data. Direct TDS-based measurements of hydrophone phase responses agreed well with calculations based on the minimum-phase model, with rms differences of 1.76° (PVDF spot-poled membrane hydrophone), 3.10° (PVDF capsule hydrophone), 3.43° (PVDF needle hydrophone), and 3.36° (ceramic needle hydrophone) over the range from 5 to 18 MHz. Therefore, phase responses for several types of hydrophones may be inferred from measurements of their magnitude responses. Calculation of phase response based on magnitude response using the minimumphase model is a relatively simple and practical alternative to direct measurement of phase.

Development and characterization of a tissue-mimicking material for high-intensity focused ultrasound

A tissue-mimicking material (TMM) for the acoustic and thermal characterization of high-intensity focused ultrasound (HIFU) devices has been developed. The material is a high-temperature hydrogel matrix (gellan gum) combined with different sizes of aluminum oxide particles and other chemicals. The ultrasonic properties (attenuation coefficient, speed of sound, acoustical impedance, and the thermal conductivity and diffusivity) were characterized as a function of temperature from 20 to 70°C. The backscatter coefficient and nonlinearity parameter B/A were measured at room temperature. Importantly, the attenuation coefficient has essentially linear frequency dependence, as is the case for most mammalian tissues at 37°C. The mean value is 0.64f(0.95) dB·cm(-1) at 20°C, based on measurements from 2 to 8 MHz. Most of the other relevant physical parameters are also close to the reported values, although backscatter signals are low compared with typical human soft tissues. Repeatable and consistent temperature elevations of 40°C were produced under 20-s HIFU exposures in the TMM. This TMM is appropriate for developing standardized dosimetry techniques, validating numerical models, and determining the safety and efficacy of HIFU devices.

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.

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).

Decomposition of Two-Component Pulses in Bone: Phantom Experiment and Simulation

Prony's method is used to separate signals that overlap in time domain. For additional information, the reader is referred to the references at the end of this paper.

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%.

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.

Measurements of ultrasonic backscattered spectral centroid shift from spine in vivo: methodology and preliminary results

Ultrasonic backscatter measurements from vertebral bodies (L3 and L4) in nine women were performed using a clinical ultrasonic imaging system. Measurements were made through the abdomen. The location of a vertebra was identified from the bright specular reflection from the vertebral anterior surface. Backscattered signals were gated to isolate signal emanating from the cancellous interiors of vertebrae. The spectral centroid shift of the backscattered signal, which has previously been shown to correlate highly with bone mineral density (BMD) in human calcaneus in vitro, was measured. BMD was also measured in the nine subjects' vertebrae using a clinical bone densitometer. The correlation coefficient between centroid shift and BMD was r = -0.61. The slope of the linear fit was -160 kHz / (g/cm(2)). The negative slope was expected because the attenuation coefficient (and therefore magnitude of the centroid downshift) is known from previous studies to increase with BMD. The centroid shift may be a useful parameter for characterizing bone in vivo.