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

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.

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.

AAPM Task Group 241: A medical physicist's guide to MRI-guided focused ultrasound body systems

Magnetic resonance-guided focused ultrasound (MRgFUS) is a completely non-invasive technology that has been approved by FDA to treat several diseases. This report, prepared by the American Association of Physicist in Medicine (AAPM) Task Group 241, provides background on MRgFUS technology with a focus on clinical body MRgFUS systems. The report addresses the issues of interest to the medical physics community, specific to the body MRgFUS system configuration, and provides recommendations on how to successfully implement and maintain a clinical MRgFUS program. The following sections describe the key features of typical MRgFUS systems and clinical workflow and provide key points and best practices for the medical physicist. Commonly used terms, metrics and physics are defined and sources of uncertainty that affect MRgFUS procedures are described. Finally, safety and quality assurance procedures are explained, the recommended role of the medical physicist in MRgFUS procedures is described, and regulatory requirements for planning clinical trials are detailed. Although this report is limited in scope to clinical body MRgFUS systems that are approved or currently undergoing clinical trials in the United States, much of the material presented is also applicable to systems designed for other applications.

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.

High-Power Gallium Nitride HIFU Transmitter With Integrated Real-Time Current and Voltage Measurement

High-Intensity Focused Ultrasound (HIFU) therapy provides a non-invasive technique with which to destroy cancerous tissue without using ionizing radiation. To drive large single-element High-Intensity Focused Ultrasound (HIFU) transducers, ultrasound transmitters capable of delivering high powers at relevant frequencies are required. The acoustic power delivered to a transducers focal region will determine the treated area, and due to safety concerns and intervening layers of attenuation, control of this output power is critical. A typical setup involves large inefficient linear power amplifiers to drive the transducer. Switched mode transmitters allow for a more compact drive system with higher efficiencies, with multi-level transmitters allowing control over the output power. Real-time monitoring of power delivered can avoid damage to the transducer and injury to patients due to over treatment, and allow for precise control over the output power. This study demonstrates a transformer-less, high power, switched mode transmit transmitter based on Gallium-Nitride (GaN) transistors that is capable of delivering peak powers up to 1.8 kW at up to 600 Vpp, while operating at frequencies from DC to 5 MHz. The design includes a 12 b 16 MHz floating Current/Voltage (IV) measurement circuit to allow real-time high-side monitoring of the power delivered to the transducer allowing use with multi-element transducers.

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.

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.

Scan Parameter Optimization for Histotripsy Treatment of S. Aureus Biofilms on Surgical Mesh

There is a critical need to develop new noninvasive therapies to treat bacteria biofilms. Previous studies have demonstrated the effectiveness of cavitation-based ultrasound histotripsy to destroy these biofilms. In this study, the dependence of biofilm destruction on multiple scan parameters was assessed by conducting exposures at different scan speeds (0.3-1.4 beamwidths/s), step sizes (0.25-0.5 beamwidths), and the number of passes of the focus across the mesh (2-6). For each of the exposure conditions, the number of colony-forming units (CFUs) remaining on the mesh was quantified. A regression analysis was then conducted, revealing that the scan speed was the most critical parameter for biofilm destruction. Reducing the number of passes and the scan speed should allow for more efficient biofilm destruction in the future, reducing the treatment time.

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).

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.

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

Accurate measurements of acoustic pressure are required for characterisation of ultrasonic transducers and for experimental validation of models of ultrasound propagation. Errors in measured pressure can arise from a variety of sources, including variations in the properties of the source and measurement equipment, calibration uncertainty, and processing of measured data. In this study, the repeatability of measurements made with four probe and membrane hydrophones was examined. The pressures measured by these hydrophones in three different ultrasound fields, with both linear and nonlinear, pulsed and steady state driving conditions, were compared to assess the reproducibility of measurements. The coefficient of variation of the focal peak positive pressure was less than 2% for all hydrophones across five repeated measurements. When comparing hydrophones, pressures measured in a spherically focused 1.1 MHz field were within 7% for all except 1 case, and within 10% for a broadband 5 MHz pulse from a diagnostic linear array. Larger differences of up to 55% were observed between measurements of a tightly focused 3.3 MHz field, which were reduced for some hydrophones by the application of spatial averaging corrections. Overall, the major source of these differences was spatial averaging and uncertainty in the complex frequency response of the hydrophones.

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).

Impact of High-Intensity Ultrasound on Strength of Surgical Mesh When Treating Biofilm Infections

The use of cavitation-based ultrasound histotripsy to treat infections on surgical mesh has shown great potential. However, any impact of the therapy on the mesh must be assessed before the therapy can be applied in the clinic. The goal of this study was to determine if the cavitation-based therapy would reduce the strength of the mesh thus compromising the functionality of the mesh. First, Staphylococcus aureus biofilms were grown on the surgical mesh samples and exposed to high-intensity ultrasound pulses. For each exposure, the effectiveness of the therapy was confirmed by counting the number of colony forming units (CFUs) on the mesh. Most of the exposed meshes had no CFUs with an average reduction of 5.4-log₁₀ relative to the sham exposures. To quantify the impact of the exposure on mesh strength, the force required to tear the mesh and the maximum mesh expansion before damage were quantified for control, sham, and exposed mesh samples. There was no statistical difference between the exposed and sham/control mesh samples in terms of ultimate tensile strength and corresponding mesh expansion. The only statistical difference was with respect to mesh orientation relative to the applied load. The tensile strength increased by 1.36 N while the expansion was reduced by 1.33 mm between different mesh orientations.

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.