A 3-D finite-element model for computation of temperature profiles and regions of thermal damage during focused ultrasound surgery exposures

Evaluation of acoustic-thermal simulations of in vivo magnetic resonance guided focused ultrasound ablative therapy

PURPOSE

To evaluate numerical simulations of focused ultrasound (FUS) with a rabbit model, comparing simulated heating characteristics with magnetic resonance temperature imaging (MRTI) data collected during in vivo treatment.

METHODS

A rabbit model was treated with FUS sonications in the biceps femoris with 3D MRTI collected. Acoustic and thermal properties of the rabbit muscle were determined experimentally. Numerical models of the rabbits were created, and tissue-type-specific properties were assigned. FUS simulations were performed using both the hybrid angular spectrum (HAS) method and k-Wave. Simulated power deposition patterns were converted to temperature maps using a Pennes' bioheat equation-based thermal solver. Agreement of pressure between the simulation techniques and temperature between the simulation and experimental heating was evaluated. Contributions of scattering and absorption attenuation were considered.

RESULTS

Simulated peak pressures derived using the HAS method exceeded the simulated peak pressures from k-Wave by 1.6 ± 2.7%. The location and FWHM of the peak pressure calculated from HAS and k-Wave showed good agreement. When muscle acoustic absorption value in the simulations was adjusted to approximately 54% of the measured attenuation, the average root-mean-squared error between simulated and experimental spatial-average temperature profiles was 0.046 ± 0.019 °C/W. Mean distance between simulated and experimental COTMs was 3.25 ± 1.37 mm. Transverse FWHMs of simulated sonications were smaller than in in vivo sonications. Longitudinal FWHMs were similar.

CONCLUSIONS

Presented results demonstrate agreement between HAS and k-Wave simulations and that FUS simulations can accurately predict focal position and heating for in vivo applications in soft tissue.

Thermal Modeling of Ultrasound Diathermy in Tissues with a Circular Inclusion near a Curved Interface

The influences of implants on the temperature field in tissues during ultrasound diathermy is controversial. In addition, most previous studies have focused on plate implants, and the effects of irregular implants and bones are seldom discussed. In this study, a hybrid computational framework per se is proposed to investigate the effects of double circular inclusions on the temperature distribution during ultrasound diathermy. The tissue–inclusion–bone structure is simplified as a two-dimensional bilayer composite model consisting of soft tissue and bone with a circular inclusion imbedded in the soft tissue. The interface between the bone layer and the soft-tissue layer is assumed as a convex surface for the incident ultrasonic waves. Multiply scattered waves originate between the two acoustic scatterers, i.e., the circular inclusion and the convex bone. The proposed computational framework consists of two kernels tackling ultrasound propagation and heat conduction problems, respectively. Making use of theoretical solutions of pressure fields, the transformed heat sources are efficiently obtained in the first kernel without sacrificing much computational burden. Temperature distributions in the composite media under ultrasound diathermy are evaluated via finite element numerical simulations in the second kernel. Numerical results indicate that the temperature distributions in the composite system obviously change when the bone layer changes from flat to convex. In addition, the inclusion size, location, material, and ultrasound operation frequency will also affect the temperature distribution and peak temperature during ultrasound diathermy. Pertinent findings could serve as a guide for clinical innovations in therapeutic ultrasounds.

Vein wall shrinkage induced by thermal coagulation with high-intensity-focused ultrasound: numerical modeling and in vivo experiments in sheep

BACKGROUND

Varicose veins are a common disease that may significantly affect quality of life. Different approaches are currently used in clinical practice to treat this pathology.

MATERIALS AND METHODS

In thermal therapy (radiofrequency or laser therapy), the vein is directly heated to a high temperature to induce vein wall coagulation, and the heat induces denaturation of the intramural collagen, which results macroscopically in vein shrinkage. Thermal vein shrinkage is a physical indicator of the efficiency of endovenous treatment. High-intensity focused ultrasound (HIFU) is a noninvasive technique that can thermally coagulate vein walls and induce vein shrinkage. In this study, we evaluated the vein shrinkage induced in vivo by extracorporeal HIFU ablation of sheep veins: six lateral saphenous veins (3.4mm mean diameter) were sonicated for 8 s with 3MHz continuous waves. Ultrasound imaging was performed before and immediately post-HIFU to quantify the HIFU-induced shrinkage.

RESULTS

Luminal constriction was observed in 100% (6/6) of the treated veins. The immediate findings showed a mean diameter constriction of 53%. The experimental HIFU-induced shrinkage data were used to validate a numerical model developed to predict the thermally induced vein contraction during HIFU treatment.

CONCLUSIONS

This model is based on the use of the k-wave library and published contraction rates of vessels immersed in hot water baths. The simulation results agreed well with those of in vivo experiments, showing a mean percent difference of 5%. The numerical model could thus be a valuable tool for optimizing ultrasound parameters as functions of the vein diameter, and future clinical trials are anticipated.

Numerical Study on the Possible Scanning Pathways to Optimize Thermal Impacts During Multiple Sonication of HIFU

Findings from numerical investigation of thermal aspects of tissue phantoms subjected to high intensity focused ultrasound (HIFU) during the process of multiple sonications have been presented. Various scanning pathways are chosen to deliver the acoustic energy and to place multiple lesions at the desired locations within the tissue. A new scanning method based on the calculation of the largest distance between any two consecutive lesions is proposed and developed, which can possibly reduce the total treatment time by eliminating the cooling period. This new approach is compared with conventional scanning methods, namely, raster scan, spiral scan from the center outwards and spiral scan from the outside to the center. Various parameters that affect the thermal response of the tissue due to the generation of multiple lesions are defined and studied so that the energy that is given to each spot can be modulated. It is found that modulation of thermal energy provides better control over HIFU exposure and heating time modulation results into a reduced treatment time. The study highlighted the potential advantages of the proposed scanning method vis-à-vis the other conventional approaches. In particular, compared to the other methods, the proposed approach resulted in the realization of almost uniform distribution of thermal energy over the entire ROI leading to almost simultaneous destruction of the affected lesions. The present study can provide the requisite guidance for HIFU-based treatment planning and also highlights the need for optimizing the scanning pathway on the basis of total number of lesions and time parameters.

Temperature Dependence of Tissue Thermal Parameters Should Be Considered in the Thermal Lesion Prediction in High-Intensity Focused Ultrasound Surgery

This study considers the temperature-dependent thermal parameters (specific heat capacity, thermal diffusivity and thermal conductivity) used when predicting the temperature rise of tissue exposed to high-intensity focused ultrasound (HIFU). Numerical analysis was performed using the Khokhlov-Zabolotskaya-Kuznetsov equation coupled with a bioheat transfer function. The thermal parameters were set as the functions of temperature using experimental data. The results revealed that, for liver tissue exposed to HIFU with a focal intensity of 3000 W/cm² for 10 s, the predicted focal temperature rise was 23% lower and the thermal lesion area 41% smaller than those predicted without considering the temperature dependence. The prediction was validated by experimental observations on thermal lesions visualized in a tissue-mimicking phantom. The present results suggest that temperature-dependent thermal parameters should be considered in the prediction of HIFU-induced temperature rise to avoid lowering ultrasonic output settings for HIFU surgery. The aim of the present study was to investigate how significantly the temperature dependence of the thermal parameters affects the thermal dose imposed on the tissue by a typical clinical HIFU device. A numerical simulation was performed using a thermo-acoustic algorithm coupling the non-linear Khokhlov-Zabolotskaya-Kuznetsov (KZK) equation (Meaney et al. 1998; Filonenko and Khokhlova 2001) and a bio-heat transfer (BHT) equation (Pennes 1948). Thermal parameters of liver tissue were modeled in the present study as functions of temperature and were incorporated into the BHT equation to compensate for the variations in thermal parameters with temperature. Experimental validation was achieved by comparing the predictions with the thermal lesions formed in the tissue-mimicking phantoms.

Simplified Theoretical Model for Temperature Evaluation in Tissue–Implant–Bone Systems during Ultrasound Diathermy

Deep heating procedures are helpful in treating joint contractures that frequently occur with fractures and joint diseases involving surgical implants and artificial joint prostheses. This study uses a one-dimensional composite medium model consisting of parallel slabs as a simplified approach to shed light on the influences of implants during ultrasound diathermy. Analytical solutions for the one-dimensional transient heat generation and conduction problem were derived using the orthogonal expansion technique and a Green’s function approach. The analytical solutions provided deep insight into the temperature profile by therapeutic ultrasound heating in the composite system. The effects of the implant material type, tissue thickness, and ultrasound operation frequency on temperature distribution were studied for clinical application. In addition, sensitivity analyses were carried out to investigate the influences of material properties on the temperature distribution during ultrasound diathermy. Based on the derived analytical solutions, the numerical simulations indicate that materials with high density, high specific heat, and low thermal conductivity may be optimal implant materials. Among available implant materials, a tantalum implant, which can achieve a lower temperature rise within the tissue (hydrogel) and bone layers during ultrasound diathermy, is a better choice thanks to its thermodynamics.

Validation of hybrid angular spectrum acoustic and thermal modelling in phantoms

In focused ultrasound (FUS) thermal ablation of diseased tissue, acoustic beam and thermal simulations enable treatment planning and optimization. In this study, a treatment-planning methodology that uses the hybrid angular spectrum (HAS) method and the Pennes' bioheat equation (PBHE) is experimentally validated in homogeneous tissue-mimicking phantoms. Simulated three-dimensional temperature profiles are compared to volumetric MR thermometry imaging (MRTI) of FUS sonications in the phantoms, whose acoustic and thermal properties are independently measured. Additionally, Monte Carlo (MC) uncertainty analysis is performed to quantify the effect of tissue property uncertainties on simulation results. The mean error between simulated and experimental spatiotemporal peak temperature rise was +0.33°C (+6.9%). Despite this error, the experimental temperature rise fell within the expected uncertainty of the simulation, as determined by the MC analysis. The average errors of the simulated transverse and longitudinal full width half maximum (FWHM) of the profiles were -1.9% and 7.5%, respectively. A linear regression and local sensitivity analysis revealed that simulated temperature amplitude is more sensitive to uncertainties in simulation inputs than in the profile width and shape. Acoustic power, acoustic attenuation and thermal conductivity had the greatest impact on peak temperature rise uncertainty; thermal conductivity and volumetric heat capacity had the greatest impact on FWHM uncertainty. This study validates that using the HAS and PBHE method can adequately predict temperature profiles from single sonications in homogeneous media. Further, it informs the need to accurately measure or predict patient-specific properties for improved treatment planning of ablative FUS surgeries.

Development and validation of a MRgHIFU non-invasive tissue acoustic property estimation technique

MR-guided high-intensity focussed ultrasound (MRgHIFU) non-invasive ablative surgeries have advanced into clinical trials for treating many pathologies and cancers. A remaining challenge of these surgeries is accurately planning and monitoring tissue heating in the face of patient-specific and dynamic acoustic properties of tissues. Currently, non-invasive measurements of acoustic properties have not been implemented in MRgHIFU treatment planning and monitoring procedures. This methods-driven study presents a technique using MR temperature imaging (MRTI) during low-temperature HIFU sonications to non-invasively estimate sample-specific acoustic absorption and speed of sound values in tissue-mimicking phantoms. Using measured thermal properties, specific absorption rate (SAR) patterns are calculated from the MRTI data and compared to simulated SAR patterns iteratively generated via the Hybrid Angular Spectrum (HAS) method. Once the error between the simulated and measured patterns is minimised, the estimated acoustic property values are compared to the true phantom values obtained via an independent technique. The estimated values are then used to simulate temperature profiles in the phantoms, and compared to experimental temperature profiles. This study demonstrates that trends in acoustic absorption and speed of sound can be non-invasively estimated with average errors of 21% and 1%, respectively. Additionally, temperature predictions using the estimated properties on average match within 1.2 °C of the experimental peak temperature rises in the phantoms. The positive results achieved in tissue-mimicking phantoms presented in this study indicate that this technique may be extended to in vivo applications, improving HIFU sonication temperature rise predictions and treatment assessment.

Effects of an implant on temperature distribution in tissue during ultrasound diathermy

The effects of an implant on temperature distribution in a tissue-mimicking hydrogel phantom during the application of therapeutic ultrasound were investigated. In vitro experiments were conducted to compare the influences of plastic and metal implants on ultrasound diathermy and to calibrate parameters in finite element simulation models. The temperature histories and characteristics of the opaque (denatured) areas in the hydrogel phantoms predicted by the numerical simulations show good correlation with those observed in the in vitro experiments. This study provides an insight into the temperature profile in the vicinity of an implant by therapeutic ultrasound heating typically used for physiotherapy. A parametric study was conducted through numerical simulations to investigate the effects of several factors, such as implant material type, ultrasound operation frequency, implant thickness and tissue thickness on the temperature distribution in the hydrogel phantom. The results indicate that the implant material type and implant thickness are the main parameters influencing the temperature distribution. In addition, once the implant material and ultrasound operation frequency are chosen, an optimal implant thickness can be obtained so as to avoid overheating injuries in tissue.

Simulation of thermal ablation by high-intensity focused ultrasound with temperature-dependent properties

An integrated computational framework was developed in this study for modeling high-intensity focused ultrasound (HIFU) thermal ablation. The temperature field was obtained by solving the bioheat transfer equation (BHTE) through the finite element method; while, the thermal lesion was considered as a denatured material experiencing phase transformation and modeled with the latent heat. An equivalent attenuation coefficient, which considers the temperature-dependent properties of the target material and the ultrasound diffraction due to bubbles, was proposed in the nonlinear thermal transient analysis. Finally, a modified thermal dose formulation was proposed to predict the lesion size, shape and location. In-vitro thermal ablation experiments on transparent tissue phantoms at different energy levels were carried out to validate this computational framework. The temperature histories and lesion areas from the proposed model show good correlation with those from the in-vitro experiments.

Ultrasound-guided therapeutic focused ultrasound: current status and future directions

This paper reviews ultrasound imaging methods for the guidance of therapeutic focused ultrasound (USgFUS), with emphasis on real-time preclinical methods. Guidance is interpreted in the broadest sense to include pretreatment planning, siting of the FUS focus, real-time monitoring of FUS-tissue interactions, and real-time control of exposure and damage assessment. The paper begins with an overview and brief historical background of the early methods used for monitoring FUS-tissue interactions. Current imaging methods are described, and discussed in terms of sensitivity and specificity of the localisation of the FUS effects in both therapeutic and sub-therapeutic modes. Thermal and non-thermal effects are considered. These include cavitation-enhanced heating, tissue water boiling and cavitation. Where appropriate, USgFUS methods are compared with similar methods implemented using other guidance modalities, e.g. magnetic resonance imaging. Conclusions are drawn regarding the clinical potential of the various guidance methods, and the feasibility and current status of real-time implementation.

Influence of temperature-dependent thermal parameters on temperature elevation of tissue exposed to high-intensity focused ultrasound: numerical simulation

High-intensity focused ultrasound (HIFU) has been used successfully as a non-invasive modality in treating solid tumors. The temperature rise HIFU irradiation causes in a tissue depends on the thermal properties of the tissue. This study was motivated by our observation that the thermal properties of a tissue vary significantly with temperature (Guntur SR, Lee KI, Paeng DG, Coleman AJ, Choi MJ. Ultrasound Med Biol 2013;39:1771-1784). This research investigated how significantly the alteration of tissue thermal parameters, in the ranges of values measured at 25°C-90°C, affects prediction of the temperature elevation of tissue under the same HIFU exposure. The numerical simulation was performed by coupling a non-linear Khokhlov-Zabolotskaya-Kuznetsov equation with a bio-heat transfer function. In the conventional method of prediction, the thermal parameters were set as constants measured at room temperature (25°C). This study compared the conventional prediction with those predicted with different thermal parameters measured at the various temperatures up to 90°C. The results indicated that the conventional method significantly overestimated the rise in focal temperature in the liver tissue exposed to a clinical HIFU field, compared with the prediction made using thermal parameters measured at temperatures that cause thermal denaturation. This finding suggests that temperature-dependent thermal parameters should be considered in predicting the temperature rise in a tissue to avoid use of an insufficient thermal dose in treatment planning for HIFU surgery.

Temperature-dependent thermal properties of ex vivo liver undergoing thermal ablation

Thermotherapy uses a heat source that raises temperatures in the target tissue, and the temperature rise depends on the thermal properties of the tissue. Little is known about the temperature-dependent thermal properties of tissue, which prevents us from accurately predicting the temperature distribution of the target tissue undergoing thermotherapy. The present study reports the key thermal parameters (specific heat capacity, thermal conductivity and heat diffusivity) measured in ex vivo porcine liver while being heated from 20 ° C to 90 ° C and then naturally cooled down to 20 ° C. The study indicates that as the tissue was heated, all the thermal parameters resulted in plots with asymmetric quasi-parabolic curves with temperature, being convex downward with their minima at the turning temperature of 35-40 ° C. The largest change was observed for thermal conductivity, which decreased by 9.6% from its initial value (at 20 ° C) at the turning temperature (35 ° C) and rose by 45% at 90 ° C from its minimum (at 35 ° C). The minima were 3.567 mJ/(m(3) ∙ K) for specific heat capacity, 0.520 W/(m.K) for thermal conductivity and 0.141 mm(2)/s for thermal diffusivity. The minimum at the turning temperature was unique, and it is suggested that it be taken as a characteristic value of the thermal parameter of the tissue. On the other hand, the thermal parameters were insensitive to temperature and remained almost unchanged when the tissue cooled down, indicating that their variations with temperature were irreversible. The rate of the irreversible rise at 35 ° C was 18% in specific heat capacity, 40% in thermal conductivity and 38.3% in thermal diffusivity. The study indicates that the key thermal parameters of ex vivo porcine liver vary largely with temperature when heated, as described by asymmetric quasi-parabolic curves of the thermal parameters with temperature, and therefore, substantial influence on the temperature distribution of the tissue undergoing thermotherapy is expected.

Thermal strain imaging: a review

Thermal strain imaging (TSI) or temporal strain imaging is an ultrasound application that exploits the temperature dependence of sound speed to create thermal (temporal) strain images. This article provides an overview of the field of TSI for biomedical applications that have appeared in the literature over the past several years. Basic theory in thermal strain is introduced. Two major energy sources appropriate for clinical applications are discussed. Promising biomedical applications are presented throughout the paper, including non-invasive thermometry and tissue characterization. We present some of the limitations and complications of the method. The paper concludes with a discussion of competing technologies.

The feasibility of using thermal strain imaging to regulate energy delivery during intracardiac radio-frequency ablation

A method is introduced to monitor cardiac ablative therapy by examining slope changes in the thermal strain curve caused by speed of sound variations with temperature. The sound speed of water-bearing tissue such as cardiac muscle increases with temperature. However, at temperatures above about 50°C, there is no further increase in the sound speed and the temperature coefficient may become slightly negative. For ablation therapy, an irreversible injury to tissue and a complete heart block occurs in the range of 48 to 50°C for a short period in accordance with the well-known Arrhenius equation. Using these two properties, we propose a potential tool to detect the moment when tissue damage occurs by using the reduced slope in the thermal strain curve as a function of heating time. We have illustrated the feasibility of this method initially using porcine myocardium in vitro. The method was further demonstrated in vivo, using a specially equipped ablation tip and an 11-MHz microlinear intracardiac echocardiography (ICE) array mounted on the tip of a catheter. The thermal strain curves showed a plateau, strongly suggesting that the temperature reached at least 50°C.

Real-time monitoring of high-intensity focused ultrasound lesion formation using acousto-optic sensing

High-intensity focused ultrasound (HIFU) is a promising modality that is used to noninvasively ablate soft tissue tumors. Nevertheless, real-time treatment monitoring with diagnostic ultrasound still poses a significant challenge since tissue necrosis, in the absence of cavitation or boiling, provides little acoustic contrast with normal tissue. In comparison, the optical properties of tissue are significantly altered accompanying lesion formation. A photorefractive crystal-based acousto-optic (AO) sensing system that uses a single HIFU transducer to simultaneously generate tissue necrosis and pump the AO interaction is used to monitor the real-time optical changes associated with thermal lesions induced in chicken breast ex vivo. It is found that the normalized change in AO response increases proportionally with the volume of necrosis. This study demonstrates AO sensing can identify the onset and growth of lesion formation in real time and, when used as feedback to guide exposures, results in more predictable lesion formation.

Dual-focus therapeutic ultrasound transducer for production of broad tissue lesions

In noninvasive high-intensity focused ultrasound (HIFU) treatment, formation of a large tissue lesion per sonication is desirable for reducing the overall treatment time. The goal of this study is to show the feasibility of enlarging tissue lesion size with a dual-focus therapeutic ultrasound transducer (DFTUT) by increasing the depth-of-focus (DOF). The proposed transducer consists of a disc- and an annular-type element of different radii of curvatures to produce two focal zones. To increase focal depth and to maintain uniform beamwidth of the elongated DOF, each element transmits ultrasound of a different center frequency: the inner element at a higher frequency for near field focusing and the outer element at a lower frequency for far field focusing. By activating two elements at the same time with a single transmitter capable of generating a dual-frequency mixed signal, the overall DOF of the proposed transducer may be extended considerably. A prototype transducer composed of a 4.1 MHz inner element and a 2.7 MHz outer element was fabricated to obtain preliminary experimental results. The feasibility the proposed technique was demonstrated through sound field, temperature and thermal dose simulations. The performance of the prototype transducer was verified by hydrophone measurements and tissue ablation experiments on a beef liver specimen. When several factors affecting the length and the uniformity of elongated DOF of the DFTUT are optimized, the proposed therapeutic ultrasound transducer design may increase the size of ablated tissues in the axial direction and, thus, decreasing the treatment time for a large volume of malignant tissues especially deep-seated targets.

Model-based ultrasound temperature visualization during and following HIFU exposure

This paper describes the application of signal processing techniques to improve the robustness of ultrasound feedback for displaying changes in temperature distribution in treatment using high-intensity focused ultrasound (HIFU), especially at the low signal-to-noise ratios that might be expected in in vivo abdominal treatment. Temperature estimation is based on the local displacements in ultrasound images taken during HIFU treatment, and a method to improve robustness to outliers is introduced. The main contribution of the paper is in the application of a Kalman filter, a statistical signal processing technique, which uses a simple analytical temperature model of heat dispersion to improve the temperature estimation from the ultrasound measurements during and after HIFU exposure. To reduce the sensitivity of the method to previous assumptions on the material homogeneity and signal-to-noise ratio, an adaptive form is introduced. The method is illustrated using data from HIFU exposure of ex vivo bovine liver. A particular advantage of the stability it introduces is that the temperature can be visualized not only in the intervals between HIFU exposure but also, for some configurations, during the exposure itself.

Noninvasive determination of in situ heating rate using kHz acoustic emissions and focused ultrasound

For high-intensity focused ultrasound (HIFU) to be widely applicable in the clinic, robust methods of treatment planning, guidance and delivery need to be developed. These technologies would greatly benefit if patient specific tissue parameters could be provided as inputs so that the treatment planning and monitoring schemes are customized and tailored on a case by case basis. A noninvasive method of estimating the local in situ acoustic heating rate using the heat transfer equation (HTE) and applying novel signal processing techniques is presented in this article. The heating rate is obtained by experimentally measuring the time required to raise the temperature of the therapeutic focus from a baseline temperature to boiling (here assumed to be 100 degrees C for aqueous media) and then solving the heat transfer equation iteratively to find the heating rate that results in the onset of boiling. The onset of boiling is noninvasively detected by measuring the time instant of onset of acoustic emissions in the audible frequency range due to violent collapse of bubbles. In vitro experiments performed in a tissue mimicking alginate phantom and excised turkey breast muscle tissue demonstrate that the noninvasive estimates of heating rate are in good agreement with those obtained independently using established methods. The results show potential for the applicability of these techniques in therapy planning and monitoring for therapeutic dose optimization using real-time acoustic feedback.

Preliminary optimization of non-destructive high intensity focused ultrasound exposures for hyperthermia applications

Due to its high degree of accuracy and non-invasive implementation, pulsed-high intensity focused ultrasound (HIFU) is a promising modality for hyperthermia applications as adjuvant therapy for cancer treatment. However, the relatively small focal region of the HIFU beam could result in prohibitively long treatment times for large targets requiring multiple exposures. In this work, finite element analysis modeling was used to simulate focused ultrasound propagation and the consequent induction of hyperthermia. The accuracy of the simulations was first validated with thermocouple measurements in hydrogel phantoms. More advanced simulations of in vivo applications using single HIFU exposures were then done incorporating complex, multi-layered tissue composition and variable perfusion for an in vivo murine xenograft tumor model. The results of this study describe the development of a preliminary methodology for optimizing spatial application of hyperthermia, through the evaluation of different HIFU exposures. These types of simulations, and their validations in vivo, may help minimize treatment durations for pulsed-HIFU induced hyperthermia and facilitate the translation of these exposures into the clinic.

Noninvasive measurement of local thermal diffusivity using backscattered ultrasound and focused ultrasound heating

Previously, noninvasive methods of estimating local tissue thermal and acoustic properties using backscattered ultrasound have been proposed in the literature. In this article, a noninvasive method of estimating local thermal diffusivity in situ during focused ultrasound heating using beamformed acoustic backscatter data and applying novel signal processing techniques is developed. A high intensity focused ultrasound (HIFU) transducer operating at subablative intensities is employed to create a brief local temperature rise of no more than 10 degrees C. Beamformed radio-frequency (RF) data are collected during heating and cooling using a clinical ultrasound scanner. Measurements of the time-varying "acoustic strain", that is, spatiotemporal variations in the RF echo shifts induced by the temperature related sound speed changes, are related to a solution of the heat transfer equation to estimate the thermal diffusivity in the heated zone. Numerical simulations and experiments performed in vitro in tissue mimicking phantoms and excised turkey breast muscle tissue demonstrate agreement between the ultrasound derived thermal diffusivity estimates and independent estimates made by a traditional hot-wire technique. The new noninvasive ultrasonic method has potential applications in thermal therapy planning and monitoring, physiological monitoring and as a means of noninvasive tissue characterization.

HIFU procedures at moderate intensities—effect of large blood vessels

A three-dimensional computational model is presented for studying the efficacy of high-intensity focused ultrasound (HIFU) procedures targeted near large blood vessels. The analysis applies to procedures performed at intensities below the threshold for cavitation, boiling and highly nonlinear propagation, but high enough to increase tissue temperature a few degrees per second. The model is based upon the linearized KZK equation and the bioheat equation in tissue. In the blood vessel the momentum and energy equations are satisfied. The model is first validated in a tissue phantom, to verify the absence of bubble formation and nonlinear effects. Temperature rise and lesion-volume calculations are then shown for different beam locations and orientations relative to a large vessel. Both single and multiple ablations are considered. Results show that when the vessel is located within about a beam width (few mm) of the ultrasound beam, significant reduction in lesion volume is observed due to blood flow. However, for gaps larger than a beam width, blood flow has no major effect on the lesion formation. Under the clinically representative conditions considered, the lesion volume is reduced about 40% (relative to the no-flow case) when the beam is parallel to the blood vessel, compared to about 20% for a perpendicular orientation. Procedures involving multiple ablation sites are affected less by blood flow than single ablations. The model also suggests that optimally focused transducers can generate lesions that are significantly larger (>2 times) than the ones produced by highly focused beams.

Experimental validation of a tractable numerical model for focused ultrasound heating in flow-through tissue phantoms

Heating from high intensity focused ultrasound (HIFU) can be used to control bleeding, both from individual blood vessels as well as from gross damage to the capillary bed. The presence of vascularity can limit one's ability to elevate the temperature owing to convective heat transport. In an effort to better understand the heating process in tissues with vascular structure we have developed a numerical simulation that couples models for ultrasound propagation, acoustic streaming, ultrasound heating and blood cooling in a Newtonian viscous medium. The 3-D simulation allows for the study of complicated biological structures and insonation geometries. We have also undertaken a series of in vitro experiments employing non-uniform flow-through tissue phantoms and designed to provide verification of the model predictions. We show that blood flow of 2 cm/s (6.4 ml/min through a 2.6 mm 'vessel') can reduce peak temperature in a vessel wall by 25%. We also show that HIFU intensities of 6.5 x 10(5) W/m2 can induce acoustic streaming with peak velocities up to 5 cm/s and this can reduce heating near a vessel wall by more than 10%. These results demonstrate that convective cooling is important in HIFU and can be accounted for within simulation models.

Mathematical modeling of temperature mapping over skin surface and its implementation in thermal disease diagnostics

In non-invasive thermal diagnostics, accurate correlations between the thermal image on skin surface and interior human pathophysiology are often desired, which require general solutions for the bioheat equation. In this study, the Monte Carlo method was implemented to solve the transient three-dimensional bio-heat transfer problem with non-linear boundary conditions (simultaneously with convection, radiation and evaporation) and space-dependent thermal physiological parameters. Detailed computations indicated that the thermal states of biological bodies, reflecting physiological conditions, could be correlated to the temperature or heat flux mapping recorded at the skin surface. The effect of the skin emissivity and humidity, the convective heat transfer coefficient, the relative humidity and temperature of the surrounding air, the metabolic rate and blood perfusion rate in the tumor, and the tumor size and number on the sensitivity of thermography are comprehensively investigated. Moreover, several thermal criteria for disease diagnostic were proposed based on statistical principles. Implementations of this study for the clinical thermal diagnostics are discussed.

Imaging of temperature-induced echo strain: preliminary in vitro study to assess feasibility for guiding focused ultrasound surgery

Ultrasonic estimation of heat-induced echo strain has been suggested as a noninvasive technique for guiding focused ultrasound (US) surgery (FUS), that is, for predicting the location of the thermal lesion before it is formed. The proposed strategy is to run the FUS system at a nonablative intensity and to use a diagnostic transducer to image the heat-induced echo strain, which, over a sufficiently small temperature range, is proportional to the temperature rise. The principal aim of this in vitro study was to determine if temperature-induced strain imaging is likely to be able to visualise the small (< 0.5%) strains that one would be restricted to in vivo. Temperature rises ranging from approximately 2 degrees C to 15 degrees C (starting at approximately 25 degrees C) were induced in bovine liver samples using an FUS system. The pre- and post-heated US images were processed to produce images of the apparent axial strain. These images were found to possess excellent spatial and contrast resolution, so that the hot spot remained clearly visible even when the spatial peak strain value was approximately 0.2% (corresponding to temperature rises on the order of 2 to 5 degrees C). Good repeatability in the strain images was observed within and between tissue samples. Artefacts due to thermoacoustic refraction were seen distal to the heated region, but they did not reduce hot spot visibility. The length of the hot spot exceeded that of the subsequent ablation (by approximately 200%), which was to be expected given that temperature imaging depicts the entire area over which the temperature has increased relative to the baseline. We conclude that temperature-induced strain imaging for the guidance of FUS in the liver is likely to be feasible, provided that it will be possible either to neglect or to correct for the additional sources of error (such as cardiac-induced motion) that will arise in vivo.

Numerical simulation of the transient temperature field from an annular focused ultrasonic transducer

Knowledge of the extent of the "heated necrosis element" from a single exposure in target tissue created by an ultrasonic beam is critical for the application of focal ultrasound (US) surgery (FUS). This study uses the O'Nell and Pennes formulas to simulate the heated necrosis element from an annular focused transducer and to examine its dependence on exposure dosage, as well as some design parameters of the transducer. Several conclusions may be drawn from our numerical results: 1. With increasing exposure, the heated necrosis element increases, but its contour becomes plumper and the influence of sound intensity I is found to be greater than that of the exposure time t. 2. To get a similar heated necrosis element, the exposure approximately satisfies a relation: It(0. 4 3)=constant. 3. Increasing the US frequency or the outer-radius of the annular transducer leads to a decrease in the heated necrosis volume.

Fundamental limitations of noninvasive temperature imaging by means of ultrasound echo strain estimation

Ultrasonic estimation of temperature-induced echo strain has been suggested as a means of predicting the location of thermal lesions formed by focused ultrasound (US) surgery before treatment. Preliminary investigations of this technique have produced optimistic results because they were carried out with rubber phantoms and used room temperature, rather than body temperature, as the baseline. The objective of the present study was to determine, through modelling, the likely feasibility of using ultrasonic temperature imaging to detect and localise the focal region of the heating beam for a medium with a realistic temperature-dependence of sound speed subjected to a realistic temperature rise. We determined the minimum ultrasonic signal-to-noise ratio (SNR) required to visualise the heated region for liver of varying fat content. Due to the small (0.5%) change in sound speed at the focus, the threshold SNR for normal liver (low fat content) was found to be at least 20 dB. This implies that temperature imaging in this tissue type will only be feasible if the effects of electronic noise can be minimised and if other sources of noise, such as cardiac-induced motion, do not substantially reduce the visibility of the focal region. For liver of intermediate fat content, the heated region could not be visualised even when the echo data were noise-free. Tissues with a very high fat content are likely to represent the most favourable conditions for ultrasonic temperature imaging.

Bio-acoustic thermal lensing and nonlinear propagation in focused ultrasound surgery using large focal spots: a parametric study

It is well known that the acoustic properties of soft tissue have a dependence on tissue temperature. This is of particular interest in focused ultrasound surgery since the mechanism of action of focused ultrasound surgery is to kill targeted tissue by inducing localized heating by ultrasound absorption, and hence cautery of that tissue. However, the act of localized heating induces a change in the acoustic properties of the targeted tissue and tissue surrounding it. This phenomenon distorts the incoming acoustic wavefront, and has been termed the thermal lens effect for this reason. Furthermore, nonlinear effects in acoustic propagation become non-negligible at the ultrasound intensities required for therapeutic action. This paper examines the importance of the thermal lens effect and nonlinear tissue properties by simulating a variety of clinically applicable phased array transducer configurations that have not yet been appropriately analysed using a full three-dimensional nonlinear treatment of acoustic propagation. The significance of the thermal lens effect is characterized by comparing the simulation of coupled acoustic and thermal propagation with an uncoupled treatment; neglecting thermal lensing typically produces a movement of 1 to 2 mm in the predicted position of the focus towards the transducer. The results also show that the classical methods of acoustic propagation can produce grossly erroneous results under certain clinically relevant transducer configurations and that an acoustic field scan with a hydrophone may not accurately predict therapeutic effect.

Optimization of power deposition and a heating strategy for external ultrasound thermal therapy

The purpose of this paper is to examine the thermal dose distribution, to configure the optimal absorbed power deposition, and to design an appropriate heating strategy for ultrasound thermal therapy. This work employs simulation programs, which are based on the transient bio-heat transfer equation and an ideal absorbed power deposition or an ideal temperature elevation within a cube of tissue, to study the optimal absorbed power deposition. Meanwhile, a simplified model of a scanned ultrasound transducer power deposition (a cone with convergent/divergent shape) is used to investigate the heating strategy for a large tumor with a sequence of heating pulses. The distribution of thermal dose equivalence defined by Sapareto and Dewey is used to evaluate the heating result for a set of given parameters. The parameters considered are the absorbed power density, heating duration, temperature elevation, blood perfusion, and the size of heating cube. The results demonstrate that the peak temperature is the key factor determining the thermal dose for this short-duration heating. Heat conduction has a very strong influence on the responses of temperature and thermal dose for a small heating cube and the boundary portion of a large heating cube. Hence, for obtaining the same therapeutic result, a higher power density is required for these two conditions to compensate the great temperature difference between the heating cube and the surrounding tissue. The influence of blood perfusion on the thermal dose is negligible on the boundary portion of the heating cube, while in the central portion it may become a crucial factor as a lower power density is used in this portion to save the delivered energy. When using external ultrasound heating method to treat a large tumor, the size of heating unit, the sequence of heating pulses, and the cooling-time interval between the consecutive heating pulses are the important factors to be determined to have an appropriate treatment within a reasonable overall treatment time.

Comparison of modelled and observed in vivo temperature elevations induced by focused ultrasound: implications for treatment planning

Two numerical models for predicting the temperature elevations resulting from focused ultrasound heating of muscle tissue were tested against experimental data. Both models use the Rayleigh-Sommerfeld integral to calculate the pressure field from a source distribution. The first method assumes a source distribution derived from a uniformly radiating transducer whereas the second uses a source distribution obtained by numerically projecting pressure field measurements from an area near the focus backward toward the transducer surface. Both of these calculated ultrasound fields were used as heat sources in the bioheat equation to calculate the temperature elevation in vivo. Experimental results were obtained from in vivo rabbit experiments using eight-element sector-vortex transducers at 1.61 and 1.7 MHz and noninvasive temperature mapping with MRI. Results showed that the uniformly radiating transducer model over-predicted the peak temperature by a factor ranging from 1.4 to 2.8, depending on the operating mode. Simulations run using the back-projected sources were much closer to experimental values, ranging from 1.0 to 1.7 times the experimental results, again varying with mode. Thus, a significant improvement in the treatment planning can be obtained by using actual measured ultrasound field distributions in combination with backward projection.

The intensity dependence of lesion position shift during focused ultrasound surgery

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.