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A GPU Accelerated Finite Differences Method of the Bioheat Transfer Equation for Ultrasound Thermal Ablation
Abstract
Over the years, high intensity focused ultrasound (FUS) therapy has become a promising therapeutic alternative for non-invasive tumor treatment. The basic idea of FUS therapy is the elevation of the tissue temperature by the application of focused ultrasound beams to focal spot in the tumor. Biothermal modeling is utilized to predict dynamic temperature distributions generated and altered by the therapeutic heating modality, tissue energy storage and dissipation, and blood flow. Implementation of biothermal modeling in the planning, monitoring, control and evaluation of MR guided Focused Ultrasound (MRgFUS) therapies can help to minimize treatment time, maximize efficacy, and ensure the safety of healthy normal tissues, while increasing clinical confidence in MRgFUS treatments. Fast calculations of thermal doses can support in planning, conduction, and monitoring of such treatments. In the current study a GPU-based method in Matlab is proposed, for fast calculations of the temperature and cumulative equivalent minutes at 43° (CEM 43°) based on the bioheat equation. The performance of our proposed method was assessed with three GPUs (GTX 750, GTX 770 and Tesla C2050) for five grid sizes. The maximum speedup was achieved with the Tesla C2050 (~29) while GTX 750 demonstrated the lower performance (~15).
... Various methods were reported for fast solutions of bio-heat transfer models; however, the study on fast thermal analysis under tissue deformation is very limited. Studies were focused on facilitating the computational efficiency by using parallel alternating direction explicit scheme [15] based on finite difference method (FDM) [16], spatial filter method based on Fast Fourier Transform (FFT) [17], fast FFT method [18], Graphics Processing Unit (GPU)-accelerated FDM [19,20], GPU-accelerated finite element methodology (FEM) [21], cellular neural network [22], multi-grid technique based on finite volume method (FVM) [23,24], dynamic mode decomposition based on meshless point collocation method [25] and model order reduction based on FDM [26]. Despite the improved computational effort by the above methods, they all consider solving the bio-heat transfer equation on a static non-moving state of soft tissue. ...
... The classical PBHT exists certain simplifications and assumptions. The blood flow in the capillaries is assumed isotropic and hence the directional-dependent blood flow heat transfer is not modelled [19,54]. The physical processes such as water evaporation and transport of vapor are not captured in the classical PBHT [25,37,55]; however, the phase change occurs when tissue temperature elevates beyond the vaporisation threshold í µí± í µí±¡ℎí µí±í µí±í µí± (í µí± í µí±¡ℎí µí±í µí±í µí± = 100℃ [36]), but the maximum temperature reached in the present work is less than í µí± = 65℃ (see Fig. 4(a)). ...
During thermal heating surgical procedures such as electrosurgery, thermal ablative treatment and hyperthermia, soft tissue deformation due to tool-tissue interaction and patients' motion can affect the distribution of induced thermal energy. Tissue temperature must be efficiently and accurately obtained from deformed tissues for precise thermal energy delivery; however, the classical Pennes bio-heat transfer can handle only the static non-moving state of soft tissue. This paper presents a formulation of bio-heat transfer under the effect of tissue deformation for fast or near real-time tissue temperature computation, based on fast explicit dynamics finite element algorithm for transient heat transfer. The proposed computation is achieved by transformation of the unknown deformed tissue state to the known initial non-moving state via a mapping function. The appropriateness and effectiveness of the proposed methodology are evaluated on a realistic virtual human liver with blood vessels to demonstrate a clinically relevant scenario of thermal ablation of hepatic cancer. Compared against the established non-linear procedures from commercial finite element analysis package, ABAQUS/CAE, the proposed methodology can achieve a typical 1.0e-3 level of normalized relative error at nodes and between 1.0e-4 and 1.0e-5 level of total errors, which is in good agreement with ABAQUS solutions. The proposed method consumes slightly more time than the formulation without soft tissue deformation, and computation performance of five different formulations are examined. The proposed method can be applied with bio-mechanical deformable models for fast or near real-time computation of non-linear bio-heat transfer, leading to translational potential in dynamic tissue temperature predictive analysis and thermal dosimetry computation for computer-integrated medical education and personalized treatments.
... Various methods were reported for fast solutions of bio-heat transfer models; however, the study on fast thermal analysis under tissue deformation is very limited. Studies were focused on facilitating the computational efficiency by using parallel alternating direction explicit scheme [15] based on finite difference method (FDM) [16], spatial filter method based on Fast Fourier Transform (FFT) [17], fast FFT method [18], Graphics Processing Unit (GPU)-accelerated FDM [19,20], GPU-accelerated finite element methodology (FEM) [21], cellular neural network [22], multi-grid technique based on finite volume method (FVM) [23,24], dynamic mode decomposition based on meshless point collocation method [25] and model order reduction based on FDM [26]. Despite the improved computational effort by the above methods, they all consider solving the bio-heat transfer equation on a static non-moving state of soft tissue. ...
... The classical PBHT exists certain simplifications and assumptions. The blood flow in the capillaries is assumed isotropic and hence the directional-dependent blood flow heat transfer is not modelled [19,54]. The physical processes such as water evaporation and transport of vapor are not captured in the classical PBHT [25,37,55]; however, the phase change occurs when tissue temperature elevates beyond the vaporisation threshold ℎ ( ℎ = 100℃ [36]), but the maximum temperature reached in the present work is less than = 65℃ (see Fig. 4(a)). ...
Background and Objectives: During thermal heating surgical procedures such as electrosurgery, thermal ablative treatment and hyperthermia, soft tissue deformation due to surgical tool-tissue interaction and patient movement can affect the distribution of thermal energy induced. Soft tissue temperature must be obtained from the deformed tissue for precise delivery of thermal energy. However, the classical Pennes bio-heat transfer model can handle only the static non-moving state of tissue. In addition, in order to enable a surgeon to visualize the simulated results immediately, the solution procedure must be suitable for real-time thermal applications.
Methods: This paper presents a formulation of bio-heat transfer under the effect of soft tissue deformation for fast or near real-time tissue temperature prediction, based on fast explicit dynamics finite element algorithm (FED-FEM) for transient heat transfer. The proposed thermal analysis under deformation is achieved by transformation of the unknown deformed tissue state to the known initial static state via a mapping function. The appropriateness and effectiveness of the proposed formulation are evaluated on a realistic virtual human liver model with blood vessels to demonstrate a clinically relevant scenario of thermal ablation of hepatic cancer.
Results: For numerical accuracy, the proposed formulation can achieve a typical 10^(-3) level of normalized relative error at nodes and between 10^(-4) and 10^(-5) level of total errors for the simulation, by comparing solutions against the commercial finite element analysis package. For computation time, the proposed formulation under tissue deformation with anisotropic temperature-dependent properties consumes 2.518×10^(-4) ms for one element thermal loads computation, compared to 2.237×10^(-4) ms for the formulation without deformation which is 0.89 times of the former. Comparisons with three other formulations for isotropic and temperature-independent properties are also presented.
Conclusions: Compared to conventional methods focusing on numerical accuracy, convergence and stability, the proposed formulation focuses on computational performance for fast tissue thermal analysis. Compared to the classical Pennes model that handles only the static state of tissue, the proposed formulation can achieve fast thermal analysis on deformed states of tissue and can be applied in addition to tissue deformable models for non-linear heating analysis at even large deformation of soft tissue, leading to great translational potential in dynamic tissue temperature analysis and thermal dosimetry computation for computer-integrated medical education and personalized treatment.
... Based on FDM, Schwenke et al. [14] studied a Graphics Processing Unit (GPU)-accelerated approach, utilising parallel execution of GPU for fast simulation of focused ultrasound thermal treatment. Kalantzis et al. [15] also studied a GPUaccelerated technique for fast simulation of focused ultrasound thermal ablation. Chen et al. [16] presented a GPU-accelerated microwave imaging method to monitor temperature during thermal therapy. ...
... Soft tissue temperature field is determined by solving the Pennes bio-heat transfer equation in 3-D [43], which mathematically describes heat transfer in tissue accounting for the bio-heating and cooling effects of heat conduction, blood perfusion, metabolic heat generation, and regional heat sources [44]. The Pennes bio-heat equation can provide suitable temperature prediction for whole body, organ, and tumour analyses [45], and therefore it has been widely used in the modelling of cancer treatment by hyperthermia and ablative methods [15,25,46,47] and other biomedical research areas [9,48,49]. The Pennes bio-heat transfer equation is given by [43]: ...
Real-time simulation of bio-heat transfer can improve surgical feedback in thermo-therapeutic treatment, leading to technical innovations to surgical process and improvements to patient outcomes; however, it is challenging to achieve real-time computational performance by conventional methods. This paper presents a cellular neural network (CNN) methodology for fast and real-time modelling of bio-heat transfer with medical applications in thermo-therapeutic treatment. It formulates nonlinear dynamics of the bio-heat transfer process and spatially discretised bio-heat transfer equation as the nonlinear neural dynamics and local neural connectivity of CNN, respectively. The proposed CNN methodology considers three-dimensional (3-D) volumetric bio-heat transfer behaviour in tissue and applies the concept of control volumes for discretisation of the Pennes bio-heat transfer equation on 3-D irregular grids, leading to novel neural network models embedded with bio-heat transfer mechanism for computation of tissue temperatures and associated thermal dose. Simulations and comparative analyses demonstrate that the proposed CNN models can achieve good agreement with the commercial finite element analysis package, ABAQUS/CAE, in numerical accuracy and reduce computation time by 304 and 772.86 times compared to those of with and without ABAQUS parallel execution, far exceeding the computational performance of the commercial finite element codes. The medical application is demonstrated using a high-intensity focused ultrasound (HIFU)-based thermal ablation of hepatic cancer for prediction of tissue temperatures and estimation of thermal dose.
... Schwenke et al. [20] studied a Graphics Processing Unit (GPU)-accelerated FDM to achieve fast simulation of focused ultrasound treatment via a parallel execution of the solution procedure on GPU; however, FDM requires a regular computation grid to approximate spatial derivatives, but human organs/tissue are irregular shapes with curvilinear boundaries, resulting in inaccuracy for accommodating soft tissue material properties and enforcing boundary conditions. He and Liu [21] developed a parallel alternating direction explicit (ADE) scheme based on FDM to solve the bio-heat equation; Carluccio et al. [22] devised a spatial filter method based on Fast Fourier Transform (FFT) with FDM to reduce computation time; Kalantzis et al. [23] studied a GPU-accelerated FDM for fast simulation of focused ultrasound thermal ablation; Dillenseger and Esneault [24] also studied an FFT-based FDM method; Chen et al. [25] presented a GPU-accelerated microwave imaging method based on FDM to monitor temperature in thermal therapy; Johnson and Saidel [26] studied an FDM-based methodology for fast simulation of radiofrequency tumor ablation; and Niu et al. [27] employed cellular neural networks (CNN) based on FDM for efficient estimation of tissue temperature field. Despite the improved computational performance by the above methods, they all suffer from the inaccuracy in describing the thermal effects of irregular boundary conditions due to using FDM for computation grid. ...
... The heat transfer in soft biological tissue may be characterized by various bio-heat transfer models, among which the most well-known is the Pennes bio-heat transfer model by Harry H. Pennes [37], which mathematically describes the heat transfer process in living biological tissue composed of solid tissue and blood flow [38]. The Pennes bio-heat transfer model can provide suitable temperature predictions in the whole body, organ, and tumor analyses [39], and therefore it has been widely used in the modeling of thermal ablation for cancer treatment [16,23,30,40] and other biomedical research areas [12,21,41,42]. ...
Real-time analysis of bio-heat transfer is very beneficial in improving clinical outcomes of hyperthermia and thermal ablative treatments but challenging to achieve due to large computational costs. This paper presents a fast numerical algorithm well suited for real-time solutions of bio-heat transfer, and it achieves real-time computation via the (i) computationally efficient explicit dynamics in the temporal domain, (ii) element-level thermal load computation, (iii) computationally efficient finite elements, (iv) explicit formulation for unknown nodal temperature, and (v) pre-computation of constant simulation matrices and parameters, all of which lead to a significant reduction in computation time for fast run-time computation. The proposed methodology considers temperature-dependent thermal properties for nonlinear characteristics of bio-heat transfer in soft tissue. Utilising a parallel execution, the proposed method achieves computation time reduction of 107.71 and 274.57 times compared to those of with and without parallelisation of the commercial finite element codes if temperature-dependent thermal properties are considered, and 303.07 and 772.58 times if temperature-independent thermal properties are considered, far exceeding the computational performance of the commercial finite element codes, presenting great potential in real-time predictive analysis of tissue temperature for planning, optimisation and evaluation of thermo-therapeutic treatments.
... Since solving a partial differential equation (PDE) in a three-dimensional domain requires significant computational time, even with simplified models, combining DE with Pennes' three-dimensional model significantly impacts performance. To reduce computational time and obtain solutions within a reasonable timeframe, we used general-purpose computing on graphics processing units (GPGPU) via the Compute Unified Device Architecture (CUDA) parallel computing platform to parallelize the implementation of the bioheat model [11,[28][29][30], i.e., minimize the time spent evaluating the objective function. ...
According to the World Health Organization, cancer is a worldwide health problem. Its high mortality rate motivates scientists to study new treatments. One of these new treatments is hyperthermia using magnetic nanoparticles. This treatment consists in submitting the target region with a low-frequency magnetic field to increase its temperature over 43 °C, as the threshold for tissue damage and leading the cells to necrosis. This paper uses an in silico three-dimensional Pennes’ model described by a set of partial differential equations (PDEs) to estimate the percentage of tissue damage due to hyperthermia. Differential evolution, an optimization method, suggests the best locations to inject the nanoparticles to maximize tumor cell death and minimize damage to healthy tissue. Three different scenarios were performed to evaluate the suggestions obtained by the optimization method. The results indicate the positive impact of the proposed technique: a reduction in the percentage of healthy tissue damage and the complete damage of the tumors were observed. In the best scenario, the optimization method was responsible for decreasing the healthy tissue damage by 59%
when the nanoparticles injection sites were located in the non-intuitive points indicated by the optimization method. The numerical solution of the PDEs is computationally expensive. This work also describes the implemented parallel strategy based on CUDA to reduce the computational costs involved in the PDEs resolution. Compared to the sequential version executed on the CPU, the proposed parallel implementation was able to speed the execution time up to 84.4 times.
... The temperature distribution of soft tissue is calculated based on the Pennes bio-heat transfer (PBHT) equation [29] in three-dimension (3-D) which has been compared to experimental data [30][31][32] to provide reliable tissue temperature predictions and is widely used in the modeling of thermal dose for cancer treatment [33][34][35][36] and other biomedical research areas [37][38][39]. PBHT is given by ...
Computation of desired thermal dose can improve the safety and effectiveness of thermal therapeutic interventions while fast bio-heat in silico simulation can enhance the real-time surgical feedback. However, the existing methods are either computationally expensive or numerically inaccurate. This article presents a new methodology for fast and accurate desired thermal dose computation. New iterative algorithms are developed to adjust control parameters to efficiently obtain the desired lesion volumes, based on efficient solutions of bio-heat transfer in soft tissue. The variation of thermal dose is investigated using single-and multi-lesion configurations, and convergence analysis is presented. The clinically relevant scenario is demonstrated using a patient-specific simulation of focused ultrasound treatment of hepatic cancers to achieve multi-lesion planning (consistent and common lesion volumes in our case) for predictable and repeatable heat exposure sequence. The proposed method provides a common approach for fast iterative computation of single-or multiple-desired thermal lesions.
... The heat transfer in soft biological tissue may be characterised by various bio-heat transfer models, among which the most well-known is the Pennes bio-heat transfer model by Harry H. Pennes [37], which mathematically describes the heat transfer process in living biological tissue composed of solid tissue and blood flow [38]. The Pennes bio-heat transfer model can provide suitable temperature predictions in the whole body, organ, and tumour analyses [39], and therefore it has been widely used in the modelling of thermal ablation for cancer treatment [16,23,30,40] and other biomedical research areas [12,21,41,42]. ...
Real-time analysis of bio-heat transfer is very beneficial in improving clinical outcomes of hyperthermia and thermal ablative treatments but challenging to achieve due to large computational costs. This paper presents a fast numerical algorithm well suited for real-time solutions of bio-heat transfer, and it achieves real-time computation via the (i) computationally efficient explicit dynamics in the temporal domain, (ii) element-level thermal load computation, (iii) computationally efficient finite elements, (iv) explicit formulation for unknown nodal temperature, and (v) pre-computation of constant simulation matrices and parameters, all of which lead to a significant reduction in computation time for fast run-time computation. The proposed methodology considers temperature-dependent thermal properties for nonlinear characteristics of bio-heat transfer in soft tissue. Utilizing a parallel execution, the proposed method achieves computation time reduction of 107.71 and 274.57 times compared to those of with and without parallelization of the commercial finite element codes if temperature-dependent thermal properties are considered, and 303.07 and 772.58 times if temperature-independent thermal properties are considered, far exceeding the computational performance of the commercial finite element codes, presenting great potential in real-time predictive analysis of tissue temperature for planning, optimization and evaluation of thermo-therapeutic treatments.
... 3 The heating mechanism involved in the thermal ablation can be characterized by various bio-heat transfer models, among which the most well-known model is the Pennes' bio-heat transfer equation. [4][5][6] Owing to its simplicity, the Pennes' bio-heat transfer equation has been widely used in the modeling of therapeutic hyperthermia for cancer treatment and other biomedical research areas. ...
Efficient simulation of heating processes in thermal ablation is of great importance for surgical simulation of thermal ablation procedures. This paper presents a Graphics Processing Unit (GPU) assisted finite element methodology for modeling and analysis of bio-heat transfer processes in the treatment of thermal ablation. The proposed methodology employs finite element method for discretization of the bio-heat equation, and the finite element modeling is implemented using the High-Level Shader Language of the Microsoft Direct3D 11. Simulations and comparison analyses are conducted, demonstrating computational performance improvement of up to 55.3 times using the proposed methodology.
... The heat transfer in soft tissues can be characterized by various bioheat transfer models, among which the most well-known model is the Pennes' bioheat transfer equation. 6,23,24 Owing to its simplicity the Pennes' bioheat transfer equation has been widely used in the modeling of thermal ablation for cancer treatment and other biomedical research areas. The Pennes' bioheat equation, 25 which expresses heat transfer in soft tissues, is given by ...
Modeling of thermomechanical behavior of soft tissues is vitally important for the development of surgical simulation of hyperthermia procedures. Currently, most literature considers only temperature-independent thermal parameters, such as the temperature-independent tissue specific heat capacity, thermal conductivity and stress–strain relationships for soft tissue thermomechanical modeling; however, these thermal parameters vary with temperatures as shown in the literature. This paper investigates the effect of temperature-dependent thermal parameters for soft tissue thermomechanical modeling. It establishes formulations for specific heat capacity, thermal conductivity and stress–strain relationships of soft tissues, all of which are temperature-dependent parameters. Simulations and comparison analyses are conducted, showing a different thermal-induced stress distribution of lower magnitudes when considering temperature-dependent thermal parameters of soft tissues.
... Parallel threads running the same instructions on multiple data (SIMD) can coalesce the memory accesses to optimally use the global memory bandwidth. Due to these properties, GPU parallelization has been applied to the simulation of bio-physical phenomena, for example elasticity (Dick et al., 2011;Han et al., 2012); wave propagation (Mehra et al., 2011;Karamalis et al., 2010); and bio-heat simulation (Kalantzis et al., 2016;Reis et al., 2016). ...
Focused ultrasound (FUS) is a noninvasive method for tissue ablation that has the potential for complete and local tumor destruction with minimal side effects. Already being used for the treatment of static organs, compensating target motion is not yet clinically available due to the complexity of the treatment. We here propose a numerical model of the therapy effects during respiratory motion to study FUS for moving liver targets. A focus lies on incorporating the motion and the computational efficiency of the simulations. A temperature model is proposed predicting the temperature distributions efficiently on the graphics processing unit by mapping the problem from the moving physical world to a static motion reference state. We also investigate the accuracy of ultrasound modeling in the highly heterogeneous propagation domain including ribs. A novel angular spectrum approach for heterogeneous media is proposed as the widely used hybrid angular spectrum method is found to be ineffective. For real-time applications, we propose an approximate ultrasound propagation model. An integrated FUS model is developed combining these model with an abdominal motion model, tissue damage, and a parameter model. The patient anatomy is automatically derived from CT images. Two clinical use-cases of the integrated model are given: A simulation-driven planning tool allows a clinician to interactively explore treatment options. And a study is performed using the model to optimize the placement of the FUS device. The model is furthermore used to study a novel motion-compensation FUS treatment system by replacing hardware and patient by model predictions. We estimate the efficiency of the treatment system in combination with a clinically available FUS device and MR imaging device (6.67 Hz image rate, 20 Hz FUS control rate) to be above 80%. This estimated efficiency of the new treatment system is expected to be already suited for clinical applications.
... Parallel threads running the same instructions on multiple data (SIMD) can coalesce the memory accesses to optimally use the global memory bandwidth. Due to these properties, GPGPU parallelization has been applied to the simulation of bio-physical phenomena, for example elasticity [36], [37]; wave propagation [38], [39]; and bioheat simulation [40], [41]. ...
Objective:
Focused ultrasound (FUS) is rapidly gaining clinical acceptance for several target tissues in the human body. Yet, treating liver targets is not clinically applied due to a high complexity of the procedure (noninvasiveness, target motion, complex anatomy, blood cooling effects, shielding by ribs, and limited image-based monitoring). To reduce the complexity, numerical FUS simulations can be utilized for both treatment planning and execution. These use-cases demand highly accurate and computationally efficient simulations.
Methods:
We propose a numerical method for the simulation of abdominal FUS treatments during respiratory motion of the organs and target. Especially, a novel approach is proposed to simulate the heating during motion by solving Pennes' bioheat equation in a computational reference space, i.e., the equation is mathematically transformed to the reference. The approach allows for motion discontinuities, e.g., the sliding of the liver along the abdominal wall.
Results:
Implementing the solver completely on the graphics processing unit and combining it with an atlas-based ultrasound simulation approach yields a simulation performance faster than real time (less than 50-s computing time for 100 s of treatment time) on a modern off-the-shelf laptop. The simulation method is incorporated into a treatment planning demonstration application that allows to simulate real patient cases including respiratory motion.
Conclusion:
The high performance of the presented simulation method opens the door to clinical applications.
Significance:
The methods bear the potential to enable the application of FUS for moving organs.
Hyperthermia is a type of cancer treatment in which cancer cells are exposed to high temperatures (up to 44–45°C). Research has shown that high temperatures can damage and kill cancer cells, by a localized and concentrated heating source. By killing cancer cells and damaging proteins and structures within cells, hyperthermia may shrink tumors, with minimal injury to normal tissues. Penne’s bio-heat equation is used to model a heat diffusion process inside a tumor, modeled as a spherical domain with magnetic nanoparticles distributed within the diseased tissue. These magnetic particles are considered as point heat sources. Heat is generated as the result of magnetic relaxation mechanisms (Brownian and Neel relaxation) by the application of alternating magnetic fields. The Bio-Heat equation is solved using Monte Carlo techniques. Monte Carlo simulations are based on departing random walkers from the point where temperature is going to be determined. The probability in each step of the random walk is given by the coefficients of the nodal temperatures after a Finite Difference Discretization of the Penne’s bio-heat diffusion equation. The main advantage of Monte Carlo simulations versus classical numerical methods lies in the possibility of solving the temperature in a specific point without solving for all the points within the domain. This feature and the fact that each random walk is independent from each other results in an easy parallelization of the computer code. Parametric studies of the temperature profiles are carried out to study the effect of different parameters like the heat generation rate, perfusion rate and diameter of the point source on the maximum temperature and on the temperature profile.
Over the past years, high intensity focused ultrasound therapy has become a promising therapeutic alternative for non-invasive tumor treatment. The basic idea of this interventional approach is to apply focused ultrasound waves to the tumor tissue such that the cells are heated and hence destroyed. Since it is quite difficult to assess the quality of this non-invasive therapy, there is a dire need for computer support in planning, conduction, and monitoring of such treatments. In this work, we propose efficient simulation techniques for focused ultrasound waves as well as their heat dis- semination using current graphics hardware as a numerical co-processor. We achieve speed-ups between 10 and 700 for the single simulation steps compared to an optimized CPU solution, overall resulting in a significant performance gain over previous approaches for simulation of focused ultrasound.
This paper describes a modeling method of the tissue temperature evolution over time in hyper or hypothermia. The tissue temperature evolution over time is classically described by Pennes' bioheat transfer equation which is generally solved by a finite difference method. In this paper we will present a method where the bioheat transfer equation can be algebraically solved after a Fourier transformation over the space coordinates. As an example, we implemented this method for the simulation of a percutaneous high intensity ultrasound hepatocellular carcinoma curative treatment and compared it with the finite difference method and experimental data.
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 24,000 W/cm(2). 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/cm(2), 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.
To test the feasibility of noninvasive magnetic resonance (MR) imaging-guided focused ultrasound surgery (FUS) of benign fibroadenomas in the breast.
Eleven fibroadenomas in nine patients under local anesthesia were treated with MR imaging-guided FUS. Based on a T2-weighted definition of target volumes, sequential sonications were delivered to treat the entire target. Temperature-sensitive phase-difference-based MR imaging was performed during each sonication to monitor focus localization and tissue temperature changes. After the procedure, T2-weighted and contrast material-enhanced T1-weighted MR imaging were performed to evaluate immediate and long-term effects.
Thermal imaging sequences were improved over the treatment period, with 82% (279 of 342) of the hot spots visible in the last seven treatments. The MR imager was used to measure temperature elevation (12.8 degrees -49.9 degrees C) from these treatments. Eight of the 11 lesions treated demonstrated complete or partial lack of contrast material uptake on posttherapy T1-weighted images. Three lesions showed no marked decrease of contrast material uptake. This lack of effective treatment was most likely due to a lower acoustic power and/or patient movement that caused misregistration. No adverse effects were detected, except for one case of transient edema in the pectoralis muscle 2 days after therapy.
MR imaging-guided FUS can be performed to noninvasively coagulate benign breast fibroadenomas.
This review takes a retrospective look at how hyperthermia biology, as defined from studies emerging from the late 1970s and into the 1980s, mis-directed the clinical field of hyperthermia, by placing too much emphasis on the necessity of killing cells with hyperthermia in order to define success. The requirement that cell killing be achieved led to sub-optimal hyperthermia fractionation goals for combinations with radiotherapy, inappropriate sequencing between radiation and hyperthermia and goals for hyperthermia equipment performance that were neither achievable nor necessary. The review then considers the importance of the biologic effects of hyperthermia that occur in the temperature range that lies between that necessary to kill substantial proportions of cells and normothermia (e.g. 39-42 degrees C for 1 h). The effects that occur in this temperature range are compelling-including inhibition of radiation-induced damage repair, changes in perfusion, re-oxygenation, effects on macromolecular and nanoparticle delivery, induction of the heat shock response and immunological stimulation, all of which can be exploited to improve tumour response to radiation and chemotherapy. This new knowledge about the biology of hyperthermia compels one to continue to move the field forward, but with thermal goals that are eminently achievable and tolerable by patients. The fact that lower temperatures are incorporated into thermal goals does not lessen the need for non-invasive thermometry or more sophisticated hyperthermia delivery systems, however. If anything, it further compels one to move the field forward on an integrated biological, engineering and clinical level.
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.
Modern ultrasound transducer material and matching layer technology has permitted us to combine the ultrasound visualization capability with production of high-intensity focused ultrasound (HIFU) on the same ceramic crystal. This development has lead to the design of a transrectal probe for noninvasive surgery of prostate tissue by HIFU. The combined capability using the same ceramic crystal simplifies treatment planning, targeting, and monitoring of tissue before and during the HIFU treatment. This mechanically scanning transrectal probe was introduced for clinical use in 1992 for noninvasive surgery of the prostate to treat benign prostatic hyperplasia (BPH) condition. This paper reviews major steps progressing from conception to the present clinical trial status of the HIFU device. During these clinical studies generation of microbubbles and cavitation were observed. Data from microbubble generation, temperature monitoring in tissue, and autopsy of HIFU-treated animal prostates are presented. Results of human clinical studies are briefly summarized to indicate performance of the device.
To calculate the in vivo temperature distribution, the impact of blood ow on heat transfer has to be accounted for [1]. Basically, two approaches can be utilized when taking the blood ow into account in a thermal model: the continuum models and the discrete vessel models. e rst approach models the thermal impact of all blood vessels with a single, global parameter; the latter models the thermal impact of each vessel individually.
This paper discusses and analyzes the reasons of fast development of GPU computing, CUDA-enabled GPU programming model, direct matrix multiplication algorithms based on CPU and CUDA-enabled GPU. In three different environments of VC++2008, Matlab 2009b and Mathematica 8, for matrices of different dimensions, we compare execution efficiency by means of runtime. For research and study, GPU Computing in mathematica software systems provides a good choice because of their advantages of low cost, ease of use, high efficiency.
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.
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To evaluate different cut-off temperature levels for a threshold-based prediction of the coagulation zone in magnetic resonance (MR)-guided radiofrequency (RF) ablation of liver tumours.
Temperature-sensitive measurements were acquired during RF ablation of 24 patients with primary (6) and secondary liver lesions (18) using a wide-bore 1.5 T MR sytem and compared with the post-interventional coagulation zone. Temperature measurements using the proton resonance frequency shift method were performed directly subsequent to energy application. The temperature maps were registered on the contrast-enhanced follow-up MR images acquired 4 weeks after treatment. Areas with temperatures above 50°, 55° and 60°C were segmented and compared with the coagulation zones. Sensitivity and positive predictive value were calculated.
No major complications occurred and all tumours were completely treated. No tumour recurrence was observed at the follow-up examination after 4 weeks. Two patients with secondary liver lesions showed local tumour recurrence after 4 and 7 months. The 60°C threshold level achieved the highest positive predictive value (87.7 ± 9.9) and the best prediction of the coagulation zone.
For a threshold-based prediction of the coagulation zone, the 60°C cut-off level achieved the best prediction of the coagulation zone among the tested levels. KEY POINTS : • Temperature monitoring can be used to survey MR-guided radiofrequency ablation • The developing ablation zone can be estimated based on post-interventional temperature measurements • A 60°C threshold level can be used to predict the ablation zone • The 50°C and 55°C temperature zones tend to overestimate the ablation zone.
Tumors implanted in the hamster flank have been irradiated in vivo with intense focused ultrasound at a spatial peak intensity of 907 W/cm2. A matrix of points was irradiated under c.w. conditions through the central plane of the tumor and perpendicular to the longitudinal axis of the sound field. A center spacing of 4 mm between matrix points and a time-on period of 2.5 sec at each point produced no cures. A spacing distance of 2 mm with 7 sec time-on period at each point increased mean survival time in non-cured animals and produced a cure rate of 29.4%. Combining the second regime of ultrasound treatment with administration of a chemotherapeutic agent (BCNU) 24 hr after irradiation did not increase mean survival time in the non-cured animals compared to the BCNU non-irradiated shams; however, the cure rate increased to 40%. Secondary tumors which were not seen in any ultrasound shams or controls were observed in all other regimes including BCNU non-irradiated shams. The incidence of secondary tumors was inversely related to the cure rate.
The relevant literature is reviewed in an attempt to clarify the mechanism of heat-dependent tumor cell destruction in vivo. Malignant cells in vivo appear to be selectively destroyed by hyperthermia in the range of 41-43 degrees C. Heat evidently affects nuclear function, expressed by an inhibited RNA, DNA and protein synthesis and characteristic arrest or delay of cells in certain locations of the cell cycle. However, as these effects appear to be reversible and are observed in normal cells as well as malignant cells, they probably do not explain the hyperthermic induced selective in vivo destruction of malignant cells. Heat-induced cytoplasmic damage appears to be of more importance. Increased lysosomal activation is observed, and is further intensified by a relatively increased anaerobic glycolysis which develops selectively in tumor cells. A hypothesis is proposed and discussed which explains the marked and selective in vivo tumor cell destruction as a consequence of the enhancing effect on the cytoplasmic damage of certain environmental factors (e.g. increased acidity, hypoxia and insufficient nutrition.
Thermal factors are believed to play a dominant role in the development of the structural and functional effects of irradiation of the nervous system with focused ultrasound at low‐megahertz frequencies. Similar mechanisms are postulated to underlie the effects of irradiation in methacrylate, which is frequently used as a test material to evaluate the influence of various factors on the results obtained. This study was undertaken to determine if thermal mechanisms alone can explain the development of trackless focal alterations (lesions) and all of their measurablecharacteristics in plastic as well as in brain. A purely thermal model is assumed and analytical prediction of lesion development and lesion size and shape for varying values of ultrasonic and thermal constants and controllable variables (frequency, focusing, dosage, target depth, etc.) is attempted. An empirical equation to describe the axial and radial ultrasonic energy distribution at the focus in water is derived. Appropriate heat transfer equations are developed for temperature distributions resulting from ultrasonic irradiation. The computed temperature profiles are plotted against nondimensionalized parameters. Temperatures at the lesion boundary were determined experimentally. Lesion dimensions read off the computed temperature profiles at the measured lesion boundary temperature are compared with experimental data. Agreement of analysis and data shows that, within the range of ultrasonic parameters used in this study, the development of lesions in the brain are explained by thermal mechanisms.
With the rapid development of clinical hyperthermia for the treatment of cancer either alone or in conjunction with other modalities, a means of measuring a thermal dose in terms which are clinically relevant to the biological effect is needed. A comparison of published data empirically suggests a basic relationship that may be used to calculate a "thermal dose." From a knowledge of the temperature during treatment as a function of time combined with a mathematical description of the time-temperature relationship, an estimate of the actual treatment calculated as an exposure time at some reference temperature can be determined. This could be of great benefit in providing a real-time accumulated dose during actual patient treatment. For the purpose of this study, a reference temperature of 43 degrees C has been arbitrarily chosen to convert all thermal exposures to "equivalent-minutes" at this temperature. This dose calculation can be compared to an integrated calculation of the "degree-minutes" to determine its prognostic ability. The time-temperature relationship upon which this equivalent dose calculation is based does not predict, nor does it require, that different tissues have the same sensitivity to heat. A computer program written in FORTRAN is included for performing calculations of both equivalent-minutes (t43) and degree-minutes (tdm43). Means are provided to alter the reference temperature, the Arrhenius "break" temperature and the time-temperature relationship both above and below the "break" temperature. In addition, the effect of factors such as step-down heating, thermotolerance, and physiological conditions on thermal dose calculations are discussed. The equations and methods described in this report are not intended to represent the only approach for thermal dose estimation; instead, they are intended to provide a simple but effective means for such calculations for clinical use and to stimulate efforts to evaluate data in terms of therapeutically useful thermal units.
QUANTITATIVE ANALYSIS of the relationship between arterial blood and tissue temperatures has not been previously attempted. Bazett and McGlone's measurements of tissue temperature indicate that the deep thermal gradient in the resting normal human forearm does not extend deeper than 2.5 cm.; deeper measurements are not reported (1). According to recent observations in this laboratory, the temperature gradient in intact human biceps muscle extended beyond this depth to approach the geometrical axis of the limb (2), as would be expected if the analytic theory of heat flow by conduction is applicable to a localized arm segment. With the stimulus of this observation, the temperatures of the normal human forearm tissues and brachial arterial blood have been measured to evaluate the applicability of heat flow theory to the forearm in basic terms of local rate of tissue heat production and volume flow of blood.
To establish clinical efficacy and safety of High Intensity Focused Ultrasound (HIFU) for the treatment of benign prostatic hyperplasia (BPH) in a multiple site clinical study.
Seven clinical sites were set up for the studies, five in the USA, one in Canada and one in Japan respectively. Sixty two patients were enrolled in these three studies. Transrectal ultrasound probes made to produce sufficient acoustic power required for focused ultrasound surgery of the prostate as well as to perform imaging of the prostate, were employed in the study. The probes ware made of 2.5, 3.0, 3.5, 4.0 and 4.5 cm focal length transducers to treat varying prostate sizes and shapes and operated at 4 MHz frequency for both imaging and treatment. The employed ultrasound device produced both transverse and longitudinal images of the prostate on the same display. The images were used for selection of tissue volume, treatment planning and monitoring of tissue during the HIFU treatment cycle. The patients in the USA and Canada were followed for two years and those in Japan were followed for one year on a regular interval. The results were evaluated for changes in the peak flow rate (Qmax in ml/s), quality of life (QOL) and International Prostate Symptom Score (IPSS).
The average pre / post treatment results at 180 days were significantly different for Qmax, QOL and IPSS 8.5/14.2 (ml/s), 4.7/2.1 and 22/10 respectively.
Under this protocol, HIFU was found safe and efficacious for the treatment of BPH. The HIFU treatment produced statistically significant results for the parameters measured with least complications. Additionally, the HIFU treatment was found to be durable.
Criteria for determining the durability of the response to transrectal high-intensity focused ultrasound (HIFU) ablation of prostate cancer have been established by calculating progression-free probability.
A series of 82 patients (mean age 71 +/- 5.7 years) with biopsy-proven localized (stage T1-T2) cancer who were not suitable candidates for radical surgery underwent transfectal HIFU ablation with the Ablatherm machine. The mean follow-up was 17.6 months (range 3-68 months). The mean serum prostate specific antigen (PSA) value and mean prostate volume were 8.11 +/- 4.64 ng/mL and 34.9 +/- 17.4 cm3, respectively. Progression was rigidly defined as any positive biopsy result, regardless of PSA concentration, or three successive PSA increases for patients with a negative biopsy (PSA velocity > or = 0.75). Times to specific events (positive biopsy and PSA elevation) were analyzed with the Kaplan-Meier survival method.
Overall, 62% of the patients exhibited no evidence of disease progression 60 months after transrectal HIFU ablation. In particular, the disease-free rate was 68% for the moderate-risk group of 50 patients (PSA < 15.0 ng/mL, Gleason sum < 8, prostate volume < 40 cm3, and number of positive biopsies < 5). For the low-risk group of 32 patients (PSA < 10 ng/mL and Gleason sum < 7), the disease-free survival rate was 83%.
Transrectal HIFU prostate ablation is an effective therapeutic alternative for patients with localized prostatic adenocarcinoma.
Focused ultrasound (US) surgery has been used to induce high temperature elevations in tissue to coagulate the proteins and kill the tissue. The introduction of noninvasive online temperature monitoring has made it possible to induce well-controlled thermal exposures. In this study, we used magnetic resonance imaging (MRI) thermometry to monitor thermal exposures near the threshold of tissue damage, and then investigated if apoptosis was induced. Rabbit brains were sonicated with an eight-sector phased array to create a large region of uniform temperature elevation at the end of a 30-s sonication. Histological examination demonstrated that apoptosis was induced in some cells. At 4 h after the sonications, the apoptotic cells constituted 9 ± 7% of identifiable cells. By 48 h after the sonications, the number of apoptotic cells had increased up to 17 ± 9%. The impact of this finding for therapy needs to be explored further. (E-mail: [email protected]
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Hyperthermia is generally regarded as an experimental treatment with no realistic future in clinical cancer therapy. This is totally wrong. Although the role of hyperthermia alone as a cancer treatment may be limited, there is extensive pre-clinical data showing that in combination with radiation it is one of the most effective radiation sensitisers known. Moreover, there are a number of large randomised clinical trials in a variety of tumour types that clearly show the potential of hyperthermia to significantly improve both local tumour control and survival after radiation therapy, without a significant increase in side-effects. Here we review the pre-clinical rationale for combining hyperthermia with radiation, and summarise the clinical data showing its efficacy.
Study of the bioheat equation with a spherical heat source for local magnetic hyperthermia
- G Gutierrez
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Research and comparison of CUDA GPU programming in Matlab and Mathematica
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