Transcranial volumetric imaging using a conformal ultrasound patch.

Accurate and continuous monitoring of cerebral blood flow is valuable for clinical neurocritical care and fundamental neurovascular research. Transcranial Doppler (TCD) ultrasonography is a widely used non-invasive method for evaluating cerebral blood flow1, but the conventional rigid design severely limits the measurement accuracy of the complex three-dimensional (3D) vascular networks and the practicality for prolonged recording2. Here we report a conformal ultrasound patch for hands-free volumetric imaging and continuous monitoring of cerebral blood flow. The 2 MHz ultrasound waves reduce the attenuation and phase aberration caused by the skull, and the copper mesh shielding layer provides conformal contact to the skin while improving the signal-to-noise ratio by 5 dB. Ultrafast ultrasound imaging based on diverging waves can accurately render the circle of Willis in 3D and minimize human errors during examinations. Focused ultrasound waves allow the recording of blood flow spectra at selected locations continuously. The high accuracy of the conformal ultrasound patch was confirmed in comparison with a conventional TCD probe on 36 participants, showing a mean difference and standard deviation of difference as -1.51 ± 4.34 cm s-1, -0.84 ± 3.06 cm s-1 and -0.50 ± 2.55 cm s-1 for peak systolic velocity, mean flow velocity, and end diastolic velocity, respectively. The measurement success rate was 70.6%, compared with 75.3% for a conventional TCD probe. Furthermore, we demonstrate continuous blood flow spectra during different interventions and identify cascades of intracranial B waves during drowsiness within 4 h of recording.

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 ag . 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 ag 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 ag .

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.

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.

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 dg : 85-1000 [Formula: see text]), resulting in 35 transducer/hydrophone combinations. Exponential functions, exp( -αx ), where x = dg /( 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.

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 pc ), 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.

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 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.

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.

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 ( pc ), peak rarefactional pressure ( pr ), 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% ( pc ), 12% ( pr ), 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.

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.

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 ( ag ) 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 aeff(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, ( aeff - ag)/ag , was fit to C /( kag)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 ag , [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.