【正文】 p system incorporating a PI controller and the dynamic system (FEM model). The transfer function of the PI controller is: Equation (3) can be described in the timedomain by: To implement this controller in software, we have to use the discrete timedomain version of (4), The second term of (5) represents the approximation of the integral term in (4) by trapezoidal numerical integration. The behavior of the PI controller is determined by the two parameters Kp and Ki. We simulated the behavior of the closedloop system with the software ANA. From invivo experiments in pigs with the RITA 500 generator and the Model 30 electrode we determined that it takes between 1 and 2 min for the tip temperature to reach a target temperature of 100176。 the model consisted of ~35,000 tetrahedral elements and ~7,000 nodes. The node spacing was small next to the electrode ( 16 mm) and larger at the model boundary (2 mm). Perfusion was included in the model according to the Pennes model [14]. The blood perfusion wbl used in this model was Sorensen, Inc., Pawtucket, RI) for solving the coupled thermoelectrical analysis. All analysis was performed on a SUN Blade1000 workstation equipped with GB of RAM and 80 GB of hard disk space. Fig. 1 shows the geometry of the RITA model 30, 4prong 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 37176。K)). J is the current density (A/m2) and E is the electric field intensity (V/m). Tbl is the temperature of blood, ρbl is the blood density (kg/m3), cbl is the specific heat of the blood (J/(kgC. The hepatic electrodes (Fig. 1) used for temperaturecontrolled 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. 14 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 ablation [311]. When using the FEM to model temperaturecontrolled ablation, the applied voltage has to be adjusted to keep the tip temperature constant. Previously, most researchers used manual adjustment of applied voltage and trialanderror methods to perform temperaturecontrolled ablation [3,58]. Implementation of temperaturecontrolled feedback in models is of importance to obtain results parable 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 previously[6]. We implemented a control algorithm for a PI controller – a monly 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. 15 Methods Finite element method RF 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: where ρ is the density (kg/m3), c is the specific heat (J/(kg at 50176。 13 finite element method Background Radiofrequency (RF) ablation has bee of considerable interest as a minimally invasive treatment for primary and metastatic liver tumors. Hepatocellular carcinoma is one of the most mon malignancies, worldwide with an estimated annual number of 500,000 deaths [1]. Surgical resection offers the best chance of longterm 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 necessary [2]. 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 electromagic power delivered to tissue can be utilized. Powercontrolled mode (P = constant), temperaturecontrolled mode (T = constant) and impedancecontrolled mode (Z constant) are monly used. The electromagic energy is converted to heat by resistive heating. Tissue damage can occur at temperatures above 43176。 radiofrequency ablation。 liver ablation。t support automating temperature control. Most researchers manually control the applied power by trial and error to keep the tip temperature of the electrodes constant. Methods We 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. Results We present results of a temperature controlled 3D 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 100176。 確認(rèn) 這項(xiàng)工作是支持 HL56413 NIH的資助。詹參與設(shè)計(jì)的研究。此外 ,如果控制參數(shù)和算法的商業(yè)設(shè)備是已知或可以測(cè)量 ,準(zhǔn)確模擬商業(yè)設(shè)備是可能的。我們進(jìn)一步用閉環(huán)控制系統(tǒng)仿真優(yōu)化控制參數(shù)。然而 ,隨著知識(shí)的實(shí)際控制參數(shù)和算法的商業(yè)設(shè)備 (如獲得測(cè)量 ),準(zhǔn)確模擬這些設(shè)備可以使用我們的方法。從我們的經(jīng)驗(yàn)中溫度分布的有限元模型達(dá)到接近穩(wěn)態(tài)仿真結(jié)束時(shí)由于長(zhǎng)期模擬次數(shù)。自加熱周期相對(duì)小得多 (1到 2分鐘。黑暗的曲線顯示結(jié)果的控制有限元模型將灌注。上面的曲線顯示提示溫度 ,較低的曲線顯示了外加電壓。在這種情況下 ,溫度最熱的電極應(yīng)該用于控制以避免組織過(guò)熱。我們的模型只包括一個(gè)季度的實(shí)際的電極。兩個(gè)超和沉降時(shí)間的提示溫度較高的情況 ,灌注同時(shí) ,電壓要求保持提示溫度高于設(shè)定溫度價(jià)值因?yàn)楣嘧⑦M(jìn)行熱了。光圖顯示的行為沒(méi)有將灌注在有限元模型中 ,黑暗的圖表顯