Dynamic Mode Decomposition for Transient Cavitation Bubbles Imaging in Pulsed High-Intensity Focused Ultrasound Therapy.

Pulsed high-intensity focused ultrasound (pHIFU) can induce sparse de novo inertial cavitation without the introduction of exogenous contrast agents, promoting mild mechanical disruption in targeted tissue. Because the bubbles are small and rapidly dissolve after each HIFU pulse, mapping transient bubbles and obtaining real-time quantitative metrics correlated with tissue damage are challenging. Prior work introduced Bubble Doppler, an ultrafast power Doppler imaging method as a sensitive means to map cavitation bubbles. The main limitation of that method was its reliance on conventional wall filters used in Doppler imaging and its optimization for imaging blood flow rather than transient scatterers. This study explores Bubble Doppler enhancement using dynamic mode decomposition (DMD) of a matrix created from a Doppler ensemble for mapping and extracting the characteristics of transient cavitation bubbles. DMD was first tested in silico with a numerical dataset mimicking the spatiotemporal characteristics of backscattered signal from tissue and bubbles. The performance of DMD filter was compared to other widely used Doppler wall filter-singular value decomposition (SVD) and infinite impulse response (IIR) high-pass filter. DMD was then applied to an ex vivo tissue dataset where each HIFU pulse was immediately followed by a plane wave Doppler ensemble. In silico DMD outperformed SVD and IIR high-pass filter and ex vivo provided physically interpretable images of the modes associated with bubbles and their corresponding temporal decay rates. These DMD modes can be trackable over the duration of pHIFU treatment using k-means clustering method, resulting in quantitative indicators of treatment progression.

Elastic Properties of Aging Human Hematoma Model In Vitro and Its Susceptibility to Histotripsy Liquefaction.

OBJECTIVE: Tissue susceptibility to histotripsy disintegration has been reported to depend on its elastic properties. This work was aimed at investigation of histotripsy efficiency for liquefaction of human hematomas, depending on their stiffness and degree of retraction over time (0-10 d). METHODS: As an in vitro hematoma model, anticoagulated human blood samples (200 mL) were recalcified at different temperatures. In one set of samples, the shear modulus was measured by shear wave elastography during blood clotting at 10℃, 22℃ and 37℃, and then daily during further aging. The ultrastructure of the samples was analyzed daily with scanning electron microscopy (SEM). Another set of blood samples (50-200 mL) were recalcified at 37℃ for density and retraction measurements over aging and exposed to histotripsy at varying time points. Boiling histotripsy (2.5 ms pulses) and hybrid histotripsy (0.2 ms pulses) exposures (2 MHz, 1% dc, P+/P-/As = 182/-27/207 MPa in situ) were used to produce either individual cigar-shaped or volumetric (0.8-3 mL) lesions in samples incubated for 3 h, 5 d and 10 d. The obtained lesions were sized, then the lysate aspirated under B-mode guidance was analyzed ultrastructurally and diluted in distilled water for sizing of residual fragments. RESULTS: It was found that clotting time decreased from 113 to 25 min with the increase in blood temperature from 10℃ to 37℃. The shear modulus increased to 0.53 ± 0.17 kPa during clotting and remained constant within 8 d of incubation at 2℃. Sample volumes decreased by 57% because of retraction within 10 d. SEM revealed significant echinocytosis but unchanged ultrastructure of the fibrin meshwork. Liquefaction rate and lesion dimensions produced with the same histotripsy protocols correlated with the increase in the degree of retraction and were lower in retracted samples versus freshly clotted samples. More than 80% of residual fibrin fragments after histotripsy treatment were shorter than 150 µm; the maximum length was 208 µm, allowing for unobstructed aspiration of the lysate with most clinically used needles. CONCLUSION: The results indicate that hematoma susceptibility to histotripsy liquefaction is not entirely determined by its stiffness, and correlates with the retraction degree.

Dynamic Mode Decomposition for Transient Cavitation Bubbles Imaging in Pulsed High Intensity Focused Ultrasound Therapy.

Pulsed high-intensity focused ultrasound (pHIFU) can induce sparse de novo inertial cavitation without the introduction of exogenous contrast agents, promoting mild mechanical disruption in targeted tissue. Because the bubbles are small and rapidly dissolve after each HIFU pulse, mapping transient bubbles and obtaining real-time quantitative metrics correlated to tissue damage are challenging. Prior work introduced Bubble Doppler, an ultrafast power Doppler imaging method as a sensitive means to map cavitation bubbles. The main limitation of that method was its reliance on conventional wall filters used in Doppler imaging and optimized for imaging blood flow rather than transient scatterers. This study explores Bubble Doppler enhancement using dynamic mode decomposition (DMD) of a matrix created from a Doppler ensemble for mapping and extracting the characteristics of transient cavitation bubbles. DMD was first tested in silico with a numerical dataset mimicking the spatiotemporal characteristics of backscattered signal from tissue and bubbles. The performance of DMD filter was compared to other widely used Doppler wall filters - singular value decomposition (SVD) and infinite impulse response (IIR) highpass filter. DMD was then applied to an ex vivo tissue dataset where each HIFU pulse was immediately followed by a plane wave Doppler ensemble. In silico DMD outperformed SVD and IIR high pass filter and ex vivo provided physically interpretable images of the modes associated with bubbles and their corresponding temporal decay rates. These DMD modes can be trackable over the duration of pHIFU treatment using k-means clustering method, resulting in quantitative indicators of treatment progression.

Treatment Planning and Aberration Correction Algorithm for HIFU Ablation of Renal Tumors.

High-intensity focused ultrasound (HIFU) applications for thermal or mechanical ablation of renal tumors often encounter challenges due to significant beam aberration and refraction caused by oblique beam incidence, inhomogeneous tissue layers, and presence of gas and bones within the beam. These losses can be significantly mitigated through sonication geometry planning, patient positioning, and aberration correction using multielement phased arrays. Here, a sonication planning algorithm is introduced, which uses the simulations to select the optimal transducer position and evaluate the effect of aberrations and acoustic field quality at the target region after aberration correction. Optimization of transducer positioning is implemented using a graphical user interface (GUI) to visualize a segmented 3-D computed tomography (CT)-based acoustic model of the body and to select sonication geometry through a combination of manual and automated approaches. An HIFU array (1.5 MHz, 256 elements) and three renal cell carcinoma (RCC) cases with different tumor locations and patient body habitus were considered. After array positioning, the correction of aberrations was performed using a combination of backpropagation from the focus with an ordinary least squares (OLS) optimization of phases at the array elements. The forward propagation was simulated using a combination of the Rayleigh integral and k-space pseudospectral method (k-Wave toolbox). After correction, simulated HIFU fields showed tight focusing and up to threefold higher maximum pressure within the target region. The addition of OLS optimization to the aberration correction method yielded up to 30% higher maximum pressure compared to the conventional backpropagation and up to 250% higher maximum pressure compared to the ray-tracing method, particularly in strongly distorted cases.

The histotripsy spectrum: differences and similarities in techniques and instrumentation.

Since its inception about two decades ago, histotripsy - a non-thermal mechanical tissue ablation technique - has evolved into a spectrum of methods, each with distinct potentiating physical mechanisms: intrinsic threshold histotripsy, shock-scattering histotripsy, hybrid histotripsy, and boiling histotripsy. All methods utilize short, high-amplitude pulses of focused ultrasound delivered at a low duty cycle, and all involve excitation of violent bubble activity and acoustic streaming at the focus to fractionate tissue down to the subcellular level. The main differences are in pulse duration, which spans microseconds to milliseconds, and ultrasound waveform shape and corresponding peak acoustic pressures required to achieve the desired type of bubble activity. In addition, most types of histotripsy rely on the presence of high-amplitude shocks that develop in the pressure profile at the focus due to nonlinear propagation effects. Those requirements, in turn, dictate aspects of the instrument design, both in terms of driving electronics, transducer dimensions and intensity limitations at surface, shape (primarily, the F-number) and frequency. The combination of the optimized instrumentation and the bio-effects from bubble activity and streaming on different tissues, lead to target clinical applications for each histotripsy method. Here, the differences and similarities in the physical mechanisms and resulting bioeffects of each method are reviewed and tied to optimal instrumentation and clinical applications.

Phase holograms for the three-dimensional patterning of unconstrained microparticles.

Acoustic radiation forces can remotely manipulate particles. Forces from a standing wave field align microscale particles along the nodal or anti-nodal locations of the field to form three-dimensional (3D) patterns. These patterns can be used to form 3D microstructures for tissue engineering applications. However, standing wave generation requires more than one transducer or a reflector, which is challenging to implement in vivo. Here, a method is developed and validated to manipulate microspheres using a travelling wave from a single transducer. Diffraction theory and an iterative angular spectrum approach are employed to design phase holograms to shape the acoustic field. The field replicates a standing wave and aligns polyethylene microspheres in water, which are analogous to cells in vivo, at pressure nodes. Using Gor'kov potential to calculate the radiation forces on the microspheres, axial forces are minimized, and transverse forces are maximized to create stable particle patterns. Pressure fields from the phase holograms and resulting particle aggregation patterns match predictions with a feature similarity index > 0.92, where 1 is a perfect match. The resulting radiation forces are comparable to those produced from a standing wave, which suggests opportunities for in vivo implementation of cell patterning toward tissue engineering applications.

Enhancement of Boiling Histotripsy by Steering the Focus Axially During the Pulse Delivery.

Boiling histotripsy (BH) is a pulsed high-intensity focused ultrasound (HIFU) method relying on the generation of high-amplitude shocks at the focus, localized enhanced shock-wave heating, and bubble activity driven by shocks to induce tissue liquefaction. BH uses sequences of 1-20 ms long pulses with shock fronts of over 60 MPa amplitude, initiates boiling at the focus of the HIFU transducer within each pulse, and the remainder shocks of the pulse then interact with the boiling vapor cavities. One effect of this interaction is the creation of a prefocal bubble cloud due to reflection of shocks from the initially generated mm-sized cavities: the shocks are inverted when reflected from a pressure-release cavity wall resulting in sufficient negative pressure to reach intrinsic cavitation threshold in front of the cavity. Secondary clouds then form due to shock-wave scattering from the first one. Formation of such prefocal bubble clouds has been known as one of the mechanisms of tissue liquefaction in BH. Here, a methodology is proposed to enlarge the axial dimension of this bubble cloud by steering the HIFU focus toward the transducer after the initiation of boiling until the end of each BH pulse and thus to accelerate treatment. A BH system comprising a 1.5 MHz 256-element phased array connected to a Verasonics V1 system was used. High-speed photography of BH sonications in transparent gels was performed to observe the extension of the bubble cloud resulting from shock reflections and scattering. Volumetric BH lesions were then generated in ex vivo tissue using the proposed approach. Results showed up to almost threefold increase of the tissue ablation rate with axial focus steering during the BH pulse delivery compared to standard BH.

Comparative Characterization of Nonlinear Ultrasound Fields Generated by Sonalleve V1 and V2 MR-HIFU Systems.

A Sonalleve magnetic resonance-guided high-intensity focused ultrasound (MR-HIFU) clinical system (Profound Medical, Mississauga, ON, Canada) has been shown to generate nonlinear ultrasound fields with shocks up to 100 MPa at the focus as required for HIFU applications such as boiling histotripsy of hepatic and renal tumors. The Sonalleve system has two versions V1 and V2 of the therapeutic array, with differences in focusing angle, focus depth, arrangement of elements, and the size of a central opening that is twice larger in the V2 system compared to the V1. The goal of this study was to compare the performance of the V1 and V2 transducers for generating high-amplitude shock-wave fields and to reveal the impact of different array geometries on shock amplitudes at the focus. Nonlinear modeling of the field in water using boundary conditions reconstructed from holography measurements shows that at the same power output, the V2 array generates 10-15-MPa lower shock amplitudes at the focus. Consequently, substantially higher power levels are required for the V2 system to reach the same shock-wave exposure conditions in histotripsy-type treatments. Although this difference is mainly caused by the smaller focusing angle of the V2 array, the larger central opening of the V2 array has a nontrivial impact. By excluding coherently interacting weakly focused waves coming from the central part of the source, the presence of the central opening results in a somewhat higher effective focusing angle and thus higher shock amplitudes at the focus. Axisymmetric equivalent source models were constructed for both arrays, and the importance of including the central opening was demonstrated. These models can be used in the "HIFU beam" software for simulating nonlinear fields of the Sonalleve V1 and V2 systems in water and flat-layered biological tissues.

Initial Assessment of Boiling Histotripsy for Mechanical Ablation of Ex Vivo Human Prostate Tissue.

Boiling histotripsy (BH) is a focused ultrasound technology that uses millisecond-long pulses with shock fronts to induce mechanical tissue ablation. The pulsing scheme and mechanisms of BH differ from those of cavitation cloud histotripsy, which was previously developed for benign prostatic hyperplasia. The goal of the work described here was to evaluate the feasibility of using BH to ablate fresh ex vivo human prostate tissue as a proof of principle for developing BH for prostate applications. Fresh human prostate samples (N = 24) were obtained via rapid autopsy (<24 h after death, institutional review board exempt). Samples were analyzed using shear wave elastography to ensure that mechanical properties of autopsy tissue were clinically representative. Samples were exposed to BH using 10- or 1-ms pulses with 1% duty cycle under real-time B-mode and Doppler imaging. Volumetric lesions were created by sonicating 1-4 rectangular planes spaced 1 mm apart, containing a grid of foci spaced 1-2 mm apart. Tissue then was evaluated grossly and histologically, and the lesion content was analyzed using transmission electron microscopy and scanning electron microscopy. Observed shear wave elastography characterization of ex vivo prostate tissue (37.9 ± 22.2 kPa) was within the typical range observed clinically. During BH, hyperechoic regions were visualized at the focus on B-mode, and BH-induced bubbles were also detected using power Doppler. As treatment progressed, hypoechoic regions of tissue appeared, suggesting successful tissue fractionation. BH treatment was twofold faster using shorter pulses (1 ms vs. 10 ms). Histological analysis revealed lesions containing completely homogenized cell debris, consistent with histotripsy-induced mechanical ablation. It was therefore determined that BH is feasible in fresh ex vivo human prostate tissue producing desired mechanical ablation. The study supports further work aimed at translating BH technology as a clinical option for prostate ablation.

Quantitative Assessment of Boiling Histotripsy Progression Based on Color Doppler Measurements.

Boiling histotripsy (BH) is a mechanical tissue liquefaction method that uses sequences of millisecond-long high intensity focused ultrasound (HIFU) pulses with shock fronts. The BH treatment generates bubbles that move within the sonicated volume due to acoustic radiation force. Since the velocity of the bubbles and tissue debris is expected to depend on the lesion size and liquefaction completeness, it could provide a quantitative metric of the treatment progression. In this study, the motion of bubble remnants and tissue debris immediately following BH pulses was investigated using high-pulse repetition frequency (PRF) plane-wave color Doppler ultrasound in ex vivo myocardium tissue. A 256-element 1.5 MHz spiral HIFU array with a coaxially integrated ultrasound imaging probe (ATL P4-2) produced 10 ms BH pulses to form volumetric lesions with electronic beam steering. Prior to performing volumetric BH treatments, the motion of intact myocardium tissue and anticoagulated bovine blood following isolated BH pulses was assessed as two limiting cases. In the liquid blood the velocity of BH-induced streaming at the focus reached over 200 cm/s, whereas the intact tissue was observed to move toward the HIFU array consistent with elastic rebound of tissue. Over the course of volumetric BH treatments tissue motion at the focus locations was dependent on the axial size of the forming lesion relative to the corresponding size of the HIFU focal area. For axially small lesions, the maximum velocity after the BH pulse was directed toward the HIFU transducer and monotonically increased over time from about 20-100 cm/s as liquefaction progressed, then saturated when tissue was fully liquefied. For larger lesions obtained by merging multiple smaller lesions in the axial direction, the high-speed streaming away from the HIFU transducer was observed at the point of full liquefaction. Based on these observations, the maximum directional velocity and its location along the HIFU propagation axis were proposed and evaluated as candidate metrics of BH treatment completeness.

Mechanical damage thresholds for hematomas near gas-containing bodies in pulsed HIFU fields.

Objective. Boiling histotripsy (BH) is a novel high intensity focused ultrasound (HIFU) application currently being developed for non-invasive mechanical fractionation of soft tissues and large hematomas. In the context of development of BH treatment planning approaches for ablating targets adjacent to gas-containing organs, this study aimed at investigation of the ultrasound pressure thresholds of atomization-induced damage to the tissue-air interface and correlation of the danger zone dimensions with spatial structure of nonlinear HIFU field parameters.Approach. A flat interface with air of freshly clotted bovine blood was used as anex vivomodel due to its homogenous structure and higher susceptibility to ultrasound-induced mechanical damage compared to soft tissues. Three 1.5 MHz transducers of differentF-numbers (0.77, 1 and 1.5) were focused at various distances before or beyond a flat clot surface, and a BH exposure was delivered either at constant, high-amplitude output level, or at gradually increasing level until a visible damage to the clot surface occurred. The HIFU pressure field parameters at the clot surface were determined through a combination of hydrophone measurements in water, forward wave propagation simulation using 'HIFU beam' software and an image source method to account for the wave reflection from the clot surface and formation of a standing wave. The iso-levels of peak negative pressure in the resulting HIFU field were correlated to the outlines of surface erosion to identify the danger zone around the BH focus.Main results. The outline of the danger zone was shown to differ from that of a typical BH lesion produced in a volume of clot material. In the prefocal area, the zone was confined within the 4 MPa contour of the incident peak-to-peak pressure; within the main focal lobe it was determined by the maximum BH lesion width, and in the postfocal area-by the transverse size of the focal lobe and position of the first postfocal pressure axial null.Significance. The incident HIFU pressure-based danger zone boundaries were outlined around the BH focus and can be superimposed onto in-treatment ultrasound image to avoid damage to adjacent gas-containing bodies.

In Vivo Aberration Correction for Transcutaneous HIFU Therapy Using a Multielement Array.

One of the challenges of transcutaneous high-intensity focused ultrasound (HIFU) therapies, especially ones relying heavily on shock formation, such as boiling histotripsy (BH), is the loss of focusing from aberration induced by the heterogeneities of the body wall. Here, a methodology to execute aberration correction in vivo is proposed. A custom BH system consisting of a 1.5-MHz phased array of 256 elements connected to a Verasonics V1 system is used in pulse/echo mode on a porcine model under general anesthesia. Estimation of the time shifts needed to correct for aberration in the liver and kidney is done by maximizing the value of the coherence factor on the acquired backscattered signals. As this process requires multiple pulse/echo sequences on a moving target to converge to a solution, tracking is also implemented to ensure that the same target is used between each iteration. The method was validated by comparing the acoustic power needed to generate a boiling bubble at one target with aberration correction and at another target within a 5-mm radius without aberration correction. Results show that the aberration correction effectively lowers the acoustic power required to reach boiling by up to 45%, confirming that it indeed restored formation of the nonlinear shock front at the focus.

B/A Measurement of Clear Cell Renal Cell Carcinoma versus Healthy Kidney Tissue.

The acoustic parameter of non-linearity B/A has been found capable of discriminating some types of pathological tissue from healthy tissue. The literature on the utility of B/A for cancer diagnostics is very limited, with measurements on the human breast and liver. This work expands the current research on cancer diagnostics by B/A assessment of eight slices of human clear cell renal cell carcinoma (ccRCC) from two patients and four slices of healthy kidney tissue from two healthy kidney samples. The Wilcoxon test identified the B/A distribution of malignant tissue as not significantly different from that of healthy tissue. An alternative way of defining outliers resulted in median B/A values of 8.1 for ccRCC and 6.8 for healthy tissue (p < 0.05). Acoustic attenuation at 2.1 MHz was significantly greater (p < 0.05) for ccRCC (1.7 dB/cm) than for healthy tissue (1.0 dB/cm). The observed differences in the measured values suggest that B/A and acoustic attenuation may represent potential diagnostic markers of ccRCC. More data and an improved experimental design are required to provide a definitive conclusion on the utility of B/A for cancer diagnostics.

Improving Burst Wave Lithotripsy Effectiveness for Small Stones and Fragments by Increasing Frequency: Theoretical Modeling and Ex Vivo Study.

Introduction and Objective: In clinical trial NCT03873259, a 2.6-mm lower pole stone was treated transcutaneously and ex vivo with 390-kHz burst wave lithotripsy (BWL) for 40 minutes and failed to break. The stone was subsequently fragmented with 650-kHz BWL after a 4-minute exposure. This study investigated how to fragment small stones and why varying the BWL frequency may more effectively fragment stones to dust. Methods: A linear elastic theoretical model was used to calculate the stress created inside stones from shock wave lithotripsy (SWL) and different BWL frequencies mimicking the stone's size, shape, lamellar structure, and composition. To test model predictions about the impact of BWL frequency, matched pairs of stones (1-5 mm) were treated at (1) 390 kHz, (2) 830 kHz, and (3) 390 kHz followed by 830 kHz. The mass of fragments >1 and 2 mm was measured over 10 minutes of exposure. Results: The linear elastic model predicts that the maximum principal stress inside a stone increases to more than 5.5 times the pressure applied by the ultrasound wave as frequency is increased, regardless of the composition tested. The threshold frequency for stress amplification is proportionate to the wave speed divided by the stone diameter. Thus, smaller stones may be likely to fragment at a higher frequency, but not at a lower frequency below a limit. Unlike with SWL, this amplification in BWL occurs consistently with spherical and irregularly shaped stones. In water tank experiments, stones smaller than the threshold size broke fastest at high frequency (p = 0.0003), whereas larger stones broke equally well to submillimeter dust at high, low, or mixed frequencies. Conclusions: For small stones and fragments, increasing frequency of BWL may produce amplified stress in the stone causing the stone to break. Using the strategies outlined here, stones of all sizes may be turned to dust efficiently with BWL.

Ultrastructural Analysis of Volumetric Histotripsy Bio-effects in Large Human Hematomas.

Large-volume soft tissue hematomas are a serious clinical problem, which, if untreated, can have severe consequences. Current treatments are associated with significant pain and discomfort. It has been reported that in an in vitro bovine hematoma model, pulsed high-intensity focused ultrasound (HIFU) ablation, termed histotripsy, can be used to rapidly and non-invasively liquefy the hematoma through localized bubble activity, enabling fine-needle aspiration. The goals of this study were to evaluate the efficiency and speed of volumetric histotripsy liquefaction using a large in vitro human hematoma model. Large human hematoma phantoms (85 cc) were formed by recalcifying blood anticoagulated with citrate phosphate dextrose/saline-adenine-glucose-mannitol solution. Typical boiling histotripsy pulses (10 or 2 ms) or hybrid histotripsy pulses using higher-amplitude and shorter pulses (0.4 ms) were delivered at 1% duty cycle while continuously translating the HIFU focus location. Histotripsy exposures were performed under ultrasound guidance with a 1.5-MHz transducer (8-cm aperture, F# = 0.75). The volume of liquefied lesions was determined by ultrasound imaging and gross inspection. Untreated hematoma samples and samples of the liquefied lesions aspirated using a fine needle were analyzed cytologically and ultrastructurally with scanning electron microscopy. All exposures resulted in uniform liquid-filled voids with sharp edges; liquefaction speed was higher for exposures with shorter pulses and higher shock amplitudes at the focus (up to 0.32, 0.68 and 2.62 mL/min for 10-, 2- and 0.4-ms pulses, respectively). Cytological and ultrastructural observations revealed completely homogenized blood cells and fibrin fragments in the lysate. Most of the fibrin fragments were less than 20 µm in length, but a number of fragments were up to 150 µm. The lysate with residual debris of that size would potentially be amenable to fine-needle aspiration without risk for needle clogging in clinical implementation.

A review on B/A measurement methods with a clinical perspective.

The nonlinear parameter of ultrasound B/A has shown to be a useful diagnostic parameter, reflecting medium content, structure, and temperature. Despite its recognized values, B/A is not yet used as a diagnostic tool in the clinic due to the limitations of current measurement and imaging techniques. This review presents an extensive and comprehensive overview of the techniques developed for B/A measurement of liquid and liquid-like media (e.g., tissue), identifying the methods that are most promising from a clinical perspective. This work summarizes the progress made in the field and the typical challenges on the way to B/A estimation. Limitations and problems with the current techniques are identified, suggesting directions that may lead to further improvement. Since the basic theory of the physics behind the measurement strategies is presented, it is also suited for a reader who is new to nonlinear ultrasound.

"HIFU Beam:" A Simulator for Predicting Axially Symmetric Nonlinear Acoustic Fields Generated by Focused Transducers in a Layered Medium.

"HIFU beam" is a freely available software tool that comprises a MATLAB toolbox combined with a user-friendly interface and binary executable compiled from FORTRAN source code (HIFU beam. (2021). Available: http://limu.msu.ru/node/3555?language=en). It is designed for simulating high-intensity focused ultrasound (HIFU) fields generated by single-element transducers and annular arrays with propagation in flat-layered media that mimic biological tissues. Numerical models incorporated in the simulator include evolution-type equations, either the Khokhlov-Zabolotskaya-Kuznetsov (KZK) equation or one-way Westervelt equation, for radially symmetric ultrasound beams in homogeneous and layered media with thermoviscous or power-law acoustic absorption. The software uses shock-capturing methods that allow for simulating strongly nonlinear acoustic fields with high-amplitude shocks. In this article, a general description of the software is given along with three representative simulation cases of ultrasound transducers and focusing conditions typical for therapeutic applications. The examples illustrate major nonlinear wave effects in HIFU fields including shock formation. Two examples simulate propagation in water, involving a single-element source (1-MHz frequency, 100-mm diameter, 90-mm radius of curvature) and a 16-element annular array (3-MHz frequency, 48-mm diameter, and 35-mm radius of curvature). The third example mimics the scenario of a HIFU treatment in a "water-muscle-kidney" layered medium using a source typical for abdominal HIFU applications (1.2-MHz frequency, 120-mm diameter, and radius of curvature). Linear, quasi-linear, and shock-wave exposure protocols are considered. It is intended that "HIFU beam" can be useful in teaching nonlinear acoustics; designing and characterizing high-power transducers; and developing exposure protocols for a wide range of therapeutic applications such as shock-based HIFU, boiling histotripsy, drug delivery, immunotherapy, and others.

Inertial Cavitation Behaviors Induced by Nonlinear Focused Ultrasound Pulses.

Inertial cavitation induced by pulsed high-intensity focused ultrasound (pHIFU) has previously been shown to successfully permeabilize tumor tissue and enhance chemotherapeutic drug uptake. In addition to HIFU frequency, peak rarefactional pressure ( p- ), and pulse duration, the threshold for cavitation-induced bioeffects has recently been correlated with asymmetric distortion caused by nonlinear propagation, diffraction and formation of shocks in the focal waveform, and therefore with the transducer F -number. To connect previously observed bioeffects with bubble dynamics and their attendant physical mechanisms, the dependence of inertial cavitation behavior on shock formation was investigated in transparent agarose gel phantoms using high-speed photography and passive cavitation detection (PCD). Agarose phantoms with concentrations ranging from 1.5% to 5% were exposed to 1-ms pulses using three transducers of the same aperture but different focal distances ( F -numbers of 0.77, 1.02, and 1.52). Pulses had central frequencies of 1, 1.5, or 1.9 MHz and a range of p- at the focus varying within 1-18 MPa. Three distinct categories of bubble behavior were observed as the acoustic power increased: stationary near-spherical oscillation of individual bubbles, proliferation of multiple bubbles along the pHIFU beam axis, and fanned-out proliferation toward the transducer. Proliferating bubbles were only observed under strongly nonlinear or shock-forming conditions regardless of frequency, and only where the bubbles reached a certain threshold size range. In stiffer gels with higher agarose concentrations, the same pattern of cavitation behavior was observed, but the dimensions of proliferating clouds were smaller. These observations suggest mechanisms that may be involved in bubble proliferation: enhanced growth of bubbles under shock-forming conditions, subsequent shock scattering from the gel-bubble interface, causing an increase in the repetitive tension created by the acoustic wave, and the appearance of a new growing bubble in the proximal direction. Different behaviors corresponded to specific spectral characteristics in the PCD signals: broadband noise in all cases, narrow peaks of backscattered harmonics in the case of stationary bubbles, and broadened, shifted harmonic peaks in the case of proliferating bubbles. The shift in harmonic peaks can be interpreted as a Doppler shift from targets moving at speeds of up to 2 m/s, which correspond to the observed bubble proliferation speeds.

Holographic extraction of plane waves from an ultrasound beam for acoustic characterization of an absorbing layer of finite dimensions.

For the acoustic characterization of materials, a method is proposed for interpreting experiments with finite-sized transducers and test samples in terms of the idealized situation in which plane waves are transmitted through an infinite plane-parallel layer. The method uses acoustic holography, which experimentally provides complete knowledge of the wave field by recording pressure waveforms at points on a surface intersected by the acoustic beam. The measured hologram makes it possible to calculate the angular spectrum of the beam to decompose the field into a superposition of plane waves propagating in different directions. Because these waves cancel one another outside the beam, the idealized geometry of an infinite layer can be represented by a sample of finite size if its lateral dimensions exceed the width of the acoustic beam. The proposed method relies on holograms that represent the acoustic beam with and without the test sample in the transmission path. The method is described theoretically, and its capabilities are demonstrated experimentally for silicone rubber samples by measuring their frequency-dependent phase velocities and absorption coefficients in the megahertz frequency range.

Maximizing mechanical stress in small urinary stones during burst wave lithotripsy.

Unlike shock wave lithotripsy, burst wave lithotripsy (BWL) uses tone bursts, consisting of many periods of a sinusoidal wave. In this work, an analytical theoretical approach to modeling mechanical stresses in a spherical stone was developed to assess the dependence of frequency and stone size on stress generated in the stone. The analytical model for spherical stones is compared against a finite-difference model used to calculate stress in nonspherical stones. It is shown that at low frequencies, when the wavelength is much greater than the diameter of the stone, the maximum principal stress is approximately equal to the pressure amplitude of the incident wave. With increasing frequency, when the diameter of the stone begins to exceed about half the wavelength in the surrounding liquid (the exact condition depends on the material of the stone), the maximum stress increases and can be more than six times greater than the incident pressure. These results suggest that the BWL frequency should be elevated for small stones to improve the likelihood and rate of fragmentation.