自动控制的有限元模型对温控射频消融术外文翻译.doc

广东工业大学华立学院本科毕业设计（论文）外文参考文献译文及原文 系 部 机械电气学部 专 业 电气工程及其自动化 年 级 2009级 班级名称 09电气（5）班 学 号 12030905002 学生姓名 蔡中杰 指导教师 刘大龙 目录外文文献译文1外文文献原文12外文文献译文自动控制的有限元模型对温控射频消融术摘 要背景有限元法(FEM)已经被用来模拟心脏和肝射频(RF)消融。有限元建模的复杂几何形状允许所不能解决的分析方法或有限差分模型。在这两个肝和心脏射频消融共同控制模式是温控方式。商业有限元软件包不支持自动温度控制。大多数研究人员手动控制应用的功率通过试验和错误保持提示温度电极的常数。方法我们实现了一个PI控制器控制程序用c+写的。程序检查提示温度在每一步和控制应用的电压以保持温度恒定。我们创建了一个闭循环系统组成的一个有限元模型和软件控制应用的电压。控制器的控制参数进行优化使用闭环系统仿真。结果我们报告一个温度可控的结果三维有限元模型的丽塔模型30电极。控制软件有效控制外加电压在有限元模型获得,保持电极在目标的温度高达100C。闭环系统仿真输出密切相关的有限元模型,并允许我们来优化控制参数。讨论闭环控制的有限元模型允许我们实现温度控制射频消融与最小的用户输入。关键词: 消融;肝脏消融;肝切除;射频消融;射频消融;有限元方法背景射频(RF)消融已成为相当重要的作为一个微创治疗原发性和转移性肝肿瘤。肝细胞癌是最常见的恶性肿瘤之一,全世界估计每年500000人死亡1。手术切除提供了最好的机会的长期生存,但很少是可能的。在许多肝硬化患者或多个肿瘤,肝储备不足以容忍切除和替代治疗的手段是必要的2。在射频消融,射频电流450到500千赫传递到组织通过电极插入percutaneously或手术期间。不同的模式控制电磁功率交付组织可以利用。功率控制模式(P =常数),温度控制模式(T =常数)和阻抗控制模式(Z 常数)是常用的。电磁能量转换为热能通过电阻加热。组织损伤可以发生在温度高于43C与加热的时候几个小时;在50C细胞坏死后发生 3分钟12。一个常用的模式是温控消融,电极的尖端温度保持在预定值,通常约100C。肝电极(图1)用于温控消融有温度传感元素(热敏电阻或热电偶)嵌入在刺技巧。传感器报告温度回发生器,然后应用适量的权力电极保持温度恒定。图1.1图1.1几何的全面部署丽塔模型30伞探针用于有限元模型的尖头叉子和远端10毫米的轴进行射频电流。研究人员一直在使用有限元方法来模拟两个心脏和肝射频消融(3 - 11)。当使用有限元模型温控消融,外加电压必须进行调整,以保持温度不变的提示。以前,大多数研究人员使用手动调节外加电压和试错的方法来执行温控消融3,5 - 8。实现温度控制在模型是重要的反馈获得的结果与临床设备,使用这种类型的控制。我们建立了一个临床用于肝脏消融电极(15计,丽塔医疗系统模型30),如前面描述的6。我们实现了一个控制算法对于一个PI控制器一个常用的控制器类型在一个c+程序来改变外加电压之间的时间步骤。我们使用一个封闭的循环系统仿真优化控制参数PI控制器。28方法有限元方法射频消融破坏组织的热能量,转化为电能。当前流从导电电极通过组织一个表面分散电极。组织在接近附近的电极头加热电阻加热。加热的组织在射频消融治疗是由bioheat方程:哪里是密度(公斤/立方米),c是比热(J /(公斤K),K是热导率(W /(mK)。J是电流密度(一个/ m2)和E是电场强度(V / m)。台是温度的血液,bl是血液密度(公斤/立方米),水泥胶结测井的比热容是血(J /(公斤K),和wbl是血液灌注(1 / s)。子是对流传热系数占血液灌注。Qm(W / m3)是由代谢过程产生的电能,是被忽视的,因为它是小的比其他条款13。方程(1)定义解决方案在空间域包括电极和组织。组织性能的假定温度独立和更详细地描述6。我们使用商业软件ABAQUS /标准6.3(Hibbitt,卡尔森&索伦森,Inc .的波塔基特,国际扶轮)解决耦合热电气分析。所有的分析是基于太阳叶片- 1000工作站配备2.5 GB内存和80 GB的硬盘空间。图1.1显示了几何的丽塔模型30、四叉电极我们用于我们的模型。电极放置在一个汽缸(80毫米,直径50毫米长度)的肝组织。外表面缸被设置为37C(热边界条件)和0 V(电边界条件)。我们进行准静态分析。由于对称的安排,我们可以减少计算时间只建模四分之一的汽缸。我们使用相同的模型在之前的一项研究3;模型包括 35000四面体元素和 7000节点。节点间距很小旁边的电极(0.2毫米)和更大的在模型边界(2毫米)。灌注是包含在模型根据是模型14。血液灌注wbl用于该模型6.4打出1 / s15。一个输入文件被提交到有限元分析中,几何、材料性质、边界条件的步骤的时间和指定的。应用电压是一个边界条件和保持常数在每个步骤。有限元分析结果文件中创建了一个温度的所有节点的有限元模型的步骤结束时写的。我们创建了一个c+程序,读取温度电极头从结果文件并创建一个新的输入文件,应用电压设置根据控制算法;C + +程序然后调用有限元分析和等待,直到下一个步骤是完成了。我们实现了一个PI控制器在我们的控制算法。闭环系统仿真因为有限元模型需要几个小时才能完成,使用有限元模型优化控制参数是不可行。因此我们使用闭环仿真调整控制器的参数,然后用这些参数的有限元模型。在实现控制器,我们分析了动态系统(即有限元模型)来控制。这个系统是由电极的烧蚀,组织,和分散电极。系统的输入变量是电压应用到电极。输出变量是温度测量电极的尖端。最初,我们确定了阶跃响应通过应用一个恒定电压为180年代的25 V。然后我们接近这个系统的传递函数的离散传递函数以下形式:我们使用了控制系统仿真软件安娜2.52(免费软件,控制工程,技术部门的。大学。维也纳/奥地利)来分析控制系统。这个软件允许我们近似系统从其阶跃响应通过递归最小平方算法,给出了参数a0、a1、a2、b1和b2的(2)。图2显示了一步反应的原始动力系统(即有限元模型)和近似根据(2)。这些参数用于近似在(2):a0 = 1.0,a1、a2 = 0.127 = -0.959,b1,b2 = -1.150 = 1.734。采样时间的近似系统10年代,因为那也是以后的采样时间使用在数字PI控制器。这确保了更精确的仿真模型的闭环控制系统。图2.1图2.1阶跃响应的原始动力系统(有限元模型)和近似。一旦我们确定了一个近似的动态系统(有限元模型),我们设计了一个反馈控制系统。有不同的方法控制提示温度如PID控制、自适应控制、神经网络预测控制和模糊逻辑控制。我们选择了相对简单的PI控制器对我们控制系统。图3显示了完整的闭环控制系统。Ts是所需的设置提示温度和Tt是当前提示温度。PI控制器的输入e = Ts - Tt。PI控制器的输出u(对应于应用电压)被送入动态系统。图2.2图2.2闭环系统中加入一个PI控制器和动态系统(有限元模型)。传递函数的PI控制器:方程(3)可以在时域的描述:实现该控制器在软件开发中,我们必须使用离散时域版(4),第二学期,(5)代表的近似积分术语(4)通过梯形数值积分。PI控制器的行为是由这两个参数Kp和接近。我们模拟闭环系统的行为与软件安装在猪体内的实验与丽塔500发电机和模型30我们认为电极需要1到2分钟的提示温度达到目标温度100C,即温度用于临床病例在我们机构。在丽塔500发电机不允许记录的提示温度信号,所以我们没有确切数据的提示温度随着时间的推移。实证性地选择参数PI控制器来减少超调,获得类似的时间行为在体内实验。我们使用的参数PI控制器是Kp = 0.02,Ki = 0.0064。图2.3显示了结果的闭环控制系统仿真。目标100C的咀温度达到100年代后开始消融。超调量为11%,148年代后达成。最大电压24.5 V应用100年代之后。图2.3图2.3时间行为的提示温度和外加电压的闭环系统。上面的曲线显示提示温度,较低的曲线显示了外加电压。光曲线显示结果的控制系统仿真。黑暗的曲线显示结果的有限元模型控制的控制软件。控制有限元模型我们实现了PI控制器的参数所引起的控制系统仿真在控制程序用c+写的。软件控制程序确定了外加电压和步骤时间。一个输入文件被创建和ABAQUS有限元分析解决了有限元模型。有限元分析结果文件的创建,其中包括在所有节点的温度。小费温度读取结果文件的控制程序。然后,确定了外加电压和步长为下一步,和有限元分析是重启与修改输入文件。减小步长(即时间,有限元分析模拟模型与恒压)总计算时间变长。作为妥协,我们选择10年代作为初始步长。注意,有限元解算器划分成更小的增量的每一步,从0.05秒。同时,有限元解算器进行收敛测试来确保增量尺寸足够小。这个计划被重复,直到消融被模拟为所需的时间。图7是一个流程图的算法实现的控制程序。初始步长是十年代。随后,步长增加一旦提示温度变化的步骤之间减少低于一定值。图2.4图2.4流程图的控制软件实现PI控制算法。我们模拟的消融了12分钟利用有限元模型和控制程序。仿真花了250分钟来运行,分为35级。单个步骤6和11分钟之间了运行在有限元分析。不使用控制程序、手动交互是必要的在每一步后手动更改输入文件进行有限元分析,并应用一个新的输入电压和设置步长。在这种情况下,运营商必须检查结果文件在每个步骤(即在6到11分钟间隔)、修改输入文件并重启有限元分析。结果与讨论图2.4显示了生成的提示温度和外加电压第一200年代的闭环系统组成的有限元模型和控制软件。没有结果显示在200年代以来几乎没有改变一旦设置提示温度了。图4还显示了结果的控制系统仿真。有很好的相关关系控制仿真和闭环系统组成的有限元模型和控制软件。我们解释这两者之间的偏差不准确的近似(见(2)和差异在步骤大小。在控制系统仿真一个常数采样时间(即步骤时间)的10年代被使用。然而,该算法实现控制程序没有使用固定步长时期。一步提高了时间如果改变提示温度的步骤之间是低于一定值。注意参数的控制器必须修改当边界条件(如灌注),电极几何形状等变化。否则会有变化的闭环系统的动态行为。图5显示了温度和电压的有限元模型由同一PI控制器两例。光图显示的行为没有将灌注在有限元模型中,黑暗的图表显示了行为相同的有限元模型与灌注(如无花果。4)。两个超和沉降时间的提示温度较高的情况,灌注同时,电压要求保持提示温度高于设定温度价值因为灌注进行热了。获得相同的性能在初始阶段在这两种情况下,不同的控制器必须被使用,如PI控制器的参数进行了修正。我们的模型只包括一个季度的实际的电极。在模型中,如果不均匀加热由于血管发生时,电极将获得不同温度下6。在这种情况下,温度最热的电极应该用于控制以避免组织过热。图3.1图3.1时间行为的提示温度和外加电压的闭环系统。上面的曲线显示提示温度,较低的曲线显示了外加电压。光曲线显示的结果没有灌注控制有限元模型。黑暗的曲线显示结果的控制有限元模型将灌注。在肝射频消融,消融次临床用于上升到35分钟。自加热周期相对小得多(1到2分钟。),它不是至关重要的时间行为的控制算法控制算法中再现了临床设备在加热期间。从我们的经验中温度分布的有限元模型达到接近稳态仿真结束时由于长期模拟次数。只要提示温度保持在一个小范围目标周围的温度在最初的加热期间,模型结果(即最终温度分布)应该没有显著差异。然而,随着知识的实际控制参数和算法的商业设备(如获得测量),准确模拟这些设备可以使用我们的方法。结 论我们实现了一个闭环控制系统,一个有限元模型,自动温控射频消融的模拟。我们进一步用闭环控制系统仿真优化控制参数。此前,研究人员经常应用恒功率,或使用耗时的试错方法来确定所需电压。此外,如果控制参数和算法的商业设备是已知或可以测量,准确模拟商业设备是可能的。作者的贡献DH进行计算机模拟。詹参与设计的研究。所有作者阅读和批准最终的手稿。确认这项工作是支持HL56413 NIH的资助。参 考 文 献1 Bosch FX, Ribes J, Borras J:Epidemiology of primary liver cancer.2 Semin Liver Dis1999,19:271-85.PubMedAbstract3 Curley SA, Cusack JC Jr, Tanabe KK, Stoelzing O, Ellis LM:Advances in the treatment of liver tumors.4 Curr Probl Surg2002,39:449-571.PubMedAbstract|PublisherFullText5 Haemmerich D, Staelin ST, Tungjitkusolmun S, Lee FT Jr, Mahvi DM, Webster JG:Hepatic bipolar radio-frequency ablation between separated multiprong electrodes.6 IEEE Trans Biomed Eng2001,48:1145-52.PubMedAbstract|PublisherFullText7 Tungjitkusolmun S, Woo EJ, Cao H, Tsai JZ, Vorperian VR, Webster JG:Finite element analyses of uniform current density electrodes for radio-frequency cardiac ablation.8 IEEE Trans Biomed Eng2000,47:32-40.PubMedAbstract|PublisherFullText9 Panescu D, Whayne JG, Fleischman SD, Mirotznik MS, Swanson DK, Webster JG:Three-dimensional finite element analysis of current density and temperature distributions during radio-frequency ablation.10 IEEE Trans Biomed Eng1995,42:879-890.PubMedAbstract|PublisherFullText11 Tungjitkusolmun S, Staelin ST, Haemmerich D, Tsai JZ, Cao H, Webster JG, Lee FT, Mahvi DM, Vorperian VR:Three-dimensional finite-element analyses for radio-frequency hepatic tumor ablation.12 IEEE Trans Biomed Eng2002,49:3-9.PubMedAbstract|PublisherFullText13 Jain MK, Wolf PD:Temperature-controlled and constant-power radio-frequency ablation: what affects lesion growth?14 IEEE Trans Biomed Eng1999,46:1405-1412.PubMedAbstract|PublisherFullText15 Chang IA, Nguyen UD:Thermal modeling of lesion growth with radiofrequency ablation devices.16 BiomedEngOnline2004,3:27.PubMedAbstract|BioMedCentralFullText|PubMedCentralFullText17 Chang I:Finite element analysis of hepatic radiofrequency ablation probes using temperature-dependent electrical conductivity.18 BiomedEngOnline2003,2:12.PubMedAbstract|BioMedCentralFullText|PubMedCentralFullText19 Liu Z, Lobo SM, Humphries S, Horkan C, Solazzo SA, Hines-Peralta AU, Lenkinski RE, Goldberg SN:Radiofrequency tumor ablation: insight into improved efficacy using computer modeling.20 AJR Am J Roentgenol2005,184:1347-52.PubMedAbstract|PublisherFullText21 Gopalakrishnan J:A mathematical model for irrigated epicardial radiofrequency ablation.22 Ann Biomed Eng2002,30:884-93.PubMedAbstract|PublisherFullText23 Graham SJ, Chen L, Leitch M, Peters RD, Bronskill MJ, Foster FS, Henkelman RM, Plewes DB:Quantifying tissue damage due to focused ultrasound heating observed by MRI.24 Magn Reson Med1999,41:321-8.PubMedAbstract|PublisherFullText25 Chato JC:Heat transfer to blood vessels.26 J Biomech Eng1980,102:110-8.PubMedAbstract27 Pennes HH:Analysis of tissue and arterial blood temperatures in the resting human forearm.28 J Appl Physiol1948,1:93-122.29 Ebbini ES, Umemura S, Ibbini M, Cain CA:A Cylindrical-section ultrasound phased-array applicator for hyperthermia cancer-therapy.30 IEEE Trans Ultrason Ferroelectr Freq Control1988,35:561-572.PublisherFullText外文文献原文Automatic control of finite element models for temperature-controlled radiofrequency ablationAbstractBackgroundThe finite element method (FEM) has been used to simulate cardiac and hepatic radiofrequency (RF) ablation. The FEM allows modeling of complex geometries that cannot be solved by analytical methods or finite difference models. In both hepatic and cardiac RF ablation a common control mode is temperature-controlled mode. Commercial FEM packages dont support automating temperature control. Most researchers manually control the applied power by trial and error to keep the tip temperature of the electrodes constant.MethodsWe implemented a PI controller in a control program written in C+. The program checks the tip temperature after each step and controls the applied voltage to keep temperature constant. We created a closed loop system consisting of a FEM model and the software controlling the applied voltage. The control parameters for the controller were optimized using a closed loop system simulation.ResultsWe present results of a temperature controlled 3-D FEM model of a RITA model 30 electrode. The control software effectively controlled applied voltage in the FEM model to obtain, and keep electrodes at target temperature of 100C. The closed loop system simulation output closely correlated with the FEM model, and allowed us to optimize control parameters.DiscussionThe closed loop control of the FEM model allowed us to implement temperature controlled RF ablation with minimal user input.Keywords:ablation; liver ablation; hepatic ablation; radiofrequency ablation; RF ablation; finite element methodBackgroundRadio-frequency (RF) ablation has become of considerable interest as a minimally invasive treatment for primary and metastatic liver tumors. Hepatocellular carcinoma is one of the most common malignancies, worldwide with an estimated annual number of 500,000 deaths1. Surgical resection offers the best chance of long-term survival, but is rarely possible. In many patients with cirrhosis or with multiple tumors, hepatic reserve is inadequate to tolerate resection and alternative means of treatment are necessary2. In RF ablation, RF current of 450 to 500 kHz is delivered to the tissue via electrodes inserted percutaneously or during surgery. Different modes of controlling the electromagnetic power delivered to tissue can be utilized. Power-controlled mode (P= constant), temperature-controlled mode (T= constant) and impedance-controlled mode (Z constant) are commonly used. The electromagnetic energy is converted to heat by resistive heating. Tissue damage can occur at temperatures above 43C with heating times of several hours; at 50C cell necrosis occurs after 3 min12. A commonly used mode is temperature-controlled ablation, where the tip temperature of the electrodes is kept at a predetermined value, usually around 100C. The hepatic electrodes (Fig.1) used for temperature-controlled ablation have temperature sensing elements (thermistors or thermocouples) embedded in the prong tips. The sensors report temperature back to the generator, which then applies an appropriate amount of power to the electrode to keep the temperature constant.Geometry of fully deployed Rita model 30 umbrella probe used in FEM model. The prongs and the distal 10 mm of the shaft conduct RF current.Researchers have been using the finite element method (FEM) to simulate both cardiac and hepatic RF ablation3-11. When using the FEM to model temperature-controlled ablation, the applied voltage has to be adjusted to keep the tip temperature constant. Previously, most researchers used manual adjustment of applied voltage and trial-and-error methods to perform temperature-controlled ablation3,5-8. Implementation of temperature-controlled feedback in models is of importance to obtain results comparable to clinical devices that use this type of control. We modeled a clinically used hepatic ablation electrode (15 gauge, RITA medical systems model 30) as described previously6. We implemented a control algorithm for a PI controller a commonly used controller type in a C+ program to change the applied voltage between the time steps. We used a closed loop system simulation to optimize control parameters for the PI controller.Methods1.3.1 Finite element methodRF ablation destroys tissue by thermal energy, which is converted from electric energy. The current flows from the conductive electrode through the tissue to a surface dispersive electrode. Tissue in close vicinity of the electrode tip is heated by resistive heating.The heating of tissue during RF ablation is governed by the bioheat equation:whereis the density (kg/m3),cis the specific heat (J/(kgK), andkis the thermal conductivity (W/(mK).Jis the current density (A/m2) andEis the electric field intensity (V/m).Tblis the temperature of blood,blis the blood density (kg/m3),cblis the specific heat of the blood (J/(kgK), andwblis the blood perfusion (1/s).hblis the convective heat transfer coefficient accounting for the blood perfusion.Qm(W/m3) is the energy generated by metabolic processes and was neglected since it is small compared to the other terms13. Equation (1) defines the solution in the spatial domain encompassing electrodes and tissue.Tissue properties were assumed temperature independent and are described in more detail in6. We used the commercial software ABAQUS/Standard 6.3 (Hibbitt, Karlsson & Sorensen, Inc., Pawtucket, RI) for solving the coupled thermo-electrical analysis. All analysis was performed on a SUN Blade-1000 workstation equipped with 2.5 GB of RAM and 80 GB of hard disk space.Fig.1shows the geometry of the RITA model 30, 4-prong electrode we used in our models. The electrode was placed within a cylinder (80 mm diameter, 50 mm length) of liver tissue. The outer surfaces of the cylinder were set to 37C (thermal boundary condition), and 0 V (electrical boundary condition). We performed quasi-static analysis. Due to the symmetry of the arrangement, we could reduce computing time by only modeling a quarter of the cylinder. We used the same model as in a previous study3; the model consisted of 35,000 tetrahedral elements and 7,000 nodes. The node spacing was small next to the electrode (0.2 mm) and larger at the model boundary (2 mm). Perfusion was included in the model according to the Pennes model14. The blood perfusionwbl used in this model was 6.410-31/s15.An input file was submitted to ABAQUS, in which geometry, material properties, step time and boundary conditions were specified. The applied voltage was one of the boundary conditions and remained constant during each step. ABAQUS created a results file in which temperatures of all nodes of the FEM model at the end of the step were written. We created a C+ program that reads the temperature at the electrode tip from the results file and creates a new input file where the applied voltage is set according to a control algorithm; the C+ program then calls ABAQUS and waits until the next step is completed. We implemented a PI controller in our control algorithm.Closed loop system simulationSince the FEM model takes several hours to complete, using the FEM model to optimize control parameters was not feasible. Therefore we used a closed loop simulation to adjust parameters of the controller, and then used these parameters in the FEM model. Before implementing the controller, we analyzed the dynamic system (i.e. the FEM model) to be controlled. This system consisted of the ablation electrode, tissue, and dispersive electrode. The input variable of the system was the voltage applied to the electrode. The output variable was the temperature measured at the tip of the electrode. Initially, we determined the step response by applying a constant voltage of 25 V for 180 s. We then approximated the transfer function of this system by a time-discrete transfer function of the following form:We used the control system simulation software ANA 2.52 (Freeware, Dept. of Control Engineering, Tech. Univ. Vienna/Austria) to analyze the control system. This software allowed us to approximate the system from its step response by a recursive least square algorithm and gave the parametersa0,a1,a2,b1andb2of (2). Fig.2shows the step responses of the original dynamic system (i.e. the FEM model) and of the approximation according to (2). The parameters used for the approximation in (2) were:a0= 1.0,a1= -0.959,a2= 0.127,b1= 1.734,b2= -1.150. The sampling time of the approximated system was 10 s, since that was also the sampling time used later in the digital PI controller. This ensured a more accurate simulation model of the closed-loop control system.Step response of the original dynamic system (FEM model) and of the approximation.Once we had identified an approximation of the dynamic system (FEM model), we designed a feedback control system. There are different ways of controlling the tip temperature such as PID control, adaptive control, neural network prediction control and fuzzy logic control. We chose the relatively simple PI controller for our control system. Fig.3shows the complete closed-loop control system.Tsis the desired set tip temperature andTtis the current tip temperature. The input of the PI controllere=Ts-Tt. The output of the PI co