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Aims: To determine quality of life (QoL) outcomes after palliation of pain from bone metastases using magnetic resonance-guided high intensity focused ultrasound (MR-guided HIFU), measured using the European Organization for Research and Treatment of Cancer (EORTC) QLQ-C15-PAL and the QLQ-BM22 questionnaires., Materials and Methods: Twenty patients undergoing MR-guided HIFU in an international multicentre trial self-completed the QLQ-C15-PAL and QLQ-BM22 questionnaires before and on days 7, 14, 30, 60 and 90 post-treatment. Descriptive statistics were used to represent changes in symptom and functional scales over time and to determine their clinical significance. QoL changes were compared in pain responders and non-responders (who were classified according to change in worst pain score and analgesic intake, between baseline and day 30)., Results: Eighteen patients had analysable QoL data. Clinically significant improvements were seen in the QoL scales of physical functioning, fatigue, appetite loss, nausea and vomiting, constipation and pain in the 53% of patients who were classified as responders at day 30. No significant changes were seen in the 47% of patients who were non-responders at this time point., Conclusion: Local treatment of pain from bone metastases with MR-guided HIFU, even in the presence of disseminated malignancy, has a substantial positive effect on physical functioning, and improves other symptomatic QoL measures. This indicated a greater response to treatment over and above pain control alone. MR-guided HIFU is non-invasive and should be considered for patients with localised metastatic bone pain and poor QoL., (Copyright © 2018 The Royal College of Radiologists. Published by Elsevier Ltd. All rights reserved.)

High-intensity focused ultrasound (HIFU) has been investigated as a tool for the treatment of cancer for many decades, but is only now beginning to emerge as a potential alternative to conventional therapies. In recent years, clinical trials have evaluated the clinical efficacy of a number of devices worldwide. In Oxford, UK, we have been using the JC HIFU system (HAIFU Technology Company, Chongqing, PR China) in clinical trials since November 2002. This is the first report of its clinical use outside mainland China. The device is non-invasive, and employs an extracorporeal transducer operating at 0.8-1.6 MHz (aperture 12-15 cm, focal length 9-15 cm), operating clinically at Isp (free field) of 5-15 KWcm(-2). The aims of the trials are to evaluate the safety and performance of the device. Performance is being evaluated through two parallel protocols. One employs radiological assessment of response with the use of follow-up magnetic resonance imaging and microbubble-contrast ultrasound. In the other, histological assessment will be made following elective surgical resection of the HIFU treated tumours. Eleven patients with liver tumours have been treated with HIFU to date. Adverse events include transient pain and minor skin burns. Observed response from the various assessment modalities is discussed.

The aim of the work is to evaluate a magnetic resonance imaging (MRI) thermometry sequence suitable for targeting of focused ultrasound (FUS) when used in vascular occlusion studies. A sliding window dual gradient echo (SW-dGRE) sequence was used. This sequence has the capability of monitoring both T1 relaxation and phase changes, which vary with temperature. Preliminary work involved quantification of the changes in T1 relaxation time with temperature and obtaining the PRF shift coefficient in polyacrylamide gel as it underwent an exothermic reaction during polymerization (avoiding the use of an external heat source). Temperature changes were visualized using thermal maps acquired with the sequence. For FUS guidance a thermal imaging technique is required with a temporal resolution <5 s, a spatial resolution of approximately 1 mm and a temperature resolution of approximately 5 degrees C. The sequence was optimized to improve the CNR (contrast to noise ratio) and SNR (signal to noise ratio) in the phase and magnitude images respectively. The PRF coefficient obtained for the polyacrylamide gel was -9.98 +/- 0.24 ppb degrees C(-1), whilst deltaT1 and temperature change were related by a proportionality factor, the T1 temperature coefficient, of 102.3 +/- 2.9 ms degrees C(-1). The sequence produces an image at every 1.4 s interval. In both magnitude and phase data, the in-plane resolution is +/- 1.2 mm and the temperature resolution is approximately 2 degrees C. The advantage of this sequence is that the temperature obtained from the magnitude data can be confirmed independently using the phase data and vice versa. Thus the sequence can essentially be crosschecked.

The effects of heat-generated changes on the attenuation of ultrasound (US) by porcine liver tissue have been studied over a frequency range of 2.0 to 5.0 MHz. Samples of fresh tissue, 4- to 5-mm thick, were pressurized and cooled before measurement. The insertion loss was measured at room temperature, using a broadband 3.5-MHz transducer of focal length 10 cm, employing a pulse-reflection technique. Fourier analysis of the results gave the frequency-dependence of the insertion loss. Samples were then heated in a water bath to a temperature in the range of 40 to 80 degrees C, for between 30 and 500 s. The insertion loss was then re-measured at room temperature. The frequency-dependence of the change in insertion loss, expressed as a coefficient, in dB/cm, was fitted by linear regression, from which the attenuation change at 3.5 MHz was determined. This change was attributed to protein coagulation. Increases of up to 2.4 dB/cm, (80 degrees C, 300 s) were found. The averaged data were fitted to a single step exponential model, resulting in a time constant on the order of 118 +/- 5 s, and an asymptotic limit to the increase of attenuation coefficient of 2.67 +/- 0.5 dB/cm., (Copyright 2003 World Federation for Ultrasound in Medicine & Biology)

Ultrasonic contrast agents are usually comprised of a stabilised shell encapsulating a gas bubble. When these are introduced in the body they increase the acoustic scattering from the tissues through which they pass, and especially from the vasculature. Their primary uses lie in cardiological and oncological imaging. However, these microbubbles have the potential to act as centres for acoustic cavitation activity, and so it is important to consider the safety of their use from an acoustic standpoint. The addition of ultrasonic contrast agents to in vitro suspensions of red blood cells has been shown to lead to haemolysis when the sample is exposed to ultrasound at levels which leave the cells unharmed in their absence. In vivo the infusion of gas bubble contrast agents into experimental animals has been shown to enhance the incidence of petechiae and haemorrhage in the intestine. The Mechanical Index (MI) thresholds for the effects seen in vitro lie within the range of MIs available with diagnostic clinical scanners, but in vivo the thresholds lie at the top end of the exposure levels available clinically. No adverse effects in humans arising from the ultrasonic exposure of these contrast agents have been reported to date.

High intensity focused ultrasound (HIFU) is a technique that was first investigated in the 1940s as a potential method of destroying selective regions within the brain to aid neurobehavioral studies. A beam of ultrasound can be brought to a tight focus at a distance from its source, and if sufficient energy is concentrated within the focus, the cells lying within this focal volume are killed, whereas those lying elsewhere are spared. This is, therefore, a noninvasive method of producing selective and "trackless" tissue destruction in deep-seated targets in the body without damage to overlying tissues. This technique is being investigated in a number of medical fields, including urology, ophthalmology, and oncology. The mechanism for cell killing is mainly thermal in origin. Renewal of interest in this technique is due to the availability of sophisticated medical imaging, which now allows the focal volume to be accurately targeted and also allows the tissue destruction to be monitored during treatment. The burgeoning field of HIFU focused ultrasound surgery (FUS) are reviewed in this article.

Modern sophisticated ultrasonographic equipment is capable of delivering substantial levels of acoustic energy into the body when used at maximum outputs. The risk of producing bioeffects has been studied by international expert groups during symposia supported by the World Federation for Ultrasound in Medicine and Biology (WFUMB). These have resulted in the publication of internationally accepted conclusions and recommendations. National ultrasound safety committees have published guidelines as well. These recommendations and safety guidelines offer valuable information to help users apply diagnostic ultrasound in a safe and effective manner. Acoustic output from ultrasound medical devices is directly regulated only in the USA and this is done by the Food and Drug Administration (FDA). However, there is also a modern trend towards self-regulation which has implications for the worldwide use of diagnostic ultrasound. It has resulted in a move away from the relatively simple scheme of FDA-enforced, application-specific limits on acoustic output to a scheme whereby risk of adverse effects of ultrasound exposure is assessed from information provided by the equipment in the form of a real-time display of safety indices. Under this option, the FDA allows a relaxation of some intensity limits, specifically approving the use of medical ultrasound devices that can expose the fetus or embryo to nearly eight times the intensity that was previously allowed. The shift of responsibility for risk assessment from a regulatory authority to the user creates an urgent need for awareness of risk and the development of knowledgeable and responsible attitudes to safety issues. To encourage this approach, it is incumbent on authorities, ultrasound societies and expert groups to provide relevant information on biological effects that might result from ultrasonographic procedures. It is obvious from the continued stream of enquiries received by ultrasound societies that effective dissemination of such knowledge requires sustained strenuous effort on the part of ultrasound safety committees. There is a strong need for continuing education to ensure that appropriate risk/benefit assessments are made by users based on an appropriate knowledge of the probability of biological effects occurring with each type of ultrasound procedure. The primary purpose of this paper is to draw attention to current safety guidelines and show the similarities and areas of general agreement with those issued by the parent ultrasound organisation, the WFUMB. It is equally important to identify gaps in our knowledge, where applicable.

Knowledge of the spatial distribution of intensity loss from an ultrasonic beam is critical for predicting lesion formation in focused ultrasound (US) surgery (FUS). To date, most models have used linear propagation models to predict intensity profiles required to compute the temporally varying temperature distributions used to compute thermal dose contours. These are used to predict the extent of thermal damage. However, these simulations fail to describe adequately the abnormal lesion formation behaviour observed during ex vivo experiments in cases for which the transducer drive levels are varied over a wide range. In such experiments, the extent of thermal damage has been observed to move significantly closer to the transducer with increased transducer drive levels than would be predicted using linear-propagation models. The first set of simulations described herein use the KZK (Khokhlov-Zabolotskaya-Kuznetsov) nonlinear propagation model with the parabolic approximation for highly focused US waves to demonstrate that both the peak intensity and the lesion positions do, indeed, move closer to the transducer. This illustrates that, for accurate modelling of heating during FUS, nonlinear effects should be considered. Additionally, a first order approximation has been employed that attempts to account for the abnormal heat deposition distributions that accompany high transducer drive level FUS exposures where cavitation and boiling may be present. The results of these simulations are presented. It is suggested that this type of approach may be a useful tool in understanding thermal damage mechanisms.

Experiments were performed to investigate the production of harmonics by high-intensity focused ultrasound (HIFU) produced by a spherical bowl; spherical radius 15 cm, frequency 1.7 MHz, as a function of beam power in excised bovine liver. The intensity of the nth harmonic, in both water and the tissue sample, varied approximately as the nth power of the incident intensity up to the point at which irreversible changes were produced in the sample. The greatest observed axial power absorption enhancement factor was approximately 6.3, and the greatest observed total absorbed power enhancement was approximately 2.3. These enhancements may have some effect on the onset of lesioning, but not much effect on its subsequent development. In water, at an intensity of about 120 W/cm2 at the focus, the -3-dB beam diameters of harmonic components were observed to vary approximately as the inverse square root of the harmonic number.

Objective: The primary aim of this phase I trial was to assess the tolerance of cancer patients to focused ultrasound (FUS) treatment in a variety of different sites and to document any associated acute or delayed toxicity. This would appear to be the first time that treatment has been given without sedation or anaesthesia., Methods: Patients with advanced and/or metastatic disease were eligible for entry into this study. Previous work has established that an in situ ablative intensity (AI) of 1500 W/cm2 Isp for 1 s achieves coagulative necrosis at the focal spot. Ultrasonic exposures of 25-100% of AI for 1 s were delivered to preselected tissue volumes. Pain questionnaires recording any side effects were completed by the patient and the investigator separately. Ultrasound images of the target volume were taken before, immediately after, and 1 week after treatment., Results: A total of 14 patients have been entered into this study to date. Seven patients were treated at their primary site and seven received treatment to one of their metastases. No treatment needed to be stopped because of pain. Eight of the 14 patients did not complain of any side effect during or after the treatment. One patient complained of mild, and two of moderate pain during the week following treatment. One patient developed an asymptomatic blister on the skin., Conclusion: Focused ultrasound is a safe, well-tolerated and non-invasive method of delivering ablative thermal energy to selected tumours. More clinical trials are needed to assess the role of this modality in the treatment of cancer.

Objective: Focused ultrasound surgery (FUS) is being developed clinically for the non-invasive treatment of soft tissue tumours of the prostate, bladder, liver, kidney, muscle and breast. In the work described in this paper, the application of FUS is extended to investigate the potential to induce vascular occlusion, with the aim of applying the technique to problems in fetal medicine and oncology., Methods: In this feasibility study the occlusion of femoral blood flow in vivo is demonstrated using an array of multiple single exposures of 1.7 MHz focused ultrasound. These were placed in two rows of four lesions at a focal depth of 5 mm. The 4660-W cm-2 (free field spatial peak intensity) 2-s exposures were placed 2 mm apart. Vascular patency was assessed using a Siemens Vision (1.5T) magnetic resonance (MR) imaging scanner with an extremity coil, and intravenous gadolinium contrast agent. FLASH and FISP MR sequences were used to obtain full 3D data sets providing information on soft tissue damage and perfusion., Results and Conclusion: Total vascular occlusion was achieved in four of nine cases and significant vascular disruption in five of nine cases. Refinement of the FUS technique and long-term studies are now indicated prior to initial clinical application in fetal medicine.

Although there have been numerous models implemented for modeling thermal diffusion effects during focused ultrasound surgery (FUS), most have limited themselves to representing simple situations for which analytical solutions and the use of cylindrical geometries sufficed. For modeling single lesion formation and the heating patterns from a single exposure, good results were achieved in comparison with experimental results for predicting lesion size, shape and location. However, these types of approaches are insufficient when considering the heating of multiple sites with FUS exposures when the time interval between exposures is short. In such cases, the heat dissipation patterns from initial exposures in the lesion array formation can play a significant role in the heating patterns for later exposures. Understanding the effects of adjacent lesion formation, such as this, requires a three-dimensional (3-D) representation of the bioheat equation. Thus, we have developed a 3-D finite-element representation for modeling the thermal diffusion effects during FUS exposures in clinically relevant tissue volumes. The strength of this approach over past methods is its ability to represent arbitrarily shaped 3-D situations. Initial simulations have allowed calculation of the temperature distribution as a function of time for adjacent FUS exposures in excised bovine liver, with the individually computed point temperatures comparing favorably with published measurements. In addition to modeling these temperature distributions, the model was implemented in conjunction with an algorithm for calculating the thermal dose as a way of predicting lesion shape. Although used extensively in conventional hyperthermia applications, this thermal dose criterion has only been applied in a limited number of simulations in FUS for comparison with experimental measurements. In this study, simulations were run for focal depths 2 and 3 cm below the surface of pig's liver, using multiple intensity levels and exposure times. The results also compare favorably to published in vitro experimental measurements, which bodes well for future application to more complex problems, such as the modeling of multiple lesion arrays within complex anatomical geometries.

The purpose of this study was to establish the feasibility of noninvasive treatment of small renal tumors with high-intensity focused ultrasound (HIFU). A 1.69-MHz extracorporeal HIFU transducer of 150-mm focal length was used. In vitro experiments with excised porcine kidneys allowed determination of suitable exposure parameters to be tested in vivo. For short exposure times (< 2 seconds), the minimum energy required to produce acute thermal damage was 500 +/- 100 Wcm-2 per second. Porcine kidneys (N = 18) were treated in vivo at a depth of 40 mm from the skin surface, with acute damage detected in 13. Damage was macroscopically and histologically discrete and confined to the target area within the kidney. Skin induration was observed after treatment in nine cases, and there was one skin burn. Transducer developments to prevent this morbidity and to improve energy deposition within the target are discussed.

Mammalian tissues have differing sensitivities to damage by physical agents such as ultrasound. This article evaluates the scientific data in terms of known physical mechanisms of interaction and the impact on pre- and postnatal tissues. Actively dividing cells of the embryonic and fetal central nervous system are most readily disturbed. As a diagnostic ultrasound beam envelopes a small volume of tissue, it is possible that the effects of mild disturbance may not be detected unless major neural pathways are involved. There is evidence that ultrasound can be detected by the central nervous system; however, this does not necessarily imply that the bioeffect is hazardous to the fetus. Biologically significant temperature increases can occur at or near to bone in the fetus from the second trimester, if the beam is held stationary for more than 30 s in some pulsed Doppler applications. In this way, sensory organs that are encased in bone may be susceptible to heating by conduction. Reports in animals and humans of retarded growth and development following frequent exposures to diagnostic ultrasound, in the absence of significant heating, are difficult to explain from the current knowledge of ultrasound mechanisms. There is no evidence of cavitation effects occurring in the soft tissues of the fetus when exposed to diagnostic ultrasound; however, the possibility exists that such effects may be enhanced by the introduction of echo-contrast agents.

Temperature rise was observed as a function of time in liver and dog prostate tissue ex vivo during heating with high-intensity focused ultrasound. The temperature rise was measured using a needle thermocouple placed at the focus. The temperature vs. time behaviour closely followed the predictions of a model based on bulk and surface heating. When the tissue temperature was raised above 50 degrees C, an increase in heating rate was seen. At higher temperatures, a point was reached at which a marked, irreversible change of tissue properties was observed, consistent with protein denaturation. The change was sometimes accompanied by a sudden further rise in temperature followed by an equally sudden fall. On dissection, regions of tissue damage (lesions) were seen, sometimes containing bubbles consistent with acoustic cavitation or vaporisation.

The relationship between spatial peak intensity and the position of ultrasound induced tissue damage was studied in in vitro tissue models, using a 1.69 MHz spherical bowl transducer. The models corresponded to the transabdominal route to the bladder and prostate, which are potential target sites for focused ultrasound surgery. The results confirm that there is a relationship between lesion position and intensity, with lesions forming, under some exposure conditions, ahead of the geometric focus. Forward growth of lesions appears to be due to changes in the absorption characteristics of the tissue in the beam path. Using a computer model, we have demonstrated that the absorption coefficient of the tissue must increase significantly in front of the focus to enable lesions to form ahead of the predicted position. A possible mechanism for this is bubble formation as a result of acoustic cavitation. The effect of nonlinear propagation in the tissue, at the intensities studied, is shown to be relatively small.

Successful application of high intensity focused ultrasound to cancer treatment requires complete ablation of tissue volumes. In order to destroy an entire tumour it is necessary to place a contiguous array of touching lesions throughout it. In a study of how best to achieve this, exposures were selected to give single lesions that were thermal in origin, while avoiding effects due to tissue water boiling and acoustic cavitation. Arrays were formed in excised bovine liver. Under some exposure conditions, lesions were found to merge in front of the focal point, and failed to cover the desired volume. Using fine wire manganin-constantan thermocouples, temperature studies revealed a substantial rise in the temperature of surrounding untreated tissue. Cooling curves showed that it was necessary to allow surrounding tissue to cool for up to 2 min before ambient temperature was reached. By allowing the tissue to cool between exposures it was possible to form arrays of overlapping lesions thus successfully ablating the complete target region.

The prospect of being able to use "minimally invasive" surgical techniques is of great interest today, particularly for reasons of health economics, patient acceptability and reduced morbidity. High intensity focused ultrasound (HIFU) has long been known to offer the potential of very precise "trackless lesioning" but has only recently, with the advent of high quality methods of medical imaging, become a practicable possibility. High intensity beams can readily be achieved using either bowel or lens focusing procedures and, by choice of a suitable acoustic frequency, regions of tissue destruction--"lesions"--can be induced at depths of up to at least 10 cm with exposure times of the order of 1 s. Theoretical and experimental evidence indicates that the primary mechanism of damage is thermal, i.e. "cooking" of the tissues. Both conventional cavitation and boiling of tissue water may complicate the situation. Furthermore, substantial non-linear behaviour is involved. On histological appearance the lesions have a spatially sharp demarcation between regions of normal and dead cells. When attempts are made to ablate a block of tissue, by creating an array of adjacent elementary lesions, a phenomenon is observed of inhibition of formation of a lesion whose placing is too close to that of a neighbour. Provided that this problem is dealt with, complete ablation of an extended block of tissue can be achieved. For animal tumours in particular, this observation is reinforced by evidence both of in vitro cell survival and of tumour growth delay experiments. Clinically, the sites accessible for HIFU treatment will be limited by the need for a suitably wide acoustic window that either is available naturally or can be provided by a relatively minor surgical procedure. Tumour sites which thus offer a realistic prospect for local control (and some of which are already the subject of phase 1 trials) include liver, bladder, kidney, prostate, breast and brain. There is also considerable interest in non-cancer applications in these and other sites.

An analytical model has been constructed for the process of formation of thermal lesions in tissue, resulting from exposure to intense, highly focused ultrasound beams such as may be used in minimally invasive surgery. The model assumes a Gaussian approximation to beam shape in the focal region and predicts, for any such focal beam, the time delay to initiation of a lesion and the subsequent time course of growth of that lesion in lateral and axial dimensions, taking into account the effects of thermal diffusion and blood perfusion. The necessary approximations and assumptions of the model are considered. Comparison of predictions with experimentally measured data on excised pig liver indicate generally good agreement. Comparisons are also made of this theory with previously published data on exposure-time dependence of lesioning threshold intensity. Deficiencies are identified in existing practice for measuring and reporting acoustic exposures for focused ultrasound surgery, and the proposal is therefore made that a quantity that would be more satisfactory, from the viewpoints both of metrology and biophysical relevance, is the intensity spatially averaged over the area enclosed by the half-pressure-maximum contour in the focal plane, as determined under linear conditions, provisionally denoted as ISAL.

This overview of bioeffects of ultrasound presents some key aspects of selected papers dealing with biophysical end-points. Its purpose is to establish a basis for exposure and dosimetric standards for medical ultrasonic equipment. It is intended to provide essential background resource material for the medical/scientific community, and more specifically for scientific working groups. This document was prepared by members of the Safety Committee of the World Federation for Ultrasound in Medicine and Biology. It was produced as a resource document in response to a request for information by Working Group 12 (Ultrasound exposure parameters) of the International Electrotechnical Commission Technical Committee 87, Ultrasonics. IEC TC 87, WG12 is the working group responsible for generating international standards for the classification of equipment by its acoustic fields based on safety thresholds. Our paper is intended to update and supplement information on the thermal mechanism provided in the publication, "WFUMB Symposium on Safety and Standardisation in Medical Ultrasound: Issues and Recommendations Regarding Thermal Mechanisms for Biological Effects of Ultrasound" (WFUMB 1992). It also provides an overview of trends in research into nonthermal mechanisms as a preliminary to the next WFUMB Symposium on Safety of Medical Ultrasound when this subject will be examined in detail by a select group of international experts. The WFUMB-sponsored workshop will take place in Utsunomiya, Japan during 11-15th July, 1994. The purpose of the meeting is to evaluate the scientific literature and to formulate internationally accepted recommendations on the safe use of diagnostic ultrasound that may be endorsed as official policy of the WFUMB. It should be noted that the current publication is not intended for review or endorsement as an official WFUMB document. It is produced as a scientific paper by individuals who are members of the WFUMB Safety Committee, and it therefore represents the opinions of the authors. Nevertheless, during the preparation of this document, contributions were received from members of the International Electrotechnical Commission Technical Committee 87 as well as many other individual experts, and the authors sincerely acknowledge their support.

Methods for quantitative imaging of ultrasound propagation properties were applied to the examination of the acoustic appearance of lesions generated by high intensity focused ultrasound in excised pig livers. Single lesions, about 10 mm maximum diameter by 30 mm long, were created in each of six liver specimens. Two dimensional images (32 by 32 points) of sound speed, mean attenuation coefficient (as a function of frequency in the range 3 to 8.5 MHz) and mean backscattering coefficient (5 to 8 MHz) were obtained in 7 mm thick sections of tissue, cut to include a cross-section through the lesion. Images of these properties, presented alongside surface photographs of the samples, provided a qualitative demonstration that attenuation coefficient was the most useful and backscattering coefficient was the least useful acoustic parameter for visualizing such lesions. Quantitatively the data demonstrated significant increases in attenuation coefficient and sound speed in lesioned liver relative to normal, whereas backscattering was shown not to change in a significant manner except when undissolved gas is the mechanism for increased acoustic scattering. Samples where gas was not fully removed following lesion production gave significant increases in backscattering at the lesion centre, but the shape and size of regions of high backscattering coefficient corresponded poorly with the shape and size of the lesions, unlike attenuation and sound speed for which such correspondence was good.

The management of some tumours presents a difficult surgical problem. Focused ultrasound surgery is a technique which provides the possibility of destroying, non-invasively, a selected volume of tissue at depth within an organ such as the liver whilst sparing overlying tissues. For the safe and effective use of this technique, it is essential to understand the way in which such a focused ultrasound surgery beam interacts with normal and malignant tissue and to study the histological response of different tissues to the ultrasonic insult. In this paper the histology of lesions in normal rat liver, as viewed by light and electron microscopy, is described.

Visible size gas bubbles can be produced in an agar based gel when irradiated with either continuous wave (CW) or pulsed ultrasound. It is shown that many aspects of the production of these bubbles can be explained in a qualitative manner by a theoretical model based upon growth of a cavitation nucleus by rectified diffusion. Quantitative predictions for the number of bubbles produced as a function of various parameters tend to be different from measured values by less than an order of magnitude. The results given here provide a useful theoretical basis for the explanation of earlier measurements of ultrasonically induced bubbles in vivo.