Phantoms for evaluating the impact of skin pigmentation on photoacoustic imaging and oximetry performance

Recent reports have raised concerns of potential racial disparities in performance of optical oximetry technologies. To investigate how variable epidermal melanin content affects performance of photoacoustic imaging (PAI) devices, we developed plastisol phantoms combining swappable skin-mimicking layers with a breast phantom containing either India ink or blood adjusted to 50-100% SO2 using sodium dithionite. Increasing skin pigmentation decreased maximum imaging depth by up to 25%, enhanced image clutter, and increased root-mean-square error in SO2 from 8.0 to 17.6% due to signal attenuation and spectral coloring effects. This phantom tool can aid in evaluating PAI device robustness to ensure high performance in all patients.

Biomechanical structure-function relations for human trabecular bone - comparison of calcaneus, femoral neck, greater trochanter, proximal tibia, and vertebra

MicroCT-based finite element models were used to compute power law relations for uniaxial compressive yield stress versus bone volume fraction for 78 cores of human trabecular bone from five anatomic sites. The leading coefficient of the power law for calcaneus differed from those for most of the other sites (p < 0.05). However, after normalizing by site-specific mean values, neither the leading coefficient (p > 0.5) nor exponent (p > 0.5) differed among sites, suggesting that a given percentage deviation from mean bone volume fraction has the same mechanical consequence for all sites investigated. These findings help explain the success of calcaneal x-ray and ultrasound measurements for predicting hip fracture risk.

Nominal Versus Actual Spatial Resolution: Comparison of Directivity and Frequency-Dependent Effective Sensitive Element Size for Membrane, Needle, Capsule, and Fiber-Optic Hydrophones

Frequency-dependent effective sensitive element radius [Formula: see text] is a key parameter for elucidating physical mechanisms of hydrophone operation. In addition, it is essential to know [Formula: see text] to correct for hydrophone output voltage reduction due to spatial averaging across the hydrophone sensitive element surface. At low frequencies, [Formula: see text] is greater than geometrical sensitive element radius a_g . Consequently, at low frequencies, investigators can overrate their hydrophone spatial resolution. Empirical models for [Formula: see text] for membrane, needle, and fiber-optic hydrophones have been obtained previously. In this article, an empirical model for [Formula: see text] for capsule hydrophones is presented, so that models are now available for the four most common hydrophone types used in biomedical ultrasound. The [Formula: see text] value was estimated from directivity measurements (over the range from 1 to 20 MHz) for five capsule hydrophones (three with [Formula: see text] and two with [Formula: see text]). The results suggest that capsule hydrophones behave according to a "rigid piston" model for k a _g ≥ 0.7 ( k = 2π /wavelength). Comparing the four hydrophone types, the low-frequency discrepancy between [Formula: see text] and a_g was found to be greatest for membrane hydrophones, followed by capsule hydrophones, and smallest for needle and fiber-optic hydrophones. Empirical models for [Formula: see text] are helpful for choosing an appropriate hydrophone for an experiment and for correcting for spatial averaging (over the sensitive element surface) in pressure and beamwidth measurements. When reporting hydrophone-based pressure measurements, investigators should specify [Formula: see text] at the center frequency (which may be estimated from the models presented here) in addition to a_g .

Hydrophone Measurements for Biomedical Ultrasound Applications: A Review

This article presents basic principles of hydrophone measurements, including mechanisms of action for various hydrophone designs, sensitivity and directivity calibration procedures, practical considerations for performing measurements, signal processing methods to correct for both frequency-dependent sensitivity and spatial averaging across the hydrophone sensitive element, uncertainty in hydrophone measurements, special considerations for high-intensity therapeutic ultrasound, and advice for choosing an appropriate hydrophone for a particular measurement task. Recommendations are made for information to be included in hydrophone measurement reporting.

US Backscatter for Liver Fat Quantification: An AIUM-RSNA QIBA Pulse-Echo Quantitative Ultrasound Initiative

Nonalcoholic fatty liver disease (NAFLD) is believed to affect one-third of American adults. Noninvasive methods that enable detection and monitoring of NAFLD have the potential for great public health benefits. Because of its low cost, portability, and noninvasiveness, US is an attractive alternative to both biopsy and MRI in the assessment of liver steatosis. NAFLD is qualitatively associated with enhanced B-mode US echogenicity, but visual measures of B-mode echogenicity are negatively affected by interobserver variability. Alternatively, quantitative backscatter parameters, including the hepatorenal index and backscatter coefficient, are being investigated with the goal of improving US-based characterization of NAFLD. The American Institute of Ultrasound in Medicine and Radiological Society of North America Quantitative Imaging Biomarkers Alliance are working to standardize US acquisition protocols and data analysis methods to improve the diagnostic performance of the backscatter coefficient in liver fat assessment. This review article explains the science and clinical evidence underlying backscatter for liver fat assessment. Recommendations for data collection are discussed, with the aim of minimizing potential confounding effects associated with technical and biologic variables.

Pulse-Echo Quantitative US Biomarkers for Liver Steatosis: Toward Technical Standardization

Excessive liver fat (steatosis) is now the most common cause of chronic liver disease worldwide and is an independent risk factor for cirrhosis and associated complications. Accurate and clinically useful diagnosis, risk stratification, prognostication, and therapy monitoring require accurate and reliable biomarker measurement at acceptable cost. This article describes a joint effort by the American Institute of Ultrasound in Medicine (AIUM) and the RSNA Quantitative Imaging Biomarkers Alliance (QIBA) to develop standards for clinical and technical validation of quantitative biomarkers for liver steatosis. The AIUM Liver Fat Quantification Task Force provides clinical guidance, while the RSNA QIBA Pulse-Echo Quantitative Ultrasound Biomarker Committee develops methods to measure biomarkers and reduce biomarker variability. In this article, the authors present the clinical need for quantitative imaging biomarkers of liver steatosis, review the current state of various imaging modalities, and describe the technical state of the art for three key liver steatosis pulse-echo quantitative US biomarkers: attenuation coefficient, backscatter coefficient, and speed of sound. Lastly, a perspective on current challenges and recommendations for clinical translation for each biomarker is offered.

Photoacoustic imaging phantoms for assessment of object detectability and boundary buildup artifacts

Standardized phantoms and test methods are needed to accelerate clinical translation of emerging photoacoustic imaging (PAI) devices. Evaluating object detectability in PAI is challenging due to variations in target morphology and artifacts including boundary buildup. Here we introduce breast fat and parenchyma tissue-mimicking materials based on emulsions of silicone oil and ethylene glycol in polyacrylamide hydrogel. 3D-printed molds were used to fabricate solid target inclusions that produced more filled-in appearance than traditional PAI phantoms. Phantoms were used to assess understudied image quality characteristics (IQCs) of three PAI systems. Object detectability was characterized vs. target diameter, absorption coefficient, and depth. Boundary buildup was quantified by target core/boundary ratio, which was higher in transducers with lower center frequency. Target diameter measurement accuracy was also size-dependent and improved with increasing transducer frequency. These phantoms enable evaluation of multiple key IQCs and may support development of comprehensive standardized test methods for PAI devices.

Spatiotemporal Deconvolution of Hydrophone Response for Linear and Nonlinear Beams-Part I: Theory, Spatial-Averaging Correction Formulas, and Criteria for Sensitive Element Size

This article reports spatiotemporal deconvolution methods and simple empirical formulas to correct pressure and beamwidth measurements for spatial averaging across a hydrophone sensitive element. Readers who are uninterested in hydrophone theory may proceed directly to Appendix A for an easy method to estimate spatial-averaging correction factors. Hydrophones were modeled as angular spectrum filters. Simulations modeled nine circular transducers (1-10 MHz; F/1.4-F/3.2) driven at six power levels and measured with eight hydrophones (432 beam/hydrophone combinations). For example, the model predicts that if a 200- [Formula: see text] membrane hydrophone measures a moderately nonlinear 5-MHz beam from an F/1 transducer, spatial-averaging correction factors are 33% (peak compressional pressure or p_c ), 18% (peak rarefactional pressure or p ), and 18% (full width half maximum or FWHM). Theoretical and experimental estimates of spatial-averaging correction factors to were in good agreement (within 5%) for linear and moderately nonlinear signals. Criteria for maximum appropriate hydrophone sensitive element size as functions of experimental parameters were derived. Unlike the oft-cited International Electrotechnical Commission (IEC) criterion, the new criteria were derived for focusing rather than planar transducers and can accommodate nonlinear signals in addition to linear signals. Responsible reporting of hydrophone-based pressure and beamwidth measurements should always acknowledge spatial-averaging considerations.

Spatiotemporal Deconvolution of Hydrophone Response for Linear and Nonlinear Beams-Part II: Experimental Validation

This article reports experimental validation for spatiotemporal deconvolution methods and simple empirical formulas to correct pressure and beamwidth measurements for spatial averaging across a hydrophone sensitive element. The method was validated using linear and nonlinear beams transmitted by seven single-element spherically focusing transducers (2-10 MHz; F /#: 1-3) and measured with five hydrophones (sensitive element diameters d_g : 85-1000 [Formula: see text]), resulting in 35 transducer/hydrophone combinations. Exponential functions, exp( -αx ), where x = d_g /( λ₁F /#) and λ₁ is the fundamental wavelength, were used to model focal pressure ratios p'/p (where p' is the measured value subjected to spatial averaging and p is the true axial value that would be obtained with a hypothetical point hydrophone). Spatiotemporal deconvolution reduced α (followed by root mean squared difference between data and fit) from 0.29-0.30 (7%) to 0.01 (8%) (linear signals) and from 0.29-0.40 (8%) to 0.04 (14%) (nonlinear signals), indicating successful spatial averaging correction. Linear functions, Cx + 1, were used to model FWHM'/FWHM, where FWHM is full-width half-maximum. Spatiotemporal deconvolution reduced C from 9% (4%) to -0.6% (1%) (linear signals) and from 30% (10%) to 6% (5%) (nonlinear signals), indicating successful spatial averaging correction. Spatiotemporal deconvolution resulted in significant improvement in accuracy even when the hydrophone geometrical sensitive element diameter exceeded the beam FWHM. Responsible reporting of hydrophone-based pressure measurements should always acknowledge spatial averaging considerations.

Tissue-mimicking phantoms for performance evaluation of photoacoustic microscopy systems

Phantom-based performance test methods are critically needed to support development and clinical translation of emerging photoacoustic microscopy (PAM) devices. While phantoms have been recently developed for macroscopic photoacoustic imaging systems, there is an unmet need for well-characterized tissue-mimicking materials (TMMs) and phantoms suitable for evaluating PAM systems. Our objective was to develop and characterize a suitable dermis-mimicking TMM based on polyacrylamide hydrogels and demonstrate its utility for constructing image quality phantoms. TMM formulations were optically characterized over 400-1100 nm using integrating sphere spectrophotometry and acoustically characterized using a pulse through-transmission method over 8-24 MHz with highly confident extrapolation throughout the usable band of the PAM system. This TMM was used to construct a spatial resolution phantom containing gold nanoparticle point targets and a penetration depth phantom containing slanted tungsten filaments and blood-filled tubes. These phantoms were used to characterize performance of a custom-built PAM system. The TMM was found to be broadly tunable and specific formulations were identified to mimic human dermis at an optical wavelength of 570 nm and acoustic frequencies of 10-50 MHz. Imaging results showed that tungsten filaments yielded 1.1-4.2 times greater apparent maximum imaging depth than blood-filled tubes, which may overestimate real-world performance for vascular imaging applications. Nanoparticles were detectable only to depths of 120-200 µm, which may be due to the relatively weaker absorption of single nanoparticles vs. larger targets containing high concentration of hemoglobin. The developed TMMs and phantoms are useful tools to support PAM device characterization and optimization, streamline regulatory decision-making, and accelerate clinical translation.

Polyacrylamide hydrogel phantoms for performance evaluation of multispectral photoacoustic imaging systems

As photoacoustic imaging (PAI) begins to mature and undergo clinical translation, there is a need for well-validated, standardized performance test methods to support device development, quality control, and regulatory evaluation. Despite recent progress, current PAI phantoms may not adequately replicate tissue light and sound transport over the full range of optical wavelengths and acoustic frequencies employed by reported PAI devices. Here we introduce polyacrylamide (PAA) hydrogel as a candidate material for fabricating stable phantoms with well-characterized optical and acoustic properties that are biologically relevant over a broad range of system design parameters. We evaluated suitability of PAA phantoms for conducting image quality assessment of three PAI systems with substantially different operating parameters including two commercial systems and a custom system. Imaging results indicated that appropriately tuned PAA phantoms are useful tools for assessing and comparing PAI system image quality. These phantoms may also facilitate future standardization of performance test methodology.

Hydrophone Spatial Averaging Correction for Acoustic Exposure Measurements From Arrays-Part I: Theory and Impact on Diagnostic Safety Indexes

This article reports underestimation of mechanical index (MI) and nonscanned thermal index for bone near focus (TIB) due to hydrophone spatial averaging effects that occur during acoustic output measurements for clinical linear and phased arrays. TIB is the appropriate version of thermal index (TI) for fetal imaging after ten weeks from the last menstrual period according to the American Institute of Ultrasound in Medicine (AIUM). Spatial averaging is particularly troublesome for highly focused beams and nonlinear, nonscanned modes such as acoustic radiation force impulse (ARFI) and pulsed Doppler. MI and variants of TI (e.g., TIB), which are displayed in real-time during imaging, are often not corrected for hydrophone spatial averaging because a standardized method for doing so does not exist for linear and phased arrays. A novel analytic inverse-filter method to correct for spatial averaging for pressure waves from linear and phased arrays is derived in this article (Part I) and experimentally validated in a companion article (Part II). A simulation was developed to estimate potential spatial-averaging errors for typical clinical ultrasound imaging systems based on the theoretical inverse filter and specifications for 124 scanner/transducer combinations from the U.S. Food and Drug Administration (FDA) 510(k) database from 2015 to 2019. Specifications included center frequency, aperture size, acoustic output parameters, hydrophone geometrical sensitive element diameter, etc. Correction for hydrophone spatial averaging using the inverse filter suggests that maximally achievable values for MI, TIB, thermal dose ( t ₄₃ ), and spatial-peak-temporal-average intensity ( [Formula: see text]) for typical clinical systems are potentially higher than uncorrected values by (means ± standard deviations) 9% ± 4% (ARFI MI), 19% ± 15% (ARFI TIB), 50% ± 41% (ARFI t ₄₃ ), 43% ± 39% (ARFI [Formula: see text]), 7% ± 5% (pulsed Doppler MI), 15% ± 11% (pulsed Doppler TIB), 42% ± 31% (pulsed Doppler t ₄₃ ), and 33% ± 27% (pulsed Doppler [Formula: see text]). These values correspond to frequencies of 3.2 ± 1.3 (ARFI) and 4.1 ± 1.4 MHz (pulsed Doppler), and the model predicts that they would increase with frequency. Inverse filtering for hydrophone spatial averaging significantly improves the accuracy of estimates of MI, TIB, t ₄₃ , and [Formula: see text] for ARFI and pulsed Doppler signals.

Hydrophone Spatial Averaging Correction for Acoustic Exposure Measurements From Arrays-Part II: Validation for ARFI and Pulsed Doppler Waveforms

This article reports the experimental validation of a method for correcting underestimates of peak compressional pressure ( pc) , peak rarefactional pressure ( pr) , and pulse intensity integral (pii) due to hydrophone spatial averaging effects that occur during output measurement of clinical linear and phased arrays. Pressure parameters ( pc , pr , and pii), which are used to compute acoustic exposure safety indexes, such as mechanical index (MI) and thermal index (TI), are often not corrected for spatial averaging because a standardized method for doing so does not exist for linear and phased arrays. In a companion article (Part I), a novel, analytic, inverse-filter method was derived to correct for spatial averaging for linear or nonlinear pressure waves from linear and phased arrays. In the present article (Part II), the inverse filter is validated on measurements of acoustic radiation force impulse (ARFI) and pulsed Doppler waveforms. Empirical formulas are provided to enable researchers to predict and correct hydrophone spatial averaging errors for membrane-hydrophone-based acoustic output measurements. For example, for a 400- [Formula: see text] membrane hydrophone, inverse filtering reduced errors (means ± standard errors for 15 linear array/hydrophone pairs) from about 34% ( pc) , 22% ( pr) , and 45% (pii) down to within 5% for all three parameters. Inverse filtering for spatial averaging effects significantly improves the accuracy of estimates of acoustic pressure parameters for ARFI and pulsed Doppler signals.

Note to Physicians and Sonographers on Potential Underestimation of Acoustic Safety Indexes for Diagnostic Array Transducers

Two scientists from the U.S. Food and Drug Administration comment on limitations of acoustic safety indexes that can arise from spatial averaging effects of hydrophones that are used to measure acoustic output.

Correction for Hydrophone Spatial Averaging Artifacts for Circular Sources

This article reports an investigation of an inverse-filter method to correct for experimental underestimation of pressure due to spatial averaging across a hydrophone sensitive element. The spatial averaging filter (SAF) depends on hydrophone type (membrane, needle, or fiber-optic), hydrophone geometrical sensitive element diameter, transducer driving frequency, and transducer F number (ratio of focal length to diameter). The absolute difference between theoretical and experimental SAFs for 25 transducer/hydrophone pairs was 7% ± 3% (mean ± standard deviation). Empirical formulas based on SAFs are provided to enable researchers to easily correct for hydrophone spatial averaging errors in peak compressional pressure ( p_c ), peak rarefactional pressure ( p_r ), and pulse intensity integral. The empirical formulas show, for example, that if a 3-MHz, F /2 transducer is driven to moderate nonlinear distortion and measured at the focal point with a 500- [Formula: see text] membrane hydrophone, then spatial averaging errors are approximately 16% ( p_c ), 12% ( p_r ), and 24% (pulse intensity integral). The formulas are based on circular transducers but also provide plausible upper bounds for spatial averaging errors for transducers with rectangular-transmit apertures, such as linear and phased arrays.

Evaluation of Fluence Correction Algorithms in Multispectral Photoacoustic Imaging

Multispectral photoacoustic imaging (MPAI) is a promising emerging diagnostic technology, but fluence artifacts can degrade device performance. Our goal was to develop well-validated phantom-based test methods for evaluating and comparing MPAI fluence correction algorithms, including a heuristic diffusion approximation, Monte Carlo simulations, and an algorithm we developed based on novel application of the diffusion dipole model (DDM). Phantoms simulated a range of breast-mimicking optical properties and contained channels filled with chromophore solutions (ink, hemoglobin, or copper sulfate) or connected to a previously developed blood flow circuit providing tunable oxygen saturation (SO₂). The DDM algorithm achieved similar spectral recovery and SO₂ measurement accuracy to Monte Carlo-based corrections with lower computational cost, potentially providing an accurate, real-time correction approach. Algorithms were sensitive to optical property uncertainty, but error was minimized by matching phantom albedo. The developed test methods may provide a foundation for standardized assessment of MPAI fluence correction algorithm performance.

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.

Directivity and Frequency-Dependent Effective Sensitive Element Size of Membrane Hydrophones: Theory Versus Experiment

It is important to know hydrophone frequency-dependent effective sensitive element size in order to account for spatial averaging artifacts in acoustic output measurements. Frequency-dependent effective sensitive element size may be obtained from hydrophone directivity measurements. Directivity was measured at 1, 2, 3, 4, 6, 8, and 10 MHz from ±60° in two orthogonal planes for eight membrane hydrophones with nominal geometrical sensitive element radii ( a_g ) ranging from 100 to [Formula: see text]. The mean precision of directivity measurements (obtained from four repeated measurements at each frequency and angle) averaged over all frequencies, angles, and hydrophones was 5.8%. Frequency-dependent effective hydrophone sensitive element radii a_eff(f) were estimated by fitting the theoretical directional response for a disk receiver to directivity measurements using the sensitive element radius ( a ) as an adjustable parameter. For the eight hydrophones in aggregate, the relative difference between effective and geometrical sensitive element radii, ( a_eff - a_g)/a_g , was fit to C /( ka_g)ⁿ , where k = 2π/λ and λ = wavelength. The functional fit yielded C = 1.89 and n = 1.36 . The root mean square difference between the data and the model was 34%. It was shown that for a given value for a_g , [Formula: see text] for membrane hydrophones far exceeds that for needle hydrophones at low frequencies (e.g., < 4 MHz when [Formula: see text]). This empirical model for [Formula: see text] provides information required for the compensation of spatial averaging artifacts in acoustic output measurements and is useful for choosing an appropriate sensitive element size for a given experiment.

Multidomain computational modeling of photoacoustic imaging: verification, validation, and image quality prediction

As photoacoustic imaging (PAI) technology matures, computational modeling will increasingly represent a critical tool for facilitating clinical translation through predictive simulation of real-world performance under a wide range of device and biological conditions. While modeling currently offers a rapid, inexpensive tool for device development and prediction of fundamental image quality metrics (e.g., spatial resolution and contrast ratio), rigorous verification and validation will be required of models used to provide regulatory-grade data that effectively complements and/or replaces in vivo testing. To address methods for establishing model credibility, we developed an integrated computational model of PAI by coupling a previously developed three-dimensional Monte Carlo model of tissue light transport with a two-dimensional (2D) acoustic wave propagation model implemented in the well-known k-Wave toolbox. We then evaluated ability of the model to predict basic image quality metrics by applying standardized verification and validation principles for computational models. The model was verified against published simulation data and validated against phantom experiments using a custom PAI system. Furthermore, we used the model to conduct a parametric study of optical and acoustic design parameters. Results suggest that computationally economical 2D acoustic models can adequately predict spatial resolution, but metrics such as signal-to-noise ratio and penetration depth were difficult to replicate due to challenges in modeling strong clutter observed in experimental images. Parametric studies provided quantitative insight into complex relationships between transducer characteristics and image quality as well as optimal selection of optical beam geometry to ensure adequate image uniformity. Multidomain PAI simulation tools provide high-quality tools to aid device development and prediction of real-world performance, but further work is needed to improve model fidelity, especially in reproducing image noise and clutter.

Correction for Spatial Averaging Artifacts in Hydrophone Measurements of High-Intensity Therapeutic Ultrasound: An Inverse Filter Approach

High-intensity therapeutic ultrasound (HITU) pressure is often measured using a hydrophone. HITU pressure waves typically contain multiple harmonics due to nonlinear propagation. As harmonic frequency increases, harmonic beamwidth decreases. For sufficiently high harmonic frequency, beamwidth may become comparable to the hydrophone effective sensitive element diameter, resulting in signal reduction due to spatial averaging. An analytic formula for a hydrophone spatial averaging filter for beams with Gaussian harmonic radial profiles was tested on HITU pressure signals generated by three transducers (1.45 MHz, F/1; 1.53 MHz, F/1.5; 3.91 MHz, F/1) with focal pressures up to 48 MPa. The HITU signals were measured using fiber-optic and needle hydrophones (nominal geometrical sensitive element diameters: 100 and [Formula: see text]). Harmonic radial profiles were measured with transverse scans in the focal plane using the fiber-optic hydrophone. Harmonic radial profiles were accurately approximated by Gaussian functions with root-mean-square (rms) differences between transverse scans and Gaussian fits less than 9% for frequencies up to approximately 50 MHz. The Gaussian harmonic beamwidth parameter σ_n varied with harmonic number n according to a power law, σ_n = σ₁/n^q where . RMS differences between experimental and theoretical spatial averaging filters were 11% ± 1% (1.45 MHz), 8% ± 1% (1.53 MHz), and 4% ± 1% (3.91 MHz). For the two more highly focused (F/1) transducers, the effect of spatial averaging was to underestimate peak compressional pressure (pcp), peak rarefactional pressure (prp), and pulse intensity integral (pii) by (mean ± standard deviation) (pcp: 4.9% ± 0.5%, prp: 0.4% ± 0.2%, pii: 2.9% ± 1%) and (pcp: 28.3% ± 9.6%, prp: 6% ± 2.4%, pii: 24.3% ± 6.7%) for the 100- and 400- [Formula: see text]-diameter hydrophones, respectively. These errors can be suppressed by the application of the inverse spatial averaging filter.

Experimental investigation of parameters influencing plasmonic nanoparticle-mediated bubble generation with nanosecond laser pulses

Plasmonic nanoparticles (PNPs) continue to see increasing use in biophotonics for a variety of applications, including cancer detection and treatment. Several PNP-based approaches involve the generation of highly transient nanobubbles due to pulsed laser-induced vaporization and cavitation. While much effort has been devoted to elucidating the mechanisms behind bubble generation with spherical gold nano particles, the effects of particle shape on bubble generation thresholds are not well understood, especially in the nanosecond pulse regime. Our study aims to compare the bubble generation thresholds of gold nanospheres, gold nanorods, and silica-core gold nanoshells with different sizes, resonances, and surface coatings. Bubble generation is detected using a multimodality microscopy platform for simultaneous, nanosecond resolution pump-probe imaging, integrated scattering response, and acoustic transient detection. Nanoshells and large (40-nm width) nanorods were found to have the lowest thresholds for bubble generation, and in some cases they generated bubbles at radiant exposures below standard laser safety limits for skin exposure. This has important implications for both safety and performance of techniques employing pulsed lasers and PNPs.

Pulsed laser damage of gold nanorods in turbid media and its impact on multi-spectral photoacoustic imaging

Innovative biophotonic modalities such as photoacoustic imaging (PAI) have the potential to provide enhanced sensitivity and molecule-specific detection when used with nanoparticles. However, high peak irradiance levels generated by pulsed lasers can lead to modification of plasmonic nanoparticles. Thus, there is an outstanding need to develop practical methods to effectively predict the onset nanoparticle photomodification as well as a need to better understand the process during PAI. To address this need, we studied pulsed laser damage of gold nanorods (GNRs) using turbid phantoms and a multi-spectral near-infrared PAI system, comparing results with spectrophotometric measurements of non-scattering samples. Transmission electron microscopy and Monte Carlo modeling were also performed to elucidate damage processes. In the phantoms, shifts in PAI-detected spectra indicative of GNR damage were initiated at exposure levels one-third of that seen in non-scattering samples, due to turbidity-induced enhancement of subsurface fluence. For exposures approaching established safety limits, damage was detected at depths of up to 12.5 mm. Typically, GNR damage occurred rapidly, over the course of a few laser pulses. This work advances the development of test methods and numerical models as tools for assessment of nanoparticle damage and its implications, and highlights the importance of considering GNR damage in development of PAI products, even for exposures well below laser safety limits.

Considerations for Choosing Sensitive Element Size for Needle and Fiber-Optic Hydrophones-Part I: Spatiotemporal Transfer Function and Graphical Guide

The spatiotemporal transfer function for a needle or reflectance-based fiber-optic hydrophone is modeled as separable into the product of two filters corresponding to frequency-dependent sensitivity and spatial averaging. The separable hydrophone transfer function model is verified numerically by comparison to a more general rigid piston spatiotemporal response model that does not assume separability. Spatial averaging effects are characterized by frequency-dependent "effective" sensitive element diameter, which can be more than double the geometrical sensitive element diameter. The transfer function is tested in simulation using a nonlinear focused pressure wave model based on Gaussian harmonic radial pressure distributions. The pressure wave model is validated by comparing to experimental hydrophone scans of nonlinear beams produced by three source transducers. An analytic form for the spatial averaging filter, applicable to Gaussian harmonic beams, is derived. A second analytic form for the spatial averaging filter, applicable to quadratic harmonic beams, is derived by extending the spatial averaging correction recommended by IEC 62127-1 Annex E to nonlinear signals with multiple harmonics. Both forms are applicable to all hydrophones (not just needle and fiber-optic hydrophones). Simulation analysis performed for a wide variety of transducer geometries indicates that the Gaussian spatial averaging filter formula is more accurate than the quadratic formula over a wider range of harmonics. Additional experimental validation is provided in Part II. Readers who are uninterested in hydrophone theory may skip the theoretical and experimental sections of this paper and proceed to the graphical guide for practical information to inform and support selection of hydrophone sensitive element size (but might be well advised to read the Introduction).

Photoacoustic oximetry imaging performance evaluation using dynamic blood flow phantoms with tunable oxygen saturation

Multispectral photoacoustic oximetry imaging (MPOI) is an emerging hybrid modality that enables the spatial mapping of blood oxygen saturation (SO2) to depths of several centimeters. To facilitate MPOI device development and clinical translation, well-validated performance test methods and improved quantitative understanding of physical processes and best practices are needed. We developed a breast-mimicking blood flow phantom with tunable SO2 and used this phantom to evaluate a custom MPOI system. Results provide quantitative evaluation of the impact of phantom medium properties (Intralipid versus polyvinyl chloride plastisol) and device design parameters (different transducers) on SO2 measurement accuracy, especially depth-dependent performance degradation due to fluence artifacts. This approach may guide development of standardized test methods for evaluating MPOI devices.

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.

Ultrasonic attenuation in parallel-nylon-wire cancellous-bone-mimicking phantoms

Attenuation coefficients between 1.5 and 3.5 MHz were measured on four parallel-nylon-wire arrays (simulating cancellous bone) with four different wire diameters (150, 200, 250, and 300 microm). Interwire spacing was 800 microm for all four parallel-nylon-wire arrays. The measured frequency dependencies of attenuation were consistent with theoretical predications based on Faran's theory, which considers the component of attenuation due to scattering of longitudinal waves.