Phase aberration induced by soft tissue inhomogeneities often complicates high-intensity focused ultrasound (HIFU) therapies by distorting the field and, previously, we designed and fabricated a bilayer gel phantom to reproducibly mimic that effect. A surface pattern containing size scales relevant to inhomogeneities of a porcine body wall was introduced between gel materials with fat- and muscle-like acoustic properties — ballistic and polyvinyl alcohol gels. Here, the phantom design was refined to achieve relevant values of ultrasound absorption and scattering and make it more robust, facilitating frequent handling and use in various experimental arrangements. The fidelity of the interfacial surface of the fabricated phantom to the design was confirmed by three-dimensional ultrasound imaging. The HIFU field distortions — displacement of the focus, enlargement of the focal region, and reduction of focal pressure — produced by the phantom were characterized using hydrophone measurements with a 1.5 MHz 256-element HIFU array and found to be similar to those induced by an ex vivo porcine body wall. A phase correction approach was used to mitigate the aberration effect on nonlinear focal waveforms and enable boiling histotripsy treatments through the phantom or body wall. The refined phantom represents a practical tool to explore HIFU therapy systems capabilities.

High intensity focused ultrasound (HIFU) treatments typically involve the ablation of tissue volumes comprising multiple focal sites. One aspect of treatment planning involves the definition of a sequence of ultrasound pulses and corresponding focal sites as the sonication trajectory. Here, numerical simulations of the thermal effects of different trajectories are performed for HIFU exposures delivered to an ex vivo bovine liver sample by a clinical array (Sonalleve V2 3.0T system, Profound Medical Corp., Canada). Simulations consider boiling histotripsy regime with millisecond-long pulses that include shocks. Focusing of the ultrasound beam in tissue was modeled by the Westervelt equation, and the temperature field was modeled by the bioheat equation. To explore different treatment strategies, trajectories were considered with discrete foci located along two or four concentric circles with radii from 2 to 8 mm. Two approaches for traversing these focal sites were compared: In the first approach each discrete focus was sonicated by a sequence of 15 pulses before moving to the next site in the trajectory. In the second approach, each focus was sonicated once before moving to the next site, with sonications over the whole trajectory repeated 15 times. The influence of the trajectory’s size and the pulsing strategy on the temperature field was analyzed. It is shown that the structure of the temperature field is more uniform with a longer time interval between repeated irradiation of each focus, and the optimal time interval ranges from three to six pulse repetition periods.

'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 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, 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 peak rarefactional pressure 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.

Histotripsy is a therapeutic ultrasound technology to liquefy tissue into acellular debris using sequences of high-power focused ultrasound pulses. Research on histotripsy has been rapidly growing in the past decade; newer applications are being proposed and evaluated for clinical use. In contrast to conventional high-intensity focused ultrasound (HIFU) thermal therapy, the major mechanism of histotripsy is mechanical, which enables localized tissue disintegration at the target sites without thermal damage to overlying and surrounding tissues. Two major approaches, cavitational histotripsy and boiling histotripsy, with two different mechanisms, have been extensively explored lately. Histotripsy therapy is being evaluated for treating cancer, thrombosis, hematomas, abscess, neurological diseases, for inducing an enhanced immune response and performing noninvasive biopsy in preclinical studies with small and large animal models. The first clinical trials using histotripsy for benign prostatic hyperplasia, liver cancer, and calcified aortic stenosis have been undertaken.

Extracorporeal boiling histotripsy (BH), a noninvasive method for mechanical tissue disintegration, is getting closer to clinical applications. However, the motion of the targeted organs, mostly resulting from the respiratory motion, reduces the efficiency of the treatment. Here, a practical and affordable unidirectional respiratory motion compensation method for BH is proposed and evaluated in ex vivo tissues. The BH transducer is fixed on a robotic arm following the motion of the skin, which is tracked using an inline ultrasound imaging probe. In order to compensate for system lags and obtain a more accurate compensation, an autoregressive motion prediction model is implemented. BH pulse gating is also implemented to ensure targeting accuracy. The system is then evaluated with ex vivo BH treatments of tissue samples undergoing motion simulating breathing with the movement of amplitudes between 5 and 10 mm, the frequency between 16 and 18 breaths/min, and a maximum speed of 14.2 mm/s. Results show a reduction of at least 89% of the value of the targeting error during treatment while only increasing the treatment time by no more than 1%. The lesions obtained by treating with the motion compensation were close in size and affected area to the no-motion case, whereas lesions obtained without the compensation were often incomplete and had larger affected areas. This approach to motion compensation could benefit extracorporeal BH and other histotripsy methods in clinical translation.

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.

Boiling histotripsy (BH) uses millisecond-long ultrasound (US) pulses with high-amplitude shocks to mechanically fractionate tissue with potential for real-time lesion monitoring by US imaging. For BH treatments of abdominal organs, a high-power multielement phased array system capable of electronic focus steering and aberration correction for body wall inhomogeneities is needed. In this work, a preclinical BH system was built comprising a custom 256-element 1.5-MHz phased array (Imasonic, Besançon, France) with a central opening for mounting an imaging probe. The array was electronically matched to a Verasonics research US system with a 1.2-kW external power source. Driving electronics and software of the system were modified to provide a pulse average acoustic power of 2.2 kW sustained for 10 ms with a 1–2-Hz repetition rate for delivering BH exposures. System performance was characterized by hydrophone measurements in water combined with nonlinear wave simulations based on the Westervelt equation. Fully developed shocks of 100-MPa amplitude are formed at the focus at 275-W acoustic power. Electronic steering capabilities of the array were evaluated for shock-producing conditions to determine power compensation strategies that equalize BH exposures at multiple focal locations across the planned treatment volume. The system was used to produce continuous volumetric BH lesions in ex vivo bovine liver with 1-mm focus spacing, 10-ms pulselength, five pulses/focus, and 1% duty cycle.

Phase aberrations induced by heterogeneities in body wall tissues introduce a shift and broadening of the high-intensity focused ultrasound (HIFU) focus, associated with decreased focal intensity. This effect is particularly detrimental for HIFU therapies that rely on shock front formation at the focus, such as boiling histotripsy (BH). In this article, an aberration correction method based on the backscattering of nonlinear ultrasound pulses from the focus is proposed and evaluated in tissue-mimicking phantoms. A custom BH system comprising a 1.5-MHz 256-element array connected to a Verasonics V1 engine was used as a pulse/echo probe. Pulse inversion imaging was implemented to visualize the second harmonic of the backscattered signal from the focus inside a phantom when propagating through an aberrating layer. Phase correction for each array element was derived from an aberration-correction method for ultrasound imaging that combines both the beamsum and the nearest neighbor correlation method and adapted it to the unique configuration of the array. The results were confirmed by replacing the target tissue with a fiber-optic hydrophone. Comparing the shock amplitude before and after phase-aberration correction showed that the majority of losses due to tissue heterogeneity were compensated, enabling fully developed shocks to be generated while focusing through aberrating layers. The feasibility of using a HIFU phased-array transducer as a pulse-echo probe in harmonic imaging mode to correct for phase aberrations was demonstrated.

Infected abscesses are walled-off collections of pus and bacteria. They are a common sequela of complications in the setting of surgery, trauma, systemic infections and other disease states. Current treatment is typically limited to antibiotics with long-term catheter drainage, or surgical washout when inaccessible to percutaneous drainage or unresponsive to initial care efforts. Antibiotic resistance is also a growing concern. Although bacteria can develop drug resistance, they remain susceptible to thermal and mechanical damage. In particular, short pulses of focused ultrasound (i.e., histotripsy) generate mechanical damage through localized cavitation, representing a potential new paradigm for treating abscesses non-invasively, without the need for long-term catheterization and antibiotics. In this pilot study, boiling and cavitation histotripsy treatments were applied to subcutaneous and intramuscular abscesses developed in a novel porcine model. Ultrasound imaging was used to evaluate abscess maturity for treatment monitoring and assessment of post-treatment outcomes. Disinfection was quantified by counting bacteria colonies from samples aspirated before and after treatment. Histopathological evaluation of the abscesses was performed to identify changes resulting from histotripsy treatment and potential collateral damage. Cavitation histotripsy was more successful in reducing the bacterial load while having a smaller treatment volume compared with boiling histotripsy. The results of this pilot study suggest focused ultrasound may lead to a technology for in situ treatment of acoustically accessible abscesses.

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.

Aberrations induced by soft tissue inhomogeneities often complicate high-intensity focused ultrasound (HIFU) therapies. In this work, a bilayer phantom made from polyvinyl alcohol hydrogel and ballistic gel was built to mimic alternating layers of water-based and lipid tissues characteristic of an abdominal body wall and to reproducibly distort HIFU fields. The density, sound speed, and attenuation coefficient of each material were measured using a homogeneous gel layer. A surface with random topographical features was designed as an interface between gel layers using a 2D Fourier spectrum approach and replicating different spatial scales of tissue inhomogeneities. Distortion of the field of a 256-element 1.5 MHz HIFU array by the phantom was characterized through hydrophone measurements for linear and nonlinear beam focusing and compared to the corresponding distortion induced by an ex vivo porcine body wall of the same thickness. Both spatial shift and widening of the focal lobe were observed, as well as dramatic reduction in focal pressures caused by aberrations. The results suggest that the phantom produced levels of aberration that are similar to a real body wall and can serve as a research tool for studying HIFU effects as well as for developing algorithms for aberration correction.

Large intra-abdominal, retroperitoneal and intramuscular hematomas are common consequences of sharp and blunt trauma and post-surgical bleeds, and often threaten organ failure, compartment syndrome or spontaneous infection. Current therapy options include surgical evacuation and placement of indwelling drains that are not effective because of the viscosity of the organized hematoma. We have previously reported the feasibility of using boiling histotripsy (BH) — a pulsed high-intensity focused ultrasound method — for liquefaction of large volumes of freshly coagulated blood and subsequent fine-needle aspiration. The goal of this work was to evaluate the changes in stiffness of large coagulated blood volumes with aging and retraction in vitro, and to correlate these changes with the size of the BH void and, therefore, the susceptibility of the material to BH liquefaction. Large-volume (55–200 mL) whole-blood clots were fabricated in plastic molds from human and bovine blood, either by natural clotting or by recalcification of anticoagulated blood, with or without addition of thrombin. Retraction of the clots was achieved by incubation for 3 h, 3 d or 8 d. The shear modulus of the samples was measured with a custom-built indentometer and shear wave elasticity (SWE) imaging. Sizes of single liquefied lesions produced with a 1.5-MHz high-intensity focused ultrasound transducer within a 30-s standard BH exposure served as the metric for susceptibility of clot material to this treatment. Neither the shear moduli of naturally clotted human samples (0.52 ± 0.08 kPa), nor their degree of retraction (ratio of expelled fluid to original volume 50%––58%) depended on the length of incubation within 0–8 d, and were significantly lower than those of bovine samples (2.85 ± 0.17 kPa, retraction 5%–38%). In clots made from anticoagulated bovine blood, the variation of calcium chloride concentration within 5––40 mmol/L did not change the stiffness, whereas lower concentrations and the addition of thrombin resulted in significantly softer clots, similar to naturally clotted human samples. Within the achievable shear modulus range (0.4–1.6 kPa), the width of the BH-liquefied lesion was more affected by the changes in stiffness than the length of the lesion. In all cases, however, the lesions were larger compared with any soft tissue liquefied with the same BH parameters, indicating higher susceptibility of hematomas to BH damage. These results suggest that clotted bovine blood with added thrombin is an acceptable in vitro model of both acute and chronic human hematomas for assessing the efficiency of BH liquefaction strategies.

In certain medical applications, transmitting an ultrasound beam through the skin to manipulate a solid object within the human body would be beneficial. Such applications include, for example, controlling an ingestible camera or expelling a kidney stone. In this paper, ultrasound beams of specific shapes were designed by numerical modeling and produced using a phased array. These beams were shown to levitate and electronically steer solid objects (3-mm-diameter glass spheres), along preprogrammed paths, in a water bath, and in the urinary bladders of live pigs. Deviation from the intended path was on average <10%. No injury was found on the bladder wall or intervening tissue.

This article reviews the most current methods and technological aspects of high‐intensity focused ultrasound (HIFU), which is termed histotripsy. The rationale for focal therapy for prostate carcinoma rather than prostatectomy, which is being used extensively throughout Europe and Asia, is presented, and an argument for why HIFU is the modality of choice for primary therapy and recurrent disease is offered. The article presents a review of the technical advances including higher ultrasound beam energy than current thermal HIFU which allows for more accurate tissue targeting, less collateral tissue damage, and faster treatment times. Finally, the article presents a discussion about the advantage of ultrasound guidance for histotripsy in preference to magnetic resonance imaging guidance primarily based on cost, ease of application, and portability.

Boiling histotripsy (BH) is a High Intensity Focused Ultrasound (HIFU) method for precise mechanical disintegration of target tissue using millisecond-long pulses containing shocks. BH treatments with real-time ultrasound (US) guidance allowed by BH-generated bubbles were previously demonstrated ex vivo and in vivo in exposed porcine liver and small animals. Here, the feasibility of US-guided transabdominal and partially transcostal BH ablation of kidney and liver in an acute in vivo swine model was evaluated for 6 animals. BH parameters were: 1.5 MHz frequency, 5–30 pulses of 1–10 ms duration per focus, 1% duty cycle, peak acoustic powers 0.9–3.8 kW, sonication foci spaced 1–1.5 mm apart in a rectangular grid with 5–15 mm linear dimensions. In kidneys, well-demarcated volumetric BH lesions were generated without respiratory gating and renal medulla and collecting system were more resistant to BH than cortex. The treatment was accelerated 10-fold by using shorter BH pulses of larger peak power without affecting the quality of tissue fractionation. In liver, respiratory motion and aberrations from subcutaneous fat affected the treatment but increasing the peak power provided successful lesion generation. These data indicate BH is a promising technology for transabdominal and transcostal mechanical ablation of tumors in kidney and liver.

Theoretical models allow design of acoustic traps to manipulate objects with radiation force. A model of the acoustic radiation force by an arbitrary beam on a solid object is validated against measurement. The lateral force in water of different acoustic beams is measured and calculated for spheres of different diameters (2–6 wavelengths λ in water) and compositions. This is the first effort to validate a general model, to quantify the lateral force on a range of objects, and to electronically steer large or dense objects with a single-sided transducer. Vortex beams and two other beam shapes having a ring-shaped pressure field in the focal plane are synthesized in water by a 1.5-MHz, 256-element focused array. Spherical targets (glass, brass, ceramic, 2–6 mm dia.) are placed on an acoustically transparent plastic plate that is normal to the acoustic beam axis and rigidly attached to the array. Each sphere is trapped in the beam as the array with the attached plate is rotated until the sphere falls from the acoustic trap because of gravity. Calculated and measured maximum obtained angles agree on average to within 22%. The maximum lateral force occurs when the target diameter equals the beam width; however, objects up to 40% larger than the beam width are trapped. The lateral force is comparable to the gravitation force on spheres up to 90 mg (0.0009 N) at beam powers on the order of 10 W. As a step toward manipulating objects, the beams are used to trap and electronically steer the spheres along a two-dimensional path.

Multi-element high-intensity focused ultrasound phased arrays in the shape of hemispheres are currently used in clinics for thermal lesioning in deep brain structures. Certain side effects of overheating non-targeted tissues and skull bones have been revealed. Here, an approach is developed to mitigate these effects. A specific design of a fully populated 256-element 1-MHz array shaped as a spherical segment (F–number, F_# = 1) and filled by randomly distributed equal-area polygonal elements is proposed. Capability of the array to generate high-amplitude shock fronts at the focus is tested in simulations by combining three numerical algorithms for linear and nonlinear field modeling and aberration correction. The algorithms are based on the combination of the Rayleigh integral, a linear pseudo-spectral time domain Kelvin–Voigt model, and nonlinear Westervelt model to account for the effects of inhomogeneities, aberrations, reflections, absorption, nonlinearity, and shear waves in the skull. It is shown that the proposed array can generate nonlinear waveforms with shock amplitudes >60 MPa at the focus deep inside the brain without exceeding the existing technical limitation on the intensity of 40 W/cm² at the array elements. Such shock amplitudes are sufficient for mechanical ablation of brain tissues using the boiling histotripsy approach and implementation of other shock-based therapies.

High intensity focused ultrasound (HIFU) is rapidly advancing as an alternative therapy for non-invasively treating specific cancers and other pathological tissues through thermal ablation. A new type of HIFU therapy — boiling histotripsy (BH) — aims at mechanical fractionation of into subcellular fragments, with a range of accompanying thermal effects that can be tuned from none to substantial depending on the requirements of the application. The degree of mechanical tissue damage induced by BH has been shown to depend on the tissue type, with collagenous structures being most resistant, and cellular structures being most sensitive. This has been reported for single BH lesions, but has not been replicated in large volumes. Such tissue selectivity effect has potential uses involving tissue decellularization for biofabrication technologies as well as mechanical ablation by BH while sparing critical structures. The goal of this study was to investigate tissue decellularization effect in larger, clinically relevant liquefied volumes of tissue, and to evaluate the accumulated thermal effect in the volumetric lesions under different exposure parameters. All BH exposures were performed with a 256-element 1.2-MHz array of a magnetic resonance imaging — guided HIFU (MR-HIFU) clinical system (Sonalleve V1, Profound Medical Inc, Mississauga, Canada). The volumetric BH lesions were produced in degassed ex vivo bovine liver using 1–10-ms long pulses with in situ shock amplitudes of 75–100 MPa at the focus and pulse repetition frequencies (PRFs) of 1–10 Hz covering a range of effects from pure mechanical homogenization to thermal ablation. Multimodal analysis of the lesions was then performed, including microstructure (histological), ultrastructure (electron microscopy), and molecular (biochemistry) methods. Results show a range of tissue effects in terms of the degree of tissue selectivity and the amount of heat generated in large BH lesions, thereby demonstrating potential for treatments tailored to different clinical applications.

Pulsed high intensity focused ultrasound was shown to enhance chemotherapeutic drug uptake in tumor tissue through inertial cavitation, which is commonly assumed to require peak rarefactional pressures to exceed a certain threshold. However, recent studies have indicated that inertial cavitation activity also correlates with the presence of shocks at the focus. The shock front amplitude and corresponding peak negative pressure (p–) in the focal waveform are primarily determined by the transducer F-number: less focused transducers produce shocks at lower p–. Here, the dependence of inertial cavitation activity on the transducer F-number was investigated in agarose gel by monitoring broadband noise emissions with a coaxial passive cavitation detector (PCD) during pulsed exposures (pulse duration 1 ms, pulse repetition frequency 1 Hz) with p– varying within 1–15 MPa. Three 1.5 MHz transducers with the same aperture, but different focal distances (F-numbers 0.77, 1.02, 1.52) were used. PCD signals were processed to extract cavitation probability, persistence, and mean noise level. At the same p–, all metrics indicated enhanced cavitation activity at higher F-numbers; specifically, cavitation probability reached 100% when shocks formed at the focus. These results provide further evidence supporting the excitation of inertial cavitation at reduced p– by waveforms with nonlinear distortion and shocks.

Multielement focused ultrasound phased arrays have been used in therapeutic applications to treat large tissue volumes by electronic steering of the focus, to target multiple simultaneous foci, and to correct aberration caused by inhomogeneous tissue pathways. There is an increasing interest in using arrays to generate more complex beam shapes and corresponding acoustic radiation force patterns for manipulation of particles such as kidney stones. Toward this end, experimental and computational tools are needed to enable accurate delivery of desired transducer vibrations and corresponding ultrasound fields. The purpose of this paper was to characterize the vibrations of a 256-element array at 1.5 MHz, implement strategies to compensate for variability, and test the ability to generate specified vortex beams that are relevant to particle manipulation. The characterization of the array output was performed in water using both element-by-element measurements at the focus of the array and holography measurements for which all the elements were excited simultaneously. Both methods were used to quantify each element’s output so that the power of each element could be equalized. Vortex beams generated using both compensation strategies were measured and compared to the Rayleigh integral simulations of fields generated by an idealized array based on the manufacturer’s specifications. Although both approaches improved beam axisymmetry, compensation based on holography measurements had half the error relative to the simulation results in comparison to the element-by-element method.

This study addresses inactivation of E. coli in either 5- or 10-mL volumes, which were 50- to 100-fold greater than used in an earlier study (Brayman et al. 2017). Cells were treated with 1-MHz pulsed high-intensity focused ultrasound (10 cycles, 2-kHz repetition frequency, +65/–12.8 MPa focal pressures). The surviving fraction was assessed by coliform assay, and inactivation demonstrated curvilinear kinetics. The reduction of surviving fraction to 50% required 2.5 or 6 min in 5- or 10-mL samples, respectively. Exposure of 5 mL for 20 min reduced the surviving fraction to ~1%; a similar exposure of 10-mL samples reduced the surviving fraction to ~10%. Surviving cells from 5-min exposures appeared normal under light microscopy, with minimal debris; after 20 min, debris dominated. Transmission electron microscopy images of insonated samples showed some undamaged cells, a few damaged but largely intact cells and comminuted debris. Cellular damage associated with substantive but incomplete levels of inactivation can be variable, ranging from membrane holes tens of nanometers in diameter to nearly complete comminution.

Maximizing the power of multi-element phased arrays is a critical factor for high intensity focused ultrasound (HIFU) applications such as histotripsy and transcostal sonications. This can be achieved by a tight packing of the array elements. Good electronic focusing capabilities are also required. Currently used quasi-random arrays with a relatively low filling factor of about 60% have this focusing ability. Here, a novel method of designing random HIFU arrays with the maximum possible filling factor (100% if no gaps between elements needed in practice are introduced) and polygonal elements of equal area and slightly different shape based on the capacity-constrained tessellation is described. The method is validated by comparing designs of two arrays with the same geometric and physical parameters: an existing 256-element array with a compact 16-spirals layout of circular elements and the proposed array with the maximum possible filling factor. Introduction of a 0.5 mm gap between the elements of the new array resulted in a reduction of its filling factor to 86% as compared with 61% for the spiral array. It is shown that for the same intensity at the elements, the proposed array provides two times higher total power while maintaining the same electronic focusing capabilities as compared to the spiral one. Furthermore, the surface of the capacity-constrained tessellation array, its boundary, and a central opening can have arbitrary shapes.

Multi-element ultrasound arrays are increasingly used in clinical practice for both imaging and therapy. In therapy, they allow electronic steering, aberration correction, and focusing. To avoid grating lobes, an important requirement for such an array is the absence of periodicity in the arrangement of the elements. A convenient solution is the arrangement of the elements along spirals. The objective of this work was to design, fabricate, and characterize an array for boiling histotripsy applications that is capable of generating shock waves in the focus of up to 100 MPa peak pressure while having a reasonable electronic steering range.

The use of shock waves for enhancing thermal effects and mechanically ablating tissue is gaining increased attention in high intensity focused ultrasound (HIFU) applications such as tumor treatment, drug delivery, noninvasive biopsy, and immunotherapy. For abdominal targets, the presence of ribs and inhomogeneous adipose tissue can affect shock formation through aberration, absorption, and diffraction. The goal of this study was to design and validate a phantom for investigating the impact of different tissue structures on shock formation in situ. A transducer with driving electronics was developed to operate at 1.2 MHz with the ability to deliver either short pulses at high powers (up to 5 kW electric power) or continuous output at moderate powers (up to 700 W). Fat and muscle layers were represented by phantoms made from polyvinyl alcohol. Ribs were 3D-printed from a photopolymer material based on 3D CT scan images. Representative targeted tissue was comprised of optically transparent alginate or polyacrylamide gels. The system was characterized by hydrophone measurements free-field in water and in the presence of a body wall or rib phantoms. Shocked waveforms with peak positive/negative pressures of +100 / –20 MPa were measured at the focus in a free field at 1 kW electric source power. When ribs were present, shocks formed at about 50% amplitude at the same power, and higher pressures were measured with ribs positioned closer to the transducer. A uniform body wall structure attenuated shock amplitudes by a smaller amount than non-uniform, and the measurements were insensitive to the axial position of the phantom. Signal magnitude loss at the focus for both the rib phantoms and abdominal wall tissue were consistent with results from real tissues. In addition, boiling histotripsy lesions were generated and visualized in the target gels. The results demonstrate that the presence of ribs and absorptive tissue-mimicking layers do not prevent shock formation at the focus. With real-time lesion visualization, the phantom is suitable for adaptation as a training tool.

Boiling histotripsy (BH) is a method of focused ultrasound surgery that noninvasively applies millisecond-length pulses with high-amplitude shock fronts to generate liquefied lesions in tissue. Such a technique requires unique outputs compared to a focused ultrasound thermal therapy apparatus, particularly to achieve high in situ pressure levels through intervening tissue. This paper describes the design and characterization of a system capable of producing the necessary pressure to transcutaneously administer BH therapy through clinically relevant overlying tissue paths using pulses with duration up to 10 ms. A high-voltage electronic pulser was constructed to drive a 1-MHz focused ultrasound transducer to produce shock waves with amplitude capable of generating boiling within the pulse duration in tissue. The system output was characterized by numerical modeling with the 3-D Westervelt equation using boundary conditions established by acoustic holography measurements of the source field. Such simulations were found to be in agreement with directly measured focal waveforms. An existing derating method for nonlinear therapeutic fields was used to estimate in situ pressure levels at different tissue depths. The system was tested in ex vivo bovine liver samples to create BH lesions at depths up to 7 cm. Lesions were also created through excised porcine body wall (skin, adipose, and muscle) with 3–5 cm thickness. These results indicate that the system is capable of producing the necessary output for transcutaneous ablation with BH.

Boiling histotripsy (BH) is a high-intensity focused ultrasound (HIFU)–based method of mechanical tissue fractionation that utilizes millisecond-long bursts of HIFU shock waves to cause boiling at the focus in milliseconds. The subsequent interaction of the incoming shocks with the vapor bubble mechanically lyses surrounding tissue and cells. The acoustic parameter space for BH has been investigated previously and an inverse dependence between the HIFU frequency and the dimensions of a BH lesion has been observed. The primary goal of the present study was to investigate in more detail the ablation rate and reliability of BH in the frequency range relevant to treatment of deep abdominal tissue targets (1–2 MHz). The second goal was to investigate the effect of focal peak pressure levels and shock amplitude on BH lesion formation, given a constant duty factor, a constant ratio of the pulse duration to the time to reach boiling and a constant number of BH pulses. A custom-built 12-element sector array HIFU transducer with F-number = 1.05 was used in all experiments. BH pulses at 5 different frequencies (1, 1.2, 1.5, 1.7 and 1.9 MHz) were delivered to optically transparent polyacrylamide gel phantoms and ex vivo bovine liver and myocardium tissue to observe cavitation and boiling bubble activity with high-speed photography and B-mode ultrasound imaging, correspondingly. In gel phantoms, a cavitation bubble cloud was shown to form prefocally and to shield the focus in all exposures at 1 and 1.2 MHz and in the highest amplitude exposures at 1.5–1.7 MHz; shielding was not observed at 1.9 MHz. In ex vivo tissue, this shielding effect was observed in 25% of exposures when peak negative in situ pressure exceeded 10.2 MPa at 1 MHz and 14.5 MPa at 1.5 MHz. When shielding occurred, the exposures resulted in mild tissue disruption in the prefocal region, but not liquefaction. The dimensions of liquefied lesions followed the inverse proportionality trend with frequency; consequently, the frequency range of 1.2–1.5 MHz appeared to be preferable for BH exposures in terms of the compromise between the ablation rate and reliability. The lesion size was independent of the duration of the BH pulses (or the total "HIFU on" time), provided that the number of pulses was constant and boiling was induced within each pulse. Thus, the use of shorter (1 ms vs. 10 ms), higher amplitude BH pulses allowed up to 10-fold reduction in treatment time for a given duty factor.

Newer imaging and therapeutic ultrasound technologies may benefit from in situ pressure levels higher than conventional diagnostic ultrasound. One example is the recently developed use of ultrasonic radiation force to move kidney stones and residual fragments out of the urinary collecting system. A commercial diagnostic 2.3 MHz C5-2 array probe has been used to deliver the acoustic pushing pulses. The probe is a curvilinear array comprising 128 elements equally spaced along a convex cylindrical surface. The effectiveness of the treatment can be increased by using higher transducer output to provide a stronger pushing force; however nonlinear acoustic saturation can be a limiting factor. In this work nonlinear propagation effects were analyzed for the C5-2 transducer using a combined measurement and modeling approach. Simulations were based on the three-dimensional Westervelt equation with the boundary condition set to match low power measurements of the acoustic pressure field. Nonlinear focal waveforms simulated for different numbers of operating elements of the array at several output power levels were compared to fiber-optic hydrophone measurements and were found to be in good agreement. It was shown that saturation effects do limit the acoustic pressure in the focal region of a diagnostic imaging probe.

Various clinical applications of high-intensity focused ultrasound have different requirements for the pressure levels and degree of nonlinear waveform distortion at the focus. The goal of this paper is to determine transducer design parameters that produce either a specified shock amplitude in the focal waveform or specified peak pressures while still maintaining quasi-linear conditions at the focus. Multiparametric nonlinear modeling based on the Khokhlov-Zabolotskaya-Kuznetsov (KZK) equation with an equivalent source boundary condition was employed. Peak pressures, shock amplitudes at the focus, and corresponding source outputs were determined for different transducer geometries and levels of nonlinear distortion. The results are presented in terms of the parameters of an equivalent single-element spherically shaped transducer. The accuracy of the method and its applicability to cases of strongly focused transducers were validated by comparing the KZK modeling data with measurements and nonlinear full diffraction simulations for a single-element source and arrays with 7 and 256 elements. The results provide look-up data for evaluating nonlinear distortions at the focus of existing therapeutic systems as well as for guiding the design of new transducers that generate specified nonlinear fields.

In this work, an effective transcranial imaging technique is proposed to compensate for distortions of ultrasound (US) field caused by skull bone. The results of an experimental study using skull phantoms and 2D synthetic array are presented. The method was used to visualize mm-sized spherical scatterers made from styrofoam as well as a soft silicone tube mimicking a blood vessel. It is shown that the proposed technique is capable to compensate for field distortion and results in improved imaging through the skull.

In medical and industrial ultrasound, it is often necessary to measure the acoustic properties of a material. A specific medical application requires measurements of sound speed, attenuation, and nonlinearity to characterize livers being evaluated for transplantation. For this application, a transmission-mode caliper device is proposed in which both transmit and receive transducers are directly coupled to a test sample, the propagation distance is measured with an indicator gage, and receive waveforms are recorded for analysis. In this configuration, accurate measurements of nonlinearity present particular challenges: diffraction effects can be considerable while nonlinear distortions over short distances typically remain small. To enable simple estimates of the nonlinearity coeffcient from a quasi-linear approximation to the lossless Burgers’ equation, the calipers utilize a large transmitter and plane waves are measured at distances of 15–50 mm. Waves at 667 kHz and pressures between 0.1 and 1 MPa were generated and measured in water at different distances; the nonlinearity coeffcient of water was estimated from these measurements with a variability of approximately 10%. Ongoing efforts seek to test caliper performance in other media and improve accuracy via additional transducer calibrations.

Various clinical applications of high intensity focused ultrasound (HIFU) have different requirements on the pressure level and degree of nonlinear waveform distortion at the focus. Applications that utilize nonlinear waves with developed shocks are of growing interest, for example, for mechanical disintegration as well as for accelerated thermal ablation of tissue. In this work, an inverse problem of determining transducer parameters to enable formation of shocks with desired amplitude at the focus is solved. The solution was obtained by performing multiple direct simulations of the parabolic Khokhlov–Zabolotskaya–Kuznetsov (KZK) equation for various parameters of the source. It is shown that results obtained within the parabolic approximation can be used to describe the focal region of single element spherical sources as well as complex transducer arrays. It is also demonstrated that the focal pressure level at which fully developed shocks are formed mainly depends on the focusing angle of the source and only slightly depends on its aperture and operating frequency. Using the simulation results, a 256-element HIFU array operating at 1.5 MHz frequency was designed for a specific application of boiling-histotripsy that relies on the presence of 90–100 MPa shocks at the focus. The size of the array elements and focusing angle of the array were chosen to satisfy technical limitations on the intensity at the array elements and desired shock amplitudes in the focal waveform. Focus steering capabilities of the array were analysed using an open-source T-Array software developed at Moscow State University.

An equivalent source model is developed for setting boundary conditions on the parabolic diffraction equation in order to simulate ultrasound fields radiated by strongly focused medical transducers. The equivalent source is defined in a plane; corresponding boundary conditions for pressure amplitude, aperture, and focal distance are chosen so that the axial solution to the parabolic model in the focal region of the beam matches the solution to the full diffraction model (Rayleigh integral) for a spherically curved uniformly vibrating source. It is shown that the proposed approach to transferring the boundary condition from a spherical surface to a plane makes it possible to match the solutions over an interval of several diffraction maxima around the focus even for focused sources with F-numbers less than unity. This method can be used to accurately simulate nonlinear effects in the fields of strongly focused therapeutic transducers using the parabolic Khokhlov–Zabolotskaya equation.

Acoustic holography is a powerful technique for characterizing ultrasound sources and the fields they radiate, with the ability to quantify source vibrations and reduce the number of required measurements. These capabilities are increasingly appealing for meeting measurement standards in medical ultrasound; however, associated uncertainties have not been investigated systematically. Here errors associated with holographic representations of a linear, continuous-wave ultrasound field are studied. To facilitate the analysis, error metrics are defined explicitly, and a detailed description of a holography formulation based on the Rayleigh integral is provided. Errors are evaluated both for simulations of a typical therapeutic ultrasound source and for physical experiments with three different ultrasound sources. Simulated experiments explore sampling errors introduced by the use of a finite number of measurements, geometric uncertainties in the actual positions of acquired measurements, and uncertainties in the properties of the propagation medium. Results demonstrate the theoretical feasibility of keeping errors less than about 1%. Typical errors in physical experiments were somewhat larger, on the order of a few percent; comparison with simulations provides specific guidelines for improving the experimental implementation to reduce these errors. Overall, results suggest that holography can be implemented successfully as a metrological tool with small, quantifiable errors.

Accurate measurement of high-amplitude, broadband shock pulses in air is an important part of laboratory-scale experiments in atmospheric acoustics. Although various methods have been developed, specific drawbacks still exist and need to be addressed. Here, a schlieren optical method was used to reconstruct the pressure signatures of nonlinear spherically diverging short acoustic pulses generated using an electric spark source (2.5 kPa, 33% μs at 10 cm from the source) in homogeneous air. A high-speed camera was used to capture light rays deflected by refractive index inhomogeneities, caused by the acoustic wave. Pressure waveforms were reconstructed from the light intensity patterns in the recorded images using an Abel-type inversion method. Absolute pressure levels were determined by analyzing at different propagation distances the duration of the compression phase of pulses, which changed due to nonlinear propagation effects. Numerical modeling base on the generalized Burgers equation was used to evaluate the smearing of the waveform caused by finite exposure time of the high-speed camera and corresponding limitations in resolution of the schlieren technique. The proposed method allows the study of the evolution of spark-generated shock waves in air starting from the very short distances from the spark, 30 mm, up to 600 mm.

Accurate measurement of high-amplitude, broadband shock pulses in air is an important part of laboratory-scale experiments in atmospheric acoustics. Although various methods have been developed, specific drawbacks still exist and need to be addressed. Here, a schlieren optical method was used to reconstruct the pressure signatures of nonlinear spherically diverging short acoustic pulses generated using an electric spark source (2.5%u2009kPa, 33%u2009%u03BCs at 10%u2009cm from the source) in homogeneous air. A high-speed camera was used to capture light rays deflected by refractive index inhomogeneities, caused by the acoustic wave. Pressure waveforms were reconstructed from the light intensity patterns in the recorded images using an Abel-type inversion method. Absolute pressure levels were determined by analyzing at different propagation distances the duration of the compression phase of pulses, which changed due to nonlinear propagation effects. Numerical modeling base on the generalized Burgers equation was used to evaluate the smearing of the waveform caused by finite exposure time of the high-speed camera and corresponding limitations in resolution of the schlieren technique. The proposed method allows the study of the evolution of spark-generated shock waves in air starting from the very short distances from the spark, 30%u2009mm, up to 600%u2009mm.

The aim of this study is to show the evidence of Mach stem formation for very weak shock waves with acoustic Mach numbers on the order of 10^-3 to 10^-2. Two representative cases are considered: reflection of shock pulses from a rigid surface and focusing of nonlinear acoustic beams. Reflection experiments are performed in air using spark-generated shock pulses. Shock fronts are visualized using a schlieren system. Both regular and irregular types of reflection are observed. Numerical simulations are performed to demonstrate the Mach stem formation in the focal region of periodic and pulsed nonlinear beams in water.

Certain modern applications of high-intensity focused ultrasound (HIFU) in medicine use the nonlinear effect of shock front formation in the focal waveform. However, an important problem remains unsolved: determination of transducer parameters that provide the given pressure levels of the shock wave field at the focus required for a specific application. In this paper, simulations based on the Khokhlov–Zabolotskaya equation are performed to test and confirm the hypothesis that angular aperture of the transducer is the main parameter that determines the characteristic amplitude of the shock front and corresponding values for the peak positive and negative pressures at the focus. A criterion for formation of a developed shock in the acoustic waveform, as well as a method for determining its amplitude is proposed. Quantitative dependences of the amplitude of the developed shock and the peak pressures in the wave profile on the angular aperture of the transducer are calculated. The effects of saturation and the range of changes of the shock waveform parameters at the focus are analyzed for a typical HIFU transducer.

Ultrasonic atomization, or the emission of a fog of droplets, was recently proposed to explain tissue fractionation in boiling histotripsy. However, even though liquid atomization has been studied extensively, the mechanisms underlying tissue atomization remain unclear. In the work described here, high-speed photography and overpressure were used to evaluate the role of bubbles in tissue atomization. As static pressure increased, the degree of fractionation decreased, and the ex vivo tissue became thermally denatured. The effect of surface wetness on atomization was also evaluated in vivo and in tissue-mimicking gels, where surface wetness was found to enhance atomization by forming surface instabilities that augment cavitation. In addition, experimental results indicated that wetting collagenous tissues, such as the liver capsule, allowed atomization to breach such barriers. These results highlight the importance of bubbles and surface instabilities in atomization and could be used to enhance boiling histotripsy for transition to clinical use.

When focused ultrasound waves of moderate intensity in liquid encounter an air interface, a chain of drops emerges from the liquid surface to form what is known as a drop-chain fountain. Atomization, or the emission of micro-droplets, occurs when the acoustic intensity exceeds a liquid-dependent threshold. While the cavitation-wave hypothesis, which states that atomization arises from a combination of capillary-wave instabilities and cavitation bubble oscillations, is currently the most accepted theory of atomization, more data on the roles of cavitation, capillary waves, and even heat deposition or boiling would be valuable. In this paper, we experimentally test whether bubbles are a significant mechanism of atomization in drop-chain fountains. High-speed photography was used to observe the formation and atomization of drop-chain fountains composed of water and other liquids. For a range of ultrasonic frequencies and liquid sound speeds, it was found that the drop diameters approximately equalled the ultrasonic wavelengths. When water was exchanged for other liquids, it was observed that the atomization threshold increased with shear viscosity. Upon heating water, it was found that the time to commence atomization decreased with increasing temperature. Finally, water was atomized in an overpressure chamber where it was found that atomization was significantly diminished when the static pressure was increased. These results indicate that bubbles, generated by either acoustic cavitation or boiling, contribute significantly to atomization in the drop-chain fountain.

In high intensity focused ultrasound (HIFU) therapy, an ultrasound beam is focused within the body to locally affect the targeted site without damaging intervening tissues. The most common HIFU regime is thermal ablation. Recently there has been increasing interest in generating purely mechanical lesions in tissue (histotripsy). This paper provides an overview of several studies on the development of histotripsy methods toward clinical applications. Two histotripsy approaches and examples of their applications are presented. In one approach, sequences of high-amplitude, short (microsecond-long), focused ultrasound pulses periodically produce dense, energetic bubble clouds that mechanically disintegrate tissue. In an alternative approach, longer (millisecond-long) pulses with shock fronts generate boiling bubbles and the interaction of shock fronts with the resulting vapour cavity causes tissue disintegration. Recent preclinical studies on histotripsy are reviewed for treating benign prostatic hyperplasia (BPH), liver and kidney tumours, kidney stone fragmentation, enhancing anti-tumour immune response, and tissue decellularisation for regenerative medicine applications. Potential clinical advantages of the histotripsy methods are discussed. Histotripsy methods can be used to mechanically ablate a wide variety of tissues, whilst selectivity sparing structures such as large vessels. Both ultrasound and MR imaging can be used for targeting and monitoring the treatment in real time. Although the two approaches utilise different mechanisms for tissue disintegration, both have many of the same advantages and offer a promising alternative method of non-invasive surgery.

A numerical model for describing the counterpropagation of one-dimensional waves in a nonlinear medium with an arbitrary power law absorption and corresponding dispersion is developed. The model is based on general one-dimensional Navier-Stokes equations with absorption in the form of a time-domain convolution operator in the equation of state. The developed algorithm makes it possible to describe wave interactions in the presence of shock fronts in media like biological tissue. Numerical modeling is conducted by the finite difference method on a staggered grid; absorption and sound speed dispersion are taken into account using the causal memory function. The developed model is used for numerical calculations, which demonstrate the absorption and dispersion effects on nonlinear propagation of differently shaped pulses, as well as their reflection from impedance acoustic boundaries.

The clinical use of high intensity focused ultrasound (HIFU) therapy for noninvasive tissue ablation has been recently gaining momentum. In HIFU, ultrasound energy from an extracorporeal source is focused within the body to ablate tissue at the focus while leaving the surrounding organs and tissues unaffected. Most HIFU therapies are designed to use heating effects resulting from the absorption of ultrasound by tissue to create a thermally coagulated treatment volume. Although this approach is often successful, it has its limitations, such as the heat sink effect caused by the presence of a large blood vessel near the treatment area or heating of the ribs in the transcostal applications. HIFU-induced bubbles provide an alternative means to destroy the target tissue by mechanical disruption or, at its extreme, local fractionation of tissue within the focal region. Here, we demonstrate the feasibility of a recently developed approach to HIFU-induced ultrasound-guided tissue fractionation in an in vivo pig model. In this approach, termed boiling histotripsy, a millimeter-sized boiling bubble is generated by ultrasound and further interacts with the ultrasound field to fractionate porcine liver tissue into subcellular debris without inducing further thermal effects. Tissue selectivity, demonstrated by boiling histotripsy, allows for the treatment of tissue immediately adjacent to major blood vessels and other connective tissue structures. Furthermore, boiling histotripsy would benefit the clinical applications, in which it is important to accelerate resorption or passage of the ablated tissue volume, diminish pressure on the surrounding organs that causes discomfort, or insert openings between tissues.

Nonlinear propagation effects are present in most fields generated by high intensity focused ultrasound (HIFU) sources. In some newer HIFU applications, these effects are strong enough to result in the formation of high amplitude shocks that actually determine the therapy and provide a means for imaging. However, there is no standard approach yet accepted to address these effects. Here, a set of combined measurement and modeling methods to characterize nonlinear HIFU fields in water and predict acoustic pressures in tissue is presented. A characterization method includes linear acoustic holography measurements to set a boundary condition to the model and nonlinear acoustic simulations in water for increasing pressure levels at the source. A derating method to determine nonlinear focal fields with shocks in situ is based on the scaling of the source pressure for data obtained in water to compensate for attenuation losses in tissue. The accuracy of the methods is verified by comparing the results with hydrophone and time-to-boil measurements. Major effects associated with the formation of shocks are overviewed. A set of metrics for determining thermal and mechanical bioeffects is introduced and application of the proposed tools to strongly nonlinear HIFU applications is discussed.

The use of projection methods is increasingly accepted as a standard way of characterizing the 3D fields generated by medical ultrasound sources. When combined with hydrophone measurements of pressure amplitude and phase over a surface transverse to the wave propagation, numerical projection can be used to reconstruct 3D fields that account for operational details and imperfections of the source. Here, we use holography measurements to characterize the fields generated by two array transducers with different geometries and modes of operation. First, a seven-element, high-power therapy transducer is characterized in the continuous-wave regime using holography measurements and nonlinear forward-projection calculations. Second, a C5-2 imaging probe (Philips Healthcare) with 128 elements is characterized in the transient regime using holography measurements and linear projection calculations. Results from the numerical projections for both sources are compared with independent hydrophone measurements of select waveforms, including shocked focal waveforms for the therapy transducer. Accurate 3D field representations have been confirmed, though a notable sensitivity to hydrophone calibrations is revealed. Uncertainties associated with this approach are discussed toward the development of holography measurements combined with numerical projections as a standard metrological tool.

High-intensity focused ultrasound (HIFU) is a treatment modality that relies on the delivery of acoustic energy to remote tissue sites to induce thermal and/or mechanical tissue ablation. To ensure the safety and efficacy of this medical technology, standard approaches are needed for accurately characterizing the acoustic pressures generated by clinical ultrasound sources under operating conditions. Characterization of HIFU fields is complicated by nonlinear wave propagation and the complexity of phased-array transducers. Previous work has described aspects of an approach that combines measurements and modeling, and here we demonstrate this approach for a clinical phased-array transducer. First, low amplitude hydrophone measurements were performed in water over a scan plane between the array and the focus. Second, these measurements were used to holographically reconstruct the surface vibrations of the transducer and to set a boundary condition for a 3-D acoustic propagation model. Finally, nonlinear simulations of the acoustic field were carried out over a range of source power levels. Simulation results were compared with pressure waveforms measured directly by hydrophone at both low and high power levels, demonstrating that details of the acoustic field, including shock formation, are quantitatively predicted.

Histotripsy treatments use high-amplitude shock waves to fractionate tissue. Such treatments have been demonstrated using both cavitation bubbles excited with microsecond-long pulses and boiling bubbles excited for milliseconds. A common feature of both approaches is the need for bubble growth, where at 1 MHz cavitation bubbles reach maximum radii on the order of 100 microns and boiling bubbles grow to about 1 mm. To explore how histotripsy bubbles grow, a model of a single, spherical bubble that accounts for heat and mass transport was used to simulate the bubble dynamics. Results suggest that the asymmetry inherent in nonlinearly distorted waveforms can lead to rectified bubble growth, which is enhanced at elevated temperatures. Moreover, the rate of this growth is sensitive to the waveform shape, in particular the transition from the peak negative pressure to the shock front. Current efforts are focused on elucidating this behavior by obtaining an improved calibration of measured histotripsy waveforms with a fiber-optic hydrophone, using a nonlinear propagation model to assess the impact on the focal waveform of higher harmonics present at the source's surface, and photographically observing bubble growth rates.

The goal of this study was to investigate theoretically the effects of nonlinear propagation in a high-intensity focused ultrasound (HIFU) field produced by a therapeutic phased array and the resultant heating of tissue behind a rib cage. Three configurations of focusing were simulated: in water, in water with ribs in the beam path and in water with ribs backed by a layer of soft tissue. The Westervelt equation was used to model the nonlinear HIFU field, and a 1 MHz phased array consisting of 254 circular elements was used as a boundary condition to the model. The temperature rise in tissue was modelled using the bioheat equation, and thermally necrosed volumes were calculated using the thermal dose formulation. The shapes of lesions predicted by the modelling were compared with those previously obtained in in vitro experiments at low-power sonications. Intensity levels at the face of the array elements that corresponded to the formation of high-amplitude shock fronts in the focal region were determined as 10 W cm^-2 in the free field in water and 40 W cm^-2 in the presence of ribs. It was shown that exposures with shocks provided a substantial increase in tissue heating, and its better spatial localization in the main focal region only. The relative effects of overheating ribs and splitting of the focus due to the periodic structure of the ribs were therefore reduced. These results suggest that utilizing nonlinear propagation and shock formation effects can be beneficial for inducing confined HIFU lesions when irradiating through obstructions such as ribs. Design of compact therapeutic arrays to provide maximum power outputs with lower intensity levels at the elements is necessary to achieve shock wave regimes for clinically relevant sonication depths in tissue.

Recent studies have shown that shockwave heating and millisecond boiling in high-intensity focused ultrasound fields can result in mechanical fractionation or emulsification of tissue, termed boiling histotripsy. Visual observations of the change in color and contents indicated that the degree of thermal damage in the emulsified lesions can be controlled by varying the parameters of the exposure. The goal of this work was to examine thermal and mechanical effects in boiling histotripsy lesions using histologic and biochemical analysis. The lesions were induced in ex vivo bovine heart and liver using a 2-MHz single-element transducer operating at duty factors of 0.005–0.01, pulse durations of 5–500 ms and in situ shock amplitude of 73 MPa. Mechanical and thermal damage to tissue was evaluated histologically using conventional staining techniques (hematoxylin and eosin, and nicotinamide adenine dinucleotide-diaphorase). Thermal effects were quantified by measuring denaturation of salt soluble proteins in the treated region. According to histologic analysis, the lesions that visually appeared as a liquid contained no cellular structures larger than a cell nucleus and had a sharp border of one to two cells. Both histologic and protein analysis showed that lesions obtained with short pulses (<10 ms) did not contain any thermal damage. Increasing the pulse duration resulted in an increase in thermal damage. However, both protein analysis and nicotinamide adenine dinucleotide-diaphorase staining showed less denaturation than visually observed as whitening of tissue. The number of high-intensity focused ultrasound pulses delivered per exposure did not change the lesion shape or the degree of thermal denaturation, whereas the size of the lesion showed a saturating behavior suggesting optimal exposure duration. This study confirmed that boiling histotripsy offers an effective, predictable way to non-invasively fractionate tissue into sub-cellular fragments with or without inducing thermal damage.

Atomization and fountain formation is a well-known phenomenon that occurs when a focused ultrasound wave in liquid encounters an air interface. High intensity focused ultrasound (HIFU) has been shown to fractionate a tissue into submicron-sized fragments in a process termed boiling histotripsy, wherein the focused ultrasound wave superheats the tissue at the focus, producing a millimetre-sized boiling or vapour bubble in several milliseconds. Yet the question of how this millimetre-sized boiling bubble creates submicron-sized tissue fragments remains. The hypothesis of this work is that the tissue can behave as a liquid such that it atomizes and forms a fountain within the vapour bubble produced in boiling histotripsy. We describe an experiment, in which a 2 MHz HIFU transducer (maximum in situ intensity of 24,000 W cm^-2) was aligned with an air–tissue interface meant to simulate the boiling bubble. Atomization and fountain formation was observed with high-speed photography and resulted in tissue erosion. Histological examination of the atomized tissue showed whole and fragmented cells and nuclei. Air–liquid interfaces were also filmed. Our conclusion was that HIFU can fountain and atomize tissue. Although this process does not entirely mimic what was observed in liquids, it does explain many aspects of tissue fractionation in boiling histotripsy.

Surgery is moving more and more toward minimally-invasive procedures — using laparoscopic approaches with instruments inserted through tiny incisions or catheters placed in blood vessels through puncture sites. These techniques minimize the risks to the patient such as bleeding complications or infection during surgery. Taken a step further, high-intensity focused ultrasound (HIFU) can provide a tool to accomplish many of the same procedures without any incision at all. This article discusses the acoustics of histotripsy — including the processes of generation and focusing of intense ultrasound, the formation of cavitation clouds and rapid boiling in tissue, and the interactions of ultrasound shock waves with bubbles leading to tissue disintegration.

High intensity focused ultrasound (HIFU) is a rapidly growing medical technology with many clinical applications. The safety and efficacy of these applications require accurate characterization of ultrasound fields produced by HIFU systems. Current nonlinear numerical models based on the KZK and Westervelt wave equations have been shown to serve as quantitatively accurate tools for HIFU metrology. One of the critical parts of the modeling is to set a boundary condition at the source. In previous studies we proposed using measurements of low-amplitude fields to determine the source parameters. In this paper, two approaches of setting the boundary condition are reviewed: The acoustic holography method utilizes two-dimensional scanning of pressure amplitude and phase and numerical back-propagation to the transducer surface. An equivalent source method utilizes one-dimensional pressure measurements on the beam axis and in the focal plane. The dimensions and surface velocity of a uniformly vibrating transducer then are determined to match the one-dimensional measurements in the focal region. Nonlinear simulations are performed for increasing pressure levels at the source for both approaches. Several examples showing the accuracy and capabilities of the proposed methods are presented for typical HIFU transducers with different geometries.

Acoustic fields of powerful ultrasound sources with Gaussian spatial apodization and initial excitation in the form of a periodic wave or single pulse are examined based on the numerical solution of the Khokhlov-Zabolotskaya-Kuznetsov equation. The influence of nonlinear effects on the spatial structure of focused beams, as well as on the limiting values of the acoustic field parameters is compared. It is demonstrated that pressure saturation in periodic fields is mainly due to the effect of nonlinear absorption at a shock front, while in pulsed fields is due to the effect of nonlinear refraction. The limiting attainable values for the peak positive pressure in periodic fields turned out to be higher than the analogous values in pulsed acoustic fields. The total energy in a beam of periodic waves decreases with the distance from the source faster than in the case of a pulsed field, but it becomes concentrated within much smaller spatial region in the vicinity of the focus. These special features of nonlinear effect manifestation provide an opportunity to use pulsed beams for more efficient delivery of wave energy to the focus and to use periodic beams for attaining higher values of pressure in the focal region.

In high intensity focused ultrasound (HIFU) applications, tissue may be thermally necrosed by heating, emulsified by cavitation, or, as was recently discovered, emulsified using repetitive millisecond boiling caused by shock wave heating. Here, this last approach was further investigated. Experiments were performed in transparent gels and ex vivo bovine heart tissue using 1, 2, and 3 MHz focused transducers and different pulsing schemes in which the pressure, duty factor, and pulse duration were varied. A previously developed derating procedure to determine in situ shock amplitudes and the time-to-boil was refined. Treatments were monitored using B-mode ultrasound. Both inertial cavitation and boiling were observed during exposures, but emulsification occurred only when shocks and boiling were present. Emulsified lesions without thermal denaturation were produced with shock amplitudes sufficient to induce boiling in less than 20 ms, duty factors of less than 0.02, and pulse lengths shorter than 30 ms. Higher duty factors or longer pulses produced varying degrees of thermal denaturation combined with mechanical emulsification. Larger lesions were obtained using lower ultrasound frequencies. The results show that shock wave heating and millisecond boiling is an effective and reliable way to emulsify tissue while monitoring the treatment with ultrasound.

Histotripsy describes treatments in which high-amplitude acoustic pulses are used to excite bubbles and erode tissue. Though tissue erosion can be directly attributed to bubble activity, the genesis and dynamics of bubbles remain unclear. Histotripsy lesions that show no signs of thermal coagulative damage have been generated with two different acoustic protocols: relatively long acoustic pulses that produce local boiling within milliseconds and relatively short pulses that are higher in amplitude but likely do not produce boiling. While these two approaches are often distinguished as 'boiling' versus 'cavitation', such labels can obscure similarities. In both cases, a bubble undergoes large changes in radius and vapor is transported into and out of the bubble as it oscillates. Moreover, observations from both approaches suggest that bubbles grow to a size at which they cease to collapse violently. In order to better understand the dynamics of histotripsy bubbles, a single-bubble model has been developed that couples acoustically excited bubble motions to the thermodynamic state of the surrounding liquid. Using this model for bubbles exposed to histotripsy sound fields, simulations suggest that two mechanisms can act separately or in concert to lead to the typically observed bubble growth. First, nonlinear acoustic propagation leads to the evolution of shocks and an asymmetry in the positive and negative pressures that drive bubble motion. This asymmetry can have a rectifying effect on bubble oscillations whereby the bubble grows on average during each acoustic cycle. Second, vapor transport to/from the bubble tends to produce larger bubbles, especially at elevated temperatures. Vapor transport by itself can lead to rectified bubble growth when the ambient temperature exceeds 100C ('boiling') or local heating in the vicinity of the bubble leads to a superheated boundary layer.

A novel numerical model was developed to simulate three-dimensional nonlinear fields generated by high intensity focused ultrasound (HIFU) arrays. The model is based on the solution to the Westervelt equation; the developed algorithm makes it possible to model nonlinear pressure fields of periodic waves in the presence of shock fronts localized near the focus. The role of nonlinear effects in a focused beam of a two-dimensional array was investigated in a numerical experiment in water. The array consisting of 256 elements and intensity range on the array elements of up to 10 W/cm² was considered. The results of simulations have shown that for characteristic intensity outputs of modern HIFU arrays, nonlinear effects play an important role and shock fronts develop in the pressure waveforms at the focus.

High-intensity focused ultrasound (HIFU) is a rapidly developing technology that is becoming more widely used for non-invasive and minimally invasive ablation of benign and malignant tumors. In addition, recent studies suggest that unique mechanical effects of HIFU may help to enhance targeted drug delivery and stimulate an anti-tumor immune response in many tumors including pancreatic tumors. However, targeting of pancreatic tumors using an extracorporeal source is often not possible due to the lack of an adequate acoustic window because of the presence of overlying bowel gas. The development of an EUS-guided HIFU transducer has many potential benefits including improved targeting, decreased energy requirements and decreased potential for injury to intervening structures.

Recent studies in high intensity focused ultrasound (HIFU) have shown significant interest in generating purely mechanical damage of tissue without thermal coagulation. Here, an approach using millisecond bursts of ultrasound shock waves and repeated localized boiling is presented. In HIFU fields, nonlinear propagation effects lead to formation of shocks only in a small focal region. Significant enhancement of heating due to absorption at the shocks leads to boiling temperatures in tissue in milliseconds as calculated based on weak shock theory. The heated and potentially necrotized region of tissue is small compared to the volume occupied by the mm-sized boiling bubble it creates. If the HIFU pulse is only slightly longer than the time-to-boil, thermal injury is negligible compared to the mechanical injury caused by the exploding boiling bubble and its further interaction with shocks. Experiments performed in transparent gels and various ex vivo and in vivo tissues have confirmed the effectiveness of this emulsification method. In addition, since mm-sized boiling bubbles are highly echogenic, tissue emulsification can be easily monitored in real-time using B-mode ultrasound imaging.

Metrology of high intensity focused ultrasound (HIFU) is critical to the advancement of clinical application of HIFU for safe and effective treatments in patients. Several methods for performing metrology of HIFU systems are available in the research laboratory setting; however, translation of these methods to the clinical setting remains in evolution. From our initial experience with clinical HIFU systems we have realized the importance of accurate acoustic characterization of HIFU systems in order to determine the parameters of the treatment protocol to result in safe and effective treatments. The acoustic parameters of the system, particularly at very high intensities, are very important to understand prior to delivering HIFU therapy to patients. Improved methods of HIFU metrology, especially to determine in situ exposure and dose, will result in a more rational approach to clinical HIFU therapy. Further advances in clinical HIFU therapy will require close cooperation between clinicians and scientists in order to make HIFU therapy safe and effective. Educating clinicians on the importance of metrology will also be important.

Numerical modeling has been shown to be an effective tool to characterize nonlinear pressure fields for single-element HIFU transducers, but it has not yet been applied for the much more complex three-dimensional (3-D) fields generated by therapeutic phased arrays. In this work, two approaches are presented to simulate nonlinear effects in the field of a 256-element focused array. A new full-diffraction approach includes rigorous 3-D simulations of the nonlinear wave equation with a boundary condition given at the elements of the array. A second simpler approach is based on the KZK model and a focused piston source as the boundary condition. The effective aperture and initial pressure of the piston source are set by matching linear simulations of the two models in the focal region. It is shown that as output power is increased, agreement in the focal waveforms of the two simulations, even when shocks were present, is maintained up to very high power outputs of the array. These results demonstrate the feasibility of using the simplified KZK model to evaluate the role of nonlinear effects in the fields of two-dimensional (2-D) phased arrays of clinical devices.

As recently shown, shock wave heating and millisecond boiling can be used to obtain mechanical emulsification of tissue with or without evident thermal damage, which can be controlled by varying the parameters of the high intensity focused ultrasound exposure. The goal of this work was to examine these bioeffects using histological and biochemical analysis. Lesions were created in ex vivo bovine heart and liver using a 2-MHz transducer and pulsing scheme with 71 MPa in situ shock amplitude, 0.01 duty factor, and 5-500 ms pulse duration. Mechanical tissue damage and viability of cells in the lesions were evaluated histologically using conventional staining techniques (H&E and NADH-diaphorase). Thermal effects were quantified by measuring denaturation of salt soluble proteins in the treated area and confirmed by histology. By visual observation, the liquefied lesions obtained with shorter pulses (< 15 ms) did not show any thermal damage that correlated well with the results of both histology and protein analysis. Increasing the pulse duration resulted in an increase in thermal damage; both protein analysis and NADH-diaphorase staining showed denaturation that was visually observed as whitening of the lesion content.

Clinical therapeutic ultrasound systems rely on the delivery of known acoustic pressures to treatment sites. Assessing the safety and efficacy of these systems relies upon characterization of ultrasound sources in order to determine the acoustic fields they produce and to understand performance changes over time. While direct hydrophone measurements of intense acoustic fields are possible, data acquisition throughout a treatment volume can be time-consuming and is only applicable to the specific source conditions tested. Moreover, measuring intense acoustic fields poses challenges for the hydrophone. An alternate approach combines low-amplitude pressure measurements with modeling of the nonlinear pressure field at various transducer power levels. In this work, low-intensity measurements were acquired for several therapeutic transducers. Pressure amplitude and phase were measured on a plane near the test transducer; the Rayleigh integral was used to back-propagate the acoustic field and mathematically reconstruct relative vibrations of the transducer surface. Such holographic reconstructions identified the vibratory characteristics of different types of transducers, including a 256-element clinical array. These reconstructions can be used to define boundary conditions for modeling and to record characteristics of transducer performance.

Shock-wave heating and millisecond boiling in high intensity focused ultrasound fields have been shown to result in mechanical emulsification of ex-vivo tissue. In this work, the same in situ exposures were applied in vivo in pig liver and in mice bearing 5-7 mm subcutaneous tumors (B16 melanoma) on the hind limb. Lesions were produced using a 2-MHz annular array in the case of pig liver (shock amplitudes up to 98 MPa) and a 3.4-MHz single-element transducer in the case of mouse tumors (shock amplitude of 67 MPa). The parameters of the pulsing protocol (1-500 ms pulse durations and 0.01-0.1 duty factor) were varied depending on the extent of desired thermal effect. All exposures were monitored using B-mode ultrasound. Mechanical and thermal tissue damage in the lesions was evaluated histologically using H&E and NADH-diphorase staining. The size and shape of emulsified lesions obtained in-vivo agreed well with those obtained in ex-vivo tissue samples using the same exposure parameters. The lesions were successfully produced both in bulk liver tissue at depths of 1-2 cm and in superficial tumors at depths less than 1 mm without damaging the skin.

Feasibility of soft tissue emulsification using shock wave heating and millisecond boiling induced by high intensity focused ultrasound was demonstrated recently. However, the mechanism by which the bubbles emulsify tissue is not well understood. High-speed photography of such exposures in transparent gel phantoms shows a milimeter-sized boiling bubble, and histological analysis in tissue samples reveals sub-micron-sized fragments. Here, a novel mechanism of tissue emulsification by the formation of a miniature acoustic fountain within the boiling bubble is tested experimentally using a 2 MHz transducer generating up to 70 MPa positive and 15 MPa negative peak pressures at the focus. The focus was positioned at or 1-2 mm off the plane interface between air and various materials including degassed water, transparent gel, thin sliced muscle tissue phantom, and ex-vivo tissue. Pulsing schemes with duty factors 0.001-0.1, and pulse durations 0.05-500 ms were used. Violent removal of micron-sized fragments and substantial displacement of the phantom surface were observed through high-speed filming. At the end of each exposure, the resulting erosion of the phantom surface and subsurface area was photographed and related to the exposure parameters.

Finite amplitude acoustic wave propagation through atmospheric turbulence is modeled using a Khokhlov-Zabolotskaya-Kuznetsov (KZK)-type equation. The equation accounts for the combined effects of nonlinearity, diffraction, absorption, and vectorial inhomogeneities of the medium. A numerical algorithm is developed which uses a shock capturing scheme to reduce the number of temporal grid points. The inhomogeneous medium is modeled using random Fourier modes technique. Propagation of N-waves through the medium produces regions of focusing and defocusing that is consistent with geometrical ray theory. However, differences up to ten wavelengths are observed in the locations of fist foci. Nonlinear effects are shown to enhance local focusing, increase the maximum peak pressure (up to 60%), and decrease the shock rise time (about 30 times). Although the peak pressure increases and the rise time decreases in focal regions, statistical analysis across the entire wavefront at a distance 120 wavelengths from the source indicates that turbulence: decreases the mean time-of-flight by 15% of a pulse duration, decreases the mean peak pressure by 6%, and increases the mean rise time by almost 100%. The peak pressure and the arrival time are primarily governed by large scale inhomogeneities, while the rise time is also sensitive to small scales.

When an intense ultrasound beam is directed at a free surface of a liquid, an acoustic fountain is produced that is typically accompanied by ejection of tiny droplets, i.e., liquid atomization. This phenomenon is usually attributed to instability of cavitation-produced capillary waves on the surface. In addition to capillary effects, a process called spallation may also contribute. Although the acoustic fountain is typically observed at a flat liquid surface, nothing prohibits the atomization from occurring at a curved surface. This brings about the possibility to create an acoustic fountain and droplet emission at the surface of a gas cavity in liquid or, similarly, in the bulk of soft biological tissue. The appropriate condition occurs when high-intensity ultrasound is focused in tissue and creates large (0.1 - 1 mm in diameter) bubbles due to acoustic cavitation or rapid boiling. To test this hypothesis, acoustic pressure distribution and the corresponding radiation force on the empty spherical cavity were calculated using finite difference modeling and spherical harmonic expansion. It is shown that in histotripsy regimes appropriate conditions appear for the atomization, which may be considered as a possible mechanism of tissue erosion.

The propagation of nonlinear spherically diverging N-waves in homogeneous air is studied experimentally and theoretically. A spark source is used to generate high amplitude (1.4 kPa) short duration (40 microseconds) N-waves; acoustic measurements are performed using microphones (3 mm diameter, 150 kHz bandwidth). Numerical modeling with the generalized Burgers equation is used to reveal the relative effects of acoustic nonlinearity, thermoviscous absorption, and oxygen and nitrogen relaxation on the wave propagation.

The results of modeling are in a good agreement with the measurements in respect to the wave amplitude and duration. However, the measured rise time of the front shock is ten times longer than the calculated one, which is attributed to the limited bandwidth of the microphone. To better resolve the shock thickness, a focused shadowgraphy technique is used. The recorded optical shadowgrams are compared with shadow patterns predicted by geometrical optics and scalar diffraction model of light propagation. It is shown that the geometrical optics approximation results in overestimation of the shock rise time, while the diffraction model allows to correctly resolve the shock width. A combination of microphone measurements and focused optical shadowgraphy is therefore a reliable way of studying evolution of spark-generated shock waves in air.

The field of spectral components of a focused finite-amplitude ultrasound beam in water behind the layer that introduces a constant shift randomly distributed over its plane is studied experimentally and numerically. Based on the focal field distributions obtained and the criterion proposed, the degree of maintenance of the focusing condition for the first six harmonics of the beam radiated at 1.1 MHz is evaluated. Several layer positions at a distance from the radiator are considered. It is shown that focusing of the higher-order harmonics may be less subjected to destruction by the phase layer than that of the wave at the fundamental frequency. The theory and experiment are compared for the 90 deg and 180 deg phase layers. For the latter case, selective destruction of focusing of the odd harmonics is demonstrated.

A method for focusing high-intensity ultrasound (HIFU) through a rib cage that aims to minimize heating of the ribs while maintaining high intensities at the focus (or foci) was proposed and tested theoretically and experimentally. Two approaches, one based on geometric acoustics and the other accounting for diffraction effects associated with propagation through the rib cage, were investigated theoretically for idealized source conditions. It is shown that for an idealized radiator, the diffraction approach provides a 23% gain in peak intensity and results in significantly less power losses on the ribs (1% vs. 7.5% of the irradiated power) compared with the geometric one.

A 2-D 1-MHz phased array with 254 randomly distributed elements, tissue-mimicking phantoms and samples of porcine rib cages are used in experiments; the geometric approach is used to configure how the array is driven. Intensity distributions are measured in the plane of the ribs and in the focal plane using an infrared camera. Theoretical and experimental results show that it is possible to provide adequate focusing through the ribs without overheating them for a single focus and several foci, including steering at plus/minus 10–15 mm off and plus/minus 20 mm along the array axis. Focus splitting caused by the periodic spatial structure of ribs is demonstrated both in simulations and experiments; the parameters of splitting are quantified. The ability to produce thermal lesions with a split focal pattern in ex vivo porcine tissue placed beyond the rib phantom is also demonstrated. The results suggest that the method is potentially useful for clinical applications of HIFU, for which the rib cage lies between the transducer(s) and the targeted tissue.

Propagation of high amplitude N-wave behind a random phase screen is modeled based on the Khokhlov-Zabolotskaya-Kuznetsov equation. One-dimensional random phase screens with Gaussian power spectrum density are considered. The effects of nonlinear propagation, random focusing, and diffraction on the statistical properties of the acoustic field behind the screen, including propagation through caustics and beyond caustics, are analyzed. Statistical distributions and mean values of the acoustic field parameters obtained within the developed diffraction model and using nonlinear geometrical acoustics approach are compared.

Nonlinear propagation effects result in the formation of weak shocks in high intensity focused ultrasound (HIFU) fields. When shocks are present, the wave spectrum consists of hundreds of harmonics. In practice, shock waves are modeled using a finite number of harmonics and measured with hydrophones that have limited bandwidths.

The goal of this work was to determine how many harmonics are necessary to model or measure peak pressures, intensity, and heat deposition rates of the HIFU fields. Numerical solutions of the Khokhlov-Zabolotskaya-Kuznetzov-type (KZK) nonlinear parabolic equation were obtained using two independent algorithms, compared, and analyzed for nonlinear propagation in water, in gel phantom, and in tissue. Measurements were performed in the focus of the HIFU field in the same media using fiber optic probe hydrophones of various bandwidths. Experimental data were compared to the simulation results.

The goal of the work was to demonstrate feasibility of HIFU tissue ablation through the rib cage using a high power 2D random phased array. A method to minimize heating ribs while maintaining high intensities at the focus of the array was proposed and tested theoretically and experimentally. A 2D 1-MHz phased array with 254 randomly distributed elements and a phantom of porcine rib cage were used in experiments. Intensity distributions were measured in the plane of the rib phantom and in the focal plane of the array using an infra-red camera. Theoretical and experimental results show that if the position and the shape of ribs are known it is possible to provide adequate focusing through the ribs without overheating them for a single focus, including steering at plus/minus 10–15 mm off and plus/minus 20 mm along the array axis. The results suggest that the method is potentially useful for clinical applications of HIFU for which the rib cage lies between the transducer and the targeted tissue.

A wide variety of treatment protocols have been employed in high intensity focused ultrasound (HIFU) treatments, and the resulting bioeffects observed include both mechanical as well as thermal effects. In recent studies, there has been significant interest in generating purely mechanical damage using protocols with short, microsecond pulses. Tissue erosion effects have been attained by operating HIFU sources using short pulses of 10–20 cycles, low duty cycles (<1%), and pulse average intensities of greater than 20 kW/cm².

The goal of this work was to use a modified pulsing protocol, consisting of longer, millisecond-long pulses of ultrasound and to demonstrate that heating and rapid millisecond boiling from shock wave formation can be harnessed to induce controlled mechanical destruction of soft tissue. Experiments were performed in excised bovine liver and heart tissue using a 2-MHz transducer. Boiling activity was monitored during exposures using a high voltage probe in parallel with the HIFU source. In situ acoustic fields and heating rates were determined for exposures using a novel derating approach for nonlinear HIFU fields. Several different exposure protocols were used and included varying the duty cycle, pulse length, and power to the source. After exposures, the tissue was sectioned, and the gross lesion morphology was observed. Different types of lesions were induced in experiments that ranged from purely thermal to purely mechanical depending on the pulsing protocol used. Therefore, shock wave heating and millisecond boiling may be an effective method for reliably generating significant tissue erosion effects.

Numerical simulations based on the Khokhlov–Zabolotskaya-type equation are currently used to characterize therapeutic high-intensity focused ultrasound fields in water and to predict bioeffects in tissue. Here results from three different algorithms that differ in calculating the nonlinear term in the equation are presented. Shock capturing schemes of Godunov type, exact implicit solution with further extrapolation of the waveform over a uniform temporal grid, and direct modeling in the frequency domain are tested. In the case of weak nonlinearity, all schemes give essentially the same solution. However, at high peak pressures around 50 MPa and strong shocks developed in the focal region, the predictions of acoustic variables and heat deposition become sensitive to the algorithm employed. The parameters of the schemes, such as number of harmonics or temporal samples and the inclusion of artificial absorption that provides consistent results, are discussed. It is shown that the spectral and Godunov-type approaches require about 6 points and implicit time domain approach needs more than 50 points in the shock to be accurate. In all schemes artificial absorption should be employed to obtain acceptable accuracy with fewer points per cycle.

The high-amplitude shock wave generated by a supersonic aircraft propagates through the atmosphere toward the ground and generates an acoustic field with non-uniform pressure distributions strongly influenced by atmospheric turbulence. Recent numerical simulations based on generalized KZK-type equation including the effects of moving inhomogeneous media will be discussed. Formation of multiple focusing and defocusing zones is predicted. Nonlinear effects are significant not only in the random focusing zones but also in shadow zones of lower-pressure levels due to scattering of high frequencies from the areas of focusing.

A statistical analysis is performed, and the results are compared to experimental data obtained in the controlled laboratory scale experiments conducted in the ECL anechoic wind tunnel. A high-power spark source is used to generate N-waves. Correlation length scales and spectra of the turbulent velocity field are measured. Statistical distributions and mean values for peak positive pressure and shock arrival time are obtained and found to be in a good agreement with modeling. In focusing areas, waveforms with amplitudes more than four times higher than those measured without turbulence are observed. Pressure amplitude probability density distributions are shown to possess autosimilarity properties when changing the intensity of turbulence.

High-intensity focused ultrasound (HIFU) transducers can be operated at high-pressure amplitudes of greater than 60 MPa and low-duty cycles of 1% or less to induce controlled bubble activity that fractionates tissue. The goal of this work was to investigate fractionation not from mechanically induced cavitation but from thermally induced boiling created by HIFU shock waves. Experiments were performed using a 2-MHz HIFU source. The focus was placed in ex vivo bovine heart and liver samples. Cavitation and boiling were monitored during exposures using a high-voltage probe in parallel with the HIFU source and with an ultrasound imaging system. Various exposure protocols were performed in which the time-averaged intensity and total energy delivered were maintained constant. The types of lesions induced in tissue ranged from purely thermal to purely mechanical depending on the pulsing protocol used. A pulsing protocol in which the pulse length was on the order of the time to boil (of only several milliseconds) and duty cycle was low (<1%) was found to be a highly repeatable method for inducing mechanical effects with little evidence of thermal damage, as confirmed by histology.

Nonlinear propagation causes high-intensity ultrasound waves to distort and generate higher harmonics, which are more readily absorbed and converted to heat than the fundamental frequency. Although such nonlinear effects have been investigated previously and found to not significantly alter high-intensity focused ultrasound (HIFU) treatments, two results reported here change this paradigm. One is that at clinically relevant intensity levels, HIFU waves not only become distorted but form shock waves in tissue. The other is that the generated shock waves heat the tissue to boiling in much less time than predicted for undistorted or weakly distorted waves.

In this study, a 2-MHz HIFU source operating at peak intensities up to 25,000 W/cm² was used to heat transparent tissue-mimicking phantoms and ex vivo bovine liver samples. Initiation of boiling was detected using high-speed photography, a 20-MHz passive cavitation detector and fluctuation of the drive voltage at the HIFU source. The time to boil obtained experimentally was used to quantify heating rates and was compared with calculations using weak shock theory and the shock amplitudes obtained from nonlinear modeling and measurements with a fiber optic hydrophone. As observed experimentally and predicted by calculations, shocked focal waveforms produced boiling in as little as 3 ms and the time to initiate boiling was sensitive to small changes in HIFU output. Nonlinear heating as a result of shock waves is therefore important to HIFU, and clinicians should be aware of the potential for very rapid boiling because it alters treatments.

Current methods of determining high intensity focused ultrasound (HIFU) fields in tissue rely on extrapolation of measurements in water assuming linear wave propagation both in water and in tissue. Neglecting nonlinear propagation effects in the derating process can result in significant errors. In this work, a new method based on scaling the source amplitude is introduced to estimate focal parameters of nonlinear HIFU fields in tissue. Focal values of acoustic field parameters in absorptive tissue are obtained from a numerical solution to a KZK-type equation and are compared to those simulated for propagation in water. Focal waveforms, peak pressures, and intensities are calculated over a wide range of source outputs and linear focusing gains. Our modeling indicates, that for the high gain sources which are typically used in therapeutic medical applications, the focal field parameters derated with our method agree well with numerical simulation in tissue. The feasibility of the derating method is demonstrated experimentally in excised bovine liver tissue.

The effect of focus splitting after propagation of focused ultrasound through a rib cage is investigated theoretically. It is shown that the mechanism of this effect is caused by the interference of waves from two or more spatially separated sources, such as intercostal spaces. Analytical estimates of the parameters of splitting are obtained, i.e., the number of foci, their amplitudes, diameter, and the distance between them, depending on the transducer parameters, as well as the dimensions of the rib cage and position of ribs relative to the radiator. Various configurations of the relative positioning of ribs and radiator are considered; it is shown which of them are the most effective for real surgical operations.

Derivation of the Khokhlov-Zabolotskaya (KZ) equation provided a new approach to describing the combined effects of nonlinear propagation and diffraction in sound beams. In this paper, historical aspects of the KZ equation and its generalizations are presented. The interest in nonlinear acoustic beams of Academician Khokhlov and his colleagues at Moscow State University was inspired in the 1960s by emerging developments in laser physics and the corresponding models of nonlinear optical beams. The two cases, acoustical and optical, represent two limiting cases of nonlinear beams in weakly and strongly dispersive media, respectively, which required different theoretical approaches. The KZ equation and analogous nonlinear evolution equations of nonlinear wave physics are reviewed.

It is illustrated how theoretical studies combined with numerical modeling resulted in predictions of new physical phenomena in nonlinear acoustic beams. Concurrently, newer applications of nonlinear acoustics such as parametric arrays, sonic booms, and medical acoustics stimulated the derivation of generalized KZ-type equations together with analytical and numerical methods to solve them. Modern applications and corresponding generalized KZ-type models that include effects such as frequency-dependent absorption, weak dispersion, scalar and vectorial inhomogeneities of the propagation medium, different orders of nonlinearity, and more accurate description of diffraction are presented.

Extensive theoretical analysis, numerical studies, and both large-scale and laboratory-scale experiments have been dedicated to the problem of shock wave propagation in air during recent years. The current interest is motivated by supersonic civil transport which is necessarily affected by problems of sonic boom propagation in the atmosphere. The high-amplitude shock wave generated by a supersonic aircraft propagates through the atmosphere toward the ground and generates an acoustic field with non-uniform pressure distribution. Temporal characteristics and spatial structure of the sonic boom are influenced by aircraft trajectory, nonlinear effects, and diffraction and scattering by inhomogeneities. We review recent results from various teams based on a generalized KZK-type equation that includes the effects of a moving inhomogeneous media. Statistical analysis of the numerical solutions is performed, and the results are compared to experimental data obtained in the controlled laboratory-scale experiments conducted in the Ecole Centrale de Lyon anechoic wind tunnel.

High intensity focused ultrasound (HIFU) therapy is an emerging medical technology in which acoustic pressure amplitudes of up to 100 MPa are used to induce tissue ablation, often in combination with real-time imaging. The ultrasound energy is typically focused into a millimeter-size volume and used to thermally coagulate the tissue of interest while ideally sparing surrounding tissue. Nonlinear effects are important in HIFU as in situ intensities for clinical applications of up to 30 000 W/cm² have been reported. Since controlled experiments are often difficult to perform, especially in vivo, modeling can aid in understanding the physical phenomena involved in HIFU-induced tissue ablation. The Khokhlov-Zabolotskaya-Kuznetsov (KZK) equation is applicable to HIFU because it includes all of the basic physical phenomena that are relevant to HIFU including acoustic beams, diffraction, focusing, nonlinear propagation, shock formation, and dissipation. In this paper, an overview of several recent advances in KZK modeling for HIFU applications are described. It is shown that shock-induced heating in tissue can cause localized boiling in milliseconds; furthermore, the bubbles associated with boiling can significantly alter HIFU treatments.

In this work, a new derating method to extrapolate nonlinear ultrasound fields in water to biological tissue is proposed and tested for therapeutic medical systems. Focal values of acoustic field parameters in absorptive tissue are obtained from a numerical solution to a KZK-type equation and are compared to those derated, using the proposed method, from the results of simulations in water. It is validated in modeling that for high gain sources, which are typically used for therapeutic medical applications, the focal field parameters in tissue can be obtained from the results obtained in water. The feasibility of the derating method is also demonstrated experimentally in water and excised bovine liver tissue using a 2 MHz HIFU source of 44 mm aperture and focal length.

Both mechanically induced acoustic cavitation and thermally induced boiling can occur during high intensity focused ultrasound (HIFU) medical therapy. The goal was to monitor the temperature as boiling was approached using magnetic resonance imaging (MRI). Tissue phantoms were heated for 20 s in a 4.7-T magnet using a 2-MHz HIFU source with an aperture and radius of curvature of 44 mm. The peak focal pressure was 27.5 MPa with corresponding beam width of 0.5 mm. The temperature measured in a single MRI voxel by water proton resonance frequency shift attained a maximum value of only 73 degrees C after 7 s of continuous HIFU exposure when boiling started. Boiling was detected by visual observation, by appearance on the MR images, and by a marked change in the HIFU source power. Nonlinear modeling of the acoustic field combined with a heat transfer equation predicted 100 degrees C after 7 s of exposure. Averaging of the calculated temperature field over the volume of the MRI voxel (0.3 x 0.5 x 2 mm(3)) yielded a maximum of 73 degrees C that agreed with the MR thermometry measurement. These results have implications for the use of MRI-determined temperature values to guide treatments with clinical HIFU systems.

Ultrasonic field mapping is an essential component of transducer characterization and of beam forming verification. Such measurements are commonly performed by displacing a hydrophone over a range of points within the field; these procedures can be time consuming. A calibrated hydrophone can provide accurate measurements of the field, subject to limitations of bandwidth and aperture of the device. A rapid qualitative 2D measurement of the spatial acoustic field can be obtained by optical means, in which the change in optical index due to the presence of acoustic pressure is imaged using a Schlieren approach.

This technique illuminates a transparent refracting acoustic medium using a plane collimated source and then focuses the transmitted light using a lens or mirror. In the absence of acoustic field, all of the light focuses to a small spot; acoustically induced refractive index perturbations cause some of the light to focus elsewhere. Obscuring the primary focal spot of unperturbed light with a mask permits imaging only the perturbations in the acoustic medium. We will describe a mirror-based Schlieren system for imaging continuous as well as pulsed fields and with color corresponding qualitatively to the intensity of the field.

The accurate measurement of pressure waveforms in high intensity focused ultrasound (HIFU) fields is complicated by the fact that many devices operate at output levels where shock waves can form in the focal region. In tissue ablation applications, the accurate measurement of the shock amplitude is important for predicting tissue heating since the absorption at the shock is proportional to the shock amplitude cubed. To accurately measure shocked pressure waveforms, not only must a hydrophone with a broad bandwidth (>100 MHz) be used, but the frequency response of the hydrophone must be known and used to correct the measured waveform.

In this work, shocked pressure waveforms were measured using a fiber optic hydrophone and a frequency response for the hydrophone was determined by comparing measurements with numerical modeling using a KZK-type equation. The impulse response was separately determined by comparing a measured and an idealized shock pulse generated by an electromagnetic lithotripter. The frequency responses determined by the two methods were in good agreement. Calculations of heating using measured HIFU waveforms that had been deconvolved with the determined frequency response agreed well with measurements in tissue phantom.

Both mechanically induced acoustic cavitation and thermally induced boiling can occur during high intensity focused ultrasound (HIFU) medical therapy. The goal was to monitor the temperature as boiling was approached using magnetic resonance imaging (MRI). Tissue phantoms were heated for 20 s in a 4.7-T magnet using a 2-MHz HIFU source with an aperture and radius of curvature of 44 mm. The peak focal pressure was 27.5 MPa with corresponding beam width of 0.5 mm.

The temperature measured in a single MRI voxel by water proton resonance frequency shift attained a maximum value of only 73 degrees C after 7 s of continuous HIFU exposure when boiling started. Boiling was detected by visual observation, by appearance on the MR images, and by a marked change in the HIFU source power. Nonlinear modeling of the acoustic field combined with a heat transfer equation predicted 100 degrees C after 7 s of exposure. Averaging of the calculated temperature field over the volume of the MRI voxel (0.3 x 0.5 x 2 mm(3)) yielded a maximum of 73 degrees C that agreed with the MR thermometry measurement. These results have implications for the use of MRI-determined temperature values to guide treatments with clinical HIFU systems.

The influence of nonlinear and diffraction effects on distortion of the spatial structure of peak positive and negative pressures in focused acoustic beams was studied for a weakly dissipative propagation medium. The problem was solved numerically based on the Khokhlov-Zabolotskaya-Kuznetsov equation for beams with uniform and Gaussian distributions of the harmonic signal amplitude at the source.

Acoustic characterization of high intensity focused ultrasound (HIFU) fields is important both for the accurate prediction of ultrasound induced bioeffects in tissues and for the development of regulatory standards for clinical HIFU devices. In this paper, a method to determine HIFU field parameters at and around the focus is proposed. Nonlinear pressure waveforms were measured and modeled in water and in a tissue-mimicking gel phantom for a 2 MHz transducer with an aperture and focal length of 4.4 cm. Measurements were performed with a fiber optic probe hydrophone at intensity levels up to 24000 W/cm². The inputs to a Khokhlov–Zabolotskaya–Kuznetsov-type numerical model were determined based on experimental low amplitude beam plots. Strongly asymmetric waveforms with peak positive pressures up to 80 MPa and peak negative pressures up to 15 MPa were obtained both numerically and experimentally. Numerical simulations and experimental measurements agreed well; however, when steep shocks were present in the waveform at focal intensity levels higher than 6000 W/cm², lower values of the peak positive pressure were observed in the measured waveforms. This underrepresentation was attributed mainly to the limited hydrophone bandwidth of 100 MHz. It is shown that a combination of measurements and modeling is necessary to enable accurate characterization of HIFU fields.

In extracorporeal electrohydraulic lithotripters, a hemi-ellipsoidal metal reflector is used to focus a spherical wave generated by an electrical discharge. The spark source is positioned at one of the ellipsoid foci (F1); this makes the reflected wave focused at the other focus (F2). Despite the common assumption that the reflector behaves as a rigid mirror, the true reflection phenomenon includes the generation and reverberation of elastic waves in the reflector, which reradiate to the medium. Although these waves are much lower in amplitude than the specularly reflected wave, they may influence cavitation at F2. To explore such effects, waves in water and a brass reflector were modeled in finite differences based on the linearized equations of elasticity. The bubble response was simulated based on a Rayleigh-type equation for the bubble radius. In addition, the role of acoustic nonlinearity was estimated by numerical modeling. It is shown that the elastic waves in the reflector give rise to a long "ringing" tail, which results in nonmonotonic behavior of the bubble radius during its inertial growth after shock wave passage. This numerical result is qualitatively confirmed by experimental observations of bubble behavior using high-speed photography.

A current topic of interest for high intensity focused ultrasound (HIFU) treatments involves the relative roles of bubbles and nonlinear acoustic propagation as heating mechanisms. At high amplitudes, nonlinear propagation leads to the generation of boiling bubbles within milliseconds; at lower amplitudes, cavitation bubbles can enhance heating through viscous dissipation, acoustic radiation, and heat conduction. In this context, understanding the physics attendant to HIFU bubbles requires consideration of gas–vapor bubble dynamics, including thermal effects in the nearby liquid. To this end, recent experimental observations with high-speed photography suggest that bubbles undergo a brief period of growth after application of HIFU has stopped. To explain this observation, a model is implemented that couples the thermodynamic state of a strongly driven bubble with thermal conditions in the surrounding liquid. From model simulations, liquid heating in the vicinity of a HIFU bubble is estimated. Calculations suggest that thermal conduction and viscous dissipation can lead to the evolution of a nontrivial thermal boundary layer. Development of a boundary layer that reaches superheated temperatures would explain the aforementioned experimental observation. As such, cavitation bubbles and boiling bubbles share important characteristics during HIFU.

Extensive outdoor and laboratory-scale experiments on sonic boom propagation in turbulent atmosphere have shown that shock wave amplitude and rise time are important parameters responsible for sonic boom annoyance. However, accurate measurement of the shock front structure with standard microphone remains a challenge due to the broadband spectrum of the N-wave shock front. In this work the experimental setup utilizing a spark source has been designed and built to investigate nonlinear N-wave propagation in homogeneous medium. Short duration (30µs) and high amplitude (1 kPa) spherically divergent N-waves were generated. In addition to acoustic measurements with 1/8" B&K microphones, the shadowgraphy method using short duration flash lamp (20 ns) and CCD camera was employed to assess the shock front structure at different distances from the spark. It is shown that the shock rise time measured by the shadowgraphy method was in a good agreement with the theoretical predictions and it was 10 times shorter than in microphone measurements. The widening of the shock in acoustic measurements was therefore due to the limited bandwidth of the microphone. The combination of modeling, acoustic and optical measurements provided an accurate calibration of the shock wave measuring system.

The characterization of high intensity focused ultrasound (HIFU) fields is important for both clinical treatment planning as well as for regulation of HIFU medical devices. In previous work, we have used a 100-µm fiber optic probe hydrophone (FOPH) to measure pressure waveforms from a 2-MHz HIFU source with 42-mm aperture and 44-mm focal length. The formation of shock waves with peak positive pressure of up to 80 MPa were measured and modeled in transparent tissue-mimicking gel phantoms and boiling was achieved in milliseconds [Canney MS, et al., J. Acoust. Soc. Am., 120:3110 (2006)].

In this work, the FOPH was also used to measure temperature changes in tissue phantoms from HIFU at peak focal intensities of 5000–20,000 W cm². Temperature measurements were obtained by first low-pass filtering the voltage signal measured from the FOPH to remove the acoustic part of the measurement. Then, calibration of voltage to temperature was performed using results from a separate calibration experiment. Experimental measurements were compared with numerical modeling using a KZK-type model for acoustic propagation coupled with a heat transfer model. In summary, temperatures of 100°C were measured at the HIFU focus in milliseconds, in agreement with modeling.

Bubble activity in high intensity focused ultrasound (HIFU) medical therapy is commonly but not rigorously divided between mechanically induced cavitation (µ size gas bubbles) and thermally induced boiling (mm size vapor bubbles). Our goal was to confirm that boiling occurred at 100<th>°C. A 2 MHz focused transducer (42 mm aperture, 44 mm focal length) was used to heat tissue phantoms in a 4.7 Tesla magnet. Temperature was measured by magnetic resonance imaging (MRI) proton resonance frequency shift and calculated from acoustic absorption. The MRI voxel was 0.3x0.5x2 mm, and acquisition time was 1.3 s. Boiling was observed as a dark spot in MRI images and fluctuation in the transducer drive voltage. At 30 MPa peak pressure, boiling occurred in 7 s. Calculations yielded 100<th>^circC in 7 s and a temperature half maximum width of 1 mm. Averaging the calculated temperature field over the MRI voxel yielded a maximum of 73<th>^circC, which was the peak temperature measured in the last MRI slice before boiling. In conclusion, boiling appeared when the peak temperature reached 100<th>°C, and the results warn that MRI monitoring alone may underestimate the peak temperatures.

The goal of this work was to determine the acoustic waveform and beam width at the focus of a therapeutic ultrasound source both in water and in a tissue phantom. The source was a 2 MHz transducer of 45 mm focal length, 42 mm diameter, operating at 50 - 300 W acoustic power. Focal waveforms and beam widths calculated with a KZK-type model were in excellent agreement with values measured with a 100-µm, 100-MHz bandwidth fiber optic probe hydrophone (FOPH). Super focusing of the peak positive pressure and a proximal shift in the peak negative pressure were observed. Shocked distorted waveforms reached 70 MPa and - 15 MPa. Surface waves on the transducer were measured and included in the model but did not significantly affect the results obtained at focus. The change of the FOPH bandwidth to 30- MHz or the diameter of hydrophone to 500-µm resulted in 20% underestimation of the measured peak positive pressure but did not affect the measured negative peak pressure. Initiation of boiling was observed in tissue phantoms in milliseconds as predicted by weak shock theory due to absorption on the shocks. Work was supported by NIH DK43881, NSBRI SMS00402, and RFBR.

Nonlinear propagation effects during high-intensity focused ultrasound (HIFU) treatments can induce shocks in the acoustic waveform, dramatically accelerate heating rates, and result in rapid boiling of tissue at the focus. Localized boiling can be used for targeting and calibration of clinical HIFU treatments. In our previous work, millimeter size boiling bubbles were observed in several milliseconds in a weakly absorptive transparent tissue phantom, and temperature rise to 100<th>°C was calculated using weak shock theory from experimentally measured and numerically simulated focal waveforms. In this work, experiments are extended to an opaque phantom that has higher attenuation (0.5 dB/cm/MHz in the new phantom versus 0.15 dB/cm/MHz in the previous one) more similar to real tissue. Focal acoustic waveforms are measured using a fiber optic probe hydrophone and time to boil is monitored using a 20-MHz acoustic detector. Modeling of experimental conditions is performed with a KZK-type numerical model. Results demonstrate that although higher source amplitude is needed to attain the same focal amplitudes in the new, more attenuative phantom, similar amplitude shocks can be formed, resulting in equally fast heating rates.

Bubbles generated by acoustic cavitation or boiling are often observed during high intensity focused ultrasound (HIFU) medical treatments. In this work, high-speed video imaging, a 20-MHz focused acoustic transducer, and the driving voltage to our 2-MHz HIFU source are used to distinguish between cavitation and boiling in a tissue-mimicking gel phantom at peak focal intensities up to 30,000 W/cm². Bubble dynamics are modeled using a reduced order model that accounts for evaporation and condensation, heat and gas transfer across the interface, and temperature changes in the surrounding liquid. The model includes vapor trapping, whereby the noncondensable gas slows diffusion of vapor to the interface, thereby limiting condensation. At the transducer focus, evidence of cavitation is observed in the first millisecond before disappearing. Boiling is observed several milliseconds later, after sufficient heating of the focal volume to 100&$176;C. The disappearance of cavitation can be explained in part by the observed motion of bubbles away from the focal region due to radiation-pressure forces and in part by the softening of bubble collapses by vapor trapping. Thus, at clinical HIFU amplitudes, bubble dynamics and their impact on image-feedback and/or therapy change dramatically in only milliseconds.

A new parabolic equation is derived to describe the propagation of nonlinear sound waves in inhomogeneous moving media. The equation accounts for diffraction, nonlinearity, absorption, scalar inhomogeneities (density and sound speed), and vectorial inhomogeneities (flow). A numerical algorithm employed earlier to solve the KZK equation is adapted to this more general case. A two-dimensional version of the algorithm is used to investigate the propagation of nonlinear periodic waves in media with random inhomogeneities. For the case of scalar inhomogeneities, including the case of a flow parallel to the wave propagation direction, a complex acoustic field structure with multiple caustics is obtained. Inclusion of the transverse component of vectorial random inhomogeneities has little effect on the acoustic field. However, when a uniform transverse flow is present, the field structure is shifted without changing its morphology. The impact of nonlinearity is twofold: it produces strong shock waves in focal regions, while, outside the caustics, it produces higher harmonics without any shocks. When the intensity is averaged across the beam propagating through a random medium, it evolves similarly to the intensity of a plane nonlinear wave, indicating that the transverse redistribution of acoustic energy gives no considerable contribution to nonlinear absorption.

Nonlinear propagation effects leading to shock formation at the focus of hig-intensity focused ultrasound (HIFU) treatments can accelerate heating and cause rapid boiling in tissue. Boiling can be utilized for targeting the treatment with B-mode ultrasound and should be taken into account when planning the treatment, because bubbles reflect ultrasound and thereby displace and distort the lesion shape. In these experiments, an HIFU transducer of 2 MHz frequency, 4 cm aperture, and 4.5 cm focal length was used to investigate heating effects from shock formation in tissue-mimicking phantoms. The time required to attain 100<th>°C at the focus was calculated with weak shock theory from the peak amplitudes calculated with a KZK-type model, and time to boiling was measured by high-speed video and a 20-MHz passive cavitation detector (PCD) for different values of phantom absorption (both lower than tissue absorption) and HIFU power (100–200 W). Boiling was observed in 3 ms at the highest power level used by the observation of visible bubbles and by a significant change in the PCD time signal and spectrum.

Different peak and average acoustic parameters determine the efficiency of different physical mechanisms of high-intensity focused ultrasound (HIFU) interaction with biological tissue. Spatial distributions of these parameters are therefore important for transducer calibration and extrapolation of measurements in water to application in tissue. In the case of linear focusing, all parameters of the acoustic field can be obtained from the spatial distribution of the wave amplitude. However, in nonlinear focused beams, each parameter has its own characteristic spatial structure, which changes with the increase of the HIFU power level. This work compares the focal size and location calculated for the peak positive and peak negative pressure, mean intensity, and effective acoustic energy absorption in water and in tissue. Numerical solutions, obtained with the KZK-type model, are analyzed for various regimes of linear, quasilinear, and strongly nonlinear propagation which includes formation of shocks. The results of simulations are validated by comparison with measurements performed with a fiberoptic probe hydrophone in water and in a tissue mimicking phantom. The peak positive pressure and effective absorption are finely focused, whereas the negative pressure, responsible for cavitation, is broad and displaced towards the transducer.

Study of coagulative lesion formation by high intensity focused ultrasound (HIFU) in tissue usually requires performing a sequence of experiments under different exposure conditions followed by tissue sectioning. This paper, inspired by the pioneering work of Frederic L. Lizzi, reports on the use of the bovine eye lens as a laboratory model to observe visually the development of HIFU-induced lesions. The first part of this work describes the measurement of the lens shape, density, sound speed and attenuation. The measured values were within the range of previously published values. In the second part, HIFU-induced lesion development was observed in real-time and compared with good agreement with theoretical simulation. Theoretical modeling included acoustic propagation, absorptive heating and thermal dose, as well as the experimentally measured lens characteristics. Thus, the transparent eye lens can be used as a laboratory phantom to facilitate the understanding of HIFU treatment in other tissues.

The accurate characterization of high intensity focused ultrasound (HIFU) fields is important for the prediction of thermal and mechanical bio-effects in tissue, as well as for the development of standards for therapeutic systems. At HIFU intensity levels, the combined effects of nonlinearity and diffraction result in the formation of asymmetric shocked waveforms and a corresponding distortion of the spatial distributions of various acoustic parameters that are responsible for different bio-effects. Acoustic probes that are capable of withstanding high pressures and that can measure waveforms with a high spatial and temporal resolution are required to capture the shock fronts and highly localized field structures that can arise at therapeutically relevant treatment regimes. An experimentally validated numerical model can also be an effective tool when direct measurements are not possible. In this work, acoustic measurements using force balance, acoustic holography, broadband fiber optic and PVDF hydrophones, were combined with simulations based on a KZK-type model to demonstrate an effective approach for the calibration of HIFU transducers in water and for derating these results to tissue.

A numerical model for simulating nonlinear pulsed beams radiated by rectangular focused transducers, which are typical of diagnostic ultrasound systems, is presented. The model is based on a KZK-type nonlinear evolution equation generalized to an arbitrary frequency-dependent absorption. The method of fractional steps with an operator-splitting procedure is employed in the combined frequency-time domain algorithm. The diffraction is described using the implicit backward finite-difference scheme and the alternate direction implicit method. An analytic solution in the time domain is employed for the nonlinearity operator. The absorption and dispersion of the sound speed are also described using an analytic solution but in the frequency domain. Numerical solutions are obtained for the nonlinear acoustic field in a homogeneous tissue-like medium obeying a linear frequency law of absorption and in a thermoviscous fluid with a quadratic frequency law of absorption. The model is applied to study the spatial distributions of the fundamental and second harmonics for a typical diagnostic ultrasound source. The nonlinear distortion of pulses and their spectra due to the propagation in tissues are presented. A better understanding of nonlinear propagation in tissue may lead to improvements in nonlinear imaging and in specific tissue harmonic imaging.

The main objective of this study was to evaluate the feasibility of the optoacoustic (OA) technique for the monitoring of HIFU therapy. Optoacoustic phenomenon is the generation of wideband ultrasonic transients through absorption of laser radiation and subsequent expansion of the heated volume. The excited OA transient can be detected by a wideband piezo-electric transducer and contains information on the distribution of optical properties (absorption and scattering) within the medium. If thermal lesions have different optical properties than the untreated tissue, the lesions will be detectable on the OA waveform. We used boiled and raw porcine liver as phantoms mimicking treated and untreated tissue correspondingly. Optical attenuation, absorption and scattering coefficients of raw and boiled porcine liver were measured by the optoacoustic technique, previously developed by our group. Measured optical absorption in raw liver was at least two times lower than in boiled liver at the laser wavelength of 1064 nm. Then OA technique was employed to detect a lesion produced by a 1.1 MHz focused ultrasound in a liver sample. The lesion was about 2 mm thick located about 1 cm below tissue surface. The feasibility and high promise of the OA approach to lesion detection was demonstrated.

The importance of nonlinear acoustic wave propagation and ultrasound-induced cavitation in the acceleration of thermal lesion production by high intensity focused ultrasound was investigated experimentally and theoretically in a transparent protein-containing gel. A numerical model that accounted for nonlinear acoustic propagation was used to simulate experimental conditions. Various exposure regimes with equal total ultrasound energy but variable peak acoustic pressure were studied for single lesions and lesion stripes obtained by moving the transducer. Static overpressure was applied to suppress cavitation. Strong enhancement of lesion production was observed for high amplitude waves and was supported by modeling. Through overpressure experiments it was shown that both nonlinear propagation and cavitation mechanisms participate in accelerating lesion inception and growth. Using B-mode ultrasound, cavitation was observed at normal ambient pressure as weakly enhanced echogenicity in the focal region, but was not detected with overpressure. Formation of tadpole-shaped lesions, shifted toward the transducer, was always observed to be due to boiling. Boiling bubbles were visible in the gel and were evident as strongly echogenic regions in B-mode images. These experiments indicate that nonlinear propagation and cavitation accelerate heating, but no lesion displacement or distortion was observed in the absence of boiling.

Direct measurement of HIFU fields in situ is important for the accurate prediction of thermal and mechanical bioeffects, as well as for the development of standards for medical systems. An experimentally validated numerical model can be an effective tool in both laboratory and clinical settings when direct measurements are not possible. Calculations with a KZK-type model and measurements with a fiberoptic probe hydrophone were employed together to characterize HIFU fields in water and in a tissue-mimicking gel. To determine the boundary conditions for simulations, the normal velocity distribution on the transducer surface was reconstructed using acoustic holography and combined with acoustic power measurements. At the focus, highly nonlinear waveforms ( 700 and –150 bars peak pressures) were obtained both experimentally and numerically, which differed significantly from waveforms linearly extrapolated from low-amplitude results. Strongly distorted shock waveforms were localized in an axial region much smaller than the half-maximum beamwidth of the transducer excited at low level. At the highest excitation levels, the simulations predicted frequency content higher than was measurable in our configuration. Simulations also show that if these frequencies are not included, predicted heating rates are significantly lower.

The investigation of high-intensity focused ultrasound (HIFU) as a tool for noninvasive thermally ablative therapy has required deeper understanding of the relative roles of nonlinear mechanisms involved in heat deposition. Attempts at quantifying the dose response to particular exposure conditions in vitro are complicated by the interplay of several mechanisms. These include microbubble cavitation, nonlinear acoustic propagation and attenuation, dependence of tissue parameters on temperature and temperature history, and formation and evolution of vapor bubbles due to boiling. One immediately evident consequence of such effects is distortion of coagulative lesion shape and size, colloquially evolving from cigars to tadpoles. Developing a quantitative understanding of the relative roles of relevant nonlinear mechanisms is not straightforward, yet is desirable for design of algorithms for therapy planning and real-time monitoring using ultrasound. A historical perspective of research toward this end will be presented along with a recommendation for suitable terminology for the various physical acoustic regimes encountered in HIFU therapy.

Two major nonlinear mechanisms are known to influence HIFU heating: acoustic nonlinearity and cavitation. Heating may also result in formation of boiling vapor bubbles that grow much larger than the cavitation bubbles. The relevant role of these phenomena was investigated experimentally and numerically in a gel phantom. HIFU pressure thresholds for shock formation, cavitation, and boiling were measured using a fiber-optic probe hydrophone, passive cavitation detection, ultrasound and optical imaging, and thermocouples. The KZK and Bio-heat equations were employed to simulate experimental conditions. Elevated static pressure was applied to suppress bubbles and increase the boiling temperature, thus isolating the pure effect of acoustic nonlinearity in comparison of heating between short, high-amplitude and long, low-amplitude pulses of equal average intensity. The experimental results indicated that both nonlinear mechanisms accelerated lesion production with acoustic nonlinearity responsible for the greater effect. It was observed that lesion distortion and migration was due to boiling detected in as little as 40 ms within the center of the lesion, in agreement with nonlinear acoustic simulations. These data indicate that acoustic nonlinearity and the boiling play a significant role earlier in HIFU treatments than previously anticipated.

Ed Carstensen has made many contributions to biomedical ultrasound but among those that are becoming more and more relevant to current clinical practice are those that determine the conditions under which cavitation is induced in vivo. For many years, it was assumed that the medical ultrasound devices were unable to induce cavitation in living tissue because either the acoustic conditions were not sufficient or the nucleation sites that are required were too small. With the advent of lithotripters and high-intensity focused ultrasound (HIFU) devices, cavitation generation in vivo is commonplace. Our current research at the University of Washington has focused on the role that cavitation plays in stone comminution and tissue damage during lithotripsy, as well as the enhancement or reduction of desirable coagulative necrosis during HIFU application. During HIFU application, we find enhanced heating that results from nonlinear acoustic wave propagation (a key Carstensen contribution) leads to vapor bubble formation. This presentation will review our recent studies in this area.

The importance of nonlinear acoustic wave propagation and ultrasound-induced cavitation in the acceleration of thermal lesion production by high intensity focused ultrasound was investigated experimentally and theoretically in a transparent protein-containing gel. A numerical model that accounted for nonlinear acoustic propagation was used to simulate experimental conditions. Various exposure regimes with equal total ultrasound energy but variable peak acoustic pressure were studied for single lesions and lesion stripes obtained by moving the transducer. Static overpressure was applied to suppress cavitation. Strong enhancement of lesion production was observed for high amplitude waves and was supported by modeling. Through overpressure experiments it was shown that both nonlinear propagation and cavitation mechanisms participate in accelerating lesion inception and growth. Using B-mode ultrasound, cavitation was observed at normal ambient pressure as weakly enhanced echogenicity in the focal region, but was not detected with overpressure. Formation of tadpole-shaped lesions, shifted toward the transducer, was always observed to be due to boiling. Boiling bubbles were visible in the gel and were evident as strongly echogenic regions in B-mode images. These experiments indicate that nonlinear propagation and cavitation accelerate heating, but no lesion displacement or distortion was observed in the absence of boiling.

The importance of nonlinear acoustic wave propagation and ultrasound-induced cavitation in the acceleration of thermal lesion production by high intensity focused ultrasound was investigated experimentally and theoretically in a transparent protein-containing gel. A numerical model that accounted for nonlinear acoustic propagation was used to simulate experimental conditions. Various exposure regimes with equal total ultrasound energy but variable peak acoustic pressure were studied for single lesions and lesion stripes obtained by moving the transducer. Static overpressure was applied to suppress cavitation. Strong enhancement of lesion production was observed for high amplitude waves and was supported by modeling. Through overpressure experiments it was shown that both nonlinear propagation and cavitation mechanisms participate in accelerating lesion inception and growth. Using B-mode ultrasound, cavitation was observed at normal ambient pressure as weakly enhanced echogenicity in the focal region, but was not detected with overpressure. Formation of tadpole-shaped lesions, shifted toward the transducer, was always observed to be due to boiling. Boiling bubbles were visible in the gel and were evident as strongly echogenic regions in B-mode images. These experiments indicate that nonlinear propagation and cavitation accelerate heating, but no lesion displacement or distortion was observed in the absence of boiling.

The goal of this work was to compare measured and numerically predicted HIFU pressure waveforms in water and a tissue-mimicking phantom. Waveforms were measured at the focus of a 2-MHz HIFU transducer with a fiber optic hydrophone. The transducer was operated with acoustic powers ranging from 2W to 300W. A KZK-type equation was used for modeling the experimental conditions. Strongly asymmetric nonlinear waves with peak positive pressure up to 80 MPa and peak negative pressure up to 20 MPa were measured in water, while waves up to 50 MPa peak positive pressure and 15 MPa peak negative pressure were measured in tissue phantoms. The values of peak negative pressure corresponded well with numerical simulations and were significantly smaller than predicted by linear extrapolation from low-level measurements. The values of peak positive pressures differed only at high levels of excitation where bandwidth limitations of the hydrophone failed to fully capture the predicted sharp shock fronts.

The effects of nonlinear enhancement of focusing gain and saturation are studied and compared for high-intensity focused ultrasound sources with an initial Gaussian shading and uniform amplitude distribution. Simulations are performed using the Khokhlov Zabolotskaya (KZ) nonlinear parabolic equation for weakly dissipative medium in a wide range of source linear focusing gains and source pressure amplitudes, including the strongly nonlinear regime with shocks. An artificial absorption proportional to the fourth power of frequency or an asymptotic frequency-domain approach is employed in the algorithm in order to reduce the number of harmonics for accurate modeling of strongly distorted waveforms with shocks. The effect of focusing gain and amplitude shading of the source on nonlinear enhancement of acoustic energy concentration and saturation levels at the focus is discussed. It is shown that nonlinear enhancement of focusing gain is different for different values of linear gain, different spatial distributions of the source amplitude, and different parameters of acoustic field. The levels of nonlinear saturation at the focus are obtained for very high source amplitudes. The results of simulations give lower enhancement and higher saturation levels compared to the known approximate analytic predictions.

Numerical simulations of focused acoustic beams are performed in water over a wide range of linear gains and source amplitudes, in order to demonstrate the combined effect of acoustic nonlinearity, diffraction, and focusing on extrapolation (derating) of the main parameters of high intensity acoustic fields at the focus from the linear theory. It is shown that nonlinear corrections to the focusing gain are different for different parameters of the acoustic field and for different values of the linear gain. Nonlinear enhancement of the focusing gain is found to be more pronounced for the peak positive pressure and for higher linear gains. The levels of nonlinear saturation for various parameters of the field at the focus are obtained for very high source amplitudes. The results of simulations give higher saturation levels compared to the approximate analytic predictions.

A classical effect of nonlinear acoustics is that a plane sinusoidal acoustic wave propagating in a nonlinear medium transforms to a sawtooth wave with one shock per cycle. However, the waveform evolution can be quite different in the near field of a plane source due to diffraction. Previous numerical simulations of nonlinear acoustic waves in the near field of a circular piston source predict the development of two shocks per wave cycle [Khokhlova et al., J. Acoust. Soc. Am. 110, 95-108 (2001)]. Moreover, at some locations the peak pressure may be up to 4 times the source amplitude. The motivation of this work was to experimentally verify and further explain the phenomena of the nonlinear waveform distortion. Measurements were conducted in water with a 47-mm-diameter unfocused transducer, working at 1-MHz frequency. For pressure amplitudes higher than 0.5 MPa, two shocks per cycle were observed in the waveform beyond the last minimum of the fundamental harmonic amplitude. With the increase of the observation distance, these two shocks collided and formed one shock (per cycle), i.e., the waveform developed into the classical sawtooth wave. The experimental results were in a very good agreement with the modeling based on the Khokhlov–Zabolotskaya–Kuznetsov (KZK) equation.

High intensity focused ultrasound (HIFU) can destroy tumors or stop internal bleeding. The primary physical mechanism in HIFU is the conversion of acoustic energy to heat, which as HIFU amplitude increases is enhanced by nonlinear acoustic propagation and nonlinear scattering from bubbles. The goal of this work is to study and separate the effects of nonlinear propagation and cavitation during HIFU heating of tissue. Transparent polyacrylamide gel was used as a tissue-mimicking phantom to visualize HIFU lesion growth. Lesion size was also measured in excised turkey breast. Lesions were produced by the same time-averaged intensity, but with different peak acoustic pressure amplitudes compensated by different duty cycles. In order to separate cavitation and nonlinear wave effects, experiments were performed under static pressure (10.34MPa) greater than the peak negative pressure amplitude of the sound waves (8.96MPa). Suppression of cavitation by overpressure was measured by reduced acoustic scattering and transmission loss in the treatment region. We found that, with the same time-averaged intensity, a shorter, higher amplitude wave created a larger lesion than a longer, lower amplitude wave with or without overpressure.

Therapeutic ultrasound is an emerging field with many medical applications. High intensity focused ultrasound (HIFU) provides the ability to localize the deposition of acoustic energy within the body, which can cause tissue necrosis and hemostasis. Similarly, shock waves from a lithotripter penetrate the body to comminute kidney stones, and transcutaneous ultrasound enhances the transport of chemotherapy agents. New medical applications have required advances in transducer design and advances in numerical and experimental studies of the interaction of sound with biological tissues and fluids. The primary physical mechanism in HIFU is the conversion of acoustic energy into heat, which is often enhanced by nonlinear acoustic propagation and nonlinear scattering from bubbles. Other mechanical effects from ultrasound appear to stimulate an immune response, and bubble dynamics play an important role in lithotripsy and ultrasound-enhanced drug delivery. A dramatic shift to understand and exploit these nonlinear and mechanical mechanisms has occurred over the last few years. Specific challenges remain, such as treatment protocol planning and real-time treatment monitoring. An improved understanding of the physical mechanisms is essential to meet these challenges and to further advance therapeutic ultrasound.

A numerical solution of the KZK-type parabolic nonlinear evolution equation is presented for finite-amplitude sound beams radiated by rectangular sources. The initial acoustic waveform is a short tone burst, similar to those used in diagnostic ultrasound. The generation of higher harmonic components and their spatial structure are investigated for media similar to tissue with various frequency dependent absorption properties. Nonlinear propagation in a thermoviscous fluid with a quadratic frequency law of absorption is compared to that in tissue with a nearly linear frequency law of absorption. The algorithm is based on that originally developed by Lee and Hamilton [J. Acoust. Soc. Am. 97, 906-917 (1995)] to model circular sources. The algorithm is generalized for two-dimensional sources without axial symmetry. The diffraction integral is adapted in the time-domain for two dimensions with the implicit backward finite difference (IBFD) scheme in the nearfield and with the alternate direction implicit (ADI) method at longer distances. Arbitrary frequency dependence of absorption is included in this model and solved in the frequency-domain using the FFT technique. The results of simulation may be used to better understand the nonlinear beam structure for tissue harmonic imaging in modern medical diagnostic scanners.

Cavitation appears to contribute to tissue injury in lithotripsy. Reports have shown that increasing pulse repetition frequency [(PRF) 0.5–100 Hz] increases tissue damage and increasing static pressure (1–3 bar) reduces cell damage without decreasing stone comminution. Our hypothesis is that overpressure or slow PRF causes unstabilized bubbles produced by one shock pulse to dissolve before they nucleate cavitation by subsequent shock pulses. The effects of PRF and overpressure on bubble dynamics and lifetimes were studied experimentally with passive cavitation detection, high-speed photography, and B-mode ultrasound and theoretically. Overpressure significantly reduced calculated (100–2 s) and measured (55–0.5 s) bubble lifetimes. At 1.5 bar static pressure, a dense bubble cluster was measured with clinically high PRF (2–3 Hz) and a sparse cluster with clinically low PRF (0.5–1 Hz), indicating bubble lifetimes of 0.5–1 s, consistent with calculations. In contrast to cavitation in water, high-speed photography showed that overpressure did not suppress cavitation of bubbles stabilized on a cracked surface. These results suggest that a judicious use of overpressure and PRF in lithotripsy could reduce cavitation damage of tissue while maintaining cavitation comminution of stones.

It is known that oscillations of single spherically symmetric bubble exposed to the ultrasound may have violent collapses. The impact of ultrasound on bubble dynamics strongly depends on the relation between the ultrasound frequency and the resonance frequency of the bubble, which depends on the bubble radius and on the diffusion of gas through the wall of the bubble. If high intensity ultrasound is applied, the effect of acoustic nonlinearity on ultrasound propagation results in generation of harmonics of the fundamental frequency and corresponding broadening of the wave spectrum. The bubbles with resonant frequencies close to the fundamental one of the wave, and to frequencies of multiple harmonics, can be therefore effectively excited. Another important effect on cavitation is gas diffusion — the quantity of gas diffused to and from the bubble during one cycle are not equal to each other. It results in the growth of bubble and decrease of its resonant frequency. The idea of the work is to study the effect of various acoustic waveforms on the dynamics of bubbles with different radii. The Gilmore–Akulichev equation is used as a mathematical model of cavitation. The solutions of the equation are obtained numerically using the fifth order Runge–Kutta method. The dynamic of bubbles exposed to harmonic ultrasound wave, periodic sawtooth waves, and frequency modulated waves are considered.

High-intensity focused ultrasound (HIFU) creates localized heating deep in tissues which can be used to necrose tumors or cauterize vessels. Imaging of the temperature field in tissue is important for guiding HIFU treatment. Temperature rise in excised and degassed bovine liver exposed to high-intensity focused ultrasound was visualized experimentally and simulated numerically. An infrared camera, which records surface temperature only, was used to measure spatial temperature distribution. Two blocks of tissue were stacked, and their interface was placed along the axis of the ultrasound beam. A single element concave transducer (2 MHz, 35-mm aperture, 51-mm radius of curvature) was used. After exposure to ultrasound, the upper piece was immediately removed, and the temperature on the axial plane was infrared imaged. The absorption coefficient of liver was measured and then used for numerical simulations. The theoretical model employs a KZK-type equation for the acoustic pressure field combined with a bioheat equation. It is shown that experiment and theory agree well on the location, shape, and dimensions of the heated region. The dependence of absorption coefficient in liver on exposure to ultrasound, to air, and to degassing process was studied.

Two theoretical models and the corresponding numerical codes for the description of nonlinear acoustic beams radiated from intense cw sources in water are presented. In the first model, diffraction effects are included using the Rayleigh integral, whereas nonlinearity and thermoviscous absorption are accounted for in a quasi-plane approximation. The simulations are performed in the time domain using the code previously developed for single-pulse propagation in medium having arbitrary frequency-dependent absorption. The second model is based on the Khokhlov–Zabolotskaya–Kuznetsov equation, which, contrary to the first model, accounts for diffraction in the parabolic approximation. The simulations are performed in the frequency domain using a novel algorithm that has been developed. A variable number of harmonics, which follows the nonlinear broadening of the wave spectrum are employed in the algorithm to speed up calculations. In order to prove the validity and the accuracy of the two codes developed, the simulation of diffraction and nonlinear effects in the near field of an intense ultrasound circular piston source in water is performed. The results of modeling obtained by both codes are compared with each other and with known experimental data, and are found to be in a good agreement. Frequency-domain code is then used for detailed study of the strongly nonlinear regime of propagation, when shocks are developed in the waveform close to the source. It is demonstrated that diffraction plays a major role in shock formation. Development of two shocks in each cycle and their further collision is predicted. It is also shown that nonlinear propagation and shock formation result at some distance in the two times excess of peak positive pressure in comparison with the maximum value obtained in the case of linear propagation. The beam total power decay due to formation of shocks as a function of the propagation distance is compared with the intensity in a plane wave propagation without diffraction. It is shown that nonlinear energy decay starts earlier for the beam, but decreases slower over longer distances.

Overpressure–elevated hydrostatic pressure–was used to assess the role of gas or vapor bubbles in distorting the shape and position of a high-intensity focused ultrasound (HIFU) lesion in tissue. The shift from a cigar-shaped lesion to a tadpole-shaped lesion can mean that the wrong area is treated. Overpressure minimizes bubbles and bubble activity by dissolving gas bubbles, restricting bubble oscillation and raising the boiling temperature. Therefore, comparison with and without overpressure is a tool to assess the role of bubbles. Dissolution rates, bubble dynamics and boiling temperatures were determined as functions of pressure. Experiments were made first in a low-overpressure chamber (0.7 MPa maximum) that permitted imaging by B-mode ultrasound (US). Pieces of excised beef liver (8 cm thick) were treated in the chamber with 3.5 MHz for 1 to 7 s (50% duty cycle). In situ intensities (ISP) were 600 to 3000 W/cm². B-mode US imaging detected a hyperechoic region at the HIFU treatment site. The dissipation of this hyperechoic region following HIFU cessation corresponded well with calculated bubble dissolution rates; thus, suggesting that bubbles were present. Lesion shape was then tested in a high-pressure chamber. Intensities were 1300 and 1750 W/cm² ( ± 20%) at 1 MHz for 30 s. Hydrostatic pressures were 0.1 or 5.6 MPa. At 1300 W/cm², lesions were cigar-shaped, and no difference was observed between lesions formed with or without overpressure. At 1750 W/cm², lesions formed with no overpressure were tadpole-shaped, but lesions formed with high overpressure (5.6 MPa) remained cigar-shaped. Data support the hypothesis that bubbles contribute to the lesion distortion.

Ultrasound has been used for decades as a means for noninvasive treatment of diseases. Low-intensity ultrasound is routinely applied in physical therapy for muscular and neurological related illnesses. In contrast, high-intensity focused ultrasound (HIFU) is used to induce coagulative necrosis of tissue for cancer treatment or hemostasis. Our efforts concern the latter. Predictions of ultrasound fields, temperature response, and lesion dynamics are obtained by a model which accounts for nonlinear sound propagation in inhomogeneous media, an arbitrary frequency power law for acoustic attenuation, and temperature time history [J. Acoust. Soc. Am. 107, No. 5, Pt. 2 (2000)]. The model is expanded from its previous version to include attenuation and sound speed dependence on temperature levels and also to consider generation of gas bubbles within the tissue. Results are presented in terms of treatment strategies that provide maximum energy transfer for coagulating the targeted tissue while minimizing damage to the surrounding area.

The results of this paper show—for an existing high intensity, focused ultrasound (HIFU) transducer—the importance of nonlinear effects on the space/time properties of wave propagation and heat generation in perfused liver models when a blood vessel also might be present. These simulations are based on the nonlinear parabolic equation for sound propagation and the bio-heat equation for temperature generation. The use of high initial pressure in HIFU transducers in combination with the physical characteristics of biological tissue induces shock formation during the propagation of a therapeutic ultrasound wave. The induced shock directly affects the rate at which heat is absorbed by tissue at the focus without significant influence on the magnitude and spatial distribution of the energy being delivered. When shocks form close to the focus, nonlinear enhancement of heating is confined in a small region around the focus and generates a higher localized thermal impact on the tissue than that predicted by linear theory. The presence of a blood vessel changes the spatial distribution of both the heating rate and temperature.

In order to simulate ultrasound propagation and subsequent thermal effects in biological media in which blood vessels and other structures may be present, a three-dimensional model has been developed that eliminates the need for symmetry constraints. The model is based on the coupled solution of the full wave nonlinear equation of sound in a lossy medium and the bioheat equation obtained by a pseudospectral finite-difference method in the time domain. It includes nonlinear sound propagation, an arbitrary frequency power law for attenuation, and is capable of treating material inhomogeneities. Unlike other models based on parabolic approximations, it is not restricted to near-axis solutions and can account for reflections and backscattered fields. The program was used to simulate the application of high-intensity focused ultrasound (HIFU) in liver with a blood vessel placed perpendicular to the axis of the transducer and near the focus. This approach follows recent work by the authors [Curra et al., IEEE Trans. Ultrason. Ferroelectr., Freq. Control (in press)]. Simulations are presented for different levels of driving pressure, sound nonlinearities, exposure times, and the relative position between the transducer focus and the blood vessel.