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

High-resolution pressure imaging via background-oriented schlieren tomography: A spatiotemporal measurement for MHz ultrasound fields and hydrophone calibration

In this work, the spatiotemporal pressure field of MHz-focused ultrasound is measured using a background-oriented schlieren technique combined with fast checkerboard demodulation and vector tomography (VT-BOS). Hydrophones have been commonly employed to directly measure the local pressure in underwater ultrasound. However, their limitations include that they disturb the acoustic field and affect the measured pressure through the spatial averaging effect. To overcome such limitations, we propose VT-BOS as a non-contact technique for acoustic field measurements using only a background image and a camera. In our experiments, VT-BOS measures focused acoustic fields with a focal width of 1.0 mm and a frequency of 4.55 MHz, capturing traveling, reflected, and standing waves. We discuss three key features of this approach: (1) the temporal evolution of pressure measured by VT-BOS and hydrophones, (2) the differences in computational cost and spatial resolution between VT-BOS and other techniques, and (3) the measurement range of VT-BOS. The results demonstrate that VT-BOS successfully quantifies spatiotemporal acoustic fields and can estimate the hydrophones' spatial averaging effect over a finite area. VT-BOS measures pressure fields of several MPa with high spatiotemporal resolution, requiring less computational and measurement time. It is used to measure pressure amplitudes from 0.4 to 6.4 MPa, with the potential to extend the range to 0.3-201.6 MPa by adjusting the background-to-target distance. VT-BOS is a promising tool for measuring acoustic pressure in the MHz and MPa ranges, critical for applications such as vessel flow measurement and hydrophone calibration.

Clinical, Safety, and Engineering Perspectives on Wearable Ultrasound Technology: A Review

Wearable ultrasound has the potential to become a disruptive technology enabling new applications not only in traditional clinical settings, but also in settings where ultrasound is not currently used. Understanding the basic engineering principles and limitations of wearable ultrasound is critical for clinicians, scientists, and engineers to advance potential applications and translate the technology from bench to bedside. Wearable ultrasound devices, especially monitoring devices, have the potential to apply acoustic energy to the body for far longer durations than conventional diagnostic ultrasound systems. Thus, bioeffects associated with prolonged acoustic exposure as well as skin health need to be carefully considered for wearable ultrasound devices. This article reviews emerging clinical applications, safety considerations, and future engineering and clinical research directions for wearable ultrasound technology.

Quantifying the Impact of Imaging Through Body Walls on Shear Wave Elasticity Measurements

In the context of ultrasonic hepatic shear wave elasticity imaging (SWEI), measurement success has been determined to increase when using elevated acoustic output pressures. As SWEI sequences consist of two distinct operations (pushing and tracking), acquisition failures could be attributed to (i) insufficient acoustic radiation force generation resulting in inadequate shear wave amplitude and/or (ii) distorted ultrasonic tissue motion tracking. In the study described here, an opposing window experimental setup that isolated body wall effects separately between the push and track SWEI operations was implemented. A commonly employed commercial track configuration was used, harmonic multiple-track-location SWEI. The effects of imaging through body walls on the pushing and tracking operations of SWEI as a function of mechanical index (MI), spanning 5 different push beam MIs and 10 track beam MIs, were independently assessed using porcine body walls. Shear wave speed yield was found to increase with both increasing push and track MI. Although not consistent across all samples, measurements in a subset of body walls were found to be signal limited during tracking and to increase yield by up to 35% when increasing electronic signal-to-noise ratio by increasing harmonic track transmit pressure.

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.

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.

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.