Investigation of the repeatability and reproducibility of hydrophone measurements of medical ultrasound fields

Remote Super-Resolution Mapping of Wave Fields

Mapping wave field in space has many applications such as optimizing design of radio antennas, improving and developing ultrasound transducers, and planning and monitoring the treatment of tumors using high-intensity focused ultrasound (HIFU). Currently, there are methods that can map wave fields remotely or locally. However, there are limitations to these methods. For example, when mapping the wave fields remotely, the spatial resolution is limited due to a poor diffraction-limited resolution of the receiver, especially when the f-number of the receiver is large. To map the wave fields locally, the receiver is either subject to damage in hazardous environments (corrosive media, high temperature, high wave intensity, and so on) or difficult to be placed inside an object. To address these limitations, in this article, the point spread function (PSF)-modulation super-resolution imaging method was applied to map pulse ultrasound wave fields remotely at a high spatial resolution, overcoming the diffraction limit of a focused receiver. For example, to map a pulse ultrasound field of a full-width-at-half-maximum (FWHM) beamwidth of 1.24 mm at the focal distance of a transmitter, the FWHM beamwidths of the super-resolution mapping of the pulse wave field with a spherical glass modulator of 0.7 mm diameter at two receiver angles (0° and 45°) were about 1.13 and 1.22 mm, respectively, which were close to the theoretical value of 1.24 mm and were much smaller than the diffraction-limited resolution (1.81 mm) of the receiver. Without using the super-resolution method to remotely map the same pulse wave field, the FWHM beamwidth was about 2.06 mm. For comparison, the FWHM beamwidth obtained with a broadband (1-20 MHz) and 0.6-mm-diameter polyvinylidene fluoride (PVDF) needle hydrophone was about 1.41 mm. In addition to the focused pulse ultrasound wave field, a pulse Bessel beam near the transducer surface was mapped remotely with the super-resolution method, which revealed high spatial frequency components of the beam.

A comparative study of experimental and simulated ultrasound beam propagation through cranial bones

Objective.Transcranial ultrasound is used in a variety of treatments, including neuromodulation, opening the blood-brain barrier, and high intensity focused ultrasound therapies. To ensure safety and efficacy of these treatments, numerical simulations of the ultrasound field within the brain are used for treatment planning and evaluation. This study investigates the accuracy of numerical modelling of the propagation of focused ultrasound through cranial bones.Approach.Holograms of acoustic fields after propagation through four human skull specimens were measured for frequencies ranging from 270 kHz to 1 MHz, using both quasi-continuous and pulsed modes. The open-source k-Wave toolbox was employed for simulations, using an equivalent-source hologram and a uniform bowl source with parameters that best matched the measured free-field pressure distribution.Main results.The average absolute error in k-Wave simulations with sound speed and density derived from CT scans compared to measurements was 15% for the spatial-peak acoustic pressure amplitude, 2.7 mm for the position of the focus, and 35% for the focal volume. Optimised uniform bowl sources achieved calculation accuracy comparable to that of the hologram sources.Significance.This method is demonstrated as a suitable tool for prediction of focal position, size and overall distribution of transcranial ultrasound fields. The accuracy of the shape and position of the focal region demonstrate the suitability of the sound speed and density mapping used here. However, large errors in pressure amplitude and transmission loss in some individual cases show that alternative methods for mapping individual skull attenuation are needed and the possibility of considerable errors in pressure amplitude should be taken into account when planning focused ultrasound studies or interventions in the human brain, and appropriate safety margins should be used.

ITRUSST consensus on standardised reporting for transcranial ultrasound stimulation

As transcranial ultrasound stimulation (TUS) advances as a precise, non-invasive neuromodulatory method, there is a need for consistent reporting standards to enable comparison and reproducibility across studies. To this end, the International Transcranial Ultrasonic Stimulation Safety and Standards Consortium (ITRUSST) formed a subcommittee of experts across several domains to review and suggest standardised reporting parameters for low intensity TUS, resulting in the guide presented here. The scope of the guide is limited to reporting the ultrasound aspects of a study. The guide and supplementary material provide a simple checklist covering the reporting of: (1) the transducer and drive system, (2) the drive system settings, (3) the free field acoustic parameters, (4) the pulse timing parameters, (5) in situ estimates of exposure parameters in the brain, and (6) intensity parameters. Detailed explanations for each of the parameters, including discussions on assumptions, measurements, and calculations, are also provided.

High-Bandwidth Heterodyne Laser Interferometer for the Measurement of High-Intensity Focused Ultrasound Pressure

As a high-end medical technology, high-intensity focused ultrasound (HIFU) is widely used in cancer treatment and ultrasonic lithotripsy technology. The acoustic output level and safety of ultrasound treatments are closely related to the accuracy of sound pressure measurements. Heterodyne laser interferometry is applied to the measurement of ultrasonic pressure owing to its characteristics of non-contact, high precision, and traceability. However, the upper limit of sound pressure measurement is limited by the bandwidth of the interferometer. In this paper, a high-bandwidth heterodyne laser interferometer for the measurement of high-intensity focused ultrasound pressure is developed and tested. The optical carrier with a frequency shift of 358 MHz is realized by means of an acousto-optic modulator. The selected electrical devices ensure that the electrical bandwidth can reach 1.5 GHz. The laser source adopts an iodine frequency-stabilized semiconductor laser with high-frequency spectral purity, which can reduce the influence of spectral purity on the bandwidth to a negligible level. The interference light path is integrated and encapsulated to improve the stability in use. An HIFU sound pressure measurement experiment is carried out, and the upper limit of the sound pressure measurement is obviously improved.

Real-Time Acoustic Simulation Framework for tFUS: A Feasibility Study Using Navigation System

Transcranial focused ultrasound (tFUS), in which acoustic energy is focused on a small region in the brain through the skull, is a non-invasive therapeutic method with high spatial resolution and depth penetration. Image-guided navigation has been widely utilized to visualize the location of acoustic focus in the cranial cavity. However, this system is often inaccurate because of the significant aberrations caused by the skull. Therefore, acoustic simulations using a numerical solver have been widely adopted to compensate for this inaccuracy. Although the simulation can predict the intracranial acoustic pressure field, real-time application during tFUS treatment is almost impossible due to the high computational cost. In this study, we propose a neural network-based real-time acoustic simulation framework and test its feasibility by implementing a simulation-guided navigation (SGN) system. Real-time acoustic simulation is performed using a 3D conditional generative adversarial network (3D-cGAN) model featuring residual blocks and multiple loss functions. This network was trained by the conventional numerical acoustic simulation program (i.e., k-Wave). The SGN system is then implemented by integrating real-time acoustic simulation with a conventional image-guided navigation system. The proposed system can provide simulation results with a frame rate of 5 Hz (i.e., about 0.2 s), including all processing times. In numerical validation (3D-cGAN vs. k-Wave), the average peak intracranial pressure error was 6.8 ± 5.5%, and the average acoustic focus position error was 5.3 ± 7.7 mm. In experimental validation using a skull phantom (3D-cGAN vs. actual measurement), the average peak intracranial pressure error was 4.5%, and the average acoustic focus position error was 6.6 mm. These results demonstrate that the SGN system can predict the intracranial acoustic field according to transducer placement in real-time.

Progress in wearable acoustical sensors for diagnostic applications

With extensive and widespread uses of miniaturized and intelligent wearable devices, continuously monitoring subtle spatial and temporal changes in human physiological states becomes crucial for daily healthcare and professional medical diagnosis. Wearable acoustical sensors and related monitoring systems can be comfortably applied onto human body with a distinctive function of non-invasive detection. This paper reviews recent advances in wearable acoustical sensors for medical applications. Structural designs and characteristics of the structural components of wearable electronics, including piezoelectric and capacitive micromachined ultrasonic transducer (i.e., pMUT and cMUT), surface acoustic wave sensors (SAW) and triboelectric nanogenerators (TENGs) are discussed, along with their fabrication techniques and manufacturing processes. Diagnostic applications of these wearable sensors for detection of biomarkers or bioreceptors and diagnostic imaging have further been discussed. Finally, main challenges and future research directions in these fields are highlighted.

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.

Classical and Learned MR to Pseudo-CT Mappings for Accurate Transcranial Ultrasound Simulation

Model-based treatment planning for transcranial ultrasound therapy typically involves mapping the acoustic properties of the skull from an X-ray computed tomography (CT) image of the head. Here, three methods for generating pseudo-CT (pCT) images from magnetic resonance (MR) images were compared as an alternative to CT. A convolutional neural network (U-Net) was trained on paired MR-CT images to generate pCT T images from either T1-weighted or zero-echo time (ZTE) MR images (denoted tCT and zCT, respectively). A direct mapping from ZTE to pCT was also implemented (denoted cCT). When comparing the pCT and ground-truth CT images for the test set, the mean absolute error was 133, 83, and 145 Hounsfield units (HU) across the whole head, and 398, 222, and 336 HU within the skull for the tCT, zCT, and cCT images, respectively. Ultrasound simulations were also performed using the generated pCT images and compared to simulations based on CT. An annular array transducer was used targeting the visual or motor cortex. The mean differences in the simulated focal pressure, focal position, and focal volume were 9.9%, 1.5 mm, and 15.1% for simulations based on the tCT images; 5.7%, 0.6 mm, and 5.7% for the zCT; and 6.7%, 0.9 mm, and 12.1% for the cCT. The improved results for images mapped from ZTE highlight the advantage of using imaging sequences, which improves the contrast of the skull bone. Overall, these results demonstrate that acoustic simulations based on MR images can give comparable accuracy to those based on CT.

Benchmark problems for transcranial ultrasound simulation: Intercomparison of compressional wave models

Computational models of acoustic wave propagation are frequently used in transcranial ultrasound therapy, for example, to calculate the intracranial pressure field or to calculate phase delays to correct for skull distortions. To allow intercomparison between the different modeling tools and techniques used by the community, an international working group was convened to formulate a set of numerical benchmarks. Here, these benchmarks are presented, along with intercomparison results. Nine different benchmarks of increasing geometric complexity are defined. These include a single-layer planar bone immersed in water, a multi-layer bone, and a whole skull. Two transducer configurations are considered (a focused bowl and a plane piston operating at 500 kHz), giving a total of 18 permutations of the benchmarks. Eleven different modeling tools are used to compute the benchmark results. The models span a wide range of numerical techniques, including the finite-difference time-domain method, angular spectrum method, pseudospectral method, boundary-element method, and spectral-element method. Good agreement is found between the models, particularly for the position, size, and magnitude of the acoustic focus within the skull. When comparing results for each model with every other model in a cross-comparison, the median values for each benchmark for the difference in focal pressure and position are less than 10% and 1 mm, respectively. The benchmark definitions, model results, and intercomparison codes are freely available to facilitate further comparisons.

Benchmark problems for transcranial ultrasound simulation: Intercomparison of compressional wave models

Computational models of acoustic wave propagation are frequently used in transcranial ultrasound therapy, for example, to calculate the intracranial pressure field or to calculate phase delays to correct for skull distortions. To allow intercomparison between the different modeling tools and techniques used by the community, an international working group was convened to formulate a set of numerical benchmarks. Here, these benchmarks are presented, along with intercomparison results. Nine different benchmarks of increasing geometric complexity are defined. These include a single-layer planar bone immersed in water, a multi-layer bone, and a whole skull. Two transducer configurations are considered (a focused bowl and a plane piston operating at 500 kHz), giving a total of 18 permutations of the benchmarks. Eleven different modeling tools are used to compute the benchmark results. The models span a wide range of numerical techniques, including the finite-difference time-domain method, angular spectrum method, pseudospectral method, boundary-element method, and spectral-element method. Good agreement is found between the models, particularly for the position, size, and magnitude of the acoustic focus within the skull. When comparing results for each model with every other model in a cross-comparison, the median values for each benchmark for the difference in focal pressure and position are less than 10% and 1 mm, respectively. The benchmark definitions, model results, and intercomparison codes are freely available to facilitate further comparisons.

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.

Low-Cost 3-D Hydrophone Scanning Tank with MATLAB GUI Control

The Focused Ultrasound Foundation has developed a low-cost, validated, open-source hydrophone scanner for the spatial characterization of ultrasound transducers. Assembly instructions and a MATLAB control graphical user interface are provided such that the device can be easily replicated for less than $1000 in roughly 40 person-hours. The low-cost scanning tank's performance was compared with data collected with a commercial automated scanning tank. Pressure measurements of a focused transducer and a planar transducer had less than a 10% difference between the two scanning systems. Two-dimensional automated scans (20 × 20 mm at 0.25-mm resolution) took the low-cost scanning tank 45 min compared with the commercial system's 30 min. A reproducibility study found that the low-cost scanner made consistent peak negative pressure measurements as reflected by the low coefficient of variation for both focused (1.88%) and planar (0.98%) transducers. The low-cost scanner described here is a viable alternative for ultrasound laboratories needing efficient, accurate characterization of ultrasound transducers.

Measurement of the temperature-dependent output of lead zirconate titanate transducers

The effect of temperature and electrical drive conditions on the output of lead zirconate titanate (PZT) transducers is of particular interest in ultrasound metrology and medical ultrasound applications. In this work, the temperature-dependent output of two single-element PZT transducers was measured between 22 °C and 46 °C. Two independent measurement methods were used, namely radiation force balance measurements and laser vibrometry. When driven at constant voltage using a 50 Ω matched signal generator and amplifier using continuous wave (CW) or quasi-CW excitation, the output of the two transducers increased on average by 0.6 % per degree, largely due to an increase in transducer efficiency with temperature. The two measurement methods showed close agreement. Similar trends were observed when using single cycle excitation with the same signal chain. However, when driven using a pulser (which is not electrically matched), the two transducers exhibited different behaviour depending on their electrical impedance. Accounting for the temperature-dependent output of PZT transducers could have implications for many areas of ultrasound metrology, for example, in therapeutic ultrasound where a coupling fluid at an increased or decreased temperature is often used.

Optical phase contrast imaging for absolute, quantitative measurements of ultrasonic fields with frequencies up to 20 MHz

The technique of phase contrast imaging, combined with tomographic reconstructions, can rapidly measure ultrasonic fields propagating in water, including ultrasonic fields with complex wavefront shapes, which are difficult to characterize with standard hydrophone measurements. Furthermore, the technique can measure the absolute pressure amplitudes of ultrasonic fields without requiring a pressure calibration. Absolute pressure measurements have been previously demonstrated using optical imaging methods for ultrasonic frequencies below 2.5 MHz. The present work demonstrates that phase contrast imaging can accurately measure ultrasonic fields with frequencies up to 20 MHz and pressure amplitudes near 10 kPa. Accurate measurements at high ultrasonic frequencies are performed by tailoring the measurement conditions to limit optical diffraction as guided by a simple dimensionless parameter. In some situations, differences between high frequency measurements made with the phase contrast method and a calibrated hydrophone become apparent, and the reasons for these differences are discussed. Extending optical imaging measurements to high ultrasonic frequencies could facilitate quantitative applications of ultrasound measurements in nondestructive testing and medical therapeutics and diagnostics such as photoacoustic imaging.

A Comparison of Different Calibration Techniques for Hydrophones Used in Medical Ultrasonic Field Measurement

The acoustic output characterization of medical ultrasonic equipment requires regular calibration of the hydrophones used to ensure the reliability of measurements. Such hydrophone calibration is offered as a service by several institutions. Various calibration techniques using a variety of ultrasonic excitation pressure waveforms comprising different pressure amplitude ranges and frequency compositions as well as different reference measurement systems have been proposed and applied over the past decades. Currently, four different setups for hydrophone calibration are available at the Physikalisch-Technische Bundesanstalt (PTB). This internal comparison study addresses the consistency of all four methods, including direct primary calibration and substitution calibration using reference hydrophones. The methods apply single-frequency tonebursts and swept tonebursts in the kPa amplitude range of quasi-linear acoustics as well as impulse excitation including nonlinear propagation. In recent years, a new primary calibration setup using a high-frequency vibrometer has been implemented at PTB, enabling the characterization of hydrophone frequency responses in modulus and phase and extending the upper frequency limit to up to 100 MHz. For the comparison in the frequency range from 0.5 MHz to 60 MHz, two passive membrane hydrophones with well-known characteristics gained from many years of measurements were used. Another membrane hydrophone with a nominal diameter of 0.2 mm and an integrated preamplifier was applied to address the frequency range up to 100 MHz. The results obtained with the different setups showed good agreement with average root-mean-square (rms) deviations of 3% (primary calibrations, 1-60 MHz) and 4% (1-100 MHz). The consistency of the implementations was thus verified in this comparison.

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.

Measurement and simulation of steered acoustic fields generated by a multielement array for therapeutic ultrasound

Modelling of fields generated by therapeutic ultrasound arrays can be prone to errors arising from differences from nominal transducer parameters, and variations in relative outputs of array elements when driven under different conditions, especially when simulating steered fields. Here, the effect of element size, element positions, relative source pressure variations, and electrical crosstalk on the accuracy of modelling pressure fields generated by a 555 kHz 32-element ultrasonic array were investigated. For this transducer, errors in pressure amplitude and focal position were respectively reduced from 20% to 4% and 3.3 mm to 1.5 mm using crosstalk prediction, and experimentally determined positions.

Synchronous temperature variation monitoring during ultrasound imaging and/or treatment pulse application: a phantom study

Ultrasound attenuation through soft tissues can produce an acoustic radiation force (ARF) and heating. The ARF-induced displacements and temperature evaluations can reveal tissue properties and provide insights into focused ultrasound (FUS) bio-effects. In this study, we describe an interleaving pulse sequence tested in a tissue-mimicking phantom that alternates FUS and plane-wave imaging pulses at a 1 kHz frame rate. The FUS is amplitude modulated, enabling the simultaneous evaluation of tissue-mimicking phantom displacement using harmonic motion imaging (HMI) and temperature rise using thermal strain imaging (TSI). The parameters were varied with a spatial peak temporal average acoustic intensity (I _spta ) ranging from 1.5 to 311 W.cm^-2, mechanical index (MI) from 0.43 to 4.0, and total energy (E) from 0.24 to 83 J.cm^-2. The HMI and TSI processing could estimate displacement and temperature independently for temperatures below 1.80°C and displacements up to ~117 μm (I _spta <311 W.cm^-2, MI<4.0, and E<83 J.cm^-2) indicated by a steady-state tissue-mimicking phantom displacement throughout the sonication and a comparable temperature estimation with simulations in the absence of tissue-mimicking phantom motion. The TSI estimations presented a mean error of ±0.03°C versus thermocouple estimations with a mean error of ±0.24°C. The results presented herein indicate that HMI can operate at diagnostic-temperature levels (i.e., <1°C) even when exceeding diagnostic acoustic intensity levels (720 mW.cm^-2 < I _spta < 207 W.cm^-2). In addition, the combined HMI and TSI can potentially be used for simultaneous evaluation of safety during tissue elasticity imaging as well as FUS mechanism involved in novel ultrasound applications such as ultrasound neuromodulation and tumor ablation.

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.

Hydrophone Spatial Averaging Artifacts for ARFI Beams from Array Transducers

This paper reports underestimation of peak compressional pressure (p _c), peak rarefactional pressure (p _r ), and pulse intensity integral (pii) due to hydrophone spatial averaging of acoustic radiation force impulse (ARFI) beams generated by clinical linear and phased arrays. Although a method exists for correcting for hydrophone spatial averaging for circularly-symmetric beams, there is presently no analogous method for rectangularly-symmetric beams generated by linear and phased arrays. Consequently, pressure parameters (p _c, p _r , and pii) from clinical arrays are often not corrected for spatial averaging. This can lead to errors in Mechanical Index (MI) and Thermal Index (TI), which are derived from pressure measurements and are displayed in real-time during clinical ultrasound scans. ARFI beams were generated using three clinical linear array transducers. Output pressure waveforms for all three transducers were measured using five hydrophones with geometrical sensitive element sizes (d_g) ranging from 85 to 1000 μm. Spatial averaging errors were found to increase with hydrophone sensitive element size. For example, if d_g = 500 μm (typical membrane hydrophone), frequency = 2.25 MHz and F/# = 1.5, then average errors are approximately -20% (p_c), -10% (p_r), and -25% (pii). Therefore, due to hydrophone spatial averaging, typical membrane hydrophones can exhibit significant underestimation of ARFI pressure measurements, which likely compromises exposure safety indexes.

Correction for Spatial Averaging Artifacts for Circularly-Symmetric Pressure Beams Measured with Membrane Hydrophones

This paper investigates experimental underestimation of pressure measurements due to spatial averaging across a hydrophone sensitive element. Empirical relationships are measured to enable correction for hydrophone spatial averaging errors in peak compressional pressure (p _c ), peak rarefactional pressure (p _r ), and pulse intensity integral (pii). The empirical relationships 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-μm membrane hydrophone, then spatial averaging errors are approximately 16% (p _c ), 12% (p _r ), and 24% (pii).

Experimental Validation of k-Wave: Nonlinear Wave Propagation in Layered, Absorbing Fluid Media

Models of ultrasound propagation in biologically relevant media have applications in planning and verification of ultrasound therapies and computational dosimetry. To be effective, the models must be able to accurately predict both the spatial distribution and amplitude of the acoustic pressure. This requires that the models are validated in absolute terms, which for arbitrarily heterogeneous media should be performed by comparison with measurements of the acoustic field. In this article, simulations performed using the open-source k-Wave acoustics toolbox, with a measurement-based source definition, were quantitatively validated against measurements of acoustic pressure in water and layered absorbing fluid media. In water, the measured and simulated spatial-peak pressures agreed to within 3% under linear conditions and 7% under nonlinear conditions. After propagation through a planar or wedge-shaped glycerol-filled phantom, the difference in spatial-peak pressure was 8.5% and 10.7%, respectively. These differences are within or close to the expected uncertainty of the acoustic pressure measurement. The -6 dB width and length of the focus agreed to within 4% in all cases, and the focal positions were within 0.7 mm for the planar phantom and 1.2 mm for the wedge-shaped phantom. These results demonstrate that when the acoustic medium properties and geometry are well known, accurate quantitative predictions of the acoustic field can be made using k-Wave.

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.

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.