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FINITE ELEMENT MODELING OF HEPATIC RADIO FREQUENCY ABLATION

by Dieter G. Haemmerich

A dissertation submitted in partial fulfillment of the requirements for the degree of

Doctor of Philosophy (Biomedical Engineering)

at the UNIVERSITY OF WISCONSIN – MADISON 2001

i ACKNOWLEDGEMENTS I am most grateful to my academic adviser Dr. John Webster for his support, encouragement, help, for holding ‘flexible’ office hours, and having time whenever I felt the need for discussion. His work ethics will always be an inspiration to me, as well as his integrity. I want to thank Dr. Willis Tompkins for his advice, and especially for his ongoing support on numerous occasions (often without my knowledge). My appreciation goes to Dr. Fred Lee, Jr. and Dr. David Mahvi for their encouragement, enthusiasm, and for providing a fruitful collaborative environment. I want to thank Dr. Daniel van der Weide and Dr. Wally Block for his participation in my committee. Further I want to express my thanks to my colleagues Dr. Supan Tungjitkusolmun, Dr. JangZern Tsai, Dr. Andrew Wright, Dr. Tyler Staelin, Chris Johnson, Young-Bin Choy, and Dr. Hong Cao for a productive collaboration. I am most grateful to my family for all their support and love. Finally I want to thank my girlfriend, Dr. Sumita Furlong, for her love, support and understanding of what it takes to complete a doctoral degree.

ii CONTENTS Acknowledgements

i

Contents

ii

Abstract

iii

Chapter I

Introduction

Chapter II

Automatic control of finite element models for

1 14

temperature-controlled hepatic radio-frequency ablation Chapter III

Hepatic bipolar radio- frequency ablation between

33

separated multiprong electrodes Chapter IV

Finite element analysis of hepatic multiple probe radio-

63

frequency ablation Chapter V

Multiple Probe Hepatic Radio-Frequency Ablation:

86

ex-vivo experiments in the porcine model Chapter VI

Hepatic bipolar radio- frequency ablation creates lesions

102

close to blood vessels – A Finite Element study Chapter VII

FEM model of Cool- Tip probe next to blood vessel:

129

Comparison to 10-prong probe Chapter VIII

Assessment of Heat Dissipation in Radio-Frequency

138

Ablation: A Finite Element Study Chapter IX

Ablation at Audio Frequencies Preferentially Targets

156

Tumor: A Finite Element Study Appendix

How to create model input files for ABAQUS Solver

174

iii FINITE ELEMENT MODELING OF HEPATIC RADIO FREQUENCY ABLATION

Dieter Haemmerich

Under the supervision of Professor John G. Webster at the University of Wisconsin-Madison

ABSTRACT Radio-Frequency (RF) ablation is a minimally invasive method for treatment of primary and metastatic hepatic tumors. A catheter is introduced transcutaneously into the tumor, and tissue is heated up by application of radio-frequency current. In this work, I present the application of the Finite Element Method (FEM) for creating models of hepatic RF ablation to evaluate and improve catheter design. In Chapter II I present an automated method for FEM modeling temperaturecontrolled RF ablation. In Chapter III I present a novel bipolar method, where current travels between two multiprong electrodes instead of between a single electrode and a dispersive electrode. I present FEM models, and in-vivo results for the bipolar method. Bipolar RF ablation creates about three times larger lesions compared to conventional RF ablation. In Chapter IV I present FEM analysis of three different methods that allow multiple usage of RF catheters simultaneously. Currently, commercial available generators only allow use of a single RF probe at a time. Use of multiple probes reduces treatment time and allows treatment of large tumors, or multiple metastases simultaneously.

iv In Chapter V I present a prototype developed from a commercial RF system, which allows use of two RF probes at a time. RF power is rapidly switched between two probes. Effectively, both probes heat up simultaneously, and by varying the time interval for which power is applied to each probe, both probes can be kept at same temperature. I present exvivo results that prove feasibility of this method. In Chapter VI I present FEM models of the bipolar method, using 10-prong probes next to a blood vessel. Local tumor recurrence is associated with tumor cell survival next to blood vessel. Bipolar RF ablation allows creation of lesions closer to blood vessels, compared to conventional RF ablation. This may reduce local recurrence rates. In Chapter VII I present FEM models of a cool-tip probe next to a blood vessel. In Chapter VIII I evaluate four different methods that allow assessment of where heat is dissipated. In Chapter IX I show FEM models of ablation, carried out at audio frequencies. Tumor exhibits significantly different conductivity compared to normal liver tissue, most notably at lower frequencies. I evaluate if ablation at lower frequencies improves performance. Ablation at low frequencies preferentially targets tumor tissue, and preserves normal liver tissue. Higher temperatures are reached within cancer tissue than in liver tissue, compared to conventional RF ablation. This may help reduce local recurrence rates.

1

Chapter I Introduction

2

1. Carcinoma and other types of cancer Cancer is abnormal tissue growth. There are four major types of cancer: carcinomas, sarcomas, lympho mas and leukemias. Carcinomas are malignant tissues that develop on the epithelial surface, and inside the organs and glands. Carcinomas make up ~88% of all cancers. Sarcomas appear in muscle, bone, fat and connective tissue, and constitute ~2% of all canc ers. Lymphomas concern the lymphatic system, and account for ~5% of all cancers. Leukemia occurs in the bone marrow, and accounts also for ~5% of all types of cancer [1].

2. Other Treatment types of hepatic malignancies Hepatic tumors belong to the catego ry of carcinoma. Primary and secondary (i.e. metastatic) hepatic tumors belong to the most common types of tumor. Malignant hepatic tumors remain a substantial clinical problem both in the United States and worldwide. There have been an estimated 56,300 deaths in the United States from colorectal cancer in 2000 [12]. The vast majority of patients who succumb from colorectal cancer show evidence of liver metastases at the time of death [13]. Further, a "stepwise" progression of colorectal carcinoma metastases from colon-to- liver-to- lung prior to entering the systemic circulation has been described due to filtering and scavenging mechanisms in the liver and lung [14]. Complete removal of both the primary tumor and limited metastases to the liver would thus confer a theoretical survival advantage in patients without evidence of systemic disease. This hypothesis has been confirmed in several clinical studies. Removal of all macroscopic tumor in hepatic-only metastatic colorectal carcinoma brings a survival advant age [15].

3 Chemotherapy and radiation therapy are ineffective for treatment of hepatic tumors [2]. The current gold standard is surgical resection. Unfortunately, less than 30% of patients with primary or secondary liver tumors are suited for surgical resection. Even in patients suited for surgical resection, 5 year survival rates are only 30 to 45% [3]. Several types of treatment are used. They generally produce a zone of necrosis at the tumor site, where the operator can control the extent of the zone. Ava ilable techniques include ethanol injection, cryosurgical ablation, interstitial laser photocoagulation, radio- frequency (RF) ablation, and microwave tumor coagulation, where RF ablation is worldwide the most commonly used technique. The most widely used methods in the US are cryosurgical ablation and radiofrequency ablation. However, several other types of treatment are investigated. Following I give a short overview of the different ablative therapies that are under investigation for treatment of liver carcinoma.

Microwave Ablation Most of the research on microwave ablation has been carried out in Japan with little research outside Japan. A microwave generator produces microwaves, typically around 2.45 GHz, with 60 W power. Needle electrodes are introduced into the tissue, usually under ultrasound guidance. A typical treatment cycle takes 60 s, where full power is applied. This produces a lesion of about 2 cm diameter. Treatment is repeated typically three times a week, until the entire tumor is ablated. We performed some experiments using microwave ablation at our institution where we used longer treatment times of 10 min. This resulted in larger lesion sizes, roughly comparable to RF ablation. It seemed to produce more uniform lesions, especially close to

4 blood vessels, as compared to RF ablation. We also noticed a much higher temperature is reached within tissue, up to ~150 °C, whereas in RF ablation we are limited to 100 °C to avoid charring. Multiple microwave probes can be used simultaneously, which can be used for treatment of multiple metastases or for creation of one large lesion. The zone of active heating extends further away than for RF ablation. This might result in more effective tumor destruction, and ultimately smaller recurrence rates. Currently there is no commercial microwave ablation system available in the US.

Laser Ablation Thermal injury is induced using a Nd YAG (Neodymium Yttrium Aluminum Garnet) Laser. A single 400 µm fiber is used to introduce the light at optical or near- infrared frequencies into the tissue, where it is converted to heat. Light energy of 2 to 2.5 W will produce a spherical volume of necrosis 2 cm in diameter [2]. Two methods have been used to increase the volume of necrosis. One method uses multiple fibers arrayed at 2 cm spacing. The other method uses cooled-tip diffuser fibers that can deposit up to 30 W over a large area. Currently, lesions with similar dimensions as RF ablation can be produced. The energy can be delivered through fibers over 10 m of distance. A big advantage is, that the fibers are compatible with MR imaging modalities.

Ethanol Ablation Worldwide, ethanol injection is the most accepted minimally invasive therapy for treating hepatic tumors. It is easy to perform, inexpensive and shows good clinical results. However, it only received little attention within the US. Ethanol causes dehydration with subsequent

5 coagulation necrosis within neoplastic cells. The size and shape of the induced zone of necrosis is not very reproducable and depends on vascula rization and other histological characteristics. In highly vascular regions, the injected fluid gets quickly removed and therefore shows little effect. The injection is performed either as an outpatient multisession technique, or during a single treatment under general anesthesia. In encapsulated hepatocellular carcinomas a lesion of up to 8 cm in diameter can be created. In small- and medium-size hepatocellular carcinoma the results of ethanol injection are comparable to surgical resection. Ethanol injection is less effective in the treatment of liver metastases compared to RF ablation.

Cryosurgery (Cryoablation) Cryosurgery uses subzero temperatures to destroy malignant tissue. The probe is cooled down to –100 °C to –150 °C, usually with liquid nitrogen or argon. Cryosurgery probes (~ 10 mm diameter) are inserted into the liver under ultrasound guidance. The treatment process usually includes two or three freeze-thaw cycles, each freeze cycle lasting 7 to 30 min. Maximum diameter of necrosis lies between 4 cm and 5 cm. Usually, cryosurgery is a method involving open surgery since the neighboring organs have to be protected against the low temperatures, and the treatment is usually associated with bleeding that occurs after thawing of the lesion. The treatment is performed under general anesthesia, and typically a 3 to 5 day hospital stay is required. Therefore cryosurgery is substantially more expensive than the other percutaneous techniques. Tissue is destroyed by cellular dehydration and denaturation of functional and structural proteins [4]. The size of the ice-ball can be monitored using ultrasound. Many patients experience at least minor complications, such as

6 low-grade fever. Other complications include hemorrhage, thrombosis and surface liver cracking [5]. Five- year survival rates vary between different studies, usually between 30 to 50% [6].

3. Radio-Frequency Ablation Radio- frequency ablation (RFA, RF ablation) is widely used for treatment of cardiac arrhythmias, where it was first introduced by Huang et al. in 1985 [7]. In the 1990s, application of RFA for hepatic ablation began to draw attention. Until recently, a major limitation in the application of RFA for tumor ablation was the small lesion size. Currently, the largest possible lesions created with RFA lie around 4 to 4.5 cm. RFA is nowadays also used for other types of tumor treatment, such as prostate or kidney tumors. For hepatic RFA, treatment times for a single lesion usually lie between 10 min and 35 min, depending upon desired lesion size. For a treatment of most tumors, multiple applications are necessary that produce overlapping lesions as shown in figure 1.

7

Figure 1. Multiple overlapping ablations are necessary to treat large tumors

RFA uses radio- frequency current, usually around 500 kHz to heat up tissue. The voltages applied are ~100 V, with applied power up to 200 W. The RFA probe is introduced transcutaneously, in a minimally invasive fashion, into the tumor. Therefore one of the major advantages of RFA over cryoablation is, that it can be applied to ambulatory patients, using only local anesthesia. The probe is guided via ultrasound. One or more dispersive electrodes are attached, usually to the patient’s back or thigh. Current flows between the probe and the dispersive electrode. The current is carried in the tissue by ions. Ionic agitation results in frictional heat. The tissue itself is directly heated, rather than the probe itself [8]. Above ~50 °C, protein denaturation results in irreversible tissue damage [9]. Above ~70 °C, coagulation occurs, where collagens are converted to glucose. Above 100 °C, water vapor develops, and tissue charring can occur. This is undesirable, since it raises the impedance and makes the

8 treatment ineffective. Therefore, impedance between the probe and the dispersive electrode is measured during the treatment, and the generator is shut down automatically if the impedance exceeds a certain value (~ 200 to 1000 Ω, depending on generator type). Two modes of operation are clinically used: impedance-controlled and temperaturecontrolled modes. In impedance-controlled mode, power is slowly increased and shut down once impedance rises above a certain level. The impedance rise is due to charring and gas formation. The other mode is temperature-controlled mode. Some of the modern ablation probes have thermocouples embedded in some of their multiple prongs (Figure 2). The thermocouple reports the tip temperatures back to the generator. In temperature-controlled mode, usually the average tip temperature (i.e. the average of all measured tip temperatures) is controlled to be kept at a certain set temperature. The set temperature usually is between 95 °C and 100 °C. The tip temperatures are shown on the generator display, and can often also be recorded. First generation probes consisted of a single electrode, which lead to a lesion of very limited size. Today, probes with up to nine retractable prongs are clinically used (see Figures 2 and 4). Apart from the multiple prong electrodes, a clinically commonly used probe is the so-called cool-tip electrode (Figure 3). This is a single electrode (~ 1.2 mm diameter), where fluid is circulated inside the electrode (usually saline at 20 °C). The electrode, and tissue close to the electrode are kept at a low temperature. More power can be applied to the electrode, and the size of the lesion is extended. Once the circulation of the coolant is stopped, tissue close to the probe is heated above the temperature necessary to destroy tissue. With this method it is not possible to use temperature-controlled mode, since the electrode is

9 cooled. Therefore, impedance-controlled mode is used. Lesion sizes of around 3 to 4 cm can be achieved using this technique. Lesion size during the procedure is monitored with ultrasound, though the lesion is much less apparent than when cryoablation is used. There is need for more effective imaging methods to determine lesion size. Figures 2, 3 and 4 show probes currently in clinically use. There currently are three companies in the US that distribute the probes, and accompanying generators. Rita Medical (Irvine, CA) uses temperature-controlled RF ablation, whereas Radionics (Burlington, MA) and RadioTherapeutics (Sunnyvale, CA) use impedance-controlled RF ablation.

Figure 2. Starburst XL probe (RITA, CA)

10

Figure 3. Cool-Tip probe (Radionics, MA)

Figure 4. LeVeen probe (RadioTherapeutics, CA)

Five- year survival rates after RF ablation treatment are around 40%, similar to cryoablation. Often tumor recurrence is observed. A recent study showed local recurrence rates of around 40% [11], which is the result of incomplete tumor ablation. Especially, underdosed regions

11 next to blood vessels that act as a heat sink are responsible for some of the recurrences observed [16]. Figure 5 shows a RF lesion created next to two large vessels (see arrows). The vessels caused a significant deflection of the lesions due to the cooling.

Major shortcomings of current RF ablation techniques are: -

Limited lesion size makes multiple applications necessary, and may result in incomplete tumor killing

-

Inability to use multiple probes simultaneously results in long treatment times

-

Temperatures produced are not sufficient, especially close to large vessels

-

Insufficient interoperative imaging modalities

Vessels

Figure 5. Blood vessels result in lesion deflection.

12

4. References [1] M. C. Kew, “The development of hepatocellular carcinoma in humans,” Cancer Surv., vol. 5, pp. 719–739, 1985. [2] G. D. Dodd III, M. C. Soulen, R. A. Kane, T. Livraghi, W. R. Lees, Y. Yamashita, A. R. Gillams, O. I. Karahan, H. Rhim, “Minimally invasive treatment of malignant hepatic tumors: at the threshold of a major breakthrough”, Radiographics, 20, pp. 9–27, 2000. [3] C. H. Scudamore, E. J. Patterson, A. M. Shapiro, A. K. Buczkowski, “Liver tumor ablation techniques”, J Invest Surg, 10, pp. 157–164, 1997. [4] B. Rubinsky, C. Y. Lee, J. Bastacky, G. Onik, “The process of freezing and the mechanism of damage during hepatic cryosurgery”, Cryobiology, 1990, 27, pp. 85–97. [5] G. Onik, D. Atkinson, R. Zemel, M. Weaver, “Cryosurgery of liver cancer”, Semin Surg oncol, 9, 309–317, 1993. [6] N. N. Korpan, “Hepatic cryosurgery for liver metastases”, Ann Surg, 225, pp. 193–201, 1997. [7] S. Nath, D. Haines, “Biophysics and pathology of catheter energy delivery systems”, Prog Cardiovasc Dis, 37, pp. 185–204, 1995. [8] L. Organ, “Electrophysiologic principles of radiofrequency lesion making”, Appl Neurophysiol, 39, pp. 69–76, 1976. [9] W. Lounsberry, V. Goldschmidt, and C. Linke, “The early histologic changes following electrocoagulation,” Gastrointest. Endosc., vol. 41, pp. 68–70, 1995.

13 [10] S. A. Curley, B. S. Davidson, R. Y. Fleming, F. Izzo, L. C. Stephens, P. Tinkey, and D. Cromeens, “Laparoscopically guided bipolar radiofrequency ablation of areas of porcine liver”, Surg. Endosc., vol. 11, pp. 729–733, 1997. [11] L. Solbiati, T. Livraghi, S. N. Goldberg, T. Ierace, F. Meloni, M. Dellanoce, L. Cova, E. F. Halpern, and G. Scott Gazelle, “Percutaneous Radio- frequency Ablation of Hepatic Metastases from Colorectal Cancer: Long-term Results in 117 Patients”, Radiology, vol. 221, pp. 159–166, 2001. [12] R. T. Greenlee, T. Murray, S. Bolden, and P. A. Wingo, “Cancer statistics”, Ca, vol. 50, pp. 7–33, 2000. [13] L. Weiss, E. Grundmann, J. Torhorst, F. Hartveit, I. Moberg, M. Eder, C. M. FenoglioPreiser, J. Napier, C. H. Horne, M. J. Lopez, “Haematogenous metastatic patterns in colonic carcinoma: an analysis of 1541 necropsies”, J Pathol, vol. 150, pp.195–203, 1986. [14] P. H. Sugarbaker, “Metastatic inefficiency: the scientific basis for resection of liver metastases from colorectal cancer”, J Surg Oncol, vol. 3(S), pp. 158–160, 1993. [15] K. S. Hughes, “Resection of the liver for colorectal carcinoma metastases: A multiinstitutional study of indications for resection”, Surgery, vol. 103, pp.278–288, 1988. [16] A. R. Gillams and W. R. Lees, “The Importance of Large Vessel Proximity in Thermal Ablation of Liver Tumours”, RSNA 1999, Chicago, IL, 1999.

14

Chapter II

Automatic control of finite element models for temperature-controlled hepatic radio-frequency ablation

This work was submitted for publication as: D. Haemmerich, S. T. Staelin, S. Tungjitkusolmun, F. T. Lee Jr., D. M. Mahvi, and J. G. Webster, “Automatic control of finite element models for temperature-controlled hepatic radio- frequency ablation”, IEEE Trans. Biomed. Eng., 2001.

15

Abstract The 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 hepatic RF ablation the most common control mode is temperature-controlled mode. Commercial FEM packages don’t support automating temperature control. Most researchers manually control the applied power by trial and error to keep the tip temperature of the probes constant. After each time step the user has to manually check temperature and empirically assign a new voltage. 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. This control system significantly reduces user time. We present results of a controlled hepatic 3-D FEM model of a RITA model 30 probe.

16

1. Introduction Radio- 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 mortality of 1,000,000 people [1]. 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 necessary [2]. In RF ablation, RF current of 450 – 460 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), temperaturecontrolled mode (T = constant) and impedance-controlled mode (Z < constant) are commonly used. The electromagnetic energy is converted to heat by ionic agitation. Temperatures above 45 ºC to 50 ºC have been shown to cause denaturation of intracellular proteins and destruction of membranes of tumor cells, eventually resulting in cell necrosis [8]. The most commonly used mode is temperature-controlled ablation, where the tip temperature of the probes is kept at a predetermined value, usually around 100 ºC. The hepatic probes (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 probe to keep the temperature constant. Researchers have been using the finite element method (FEM) to simulate both cardiac and hepatic RF ablation [3][4][5][6][7]. When using the FEM to model temperature-

17 controlled ablation, the applied voltage has to be adjusted to keep the tip temperature constant. Previously, researchers used manual adjustment of applied voltage and trial-anderror methods to perform temperature-controlled ablation [3][5][6][7]. We have found no use of a feedback control system in conjunction with the FEM to model temperature-controlled ablation. We modeled a commonly used hepatic ablation probe (15 gauge, RITA medical systems model 30) as described previously [7]. We implemented a control algorithm for a PI controller in a C++ program to change the applied voltage between the time steps.

2. Finite element method RF ablation destroys tissue by thermal energy, which is converted from electric energy. The current flows from the conductive probe through the tissue to a surface dispersive electrode. Tissue in close vicinity of the probe tip is heated by ionic agitation.

The heating of tissue during RF ablation is governed by the bioheat equation:

∂T = ∇ ⋅ k∇T + J ⋅ E − hbl (T − Tbl ) − Qm ∂t hbl = ρ blc bl wbl ρc

(1)

where ρ is the density (kg/m3 ), c is the specific heat (J/(kg⋅K)), and k is the thermal conductivity (W/(m⋅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), cb l is the specific heat of the blood (J/(kg⋅K)), and wb l is the blood perfusion (1/s). hbl is the convective heat

18 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 terms [9]. Tissue properties were assumed temperature independent and are described in more detail in [6]. We used the commercial software ABAQUS/Standard 5.8 (Hibbitt, Karlsson & Sorensen, Inc., Pawtucket, RI) for solving the coupled thermo-electrical analysis. All analysis was performed on a HP-C180 workstation equipped with 1.1 GB of RAM and 34 GB of hard disk space. Tungjitkusolmun et al. [3] provide a detailed description of the FEM modeling process. Fig. 1 shows the geometry of the RITA model 30, 4-prong probe we used in our models. The probe was placed within a cylinder (80 mm diameter, 50 mm length) of liver tissue. The outer surfaces of the cylinder are set to 37 °C (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. The model consisted of ~35,000 tetrahedral elements and ~7,000 nodes. The node spacing is small next to the probe (0.2 mm) and larger at the model boundary (2 mm). Perfusion was included in the model according to the Pennes model [10]. The blood perfusion wb l used in this model is 6.4·10–3 1/s. An input file is submitted to ABAQUS, in which geometry, material properties, step time and boundary conditions are specified. The applied voltage is one of the boundary conditions and remains constant during each step. ABAQUS creates a results file in which temperatures of all nodes of the FEM model at the end of the step are written. We created a C++ program that reads the temperature at the probe tip from the results file and creates a

19 new input file where the applied voltage is set according to a control algorithm. We implemented a PI controller in our control algorithm.

3. Closed loop system simulation Before implementing the controller, we analyzed the dynamic system (i.e. the FEM model) to be controlled. This system consists of the ablation probe, tissue, and dispersive electrode. The input variable of the system is the voltage applied to the probe. The output variable is the temperature measured at the tip of the probe. Initially, we determined the step response by applying constant voltage for 180 s. We then approximated the transfer function of this system by a time-discrete transfer function of the following form:

G ( z) =

b1z + b2 z 2 a0 + a1z + a2 z 2

(2)

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 allows us to approximate the system from its step response by a recursive least square algorithm and gives the parameters a0, a1, a 2, b1 and b2 of (2). Fig. 2 shows 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) are: a0=1.0, a 1 = -0.959, a2 = 0.127, b1 = 1.734, b2 = –1.150. The sampling time of the approximated system was 10 s, since that is also the sampling time used la ter in the digital PI controller. This ensured a more accurate simulation model of the closed-loop control system.

20 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. 3 shows the complete closed- loop control system. Ts is the desired set tip temperature and Tt is the current tip temperature. The input of the PI controller e = Ts – Tt. The output of the PI controller u (corresponds to the applied voltage) is fed into the dynamic system. The PI controller is described in the time-domain by,

t

u = K p e + K i ⋅ ∫ e (τ )d τ

(3)

0

To implement this controller in software, we have to use the discrete time-domain version of (3),

e m + e m −1 ∆t 2 m =1 n

u n = K p en + K i ∑

(4)

The second term of (4) represents the approximation of the integral term in (3) 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 closed-loop system with the software ANA. From in- vivo experiments in pigs with the RITA 500 generator and the Model 30 probe we determined tha t it takes between 1 and 2 min for the tip temperature to reach a target

21 temperature of 100 °C. The RITA 500 generator does not allow recording of the tip temperature so we don’t have exact data of the tip temperature over time. We empirically chose parame ters for the PI controller to minimize overshoot and obtain similar temporal behavior as in the in- vivo experiments. The parameters we used for the PI controller are Kp = 0.02, Ki = 0.0064. Fig. 4 shows the results of the closed- loop control system simulation. The target tip temperature of 100 ºC is reached 100 s after start of the ablation. The maximum overshoot is 11%, which is reached after 148 s. The maximum voltage of 24.5 V is applied after 100 s.

4. Controlled FEM model We implemented the PI controller with the parameters resulting from the control system simulation in a control program written in C++. The software control program determines the applied voltage and the step time. An input file for ABAQUS is created and ABAQUS solves the FEM model. ABAQUS creates a result file, which includes the temperatures at all nodes. The tip temperature is read from the result file by the control program. The program then determines the applied voltage and step size for the next step, and ABAQUS is restarted with the modified input file. With decreasing step size (i.e. time that ABAQUS simulates the model with constant voltage) total computation time gets longer. As a compromise, we chose 10 s as the initial step size. It should be noted, that the FEM solver divides each step into smaller increments, starting at 0.05s. Also the FEM solver performs convergence tests to ensure that the increment size is sufficiently small. This scheme is repeated until the ablation has been simulated for the desired time. Fig. 6 is a flow chart of the algorithm implemented in the control program. The initial step

22 size is 10 s. Subsequently, the step size increases once the tip temperature change between the steps decreases below a certain value. We simulated ablation for 12 min using the FEM model and the control program. The simulation took 250 min to run and was divided into 35 steps. The individual steps took between 6 and 11 min to run in ABAQUS. Without using the control program, manual interaction would be necessary after each step to manually change the input file for ABAQUS and apply a new input voltage and set the step size. In this case the operator would have to check the results file after each step (i.e. in 6 to 11 min intervals), modify the input file and restart ABAQUS. Fig. 4 shows the resulting tip temperature and the applied voltage for the first 200 s of the closed loop system consisting of the FEM model and the control software. No results are shown after 200 s since there is little change once the set tip temperature is reached. Fig. 4 also shows the results of the control system simulation. There is good correlation between the control simulation and the closed loop system consisting of the FEM model and the control software. We explain deviations between the two by inaccuracies of the approximation (see (2)) and differences in step sizes. In the control system simulation a constant sampling time (i.e. step time) of 10 s was used. However, the algorithm implemented in the control program did not use constant step times. Step time was increased if the change in tip temperature between the steps was below a certain value. Note that the parameters of the controller must be modified when boundary conditions (e.g. perfusion), probe geometry etc. are changed. Otherwise there will be changes in the dynamic behavior of the closed- loop system. Fig. 5 shows the temperature and voltage of the FEM model controlled by the same PI controller

23 for two cases. The light graphs show the behavior without incorporating perfusion in the FEM model, the dark graphs show the behavior of the same FEM model with perfusion (as in Fig. 4). Both the overshoot and the settling time of tip temperature for the case with perfusion are higher. Also, the voltage required to keep the tip temperature at the set temperature value is higher because the perfusion carries heat away. To obtain the same performance during the initial period in both cases, different controllers have to be used, e.g. the parameters of the PI controller have to be modified. In hepatic RF ablation, ablation times clinically used go up to 35 min. Since the heatup period is comparibly much smaller (1–2 min.), it is not of essential importance that the temporal behaviour of the control algorithm reproduces the control algorithm used in clinical devices during the heat-up period. From our experience, the temperature distribution in the FEM model reaches close to steady state at the end of the simulation due to the long simulation times. As long as the tip temperature is kept within a small range around the target temperature after the initial heat- up period, the model results (i.e. final temperature distribution) should not differ significantly. Therefore, the type of controller used does not affect the model outcome, and a simple controller as the PI-controller used in this paper should be sufficient.

5. Conclusion We studied how a control program can improve simulation of RF ablation by FEM in temperature controlled mode. When trial-and-error methods are used to manually adjust the applied voltage, user interaction is necessary after each step. This is a very time consuming and tiresome process, since the user has to wait until a step is completed before adjusting

24 applied voltage and resubmitting the new file to the FEM solver. The scheme described above greatly improves efficiency since no human interaction is necessary during the simulation. Different control methods can easily implemented in the control program. Unfortunately the control algorithms used in commercial devices are not known. Otherwise, an even more accurate closed- loop system could be created which accurately simulates the heat-up period. However, as the heat- up period usually is not of major importance, the simple PI controller used above is sufficient.

25

6. References [1] M. C. Kew, “The development of hepatocellular carcinoma in humans,” Cancer Surv., vol. 5, pp. 719–739, Apr., 1986. [2] S. A. Curley, B. S. Davidson, R. Y. Fleming, F. Izzo, L. C. Stephens, P. Tinkey, and D. Cromeens, “Laparoscopically guided bipolar radiofrequency ablation of areas of porcine liver,” Surg. Endosc., vol. 11, pp. 729–733, July, 1997. [3] S. Tungjitkusolmun, E. J. Woo, H. Cao, J.- Z. Tsai, V. R. Vorperian, and J. G. Webster, “Thermal-electrical finite element modeling for radio- frequency cardiac ablation: effects of changes in myocardial properties,” Med. Biol. Eng. Comput., vol. 38, pp. 562–568, Sept., 2000. [4] S. Tungjitkusolmun, E. J., Woo, H. Cao, J.- Z. Tsai, V. R. Vorperian, and J. G. Webster, “Finite element analyses of uniform current density electrodes for radio-frequency cardiac ablation,” IEEE Trans Biomed. Eng., vol. 47, pp. 32-40, Jan., 2000. [5] D. Panescu, J. G. Whayne, D. Fleischman, M. S. Mirotznik, D. K. Swanson, and J. G. Webster, “Three-dimensional finite element analysis of current density and temperature distributions during radio-frequency ablation,” IEEE Trans. Biomed. Eng., vol. 42, pp. 879– 890, Sept., 1995. [6] S. Tungjitkusolmun, S. T. Staelin, D. Haemmerich, J.-Z., H. Cao, V. R. Vorperian, F. T. Lee jr., D. M. Mahvi, J. G. Webster, “Three-dimensional finite element analyses for radiofrequency hepatic tumor ablation”, IEEE Trans. Biomed. Eng., accepted 2001.

26 [7] M. K. Jain, P. D. Wolf, “Temperature-controlled and constant-power radio- frequency ablation: what affects lesion growth?”, IEEE Trans. Biomed. Eng., vol. 46, pp. 1405-1412, Dec., 1999. [8] L. Buscarini, S. Rossi, F. Fornari, M. Di Stasi, and E. Buscarini, “Laparoscopic ablation of liver adenoma by radiofrequency electrocauthery,” Gastrointest. Endosc., vol. 41, pp. 68– 70, Jan., 1995. [9] J. Chato, “Heat transfer to blood vessels,” ASME Trans Biomech Eng, vol. 102, pp. 110– 118, May, 1980. [10] H. Arkin, L. X. Xu, K. R. Holmes, “Recent Developments in modeling heat transfer in blood perfused tissues”, IEEE Trans. Biomed. Eng., vol. 41, pp. 97–107, Feb., 1994.

27 7. Figure Legends Figure 1: 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. Figure 2: Step response of the original dynamic system (FEM model) and of the approximation Figure 3: Closed loop system incorporating a PI controller and the dynamic system (FEM model). Figure 4: Temporal behavior of tip temperature and applied voltage of the closed loop system. The upper curves show the tip temperature, the lower curves show the applied voltage. The light curves show the results of the control system simulation. The dark curves show the results of the FEM model controlled by the control software. Figure 5: Temporal behavior of tip temperature and applied voltage of the closed loop system. The upper curves show the tip temperature, the lower curves show the applied voltage. The light curves show the results of the controlled FEM model without perfusion. The dark curves show the results of the controlled FEM model incorporating perfusion. Figure 6: Flowchart of the control software implementing a PI control algorithm.

28

Stainless steel shaft, conducting, 10 mm length, 2 diameter mm

15 mm Stainless steel shaft, insulated

Ni -Ti retractable electrodes, 0.5 mm diameter

Figure 1. 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.

29

Figure 2. Step Response of the original dynamic system (FEM model) and of the approximation.

H(z) + Ts

e –

PI controller

G(z) u

Dynamic system (FEM)

Tt

Figure 3. Closed Loop system incorporating a PI controller and the dynamic system (FEM model).

30

Figure 4. Temporal behavior of tip temperature and applied voltage of the closed loop system. The upper curves show the tip temperature, the lower curves show the applied voltage. The light curves show the results of the control system simulation. The dark curves show the results of the FEM model controlled by the control software.

31

Tip temp., controlled FEM, no perfusion

T (ºC), V (V)

120 100

Voltage, controlled FEM, no perfusion

80

Tip temp., controlled FEM, with perfusion

60

Voltage, controlled FEM, with perfusion

40 20 0 0

50

100

150

200

t (s) Figure 5. Temporal behavior of tip temperature and applied voltage of the closed loop system. The upper curves show the tip temperature, the lower curves show the applied voltage. The light curves show the results of the controlled FEM model without perfusion. The dark curves show the results of the controlled FEM model incorporating perfusion.

32 Initial conditions: Step size = 10 s Ts = 100 °C Ablation time=200 s

PI control algorithm: Calculate applied voltage (u)

Create ABAQUS input file

Run ABAQUS FEM solver

Read tip temperature (Tt ) from ABAQUS results file

Change in Tt < 1.5 °C

Yes Step size := Step size * 2

No

End of ablation?

Yes STOP

No

Figure 6. Flowchart of the control software implementing a PI control algorithm.

33

Chapter III

Hepatic bipolar radio-frequency ablation between separated multiprong electrodes

This work was published as: D. Haemmerich, S.T. Staelin, S. Tungjitkusolmun, F.T. Lee Jr., D.M. Mahvi, and J.G. Webster, “Hepatic bipolar radio- frequency ablation between separated multiprong electrodes”, IEEE Trans. Biomed. Eng., 48, 1145–1152, 2001.

34 ABSTRACT Radio- frequency (RF) ablation has become an important means of treatment of nonresectable primary and metastatic liver tumors. Major limitations are small lesion size, which make multiple applications necessary and incomplete killing of tumor cells, resulting in high recurrence rates. We examined a new bipolar RF ablation method incorporating two probes with hooked electrodes (RITA model 30). We performed monopolar and bipolar in-vivo experiments on three pigs. The electrodes were 2.5 cm apart and rotated 45º relative to each other. We used temperature-controlled mode at 95 ºC. Lesion volumes were 3.9 ± 1.8 cm3 (n = 7) for the monopolar case and 12.2 ± 3 cm3 (n = 10) for the bipolar case. We generated finite element models (FEMs) of monopolar and bipolar configurations. We analyzed the distribution of temperature and electric field of the finite element model. The lesion volumes for the FEM are 7.95 cm3 for the monopolar and 18.79 cm3 for the bipolar case. The new bipolar method creates larger lesions and is less dependent on local inhomogenities in liver tissue—such as blood perfusion—compared to monopolar RF ablation. A limitation of the new method is that the power dissipation of the two probes cannot be controlled independently in response to different conditions in the vicinity of each probe. This may result in nonuniform lesions and decreased lesion size.

35

1. Introduction Radio- 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 mortality of 1,000,000 people [1]. 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 necessary [2]. In RF ablation, RF current 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 ionic agitation. Temperatures above 45 ºC to 50 ºC have been shown to cause denaturation of intracellular proteins and destruction of membranes of tumor cells, eventually resulting in cell necrosis [3]. One of the major limitations of this technique is the extent of induced necrosis. When tumors greater than 2 cm are treated, multiple applications are necessary to obtain complete tumor necrosis. Often tumor cells survive, which leads to high recurrence rates [4], [5], [6], [7]. Several methods have been investigated for increasing lesion size and improving efficacy. Internally cooled probes have been used [8], [9]. Pulsed techniques have been used to further increase necrosis diameter created by internally cooled probes [10]. Interstitial saline infusion creates larger lesions by cooling and increasing effective electrode area [11], [12], [13]. The cooling effects of large blood vessels and vascular perfusion can be minimized by the Pringle maneuver, in which vascular inflow

36 occlusion is performed by clamping the hepatic artery and portal vein [14]. However, the Pringle requires a major surgical procedure, which negates one of the major advantages of RF ablation—the use in a minimally invasive fashion (percutaneous or laporoscopic). Vasoactive pharmacologic agents have also been used to reduce blood flow to the liver [15] to reduce the blood cooling effect. Bipolar RF ablation has been shown to create larger lesions using two needle electrodes compared to monopolar ablation using a single needle electrode [2], [13], [16]. We investigated the potential of a novel bipolar RF ablation technique using two parallel oriented, hooked electrodes (model 30, RITA Medical Systems, Mountain View, CA). There have been many finite element method (FEM) studies of cardiac RF ablation [17], [18] but few FEM modeling studies on hepatic ablation [19]. We initially generated FEM models to analyze differences in distribution of temperature and electric field intensity. We created monopolar and bipolar lesions in-vivo in pig liver and compared the results to the FEM model.

2. Materials and Methods We used a RITA 500 RF generator and RITA 4-prong 15 gauge probes (model 30, RITA Medical Systems, See Fig. 1) for creating monopolar and bipolar lesions. For clinical use, the probe is inserted with retracted prongs. Once the probe is in place, the prongs are deployed. The prongs can be deployed to a maximum diameter of 3 cm. A thermistor is located in the tip of each of the prongs. The thermistors allow temperature monitoring with an accuracy of ±2 ºC from 35 ºC to 100 ºC and ±5 ºC over 100 ºC. The shaft of the probe is insulated to within 1 cm of the tip. For creating bipolar lesions, we attached a second probe to the

37 generator replacing the dispersive electrode using a modified cable for connection. Fig. 2 and Fig. 3 show the electrical configuration for monopolar and bipolar ablation, respectively. The control circuit varies the applied power so that the temperature, which is monitored by the thermistors, is kept constant.

A. Bioheat Equation Joule heating arises when an electric current passes through a conductor. Electromagnetic energy is converted into heat. The heating of tissue during RF ablation is governed by the bioheat equation:

∂T = ∇ ⋅ k∇T + J ⋅ E − hbl (T − Tbl ) − Qm ∂t hbl = ρ blc bl wbl ρc

where ρ is the density (kg/m3 ), c is the specific heat (J/kg⋅K), and k is the thermal conductivity (W/m⋅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/kg⋅K), and wbl is the blood perfusion (L/s). hbl is 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 terms. In the Pennes model described in the bioheat equation, the energy exchange between blood and tissue is modeled as a nondirectional heat source. One major assumption is that the heat transfer related to perfusion between tissue and blood occurs in the capillary bed, which turned out not to be fully correct. The main thermal equilibrium process takes place in the

38 pre- or postcapillary vessels. Nevertheless, the Pennes model describes blood perfusion with acceptable accuracy, if no large vessels are nearby [20]. The blood perfusion in hepatic tissue used in the FEM was wbl = 6.4 × 10–3 [21].

B. Finite element method We created finite element method (FEM) models for monopolar and bipolar ablation. For all FEM analyses, we used a RITA model 30, 4-prong probe. Initially we created different FEM model for bipolar ablation where we varied probe distance in 0.5 cm increments. We found the ideal distance (i.e. largest lesion size) at 2 cm probe distance. Fig. 1 shows the geometry of the probe model. For the bipolar model, the distal probe shaft was considered insulated, except for the most distal 2 mm. In the actual probe, the shaft tip is cut at an angle. Even though we insulated the outside of the shaft, the inside still conducts and contributes towards lesion formation. We created a similar situation in the model by considering the distal 2 mm of the distal probe conducting. The probes were placed within a cylinder (80 mm diameter) of liver tissue in this formation. Due to the symmetry of the arrangement, we could reduce computing time by only modeling a quarter of the cylinder. Table 1 lists the material properties used in the model, which were taken from the literature [22] [23]. We set the initial temperature of the liver tissue and temperature at the boundary of the model to 37 ºC. Blood perfusion was modeled according to the Pennes model [24]. We simulated ablation for 12 min. The maximum temperature of hepatic tissue was kept at 95 ºC by varying the voltage applied to the electrodes. The lesion size was determined using the 50 ºC margin (i.e. tissue above 50 ºC is considered destroyed). The bipolar model consisted of

39 ~63,000 tetrahedral elements and ~12,000 nodes. The monopolar model consisted of ~35,000 tetrahedral elements and ~7,000 nodes. We used PATRAN Version 9.0 (The MacNeal-Schwendler Co., Los Angeles, CA) to generate the geometric models, assign material properties, assign boundary conditions and perform meshing. After creating the model, PATRAN generates an input file for the ABAQUS/Standard 5.8 (Hibbitt, Karlsson & Sorensen, Inc., Pawtucket, RI) solver. A coupled thermo-electrical analysis was performed by ABAQUS. For postprocessing we used the built- in module ABAQUS/POST to generate profiles of temperature and electric field intensity. All analysis was performed on a HP-C180 workstation equipped with 1.1 GB of RAM and 34 GB of hard disk space. Tungjitkusolmun et al. [17] provide a detailed description of the FE modeling process.

C. In-vivo studies We used three domestic pigs (30 to 40 kg) for the in-vivo experiments. We obtained preapproval for all animal experiments from the Institutional Animal Care and Use Committee, University of Wisconsin, Madison. All procedures were performed with the animals under general anesthesia. Induction of anesthesia was achieved by using an intramuscular injection of tiletamine hydrochloride and zolazepam hydrochloride and xylazine hydrochloride. The animals were then intubated and maintained on inhaled halothane. Once adequate anesthesia was achieved, the abdomen was opened. The placement of the electrodes was guided by ultrasonic imaging to avoid blood vessel rupture and placement near large vessels. The probes were inserted with retracted prongs. The prongs were deployed once the probes were placed at the desired position. For monopolar ablations, the dispersive electrode was placed on the subjects back posterior to the liver. We performed

40 preliminary in-vivo experiments with bipolar configuration at probe distances of 3.5 cm, 3 cm and 2.5cm. When the distance was 3.5 cm and 3 cm, in some cases we found a gap of viable tissue between two lesions created by the two probes after performing ablation. Subsequently, probes were placed 2.5 cm apart. Furthermore, probes were rotated 45º relative to each other, and no dispersive electrode was used. The distal 10 mm of the distal probe shaft were insulated using epoxy resin (see Fig. 4). Both monopolar and bipolar ablations were performed for 12 min using temperature-controlled mode at 95 ºC. After the experiments were completed, the animal was sacrificed and the ablated liver lobes were resected. The liver was placed in 10% formalin for fixation. After fixation, the tissue was cut into slices 3 to 5 mm thick and the slices were scanned at a resolution of 300 dpi to obtain digital images. We measured the lesion area of each slice using the software ImageJ Version 1.16 (NIH). The lesion border was determined by optical inspection. The pale central area of the RF lesion has been shown to correspond to the zone of necrosis [25]. Lesion volume was computed by multiplying the lesion area of each slice by slice thickness, and summating results for all slices.

3. Results

A. In-vivo studies We created 7 monopolar and 10 bipolar lesions. Tables 2 and 3 show the lesion volumes of the resulting bipolar and monopolar lesions respectively. For monopolar ablation, lesion volumes were 3.9 ± 1.8 cm3. For bipolar ablation, lesion volumes were 12.2 ± 3 cm3. Figs. 5 and 6 show typical monopolar and bipolar lesions, respectively. Fig. 7 shows a bipolar lesion

41 with severe charring around the shaft of the distal probe. Fig. 8 shows a bipolar lesion where the two probes have been heated nonuniformly.

B. Finite Ele ment Method We generated models of monopolar and bipolar ablation and analyzed the distribution of temperature and electric field intensity. Figs. 9 and 10 show the profiles of the temperature distributions of monopolar and bipolar ablation, respectively. The lesion volumes were 7.95 cm3 for monopolar ablation and 18.79 cm3 for bipolar ablation. The monopolar model shows a mushroom shaped lesion while the bipolar model resembles the shape of a cylinder. Figs. 11 and 12 show the electric field intensity of monopolar and bipolar ablation, respectively.

4. Discussion We propose a new bipolar method for creating larger and more controllable lesions (i.e. less dependent on local inhomogeneities in liver tissue such as blood perfusion). In the bioheat equation, the term J⋅E represents the power density p of the electromagnetic field, which is converted into thermal energy. The electric field intensity E can be expressed as E = J⋅ρ, where ρ is the electric resistivity. Therefore the power density can also be expressed as p = E2 /ρ. Fig. 11 shows that the electric field intensity is high only very close to the probe; hence active heating is also limited to this region. We hypothesized that we could extend the zone of high field intensity further away from the probe using the bipolar configuration and thereby extend the zone of active heating.

42 In the ideal case of two parallel plates at different voltages extending infinitely in all directions, electric field intensity is homogenous. Then the deposition of electric energy is homogeneous, if the electrical resistivity of the material in between the plates is constant. When the plates have finite dimensions and the distance between the plates is small compared to the plate dimensions, a homogenous electric field gradient develops in-between the plates except for the plate edges. Fig. 13 shows this situation for the electric field gradient of two plates. We tried to create a similar case by using two umbrella electrodes placed parallel to each other at a close distance. We examined the electric field between two such probes with a FEM model. Figs. 11 and 12 show the electric field intensity for the monopolar and bipolar configurations. For the bipolar configuration we see increased field intensity between the probes. However, for probes with four prongs this increase is not sufficient to contribute significantly towards heating (note the scale, where the shades of gray correspond to field intensity from zero to 1/3 of the maximum intensity. Black covers the range above 1/3 of maximum field intensity). Therefore probes with a large number of prongs are necessary for the heating between probes to become considerable. Disadvantages of using probes with a higher number of prongs are increased risk of blood vessel rupture and the necessity for a larger gauge needle to house the prongs. Larger gauge probes are associated with a higher complication rate when placed in the liver. Intrahepatic hemorrhages and tumor seeding along the needle tract are more likely to occur [26]. The major contribution towards larger lesion size of bipolar ablation is based on a thermodynamic effect. If two lesions are created separately with electrodes at the same position as in a bipolar ablation, the total lesion size is smaller than a single bipolar lesion. In

43 monopolar ablation, heat is diverted from the ablation site in all directions. In the bipolar case however, one probe is thermally shielded by the opposing second probe, which also actively heats the tissue in its proximity. There is less cooling in the direction towards the collateral probe than exists in monopolar ablation. Heat is trapped between the two probes and higher temperatures are reached. This results in a lesion of larger size than that of two lesions produced sequentially by monopolar ablation with probes placed at the same position. The temperature distributions for monopolar and bipolar ablation shown in Figs. 9 and 10 show increased lesion size between the probes in bipolar configuration. A zone of high temperature is created between the probes, which results in more effective killing of tumor cells in this zone. Furthermore, dependence of lesion size on local differences in cooling mediated by perfusion is reduced. This is supported by the fact that the standard deviation of bipolar ablation lesion size relative to its mean is smaller than for the monopolar case. The average lesion size created in-vivo with bipolar RF ablation (V = 12.2 ± 3 cm3) was 210% larger than average lesion size of lesions created with monopolar RF ablation (V = 3.9 ± 1.8 cm3). The results obtained from FEM analysis show only 136% increase of bipolar (V = 18.79 cm3 ) versus monopolar (V = 7.95 cm3 ). However, the conditions between the FEM model and the in-vivo experiments have to be considered different. In the FEM model we used temperature independent tissue properties due to lack of data. We also considered blood perfusion to be constant whereas actually blood perfusion drops as coagulation occurs with high temperatures. Furthermore, we didn’t consider the impact of large blood vessels close to the ablation site. Due to these inaccuracies in the FEM model we obtain different results for the model and the experiment. However, both the FEM model and the in-vivo

44 experiments show a more than two- fold increase in lesio n size, which demonstrates superior performance of the bipolar configuration. Figs. 5 and 9 both show the typical mushroom shaped lesion observed after RF ablation utilizing umbrella probes. The lesion shape generated by bipolar ablation resembles a cylinder (see Figs. 6 and 10). It is easier to encompass tumors with a cylindrical bipolar lesion than with a mushroom shaped monopolar lesion. McGahan et. al. [16] made extensive bipolar RF ablation experiments in- vitro using two needle electrodes. They found an ideal distance between the two needle electrodes. The situation is similar in our bipolar ablation method. When electrode distance is too far, two small, unfused lesions are generated instead of one large lesion. The sum of the small lesions in this case is smaller than the larger lesion created using a smaller gap. Since the intention is to kill a tumor located in between the electrodes, a continuous lesion between the electrodes has to be produced and therefore distance must be kept less than a certain limit. The liver is a very heterogeneous organ, particularly in regards to vascularity. Therefore, for the in-vivo experiments there is no distance of probe spacing that is ideal for all cases. The ideal gap between the two probes depends upon the local properties of the ablation site and is different for each ablation. We performed preliminary in-vivo experiments with probe distances of 3.5 cm, 3 cm and 2.5cm. When the distance was 3.5 cm and 3 cm, in some cases we found a gap of viable tissue between two lesions created by the two probes after performing ablation. We chose a distance of 2.5 cm for subsequent experiments. A different distance might be appropriate if hooked probes with other geometries are used (e.g. 10 prong umbrella probe from Radiotherapeutics, Sunnyvale, CA).

45 We rotated the probes 45º relative to each other to achieve more uniform current distribution and heating in between the probes. We did not perform any experiments to prove that this rotation is beneficial. We also insulated the distal 10 mm of the probe shafts. When probes are used for conventional monopolar ablation, the distal 10 mm of the shaft is not insulated and is electrically active (see Fig. 1). Initial experiments, where this section of the distal probe was not insulated, showed occurrences of charring around the distal portion of the shaft (see Fig. 7), which eventually resulted in impedance rise. Impedances above 200 Ω trigger generator shut-down. This is a safety feature to avoid charring and boiling. An explanation for the rise in impedance is that the temperature at the uninsulated shaft exceeded the temperature monitored at the probe tips. The region around the uninsulated shaft was heated more because it was closer to the second probe resulting in higher local current density. Temperatures above 100 ºC cause boiling, vaporization and charring, which raises impedance. We solved this problem by insulating this region on the distal probe shaft using epoxy resin. A limitation of the bipolar method described in this study is that temperature was measured at only one probe. In RF ablation, most of the active heating occurs within a range of a few millimeters from the electrodes. Similar resistivity and current density are present in the vicinity of both probes. Therefore a comparable amount of energy is converted into heat next to each of the two probes. If one probe is cooled more by blood perfusion than the other, more heat energy is carried away. One probe reaches a higher temperature than the other. If the cooler probe is temperature-controlled at 95 ºC, the uncontrolled probe reaches temperatures above 95 ºC, which can lead to boiling and vaporization. Impedance rises, and

46 the RF generator shuts down. In four cases during bipolar ablation the impedance showed a sudden rise resulting in shut-down of the generator. In these cases, we switched the connections of the probes so that the temperature of the previously overheating probe was measured. If the temperature of the hotter probe is controlled to be kept at 95 ºC, the other probe does not reach this temperature and heating near this probe is less. Fig. 8 shows a lesion, where one probe produced only a minor lesion because the desired temperature was not reached. When treating large tumors with current RF ablation techniques, multiple ablations often must be performed on the same tumor to obtain complete necrosis of tumor tissue. Bipolar RF ablation exhibited superior performance compared to monopolar ablation, creating lesions about three times as large in in-vivo experiments. The proposed bipolar method may kill all tumor cells with a single application, which reduces treatment time. Since both probes can be inserted from the same site, insertion is only minimally more complicated compared to insertion of a single probe. Ultrasound guided placement can be used to place the probes on opposite sides of the tumor to be treated. Ultimately, a probe where two sets of electrodes at a specified distance are held within a single catheter could be manufactured. Different probes with variable distances between prong arrays, each specified for a certain tumor size, could be produced.

47

5. References [1] M. C. Kew, “The development of hepatocellular carcinoma in humans,” Cancer Surv., vol. 5, pp. 719–739, 1985. [2] S. A. Curley, B. S. Davidson, R. Y. Fleming, F. Izzo, L. C. Stephens, P. Tinkey, D. Cromeens, “Laparoscopically guided bipolar radiofrequency ablation of areas of porcine liver”, Surg. Endosc., pp. 729–733, 1997. [3] W. Lounsberry, V. Goldschmidt, C. Linke, “The early histologic changes following electrocoagulation,” Gastrointest. Endosc., vol. 41, pp. 68–70, 1995. [4] S. Rossi, M. Di Stasi, E. Buscarini, P. Quaretti, F. Garbagnati, L. Squassante, C. T. Paties, D. E. Silverman, L. Buscarini, “Percutaneous RF interstitial thermal ablation in the treatment of hepatic cancer,” Am. J. Roentgenol., vol. 167, pp. 759–768, 1996. [5] L. R. Jiao, P. D. Hansen, R. Havlik, R. R. Mitry, M. Pignatelli, N. Habib, “Clinical shortterm results of radiofrequency ablation in primary and secondary liver tumors,” Am. J. Surgery, vol. 177, pp. 303–306, 1999. [6] L. Solbiati, T. Ierace, S. N. Goldberg, S. Sironi, T. Livraghi, R. Fiocca, G. Servadio, G. Rizzatto, P. R. Mueller, A. Del Maschio, G. S. Gazelle, “Percutaneous US- guided radiofrequency tissue ablation of liver metastases: treatment and follow- up in 16 patients,” Radiology, vol. 202, pp. 195–203, 1997. [7] S. A. Curley, F. Izzo, P. Delrio, L. M. Ellis, J. Granchi, P. Vallone, F. Fiore, S. Pignata, B. Daniele, F. Cremona, “Radiofrequency ablation of unresectable primary and metastatic hepatic malignancies,” Ann. Surg., vol. 230, pp. 1–8, 1999.

48 [8] S. N. Goldberg, G. S. Gazelle, L. Solbiati, W. J. Rittman, P. R. Mueller, “Radiofrequency tissue ablation: increased lesion diameter with a perfusion electrode,” Acad. Radiol., vol. 3, pp. 636–644, 1996. [9] T. A. Lorentzen, “A cooled needle electrode for radio-frequency tissue ablation: thermodynamic aspects of improved performance compared with conventional needle design,” Acad. Radiol., vol. 3, pp. 556–563, 1996. [10] S. N. Goldberg, M. C. Stein, G. S. Gazelle, R. G. Sheiman, J. B. Kruskal, M. E. Clouse, “Percutaneous radiofrequency tissue ablation: Optimization of pulsed-radiofrequency technique to increase coagulation necrosis”, J. Vasc. Interv. Radiol, vol.10, pp. 907–916, 1999. [11] Y. Miao, Y. Ni, S. Mulier, K. Wang, M. F. Hoez, P. Mulier, F. Penninckx, J. Yu, I. De Scheerder, A. L. Baert, G. Marchal, “Ex vivo experiment on radiofrequency liver ablation with saline infusion through a screw-tip cannulated electrode,” J. Surg. Res., vol. 71, pp. 18– 26, 1997. [12] R. S. Mittleman, S. K. Huang, W. T. De Guzman, H. Cuenoud, A. B. Wagshal, L. A. Pires, “Use of saline infusion electrode catheter for improved energy delivery and increased lesion size in radiofrequency catheter ablation,” PACE, vol. 18, pp. 1022–1027, 1995. [13] F. Burdio, A. Guemes, J. M. Burdio, T. Castiella, M. A. De Gregorio, R. Lozano, T. Livraghi, “Hepatic lesion ablation with bipolar saline-enhanced radiofrequency in the audible spectrum”, Acad. Radiol., vol. 6, pp. 680–686, 1999. [14] E. Delva, Y. Camus, B. Nordlinger, “Vascular occlusions for liver resections,” Ann. Surg., vol. 209, pp. 297–304, 1989.

49 [15] S. N. Goldberg, P. F. Hahn, E. F. Halpern, R. M. Fogle, G. S. Gazelle, “Radiofrequency tissue ablation: effect of pharmacologic modulation of blood flow on coagulation diameter,” Radiology, vol. 209, pp. 761–767, 1998. [16] J. P. McGahan, W.-Z. Gu, J. M. Brock, H. Tesluk, C. D. Jones, “Hepatic ablation using bipolar radiofrequency electrocautery”, Acad. Radiol., vol. 3, pp. 418–422, 1996. [17] S. Tungjitkusolmun, E. J. Woo, H. Cao, J.-Z. Tsai, V. R. Vorperian, J. G. Webster, “Thermal-electrical finite element modeling for radio frequency cardiac ablation: effects of changes in myocardial properties,” Med. Biol. Eng. Comput., vol. 38, 562–568, 2000. [18] S. Tungjitkusolmun, E. J. Woo, H. Cao, J.-Z. Tsai, V. R. Vorperian, J. G. Webster, “Finite element analyses of uniform current density electrodes for radio-frequency cardiac ablation,” IEEE Trans. Biomed. Eng., vol. 47, pp. 32–40, 2000. [19] M. G. Curley, P. S. Hamilton, “Creation of large thermal lesions in liver using salineenhanced RF ablation,” Proc. 19th Annu. Int. Conf. IEEE Eng. Med. Biol. Soc. (Chicago, 1997) (Piscataway, NJ: IEEE), pp. 2516–2519. [20] H. Arkin, L. X. Xu, K. R. Holmes, “Recent developments in modeling heat transfer in blood perfused tissues”, IEEE Trans. Biomed. Eng., 41, pp. 97–107, 1994. [21] E. S. Ebbini, S.-I. Umemura, M. Ibbini, C. A. Cain, “A cylindrical-section ultrasound phased-array applicator for hyperthermia cancer therapy,” IEEE Trans. Biomed. Eng., vol. 35, pp. 561–572, 1988. [22] D. Panescu, J. G. Whayne, S. D. Fleischman, M. S. Mirotznik, D. K. Swanson J. G. Webster, “Three-dimensional finite eleme nt analysis of current density and temperature

50 distributions during radio-frequency ablation,” IEEE Trans. Biomed. Eng., vol. 42, pp. 879–890, 1995. [23] J. W. Valvano, J. R. Cochran, K. R. Diller, “Thermal conductivity and diffusivity of biomaterials measured with self- heating thermistors”, Int. J. Thermophys., vol. 6, pp. 301– 311, 1985. [24] H. H. Pennes, “Analysis of tissue and arterial blood temperatures in resting forearm,” J. Appl. Phys., vol. 1, pp. 93–122, 1948. [25] C. H. Cha, F. T. Lee, J. M. Gurney, B. K. Markhardt, T. F. Warner, F. Kelcz, D. M. Mahvi, “CT versus sonography for monitoring radiofrequency ablation in a porcine liver”, Am. J. Roentgenol., vol. 3, pp. 705–711, 2000. [26] G. D. Dodd III, M. C. Soulen, R. A. Kane, T. Livraghi, W. R. Lees, Y. Yamashita, A. R. Gillams, O. I. Karahan, H. Rhim, “Minimally invasive treatment of malignant hepatic tumors: at the threshold of a major breakthrough”, Radiographics, 20, pp. 9–27, 2000.

51 6. Figure Legends Figure 1. Geometry of fully deployed Rita model 30 umbrella probe used in FEM. The prongs and the distal 10 mm of the shaft conduct RF current. The orientation of the coordinates is shown at the bottom. Figure 2. Electrical configuration of monopolar ablation. Figure 3. Electrical configuration of bipolar ablation. Figure 4. Arrangement of two probes for bipolar ablation. Figure 5. In-vivo, monopolar lesion. Lesion volume V = 3.0 cm3 Figure 6. In-vivo, bipolar lesion. Lesion volume V = 14.2 cm3 Figure 7. In-vivo, bipolar lesion, severe charring around uninsulated shaft of distal probe, lesion volume V = 12.2 cm3 Figure 8. Nonuniform heating. Lower probe creates smaller lesion due to lower temperature. Lesion volume V = 10.3 cm3. Figure 9. Monopolar RF ablation: Temperature distribution after 12 min RF ablation in temperature-controlled mode, T = 95 °C. The distal 10 mm of the shaft and the prongs conduct current. The gray part of the shaft is insulated. The outermost border (lightest gray) marks the 50 °C margin, which is considered the lesion border. Lesion size V = 7.95 cm3. Figure 10. Bipolar RF ablation: Temperature distribution after 12 min RF ablation in temperature-controlled mode, T = 95°C. Only the prongs conduct current. The shafts (gray) are insulated, except for the distal 2 mm of the distal shaft. The outermost border (lightest gray) marks the 50 °C margin, which is considered the lesion border. Lesion size V = 18.79 cm3.

52 Figure 11. Monopolar RF ablation: Electric field strength. The distal 10 mm of the shaft and the prongs conduct current. The gray part of the shaft is insulated. Figure 12. Bipolar RF ablation: Electric field strength. The distal 2 mm of the distal probe shaft and the prongs of both probes conduct current. The gray parts of the shafts are insulated. Figure 13. Two parallel plates:electric field intensity. Homogenous electric field is created, except at the plate edges.

53

Element

Material

ρ [kg/m 3]

c [J/kg⋅ K]

k [W/m⋅ K]

σ [S/m]

Electrode

Ni–Ti

6450

840

18

1 × 108

Shaft

Stainless steel

21500

132

71

4 × 106

Tissue

Liver

1060

3600

0.512

0.333

Table 1. Material properties used in FEM

Lesion #

Subject #

Lesion Volume (cm3)

1

1

14.2

2

1

10.3

3

1

16.8

4

2

5

Lesion #

Subject #

Lesion Volume (cm3)

13.8

1

1

6.9

2

8.3

2

2

3.1

6

2

14.5

3

2

2.5

7

3

11.6

4

2

3.5

8

3

12.2

5

2

3.0

9

3

13.4

6

3

6.1

10

3

6.9

7

3

2.5

Average

3.9

Average

12.2

(StdDev.)

(± 1.8)

(StdDev.)

(± 3)

Table 2. Lesion Sizes, in-vivo, bipolar

Table 3. Lesion Sizes, in-vivo, monopolar

54

Stainless steel shaft, conducting, 10 mm length, 2 mm diameter

15 mm Stainless steel shaft, insulated

Ni-Ti Electrodes, 0.5 mm diameter

Figure 1.

Geometry of fully deployed Rita model 30 umbrella probe used in FEM. The

prongs and the distal 10 mm of the shaft conduct RF current. The orientation of the coordinates is shown at the bottom.

460 kHz ac 460 kHz ac Control circuit

Dispersive electrode

T

T

Cont rol circuit

Probe Figure 2. Electrical configuration of

Figure 3. Electrical configuration of bipolar

monopolar ablation

ablation.

55

Insulated (covered with expoxy resin) Not insulated

Figure 4. Arrangement of two probes for bipolar ablation.

Figure 5. In-vivo,monopolar lesion. Lesion volume V = 3.0 cm3

56

Figure 6. In-vivo, bipolar lesion. Lesion volume V = 14.2 cm3

Figure

7.

In-vivo,

bipolar

lesion,

severe

charring

around

uninsulated shaft of distal probe, lesion volume V = 12.2 cm3

57

Figure 8. Nonuniform heating. Lower probe creates smaller lesion due to lower temperature. Lesion volume V = 10.3 cm3.

58 T (°C) 37 50 55 60 65 70 75 80 85 90 95

Figure 9.

1 cm

Monopolar RF ablation: Temperature distribution after 12 min RF ablation in

temperature-controlled mode, T = 95°C. The distal 10 mm of the shaft and the prongs conduct current. The gray part of the shaft is insulated. The outermost border (lightest gray) marks the 50°C margin, which is considered lesion border. Lesion size V = 7.95 cm3.

59

T (°C) 37 50 55 60 65 70 75 80 85 90 95 1 cm

Figure 10. Bipolar RF ablation: Temperature distribution after 12 min RF ablation in temperature-controlled mode, T = 95°C. Only the prongs conduct current. The shafts (gray) are insulated. The outermost border (lightest gray) marks the 50 °C margin, which is considered lesion border. Lesion size V = 18.79 cm3.

60 E (V/cm) 0 0.7 1.4 2.1 2.8 3.5 4.2 4.9 5.6 6.2 6.9 20.8

1 cm

Figure 11. Monopolar RF ablation: Electric field strength. The distal 10 mm of the shaft and the prongs conduct current. The gray part of the shaft is insulated.

61 E (V/cm) 0 0.6 1.2 1.8 2.4 2.9 3.5 4.1 4.7 5.3 5.9 17.6

1 cm

Figure 12. Bipolar RF ablation: Electric field strength. The distal 2 mm of the distal probe shaft and the prongs of both probes conduct current. The gray parts of the shafts are insulated.

62 E (V/cm) 0.1 0.21 0.42 0.62 0.82 1.02 1.23 1.43 1.63 1.84 2.04 2.24 2.45

1 cm

2.65 Figure 13. Two parallel plates:electric field intensity. Homogenous electric field is created, except at the plate edges.

63

Chapter IV

Finite element analysis of hepatic multiple probe radio-frequency ablation

This work was submitted as: D. Haemmerich, S. Tungjitkusolmun, S. T. Staelin, F. T. Lee Jr., D. M. Mahvi, and J. G. Webster, “Finite element analysis of hepatic multiple probe radio- frequency ablation”, IEEE Trans. Biomed. Eng., submitted 2001.

64

Abstract Radio- frequency (RF) ablation is an important means of treatment of nonresectable primary and metastatic liver tumors. RF ablation, unlike cryoablation (a method of tumor destruction that utilizes cold rather than heat) must be performed with a single probe placed serially. The ablation of any but the smallest tumor requires the use of multiple overlapping treatment zones. We evaluated the performance of a configuration incorporating two hooked probes (RITA model 30). The probes were lined up along the same axis in parallel 25 mm apart. Three different modes applied voltage to the probes. The first mode applied energy in monopolar mode (current flows from both probes to a dispersive electrode). The second mode applied the energy to the probes in bipolar mode (current flows from one probe to the other). The third method applied the energy sequentially in monopolar mode (in 5 s intervals switched between the probes). We used the Finite element method (FEM) and analyzed the electric potential profile and the temperature distribution at the end of simulation of a 12 min ablation. The alternating monopolar mode allowed precise independent control of the amount of energy deposited at each probe. The bipolar mode created the highest temperature in the area between the probes in the configuration we examined. The monopolar mode showed the worst performance since the two probes in close vicinity create a disadvantageous electric field configuration. We thus conclude that alternating monopolar RF ablation superior to the other two methods.

65 1. Introduction Radio- frequency (RF) ablation is increasingly utilized as a minimally invasive treatment for primary and metastatic liver tumors. Primary hepatocellular carcinoma is a significant worldwide public health problem with an estimated annual mortality of 1,000,000 [1]. Surgical resection offers the best chance of long-term survival, but is rarely possible. In many patients with cirrhosis or multiple tumors hepatic reserve is inadequate to tolerate resection and alternative means of treatment that target the tumor, but preserve uninvolved liver are necessary [2]. In RF ablation, RF current is delivered to the tissue via electrodes inserted percutaneously or during surgical exploration. 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 used. The most commonly used mode is temperature-controlled ablation. Tumor cell death results from the conversion of electromagnetic energy to heat by ionic agitation. Temperatures above 45 ºC to 50 ºC cause denaturation of intracellular proteins and destruction of membranes of tumor cells, eventually resulting in cell necrosis [3]. One of the major limitations of this technique is the inability to use multiple probes simultaneously. When tumors greater than 2 cm are treated, multiple applications are necessary to obtain complete tumor necrosis. Often tumor cells survive, which leads to high recurrence rates [4], [5], [6]. In cases where multiple tumors are present, these must be treated sequentially. Treatment time could be drastically reduced, if multiple tumors could be treated simultaneously. Several methods have been investigated for increasing lesion size and improving efficacy. Internally cooled probes have been used [7], [8]. Pulsed techniques have

66 been used to further increase necrosis diameter created by internally cooled probes [9]. Interstitial saline infusion creates larger lesions by cooling and increasing effective electrode area [10], [11], [12]. The cooling effects of large blood vessels and vascular perfusion can be minimized by clamping the hepatic artery and portal vein and occluding vascular inflow [13]. Inflow occlusion however requires a major surgical procedure, which negates one of the major advantages of RF ablation—the use in a minimally invasive fashion (percutaneous or laparoscopic). Bipolar RF ablation has been shown to create larger lesions using two needle electrodes compared to monopolar ablation using a single needle electrode, when the two probes are placed close to each other [2], [14], [12]. However, there have been no other studies investigating possible simultaneous usage of multiple ablation probes. There have been many finite element method (FEM) studies of cardiac RF ablation [15], [16] but only few FEM studies on hepatic ablation [17]. We generated FEM models to analyze differences in distribution of temperature and electric field potential. We investigated the potential of three different modes that could be employed to allow the usage of multiple probes simultaneously. We placed two commonly used hooked electrodes (model 30, RITA medical systems, Mountain View, CA) in parallel. The first mode applied energy in monopolar mode (current flows from both probes to a dispersive electrode). The second mode applied energy to the probes in bipolar mode (current flows from one probe to the other). The third mode applied energy sequentially in monopolar mode (in 5 s intervals current is switched either from one or the other probe to the ground pad).

67 2. Methods

A. The Bioheat Equation RF ablation destroys tissue by converting electric energy into thermal energy. The current flows from the conductive probe through the tissue to a surface dispersive electrode. Tissue in close vicinity of the probe tip is heated by ionic agitation. The heating of tissue during RF ablation is governed by the bioheat equation:

∂T = ∇ ⋅ k∇ T + J ⋅ E − hbl (T − Tbl ) − Qm (1) ∂t hbl = ρblcbl wbl ρc

where ρ is the density (kg/m3), c is the specific heat (J/(kg⋅K)), and k is the thermal conductivity (W/(m⋅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/(kg⋅K)), and wbl is the blood perfusion (1/s). hbl is 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 terms [8].

B. Finite Element Analysis Software We used PATRAN Version 9.0 (The MacNeal-Schwendler Co., Los Angeles, CA) to generate the geometric models, assign material properties, assign boundary conditions and perform meshing. After creating the model, PATRAN generates an input file for the ABAQUS/Standard 5.8 (Hibbitt, Karlsson & Sorensen, Inc., Pawtucket, RI) solver. A

68 coupled thermo-electrical analysis was performed by ABAQUS. For postprocessing we used the built- in module ABAQUS/POST to generate profiles of temperature and electric field potential. All analysis was performed on a HP-C180 workstation equipped with 1.1 GB of RAM and 34 GB of hard disk space. Tungjitkusolmun et al. [15] provide a detailed description of the FEM modeling process.

C. Model Geometry Fig. 1 shows that we created FEM models of two RITA model 30, 4-prong probes, axially lined up in parallel. The probes have thermistors placed in each prong tip. In temperaturecontrolled mode the temperature sensed by the thermistors is used to control the applied power. The probes were placed 2.5 cm apart. In the actual probes, the prongs and the last 5 mm of the shaft are conducting. In our model only the prongs are conducting, and the shaft is insulated. We insulated the shaft completely, because otherwise a disadvantageous current distribution would result when using the bipolar mode. We placed the probes within a 80 mm diameter cylinder of liver tissue in this formation. Due to the symmetry of the arrangement, we could reduce computing time by modeling only a quarter of the cylinder. Table 1 lists the material parameters used in the FEM model. We neglected blood perfusion. We set the initial temperature of the liver tissue and temperature at the boundary of the model to 37 ºC. We simulated ablation for 12 min. The maximum temperature of hepatic tissue was kept at 95 ºC by varying the voltage applied to the electrodes. The model consisted of ~63,000 tetrahedral elements and ~12,000 nodes.

69 D. Energy Delivery Scheme for Multiple Probes We used the same model geometry for all three types of energy delivery. Also, for all three types we controlled the applied energy (i.e. voltage) so that the tip temperature was kept at 95 ºC (temperature-controlled mode). We simulated ablation for 12 min. The monopolar mode applied the same voltage to both probes. Current flows from the probe prongs to the dispersive electrode. The bipolar mode passes current between the two probe prongs. We controlled the applied voltage so that the probe tips of the upper probe was kept at 95 ºC. The upper probe tips get hotter because of the nonsymmetrical configuration of the two probes. The alternating monopolar scheme passed current from only one of the probe prongs to the dispersive electrode. After 5 s, the voltage alternately switches from the upper probe to the lower probe with all current collected by the dispersive electrode. The applied voltage is controlled independently for each of the two probes so that the average tip temperature of both probes is kept at 95 ºC by independently controlling the applied voltage to each probe. The tip temperature is not constant in this case since one probe cools off while power is delivered to the other probe and vice versa.

3. Results For each of the three modes we show the temperature distribution at the end of the 12 min ablation period and the electric potential profile. For the monopolar mode, Fig. 2 shows the electric potential profile and Fig. 3 shows the temperature distribution. For the bipolar mode, Fig. 4 shows the electric potential profile and Fig. 5 shows the temperature distribution. For the alternating monopolar mode, Fig. 6 shows the electric potential profile and Fig. 7 shows

70 the temperature distribuation. Fig. 8 shows the progress of upper and lower tip temperatures for the alternating monopolar mode starting 6 min after start of ablation.

4. Discussion The aim of all three modes used in this study is to allow usage of multiple probes simultaneously while performing ablation. In the configuration we used in the FEM model, the probes are positioned 25 mm apart. This configuration is useful for treating large tumors, which cannot be treated with a single application using a single probe. The configuration has an advantage based on a thermodynamic effect. If two lesions were created separately with electrodes at the same position as in a bipolar ablation, the total lesion size would be smaller than a single bipolar lesion. When only using a single probe, heat is diverted from the ablation site in all directions. When using two probes in close vicinity, one probe is thermally shielded by the opposing second probe, which also actively heats the tissue in its proximity. There is less cooling in the direction towards the collateral probe than would exist in monopolar ablation. Heat is trapped between the two probes and higher temperatures are reached. This results in a lesion of larger size than that of two lesions produced sequentially by ablation with probes placed at the same position. A zone of high temperature is created between the probes, which results in more effective killing of tumor cells in this zone. However, the configuration of the probes is not limited to that in Fig. 1. With all three modes, probes can be placed further apart, as is necessary when treating multiple tumors. In the following sections we evaluate and compare the performance of each method.

71 A. Monopolar Mode The main disadvantage of the monopolar mode is that current applied to both probes travels outward (toward a cutaneous grounding pad) with little traveling between them. Fig. 2 shows the electric potential created when the probes are placed close to each other. There is a large area of relatively constant electric potential between the two probes. The field gradient is small between the probes, and there is reduced power deposition in this area. Fig. 3 shows that the temperature between the two probes is far less than the temperature reached when using the bipolar or the alternating monopolar mode. This effect is less pronounced when the probes are placed further apart. However, for a configuration where the probes are close to each other, this mode is not desirable. Another criteria for evaluating performance of the methods is the ease with which different amounts of energy can be deposited in the vicinity of each of the probes. The liver is a very heterogeneous and well-perfused organ. Significantly different conditions may exist in the vicinity of each of the probes. In RF ablation, most of the active heating occurs in a range of a few millimeters from the electrodes. We can assume that similar resistivity and current density are present in the vicinity of both probes. Therefore a comparable amount of energy is converted into heat next to each of the two probes, if we apply the same voltage. If one probe is cooled more by blood perfusion than the other, more heat energy is carried away. One probe reaches a lower temperature than the other. The cooler probe then would have to carry a higher voltage than the other, so more energy is converted to heat in the vicinity of this probe. When two different voltages are applied to the two probes, current flows from each of the probes towards the dispersive electrode. Additionally current flows between the probes, which might

72 also cause undesirable effects depending on the distance and voltage difference between the probes.

B. Bipolar Mode One way to solve the problem of the monopolar mode that arises from the disadvantageous electric field distribution is to use the bipolar mode. In the bipolar mode current passes between the two probes. Then no dispersive electrode is necessary. Fig. 4 shows the electric potential profile created using the bipolar mode. There are no areas of constant potential between the probes as occur when using the monopolar mode. More energy is converted to heat between the probes compared to the monopolar mode. Fig. 5 shows the temperature distribution for the bipolar mode. The bipolar mode is especially advantageous with the two probes in close proximity as we used in our simulation. The electric field gradient does not show large changes in the region between the probes. This leads to a more homogenous deposition of energy between the probes. The zone of active heating extends further away from the probes since the electric field gradient does not drop as sharply as in the monopolar mode. Tissue is preferentially heated in the region between the probes and reaches much higher temperatures than in the monopolar mode (Fig. 3). This advantage is not present, when the two probes are placed far apart. When the probes are placed close to each other, the orientation of the probes relative to each other must be considered. If the probes are not placed symmetrically to a plane perpendicular to a plane that encompasses both of the probe axes, the sections of the probe that point towards the other probe will get hotter. One disadvantage when using the bipolar mode is that only two probes can be used at the same time. For treating multiple tumors this means that only two tumors can be treated

73 simultaneously. Another problem arises from the fact that all the current originating from one probe must also enter the second probe. We assume similar resistivity and current density in the vicinity of both probes, as for the monopolar mode. Then there is a comparable amount of electric energy converted to heat in the vicinity of both probes. When there is different amount of cooling at the location of each of the probes due to differences in perfusion, one probe reaches a lower temperature than the other. When using the bipolar scheme there is no way to independently control the amounts of heat generated in the vicinity of each of the probes.

C. Alternating Monopolar Mode The alternating monopolar mode solves most problems present in the two other modes. At one instant in time current flows from only one of the probes towards the dispersive electrode. The probe from which the current flows to the dispersive electrode is changed after 5 s. So the applied voltage alternates between the two probes at 5 s intervals. Fig. 8 shows the progress of tip temperatures of the upper and lower probe after equilibrium is reached (t = 0 corresponds to 6 min after start of the ablation). During the 5 s interval we used, the tip temperature varies between 86 and 103 °C. Since tighter control of temperature is desirable, ideally a lower interval should be used (e.g. 1 s). However, with shorter intervals the amount of time a FEM simulation takes to run increases. We used the 5 s interval as a compromise. The alternating monopolar mode can be extended to more than two probes, so there is no limit on how many probes to use. Different amount of energy can be converted to heat at each of the probes easily by applying different voltages to the probes. In the bipolar mode, this is not possible. Also in the monopolar mode, this can only be done with limitations.

74 Another way to deposit different amounts of energy to each of the probes is not to apply different vo ltages, but to apply the same voltage for different time intervals to each of the probes. Fig. 6 shows the electric potential during the interval when voltage is applied to the lower probe. Since voltage is only applied to one of the probes, the probes do not interfere with each other as is the case for the monopolar mode. However, in a configuration where the probes are close to each other, the bipolar mode is advantageous. In the bipolar mode the electric field gradient does not drop as sharply as in the alternating monopolar mode and also stays fairly constant in the region between the probes. This advantage also becomes apparent when comparing the temperature distributions of the alternating monopolar and the bipolar modes. Fig. 7 shows that the temperature distribution of the alternating monopolar mode yields lower temperatures than the bipolar mode (Fig. 5). However, the alternating monopolar mode still shows significantly better results than the monopolar mode (Fig. 3) This advantage of the bipolar mode over the alternating monopolar mode is much less pronounced when the probes are moved far away from each other. Then the electric field gradient and current distribution more closely matches that in the alternating monopolar mode.

5. Conclusion The alternating monopolar mode is the only mode where we can easily control the heat deposited at each probe. For treatment of multiple tumors with multiple probes, this mode is the most suitable. When probes are placed close to each other (e.g. to treat a large tumor), the

75 bipolar mode creates the highest temperatures in the region between the two probes. The monopolar mode is the most disadvantageous one of the three modes.

76

6. References [1] M. C. Kew, “The development of hepatocellular carcinoma in humans,” Cancer Surv., vol. 5, pp. 719–739, 1985. [2] S. A. Curley, B. S. Davidson, R. Y. Fleming, F. Izzo, L. C. Stephens, P. Tinkey, D. Cromeens, “Laparoscopically guided bipolar radiofrequency ablation of areas of porcine liver”, Surg. Endosc., pp. 729–733, 1997. [3] W. Lounsberry, V. Goldschmidt, C. Linke, “The early histologic changes following electrocoagulation,” Gastrointest. Endosc., vol. 41, pp. 68–70, 1995. [4] S. Rossi, M. Di Stasi, E. Buscarini, P. Quaretti, F. Garbagnati, L. Squassante, C. T. Paties, D. E. Silverman, L. Buscarini, “Percutaneous RF interstitial thermal ablation in the treatment of hepatic cancer,” Am. J. Roentgenol., vol. 167, pp. 759–768, 1996. [5] L. R. Jiao, P. D. Hansen, R. Havlik, R. R. Mitry, M. Pignatelli, N. Habib, “Clinical shortterm results of radiofrequency ablation in primary and secondary liver tumors,” Am. J. Surgery, vol. 177, pp. 303–306, 1999. [6] L. Solbiati, T. Ierace, S. N. Goldberg, S. Sironi, T. Livraghi, R. Fiocca, G. Servadio, G. Rizzatto, P. R. Mueller, A. Del Maschio, G. S. Gazelle, “Percutaneous US- guided radiofrequency tissue ablation of liver metastases: treatment and follow- up in 16 patients,” Radiology, vol. 202, pp. 195–203, 1997. [7] S. N. Goldberg, G. S. Gazelle, L. Solbiati, W. J. Rittman, P. R. Mueller, “Radiofrequency tissue ablation: increased lesion diameter with a perfusion electrode,” Acad. Radiol., vol. 3, pp. 636–644, 1996.

77 [8] T. A. Lorentzen, “A cooled needle electrode for radio-frequency tissue ablation: thermodynamic aspects of improved performance compared with conventional needle design,” Acad. Radiol., vol. 3, pp. 556–563, 1996. [9] S. N. Goldberg, M. C. Stein, G. S. Gazelle, R. G. Sheiman, J. B. Kruskal, M. E. Clouse, “Percutaneous radiofrequency tissue ablation: optimization of pulsed-radiofrequency technique to increase coagulation necrosis”, J. Vasc. Interv. Radiol, vol.10, pp. 907–916, 1999. [10] Y. Miao, Y. Ni, S. Mulier, K. Wang, M. F. Hoez, P. Mulier, F. Penninckx, J. Yu, I. De Scheerder, A. L. Baert, G. Marchal, “Ex vivo experiment on radiofrequency liver ablation with saline infusion through a screw-tip cannulated electrode,” J. Surg. Res., vol. 71, pp. 18–26, 1997. [11] R. S. Mittleman, S. K. Huang, W. T. De Guzman, H. Cuenoud, A. B. Wagshal, L. A. Pires, “Use of saline infusion electrode catheter for improved energy delivery and increased lesion size in radiofrequency catheter ablation,” PACE, vol. 18, pp. 1022–1027, 1995. [12] F. Burdio, A. Guemes, J. M. Burdio, T. Castiella, M. A. De Gregorio, R. Lozano, T. Livraghi, “Hepatic lesion ablation with bipolar saline-enhanced radiofrequency in the audible spectrum”, Acad. Radiol., vol. 6, pp. 680–686, 1999. [13] E. Delva, Y. Camus, B. Nordlinger, “Vascular occlusions for liver resections,” Ann. Surg., vol. 209, pp. 297–304, 1989. [14] J. P. McGahan, W.-Z. Gu, J. M. Brock, H. Tesluk, C. D. Jones, “Hepatic ablation using bipolar radiofrequency electrocautery”, Acad. Radiol., vol. 3, pp. 418–422, 1996.

78 [15] S. Tungjitkusolmun, E. J. Woo, H. Cao, J.-Z. Tsai, V. R. Vorperian, J. G. Webster, “Thermal-electrical finite element modelling for radio-frequency cardiac ablation: effects of changes in myocardial properties,” Med. Biol. Eng. Comput., vol. 38, pp, 562–568, September 2000. [16] S. Tungjitkusolmun, E. J. Woo, H. Cao, J.-Z. Tsai, V. R. Vorperian, J. G. Webster, “Finite element analyses of uniform current density electrodes for radio- frequency cardiac ablation,” IEEE Trans. Biomed. Eng., vol. 47, pp. 32–40, 2000. [17] M. G. Curley, P. S. Hamilton, “Creation of large thermal lesions in liver using salineenhanced RF ablation,” Proc. 19th Ann. Int. Conf. IEEE Eng. Med. Biol. Soc. (Chicago, 1997) (Piscataway, NJ: IEEE), pp. 2516–2519.

79

7. Tables and Figures Table 1. Material properties used in FEM Figure 1. Geometry of the probe arrangement used in the FEM. Only the prongs conduct RF current. The orientation of the coordinates is shown at the bottom Figure 2. Electric potential of monopolar RF ablation FEM. The scale on the left shows potential in volts. Figure 3. Monopolar RF ablation: Temperature distribution after 12 min RF ablation in temperature-controlled mode, T = 95°C. The outermost border (lightest gray) marks the 50 °C margin, which is considered lesion border. Figure 4. Electric potential of bipolar RF ablation FEM. The scale on the left shows potential in volts. Figure 5. Monopolar RF ablation: Temperature distribution after 12 min RF ablation in temperature-controlled mode, T = 95 °C. The outermost border (lightest gray) marks the 50 °C margin, which is considered lesion border. Figure 6. Electric potential of alternating monopolar RF ablation FEM model. The scale on the left shows potential in volts. Figure 7. Alternating monopolar RF ablation: Temperature distribution after 12 min RF ablation in temperature-controlled mode, T = 95 °C. Only the prongs conduct current. The shafts (gray) are insulated. The outermost border (lightest gray) marks the 50 °C margin, which is considered lesion border.

80 Figure 8. Progress of upper and lower probe tip temperature during alternating monopolar ablation. The point t = 0 corresponds to 6 min after start of ablation.

81

Element

Material

ρ [kg/m3 ]

c [J/kg⋅K]

k [W/m⋅K]

σ [S/m]

Electrode

Ni–Ti

6450

840

18

1⋅10 8

Shaft

Stainless Steel

21500

132

71

4⋅10 6

3600

0.512

0.333

Tissue Liver 1060 Table 1. Material properties used in FEM

Ni-Ti retractable electrodes, 0.5 mm diameter

Stainless steel insulated

shaft,

25 mm

Figure 1. Geometry of the probe arrangement used in the FEM. Only the prongs conduct RF current. The orientation of the coordinates is shown at the bottom.

82

Figure 2. Electric potential of monopolar RF ablation FEM. The scale on the left shows potential in volts.

Figure 3. Monopolar RF ablation: Temperature distribution after 12 min RF ablation in temperature-controlled mode, T = 95 °C. The outermost border (lightest gray) marks the 50 °C margin, which is considered lesion border.

83

Figure 4. Electric potential of bipolar RF ablation FEM. The scale on the left shows potential in volts.

Figure 5. Bipolar RF ablation: Temperature distribution after 12 min RF ablation in temperature-controlled mode, T = 95 °C. The outermost border (lightest gray) marks the 50 °C margin, which is considered lesion border.

84

Figure 6. Electric potential of alternating monopolar RF ablation FEM. The scale on the left shows potential in volts.

85

Figure 7. Alternating monopolar RF ablation: Temperature distribution after 12 min RF ablation in temperature-controlled mode, T = 95 °C. Only the prongs conduct current. The shafts (gray) are insulated. The outermost border (lightest gray) marks the 50 °C margin, which is considered lesion border.

110

T (°C)

100

90 Upper probe Lower probe 80

70

60 0

5

10

15

20

25

30

t (s)

Figure 8. Progress of upper and lower probe tip temperature during alternating monopolar ablation. The point t = 0 corresponds to 6 min after start of ablation.

86

Chapter V

Multiple Probe Hepatic Radio-Frequency Ablation: ex-vivo experiments in the porcine model

This work was published as: D. Haemmerich, F. T. Lee Jr., A. W. Wright, D. M. Mahvi, and J. G. Webster, “Multiple Probe Hepatic Radio-Frequency Ablation: ex-vivo experiments in the porcine model”, Proceedings EMBC 2001, Istanbul, 2001.

87

Abstract Radio- frequency (RF) ablation is an important means of treatment of nonresectable primary and metastatic liver tumors. The RF ablation of any but the smallest tumor requires the use of multiple overlapping treatment zones. Commercially available RF ablation generators, unlike cryoablation (a method of tumor destruction that utilizes cold rather than heat), are only capable of driving a single RF probe at a time. Using multiple probes simultaneously in RF ablation is desirable for treating large tumors and for treating multiple tumor metastases. Bipolar RF ablation, which has been previously studied by other groups, allows simultaneous usage of two probes. The energy converted to heat at each probe for bipolar RF ablation is necessarily equal. There have been no investigations of other methods that allow usage of multiple RF probes simultaneously. We investigate feasibility of a new method, where power is applied in a alternating fashion between two or more probes. This method allows independent control of the amount of energy deposited at each probe. We performed ex- vivo experiments with one (i.e conventional ablation) and with two probes. In the two-probe experiment, both probes reached target temperature and created lesions of sizes comparable to conventional RF ablation.

88

1. Introduction Radio- frequency (RF) ablation is increasingly utilized 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 mortality of 1,000,000 [1]. Surgical resection offers the best chance of long-term survival, but is rarely possible. In many patients with cirrhosis or multiple tumors hepatic reserve is inadequate to tolerate resection and alternative means of treatment that target the tumor, but preserve uninvolved liver are necessary [2]. Cryoablation and RF ablation are the most commonly used therapies for cases where surgical resection is not possible. In cryoablation, cold is used to destroy tissue. Cryoablation, unlike RF ablation, allows simultaneous application of multiple probes. Simultaneous application of multiple probes is desirable for treatment of large tumors, and for coincident treatment of metastases. In RF ablation, RF current 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), temperaturecontrolled mode (T = constant) and impedance-controlled mode (Z < constant) are used. The most commonly used mode is temperature-controlled ablation. Tumor cell death results from the conversion of electromagnetic energy to heat by ionic agitation. Temperatures above 45 ºC to 50 ºC cause denaturation of intracellular proteins and destruction of membranes of tumor cells, eventually resulting in cell necrosis [3]. One of the major limitations of this technique is the inability to use multiple probes simultaneously. When tumors greater than 2 cm are treated, multiple applications are necessary to obtain complete tumor necrosis. Often

89 tumor cells survive, which leads to high recurrence rates [5]. In cases where multiple tumors are present, these must be treated sequentially. Treatment time could be drastically reduced, if multiple RF probes could be employed simultaneously. Several methods have been investigated for increasing lesion size and improving efficacy. Internally cooled probes have been used [7]. Interstitial saline infusion creates larger lesions by cooling and increasing effective electrode area [10]. The cooling effects of large blood vessels and vascular perfusion can be minimized by clamping the hepatic artery and portal vein and occluding vascular inflow [12]. Inflow occlusion however requires a major surgical procedure, which negates one of the major advantages of RF ablation—use in a minimally invasive procedure (percutaneous or laparoscopic). Bipolar RF ablation has been shown to create larger lesions using two needle electrodes, compared to conventional ablation using a single needle electrode, when the two probes are placed close to each other [2]. There have been no investigations of methods other than bipolar ablation that allow usage of multiple RF probes simultaneously. We investigated the potential of a novel method where power is applied alternating between two probes. The temperature of both probes’ prongs are transferred to a computer. The computer controls the period for which power is applied to each probe via an electronic switch, so that both probes are kept at the same temperature. The method can also be extended to more probes.

2. Methods The system for RF ablation using two probes (probe A and probe B) simultaneously is outlined in Fig. 1. The tip temperatures of both probes (TA,i , TB,i) are reported to the RF

90 generator, which relays the values to a PC. The PC is running a software implemented PI controller, which controls an electronic switch via a D/A-converter (Module DI-220, DataQ Instruments, Akron, OH) connected to the PC’s parallel port. The power P is relayed to probes A and B via the electronic switch, so that the average tip temperature of the two probes is kept equal. The signal CA/B determines, which probe the power is relayed to. At a certain time during ablation, current flows either from probe A or from probe B towards the ground pad. For all ex-vivo experiments we used the Rita 1500 RF generator and Rita model-90 multi-prong probes (Rita Medical Systems, Mountain View, CA). The prongs of this probe can be extended to 5 cm. We only extended the prongs to 3 cm to ensure that both probes reach target temperature, since the power is shared between two probes. Each model-90 probe has 5 thermocouples placed at the prong tips, which report the tip temperatures to the RF generator. The RF generator allows for monitoring of 9 temperatures. We monitored all 5 tip temperatures of probe A (TA,i), and 4 tip temperatures of probe B (TB,i). As a specimen we used liver tissue that we acquired from a local butcher. We performed ex-vivo experiment #1, where we ablated the tissue with a single probe, at 90 °C temperature-controlled mode for 12 min. The tissue was immersed in physiological saline solution. The saline and tissue were both at 20 °C at the beginning of the experiment. We used software provided by Rita to record temperature and applied power during ablation. We used the results of experiment #1 to analyze the dynamic system to be controlled and to create an approximation of this system. We then created a computer simulation of the

91 closed- loop system. The dynamic system consisted of the ablation probe, tissue, and dispersive electrode. Since we wanted to drive two probes with the RF generator, we needed to include two dynamic systems (A and B) in the computer simulation. The input variable of the system was the power applied, the output variable was the average temperature of the probe prongs. We used the recorded temperature and power data of experiment #1 to approximate the transfer function of the dynamic system A by a 9th order linear discrete state space model, as given in (1).

x( n +1 ) = A ⋅ x( n ) + B ⋅ u( n ) y( n ) = C ⋅ x( n ) + D ⋅ u( n )

(1)

In (1), u is the input, x is the state and y is the output.

We used MATLAB (Mathworks, Natick, MA) to determine the approximated state space model of the dynamic system A (i.e. we determined matrices A, B, C and D). Using the same method we created a second state space model for the dynamic system B. The input data (i.e. powers) were not changed, but the output data (i.e. temperatures) were scaled to 80% of the data used for the first model. The model of dynamic system B approximated a situation where higher blood perfusion is present near probe B compared to probe A (i.e. it needs higher power to reach same temperature). We then created a closed- loop system in MATLAB/Simulink including the two state space models (A and B) and a PI controller that controls the power delivered to each of the probes. The closed- loop system is shown in Fig. 2. Under the assumption that the switching of power between the two probes occurs faster

92 than the time constant for change of probe tip temperatures (i.e. we neglect the ripple in tip temperatures), we introduced a control variable α (-0.5 < α < 0.5). The limiter in Fig. 2 ensures that variable α stays within its limits. This variable α determined the distribution of total power P between probes A and B. The power ((0.5 + α) · P) was delivered to probe A, power ((0.5 – α) · P) was delivered to probe B. The input of the controller was the temperature difference of the average prong tip temperatures of probes A and B. The time course of power P used in the control system simulation was taken from the data acquired for the ex-vivo experiment #1 described above. The time discrete formulation of a PI controller is given by (2). n e +e m m −1 ∆ t

u n = K p en + K i ∑

m =1

(2)

2

In (2) ∆t is the sampling time, Kp and Ki are the control parameters. Using the computer simulation we determined the control parameters by means of the Ziegler–Nichols method.

We implemented this PI controller in software using Visual Basic (Microsoft, Redmond, WA) on a PC. We used software provided by Rita to obtain temperature and applied power during ablation. The PI controller software acquired the temperature data of the two probes every 2 s from the Rita software (i.e. sampling time ∆t = 2 s). The sampling time ∆t corresponds to the sample & hold element in Fig 2. Due to limitations in the Rita software, temperature could not be acquired at smaller time intervals. The PI controller software controlled an electronic switch via a D/A-converter. Depending on the variable α., Power

93 was delivered to probe A for ((0.5 + α) · T) seconds, and to probe B for ((0.5 – α) · T) seconds. We chose T to be 1 s, so that the ripple in temperature of the probe tips was negligible. We designed the following ex-vivo experiment #2 to determine performance of the PI controller. We used two pieces of liver, where the initial temperatures of the two pie ces were different. One piece was at 17 °C initial temperature, whereas the 2nd piece was at 27 °C initial temperature. Both pieces of tissue were immersed in 27 °C physiological saline solution. We performed RF ablation for 12 min, at a target temperature of 90 °C. The RF generator controlled the applied power to keep average tip temperature of probe A at target temperature. The PI controller controlled the switch, i.e. it governed how power is distributed between the two probes, to keep both probes at same average tip temperature.

3. Results The obtained lesion dimension from experiment #1 where RF ablation was performed the conventional way (i.e. single probe), was 2.3 cm. Fig. 3 shows the time course of variable α (a), and of the difference in average tip temperature of the two probes (b) for experiment #2, for the first 150 s of the experiment. Fig. 4. shows the time course of average tip temperatures of probes A and B. Target temperature of 90 °C was reached for both probes after 350 s. The average tip temperature of the two probes was kept within the range of 89.2 °C – 92 °C during the 12 min ablation procedure. The obtained lesion dimensions were 2.3 cm for tissue sample A (initial temperature 17 °C) and 2.5 cm for tissue sample B (initial temperature 27 °C).

94 4. Discussion We evaluated a novel method that allows usage of multiple RF probes. The scheme has been examined by means of an ex-vivo experiment using two probes. The method can be extended to more probes if necessary. Other investigators examined feasability of bipolar RF ablation, where current is passed between two probes. Bipolar ablation is limited to two probes and cannot be extended to a greater number of probes. Another disadvantage is that bipolar ablation does not allow independent control of amount of energy deposited at each probe. All current originating at one probe must enter the other probe. If we assume that similar resistivity and current density are present in the vicinity of both probes, a comparable amount of energy is converted into heat next to each of the two probes. The liver is a very heterogeneous organ, with varying conditions in terms of blood perfusion. If one probe experiences more cooling due to higher blood perfusion than the other, more heat energy is carried away. In bipolar RF ablation, one probe then reaches a lower temperature than the other. With the method presented in this paper, the applied power can be independently distributed between both probes. In experiment #2, the two tissue samples (tissues A and B) had 10 °C of difference in initial temperature. Tissue A had 17 °C initial temperature, tissue B had 27 °C initial temperature. Within 40 s, the average probe tip temperatures were equalized by applying more power to the probe that was inserted into the cooler tissue. The parameter α determines how the power is distributed between the probes. Initially during experiment #2, α increased almost up to its maximum of 0.5 (i.e. all power is applied to probe B), and returned to zero as the average tip temperatures of the two probes were

95 equilibrated. Fig. 4 shows the temperature time course of both probes A and B during the first 500 s of ablation. Both probes reached the target temperature of 90 °C after 320 s, and were kept within 89.2 °C – 92 °C during the subsequent ablation procedure. The PI controller performed as expected in the ex-vivo experiment. For experiment #1, target temperature was reached faster than for experiment #2, after only 170 s. This shorter time stems from the fact that for experiment #2, the power was at maximum (i.e. 150 W) for the first 120 s, i.e. the power rating of the generator was not sufficient. The two resulting lesion dimensions of experiment #2 were similar, where the initially cooler sample had a slightly smaller lesion. The tissue sample A with lower initial temperature had a lesion of 2.3 cm diameter, tissue sample B had a lesion of 2.5 cm diameter. Both lesions were similar in dimension to the lesion created in experiment #1 (conventional RF ablation using a single probe), which had 2.3 cm diameter. In our experiment, the power was switched in ~0.5 s intervals between the probes. It has to be considered that by switching the RF generator output, a low- frequency component is introduced into the RF signal. This low- frequency component could excite nerves and tissue (e.g. cardiac tissue). For clinical application it is therefore desirable to switch at frequencies where no excitation is possible, i.e. above 20 kHz.

5. Conclusion The method presented is superior to bipolar RF ablation and conventional RF ablation. It allows simultaneous application of two or more probes. Power can be distributed between the probes to allow temperature-controlled ablation of all probes. The scheme can be used to increase lesion size for ablation of large tumors, or to treat multiple tumor metastases

96 simultaneously. The treatment time can thereby be greatly reduced compared to conventional RF ablation, where ablation has to be performed sequentially.

97

6. References [1] M. C. Kew, “The development of hepatocellular carcinoma in humans,” Cancer Surv., vol. 5, pp. 719–739, 1985. [2] S. A. Curley, B. S. Davidson, R. Y. Fleming, F. Izzo, L. C. Stephens, P. Tinkey, D. Cromeens, “Laparoscopically guided bipolar radiofrequency ablation of areas of porcine liver”, Surg. Endosc., pp. 729–733, 1997. [3] W. Lounsberry, V. Goldschmidt, C. Linke, “The early histologic changes following electrocoagulation,” Gastrointest. Endosc., vol. 41, pp. 68–70, 1995. [4] L. R. Jiao, P. D. Hansen, R. Havlik, R. R. Mitry, M. Pignatelli, N. Habib, “Clinical shortterm results of radiofrequency ablation in primary and secondary liver tumors,” Am. J. Surgery, vol. 177, pp. 303–306, 1999. [5] S. N. Goldberg, G. S. Gazelle, L. Solbiati, W. J. Rittman, P. R. Mueller, “Radiofrequency tissue ablation: increased lesion diameter with a perfusion electrode,” Acad. Radiol., vol. 3, pp. 636–644, 1996. [6] Y. Miao, Y. Ni, S. Mulier, K. Wang, M. F. Hoez, P. Mulier, F. Penninckx, J. Yu, I. De Scheerder, A. L. Baert, G. Marchal, “Ex vivo experiment on radiofrequency liver ablation with saline infusion through a screw-tip cannulated electrode,” J. Surg. Res., vol. 71, pp. 18– 26, 1997. [7] E. Delva, Y. Camus, B. Nordlinger, “Vascular occlusions for liver resections,” Ann. Surg., vol. 209, pp. 297–304, 1989.

98

7. Figure Legends Figure 1. Block diagram of multiple probe RF ablation system. Figure 2. Block diagram of closed- loop system as used in computer simulation. Figure 3. Results of ex-vivo experiment #2, 12 min ablation with two probes. The time course of (a) control variable α, and (b) difference in average tip temperature between probes A and B, is shown for first 150 s of the experiment. Figure 4. Time course of average tip temperatures.

99

T A,i , TB,i

RF Generator T B,i

PC (PI controller)

T A,i Probe A

P

PA

Switch Probe B Ground Pad

CA/B

PB

Tissue

Figure 1. Block diagram of multiple probe RF ablation system.

P(t)

PA

Power

x( n + 1 ) = A ⋅ x( n ) + B ⋅ u( n ) y( n ) = C ⋅ x( n ) + D ⋅ u( n )

TA + –

Dynamic System (Probe A)

PB

x( n +1 ) = A ⋅ x( n ) + B ⋅ u( n ) y( n ) = C ⋅ x( n ) + D ⋅ u( n )

TA-T B

TB

S&H

α PI Controller

Sample & Hold (2 s)

Dynamic System (Probe B)

0.5 – α

+ –

0.5 + α

+ +

0.5 Limiter [-0.5, 0.5] Constant

Figure 2. Block diagram of closed-loop system as used in computer simulation.

100

0.5 0.4 0.3

(a)

0.2 0.1 0 -0.1

0

50

100

150

Time (s)

15

T A-T B (°C)

10

(b)

5 0 -5 -10

0

50

100

150

Time (s)

Figure 3. Results of ex-vivo experiment #2, 12 min ablation with two probes. The time course of (a) control variable α, and (b) difference in average tip temperature between probes A and B, is shown for first 150 s of the experiment.

101

Average Tip Temperature (°C)

100 80 60 Probe A Probe B

40 20 0 0

100

200

300

400

Time (s)

Figure 4. Time course of average tip temperatures.

500

102

Chapter VI

Hepatic bipolar radio-frequency ablation creates lesions close to blood vessels - A Finite Element study

This work was submitted as:

D. Haemmerich, A. W. Wright, D. M. Mahvi, F. T. Lee Jr., and J. G. Webster, “Hepatic bipolar radio-frequency ablation creates lesions close to blood vessels - A Finite Element study”, IEEE Trans. Biomed. Eng., submitted 2001.

103

Abstract Radio- frequency (RF) ablation has become an important means of treatment of nonresectable primary and metastatic liver tumors. Recurrence of treated tumors is associated with cancer cell survival next to blood vessels. We examine the performance of classical monopolar, and two configurations of bipolar RF ablation using the LeVeen 10-prong catheter (Radio Therapeutics, Sunnyvale, CA). We created models using the finite element method of monopolar and bipolar configurations in 5 mm distance of a large blood vessel with 1 cm diameter. In one bipolar configuration, the probes were oriented in the same axial direction (asymmetric configuration); in the second bipolar configuration the two probes were facing each other (symmetric configuration). We analyzed the distribution of temperature and current density. The distance between the formed lesion and the blood vessel was 2.3 mm for monopolar, 1.8 mm for asymmetric bipolar and 1.0 mm for symmetric bipolar configuration. The symmetric bipolar method was the only one that produced continuous lesions encompassing the vessel. Symmetric bipolar RF ablation creates lesions significantly closer to blood vessels compared to monopolar RF ablation. This may reduce tumor cell survival next to blood vessels and reduce recurrence rates. However, the symmetric bipolar method may be difficult to apply in practice.

104

1. Introduction Radio- 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 mortality of 1,000,000 people [1]. 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 necessary [2]. In RF ablation, RF current is delivered to the tissue via electrodes inserted percutaneously or during surgery. Different modes of controlling the electromagnetic power delivered to tissue are 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 ionic agitation. Temperatures above 45 ºC to 50 ºC have been shown to cause denaturation of intracellular proteins and destruction of membranes of tumor cells, eventually resulting in cell necrosis [3]. The liver is a highly perfused organ, and therefore large blood vessels represent a heat sink that draw heat away and thereby limit lesions. Often tumor cells survive, which leads to high recurrence rates [4], [5], [6], [7]. More specifically, cancer cell survival next to large blood vessels is correlated with tumor recurrence after RF ablation treatment [22]. The cooling effects of large blood vessels and vascular perfusion can be minimized by the Pringle maneuver, in which vascular inflow occlusion is performed by clamping the hepatic artery and portal vein [8]. However, the Pringle requires a major surgical procedure, which negates one of the major advantages of RF ablation—the use in a minimally invasive fashion (percutaneous or laporoscopic).

105 Vasoactive pharmacologic agents have also been used to reduce blood flow to the liver [9] to reduce the blood cooling effect. Bipolar RF ablation has been shown to create larger lesions using needle electrodes [2], [10], [11] and using multiple prong probes [12]. We created FEM models of monopolar and bipolar RF ablation with multiple prong electrodes, next to a blood vessel. We compare current density, temperature distribution and distance between lesion and vessel wall for monopolar and two bipolar configurations.

2. Materials and Methods

A. Bioheat Equation Joule heating arises when an electric current passes through a conductor. Electromagnetic energy is converted into heat. The heating of tissue during RF ablation is governed by the bioheat equation, which was first introduced by Pennes in 1948 [13]: ∂T = ∇ ⋅ k∇T + J ⋅ E − hbl (T − Tbl ) − Qm ∂t hbl = ρ blc bl wbl ρc

where ρ is the density (kg/m3), c is the specific heat (J/(kg⋅K)), and k is the thermal conductivity (W/(m⋅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/(kg⋅K)), and wbl is the blood perfusion (L/s). hbl is 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 terms.

106 In the Pennes model described in the bioheat equation, the energy exchange between blood and tissue is modeled as a nondirectional heat source. One major assumption is that the heat transfer related to perfusion between tissue and blood occurs in the capillary bed, which turned out not to be fully correct. The main thermal equilibrium process takes place in the pre- or postcapillary vessels. Nevertheless, the Pennes model describes blood perfusion with acceptable accuracy, if no large vessels are nearby [14]. The blood perfusion in hepatic tissue used in the FEM model was wbl = 6.4 × 10–3 [15].

B. Finite element method We created finite element method (FEM) models for monopolar and bipolar ablation. For all FEM analyses, we used a LeVeen, 10-prong probe (Radio Therapeutics, Sunnyvale, CA) with 3 cm diameter (when prongs are extended). The prongs are of rectangular cross-section, measuring 0.4 mm × 0.3 mm (width × height). The shaft is 2.3 mm in diameter, and is insulated—only the tines conduct current. In the bipolar configuration, the two probes are placed 20 mm apart, with the vessel centered in between (i.e. the vessel is 5 mm away from the probes). We created three different geometrical configurations: monopolar, asymmetric bipolar and symmetric bipolar. Fig. 1 shows the geometry of the probe model for the asymmetric bipolar configuration where both probes are oriented in the same direction axially. In the bipolar configurations current was flowing between the two probes (i.e. one of the probes was assigned to ground potential). In the monopolar configuration only the lower probe was present next to the blood vessel, and ground potential was assigned to the model boundaries. In the symmetric bipolar configuration, the upper probe was rotated 180°, i.e. the

107 two probes were positioned contra-axially. We created an additional model using the symmetric bipolar configuration where we altered the conductivity of the blood inside the vessel to be the same as tissue conductivity. In all models, probes and vessel were surrounded by a cylinder of liver tissue, 100 mm long and 100 mm in diameter. Due to the symmetry of the arrangement, we could reduce computing time by only modeling half of the geometry shown in Figure 1. Table 1 lists the material properties used in the model, which were taken from the literature [16] [17]. We set the initial temperature of the liver tissue and temperature at the boundary of the model to 37 ºC. Blood perfusion was modeled according to the Pennes model [13]. Since for large blood vessels the blood temperature in the vessel is unaffected by the surrounding temperature field [18], we set the temperature of the blood vessel to 37 °C as an additional boundary condition. This can be considered the worst case (i.e. very high heat transfer coefficient between vessel and tissue). In clinical application, the amount of power applied to the LeVeen probe is controlled via impedance control; i.e. power is reduced once impedance rises a certain amount above baseline impedance due to desiccation and vaporization [19]. However, we were unable to simulate this process in our FEM models due to lack of information on the change of tissue properties above 100 °C. We used temperature control in a way that maximum temperature within hepatic tissue is kept at 95 °C for the duration of the treatment. We simulated ablation for 12 min; in our models we did not observe any significant change in lesion dimensions beyond that time. The maximum temperature of hepatic tissue was kept at 95 ºC by varying the voltage applied to the electrodes. The lesion size was determined using the 50 ºC margin (i.e. tissue above 50 ºC is considered destroyed) at the end of the simulation. The bipolar

108 FEM models consisted of ~255,000 tetrahedral elements, the monopolar model consisted of ~160,000 tetrahedral elements. We used a nonuniform mesh; mesh size was 0.2 mm close to the probe where we see large temperature and current gradients, and 5 mm at the model boundaries. We used PATRAN Version 2000 (The MacNeal-Schwendler Co., Los Angeles, CA) to generate the geometric models, assign material properties, assign boundary conditions and perform meshing. After creating the model, PATRAN generates an input file for the ABAQUS/Standard 5.8 (Hibbitt, Karlsson & Sorensen, Inc., Pawtucket, RI) solver. A coupled thermo-electrical analysis was performed by ABAQUS. For postprocessing we used the built- in module ABAQUS/POST to generate profiles of temperature and electric field intensity. All analysis was performed on a HP-C180 workstation equipped with 1.1 GB of RAM and 34 GB of hard disk space. Tungjitkusolmun et al. [20] provide a detailed description of the FEM modeling process.

3. Results We generated FEM models of monopolar and bipolar ablation and analyzed the distribution of temperature and current density distribution at the end of a 12 min ablation simulation. Temperature and current density maps were generated for two planes. Plane 1 was oriented perpendicular to the blood vessel axis, through the catheter axis (parallel to x–z plane in Figure 1); plane 2 was oriented through the vessel axis (i.e. along the vessel), and through the catheter axis (parallel to y–z plane in Figure 1). Due to the probe geometry, plane 1 is cutting through the tines whereas plane 2 is cutting in between two neighboring tines. Figures 2 and 3 show the temperature map for the monopolar configuration in plane 1 and plane 2, respectively. The distance between lesion and vessel wall is 2.3 mm. Figure 4 shows the

109 current density map for the monopolar configuration in plane 1. Figure 5 shows the temperature map for the asymmetric bipolar configuration in plane 1. The distance between the lower lesion and vessel wall is 1.8 mm. Figures 6 and 7 show the temperature maps for the symmetric bipolar configuration in plane 1 and plane 2, respectively. The distance between lesion and vessel wall is 1.0 mm. Figure 8 shows the temperature map in plane 1 for the symmetric bipolar configuration, where blood conductivity inside the vessel has been altered to be the same as tissue conductivity. Figure 9 shows the current density map for the symmetric bipolar configuration in plane 1. Figure 10 shows the current density map for the symmetric bipolar configuration with altered blood conductivity in plane 1. The distance between lesion and vessel wall is 1.2 mm.

4. Discussion It is well known that cooling mediated by large blood vessels has a major impact on lesion formation during hepatic RF ablation [21]. More specifically, tumor recurrence is associated with incomplete destruction of cancer cells close to blood vessels [22]. We examined the performance of bipolar RF ablation next to a large blood vessel compared to monopolar RF ablation. Figures 2 and 3 show the temperature distribution at the end of ablative treatment for the monopolar configuration, which is currently clinically used. In both figures we observe a large deflection of the lesion caused by the vessel. This may result in thermal underdosage of a tumor located close to this vessel, ultimately leading to recurrence. We compared two methods of bipolar RF ablation using the same probe as was used in the monopolar configuration. First we examined the asymmetric bipolar configuration. The temperature map for this case is shown in figure 5, where we observe less deflection of the

110 lesion created by the lower probe. The lesion created by the lower probe is also closer to the vessel compared to the monopolar configuration. The distance between lesion and vessel was 2.3 mm for the monopolar and 1.8 mm for the asymmetric bipolar configuration. However, we notice that only the upper tine tips reach the set temperature of 95 °C whereas the lower tine tips only reach around 70 °C. This stems from the nonsymmetry of the configuration, where the upper probe tines point towards the lower probe and therefore create higher current density at the tine tips in contrast to the lower tine tips, which point away from the upper probe. The upper probe tines greatly limit the total amount of energy that can be dissipated by the two probes. A large improvement over the asymmetric bipolar configuration is achieved by flipping the upper probe, which leads to a symmetric bipolar configuration. Figures 6 and 7 show the resulting temperature distribution. We now observe a confluent lesion surrounding the blood vessel, and the lesion extends much closer to the vessel. The distance between the vessel and the le sion now is 1.0 mm, which is less than half the distance we observed in the monopolar configuration. The superior performance of the bipolar configuration is partially to the thermally synergistic effect due to the simultaneous creation of two lesions close to each other. Two probes in close proximity to each other create a larger lesion than two separate lesions created by a single probe. This effect has been previously observed during microwave ablation using multiple probes [23]. A second effect is the increased current density in between the two probes. In previous experiments where we evaluated the performance of bipolar RF ablation using 4-tine multiprong probes, we observed only negligible increase in current density in between the probes [12]. However, with the 10-tine probes used in this study, we see a substantial increase in current density in

111 between the probes compared to the monopolar configuration. The current density maps resulting from monopolar and symmetric bipolar configuration are shown in Figures 4 and 9, respectively. Due to the increase in current density in between the probes, the zone of active heating (i.e. not considering lesion formation caused by thermal conduction) extends further towards the collateral probe (i.e. towards the blood vessel). This effect may contribute significantly to the lesion extending closer to the vessel. This confirms the hypothesis stated in [12], that bipolar RF ablation using multiprong probes is more effective, the more tines the probe has, in that it causes a more significant increase in current density in between the two probes. However, the increase in current density in between the probes seen in figure 9 might be partially due to the blood vessel located in between the probes. Blood has a much higher conductivity compared to liver tissue (see Table 1) and therefore current is ‘channeled’ towards the blood vessel (see Figure 9). This effect is smaller for smaller vessel sizes since then the area of blood also is smaller. To examine the significance of the channeling of current caused by the vessel, we modified the symmetric bipolar model by altering the conductivity of the blood inside the vessel to be the same as the tissue conductivity. Figure 8 shows the temperature distribution, and figure 10 shows the current density distribution resulting from this modified bipolar model. We only observe a slight change in lesion appearance for the modified model (Figure 8) compared to the original model (Figure 7). The distance between lesion and vessel for the modified model (Figure 8) is 1.2 mm (in the vertical direction) compared to 1.0 mm for the original model (Figure 7). However, we see that in the modified model the lesion is closer to the vessel in the horizontal direction (1.8

112 mm) compared to the original model (2.3 mm). This is the result of the absence of the current channeling in the modified model (Figure 10), which was present in the original model (Figure 9). Nevertheless we still get a confluent lesion surrounding the vessel and conclude, that the symmetric bipolar configuration creates lesions much closer to a blood vessel, largely independent of vessel size and the vessel- mediated current channeling effect. A disadvantage of the symmetric bipolar configuration is that the two ablation catheters have to be inserted from two opposing sides, which may not always be possible. A single catheter that contains two sets of tines that can extend in a symmetric bipolar configuration also may be difficult to design. Comparably, the symmetric bipolar configuration is much simpler to implement in practice. Two catheters can be easily lined up axially and introduced together into the tissue. However, the symmetric bipolar configuration exhibits inferior performance. It should be pointed out, that the vessel is kept at 37 °C for the simulation, and that this represents the worst-case scenario. In reality, both monopolar and bipolar RF ablation might create continuous lesions up to the vessel wall, depending on distance between vessel and probe, and vessel size. Nevertheless we show, that bipolar RF ablation is more effective in creating lesions next to a vessel.

5. Conclusion

We evaluated the clinically used monopolar configuration, an asymmetric and a symmetric bipolar configuration in close proximity to a large blood vessel. The symmetric bipolar configuration created a lesion fully encompassing the vessel. The lesion was also closest to the blood vessel, but the symmetric bipolar method may be difficult to apply in practice. The

113 asymmetric bipolar method performs better than the monopolar method, but only the upper probe reaches set temperature and therefore limits energy deposition by the lower probe. No confluent lesion is produced. The monopolar method showed worst performance. We conclude that the use of bipolar RF ablation may reduce recurrence rates associated with tumor cell survival close to blood vessels.

114

6. References [1] M. C. Kew, “The development of hepatocellular carcinoma in humans,” Cancer Surv., vol. 5, pp. 719–739, 1985. [2] S. A. Curley, B. S. Davidson, R. Y. Fleming, F. Izzo, L. C. Stephens, P. Tinkey, D. Cromeens, “Laparoscopically guided bipolar radiofrequency ablation of areas of porcine liver”, Surg. Endosc., pp. 729–733, 1997. [3] W. Lounsberry, V. Goldschmidt, C. Linke, “The early histologic changes following electrocoagulation,” Gastrointest. Endosc., vol. 41, pp. 68–70, 1995. [4] S. Rossi, M. Di Stasi, E. Buscarini, P. Quaretti, F. Garbagnati, L. Squassante, C. T. Paties, D. E. Silverman, L. Buscarini, “Percutaneous RF interstitial thermal ablation in the treatment of hepatic cancer,” Am. J. Roentgenol., vol. 167, pp. 759–768, 1996. [5] L. R. Jiao, P. D. Hansen, R. Havlik, R. R. Mitry, M. Pignatelli, N. Habib, “Clinical shortterm results of radiofrequency ablation in primary and secondary liver tumors,” Am. J. Surgery, vol. 177, pp. 303–306, 1999. [6] L. Solbiati, T. Ierace, S. N. Goldberg, S. Sironi, T. Livraghi, R. Fiocca, G. Servadio, G. Rizzatto, P. R. Mueller, A. Del Maschio, G. S. Gazelle, “Percutaneous US- guided radiofrequency tissue ablation of liver metastases: treatment and follow- up in 16 patients,” Radiology, vol. 202, pp. 195–203, 1997. [7] S. A. Curley, F. Izzo, P. Delrio, L. M. Ellis, J. Granchi, P. Vallone, F. Fiore, S. Pignata, B. Daniele, F. Cremona, “Radiofrequency ablation of unresectable primary and metastatic hepatic malignancies,” Ann. Surg., vol. 230, pp. 1–8, 1999.

115 [8] E. Delva, Y. Camus, B. Nordlinger, “Vascular occlusions for liver resections,” Ann. Surg., vol. 209, pp. 297–304, 1989. [9] S. N. Goldberg, P. F. Hahn, E. F. Halpern, R. M. Fogle, G. S. Gazelle, “Radio- frequency tissue ablation: effect of pharmacologic modulation of blood flow on coagulation diameter,” Radiology, vol. 209, pp. 761–767, 1998. [10] F. Burdio, A. Guemes, J. M. Burdio, T. Castiella, M. A. De Gregorio, R. Lozano, T. Livraghi, “Hepatic lesion ablation with bipolar saline-enhanced radiofrequency in the audible spectrum”, Acad. Radiol., vol. 6, pp. 680–686, 1999. [11] J. P. McGahan, W.-Z. Gu, J. M. Brock, H. Tesluk, C. D. Jones, “Hepatic ablation using bipolar radiofrequency electrocautery”, Acad. Radiol., vol. 3, pp. 418–422, 1996. [12] D. Haemmerich, S. T. Staelin, S. Tungjitkusolmun, F. T. Lee Jr., D. M. Mahvi, J. G. Webster, “Hepatic bipolar radio- frequency ablation between separated multiprong electrodes”, IEEE Trans. Biomed. Eng., vol. 48, 1145–1152, 2001. [13] H. H. Pennes, “Analysis of tissue and arterial blood temperatures in resting forearm,” J. Appl. Phys., vol. 1, pp. 93–122, 1948. [14] H. Arkin, L. X. Xu, K. R. Holmes, “Recent developments in modeling heat transfer in blood perfused tissues”, IEEE Trans. Biomed. Eng., 41, pp. 97–107, 1994. [15] E. S. Ebbini, S.-I. Umemura, M. Ibbini, C. A. Cain, “A cylindrical-section ultrasound phased-array applicator for hyperthermia cancer therapy,” IEEE Trans. Biomed. Eng., vol. 35, pp. 561–572, 1988. [16] D. Panescu, J. G. Whayne, S. D. Fleischman, M. S. Mirotznik, D. K. Swanson J. G. Webster, “Three-dimensional finite element analysis of current density and temperature

116 distributions during radio- frequency ablation,” IEEE Trans. Biomed. Eng., vol. 42, pp. 879–890, 1995. [17] J. W. Valvano, J. R. Cochran, K. R. Diller, “Thermal conductivity and diffusivity of biomaterials measured with self- heating thermistors”, Int. J. Thermophys., vol. 6, pp. 301– 311, 1985. [18] J. Chato, “Heat transfer to blood vessels”, ASME Trans. Biomed. Eng., vol. 102, pp. 110-118, 1980. [19] J. P. McGahan, G. D. Dodd III, “Radiofrequency ablation of the liver: current status”, AJR, vol. 176, pp. 3–16, 2001. [20] S. Tungjitkusolmun, E. J. Woo, H. Cao, J.-Z. Tsai, V. R. Vorperian, J. G. Webster, “Thermal-electrical finite element modeling for radio frequency cardiac ablation: effects of changes in myocardial properties”, Med. Biol. Eng. Comput., vol. 38, 562–568, September 2000. [21] D. S. Lu, M. P. Wang, D. J. Vodopich, S. S. Raman. “The effect of vessels on hepatic RF lesion creation: assessment of the “heat sink effect”, RSNA 2000, Chicago, IL, 2000. [22] A. R. Gillams W. R. Lees, “The importance of large vessel proximity in the rmal ablation of liver tumours”, RSNA 1999, Chicago, IL, 1999. [23] A. W. Wright, F. T. Lee Jr., C. D. Johnson, D. M. Mahvi, “Microwave ablation of hepatic tissue: simultaneous use of multiple probes results in large areas of tissue necrosis”, RSNA 2001, Chicago, IL, 2001.

117 7. Figure Legends Figure 1. Geometry of asymmetric bipolar model. Figure 2. Temperature map of monopolar configuration in plane 1. The circle represents the vessel wall, the gray block represents the shaft and the white arcs represent the tines. The outermost gray border marks the 50 °C margin. Figure 3. Temperature map of monopolar configuration in plane 2. The line represents the vessel wall. The outermost gray border marks the 50 °C margin. Figure 4. Current density map of monopolar configuration in plane 1. The circle represents the vessel wall, the gray block represents the shaft and the white arcs represent the tines. Figure 5. Temperature map of asymmetric bipolar configuration in plane 1. The circle represents the vessel wall, the gray block represents the shaft and the white arcs represent the tines. The outermost gray border marks the 50 °C margin. Figure 6. Temperature map of symmetric bipolar configuration in plane 2. The lines represent the vessel wall and the gray block represents the shaft. The outermost gray border marks the 50 °C margin. Figure 7. Temperature map of symmetric bipolar configuration in plane 1. The circle represents the vessel wall, the gray block represents the shaft and the white arcs represent the tines. The outermost gray border marks the 50 °C margin. Figure 8. Temperature map of symmetric bipolar configuration in plane 1. Blood conductivity is altered to be same as tissue conductivity. The circle represents the vessel wall, the gray block represents the shaft and the white arcs represent the tines. The outermost gray border marks the 50 °C margin.

118 Figure 9. Current density map of symmetric bipolar configuration in plane 1. The circle represents the vessel wall, the gray block represents the shaft and the white arcs represent the tines. Figure 10. Current density map of symmetric bipolar configuration in plane 1. Blood conductivity is altered to be same as tissue conductivity. The circle represents the vessel wall, the gray block represents the shaft and the white arcs represent the tines.

119

Element

Material

ρ [kg/m3]

c [J/kg⋅K]

k [W/m⋅K]

Tines

Fe

21500

132

71

σ [S/m] at 500 kHz 4 × 106

Shaft

Polyurethane

70

1045

0.026

10–5

Blood

Blood

1000

4180

0.543

0.667

Tissue

Liver

1060

3600

0.512

0.333

Table 1. Material properties used in FEM.

Vessel Tines (Fe) y

z x

Shaft (PU)

Figure 1. Geometry of asymmetric bipolar model.

120 T (°C) 37 50 55 60 65 70 75 80 85 90 95

Figure 2. Temperature map of monopolar configuration in plane 1. The circle represents the vessel wall, the gray block represents the shaft and the white arcs represent the tines. The outermost gray border marks the 50 °C margin.

121

T (°C) 37 50 55 60 65 70 75 80 85 90 95

Figure 3. Temperature map of monopolar configuration in plane 2. The line represents the vessel wall. The outermost gray border marks the 50 °C margin.

122 J (10-3·A/m2) 0 0.5 1.0 1.4 1.9 2.4 2.9 3.3 3.8 4.3 4.8

Figure 4. Current density map of monopolar configuration in plane 1. The circle represents the vessel wall, the gray block represents the shaft and the white arcs represent the tines.

123

T (°C) 37 50 55 60 65 70 75 80 85 90 95

Figure 5. Temperature map of asymmetric bipolar configuration in plane 1. The circle represents the vessel wall, the gray block represents the shaft and the white arcs represent the tines. The outermost gray border marks the 50 °C margin.

124 T (°C) 37 50 55 60 65 70 75 80 85 90 95

Figure 6. Temperature map of symmetric bipolar configuration in plane 2. The lines represent the vessel wall and the gray block represents the shaft. The outermost gray border marks the 50 °C margin.

125

T (°C) 37 50 55 60 65 70 75 80 85 90 95

Figure 7. Temperature map of symmetric bipolar configuration in plane 1. The circle represents the vessel wall, the gray block represents the shaft and the white arcs represent the tines. The outermost gray border marks the 50 °C margin.

126 T (°C) 37 50 55 60 65 70 75 80 85 90 95

Figure 8. Temperature map of symmetric bipolar configuration in plane 1. Blood conductivity is altered to be same as tissue conductivity. The circle represents the vessel wall, the gray block represents the shaft and the white arcs represent the tines. The outermost gray border marks the 50 °C margin.

127 J (10-3·A/m2) 0 0.4 0.8 1.2 1.6 2.0 2.4 2.8 3.2 3.6 4.0

Figure 9. Current density map of symmetric bipolar configuration in plane 1. The circle represents the vessel wall, the gray block represents the shaft and the white arcs represent the tines.

128 J (10-3·A/m2) 0 0.4 0.8 1.2 1.6 2.0 2.4 2.8 3.2 3.6 4.0

Figure 10. Current density map of symmetric bipolar configuration in plane 1. Blood conductivity is altered to be same as tissue conductivity. The circle represents the vessel wall, the gray block represents the shaft and the white arcs represent the tines.

129

Chapter VII

FEM model of Cool-Tip probe next to blood vessel: Comparison to 10-prong probe

130

1. Methods Similarly to the monopolar geometry I used in chapter VI, I created a model of a cool-tip probe (Radionics, Burlington, MA) next to a blood vessel. The probe was oriented parallel to the vessel axis, at 5 mm distance. Figure 1 shows the model geometry. Only the most distal 25 mm of the needle (from the tip to the black ring in figure 1) is electrically and thermally conducting. The remaining part of the probe is covered with an insulating layer. The cool-tip probe is a 17-gauge needle probe, within which saline solution around 20 °C is circulated. Thereby the probe, and also tissue in proximity to the probe is being cooled. This enables more power dissipation within the tissue and thereby allows creation of larger lesions compared to a needle probe without cooling. Since the probe is at constant temperature, we cannot use temperature-controlled mode with this type of probe. Like the 10-prong probe modeled in chapter VI, the cool- tip probe also uses the impedance-controlled mode. The maximum temperature reached within the tissue by the cool- tip probe is around 80 °C [1]. I was unable to simulate impedance control in our FEM models due to lack of information on the change of tissue properties with temperature. Therefore in the model I assumed that a maximum temperature of 80 °C is present within the tissue for the duration of the treatment. I simulated RF ablation for 12 min, which is the standard time used in clinical practice [1]. In clinical practice, at the end of the treatment the saline cooling is stopped for a minute while still applying RF energy to destroy the tissue right next to the probe, which did not heat up due to the cooling.

131 I used the same boundary conditions as in chapter VI, except for another additional thermal boundary condition: The probe tip is kept at a constant temperature of 20 °C, since it is cooled by the saline solution.

2. Discussion I present the results of the FEM model in two planes. Plane 1 contains both the vessel axis and the probe axis. Plane 2 cuts the vessel and probe cross-sectional at a 12 mm distance from the probe tip. Figure 2 shows the current density map in plane 1. We observe hot spots both at the probe tip, and at the boundary between insulated and conducting portion of the probe. These hot spots are also evident in figure 3, which shows the temperature distribution in plane 1. The borderline between white and light gray represents the lesion border (50 °C). We notice a small region around the probe that is below 50 °C since the probe is kept at 20 °C. The lesion extends further towards the blood vessel compared to the multiple-prong probe presented in chapter VI. The distance between lesion and vessel is 1.2 mm compared to 2.3 mm for the 10-prong probe presented in chapter VI. However, note that the two configurations are not directly comparable. The cool-tip probe is at a constant distance of 5 mm from the blood vessel. The 10-prong probe had only a small portion of the probe at 5 mm distance, but most of the probe was further away with the furthest part at a distance of around 15 mm from the vessel due to the more complex probe geometry. Nevertheless due to the simpler probe geometry, it is easier to create lesions close to a vessel with the cool-tip probe. Figure 4 shows the temperature distribution in plane 2, which is cross-sectional in the center of the conducting part. The maximum temperature that is reached in this plane is only

132 around 65 °C. Note that the presence of the hot spots limits the extent of lesion formation. We would be able to create a larger lesion if we were able to reduce the hot spots. Tungjitkusolmun et al. presented ways to reduce hot spots for a cardiac ablation catheter [2].

133

3. References [1] J. P. McGahan, G. D. Dodd III, “Radiofrequency ablation of the liver: current status”, AJR, vol. 176, pp. 3-16, 2001. [2] S. Tungjitkusolmun, E. J. Woo, H. Cao, J.-Z. Tsai, V. R. Vorperian, J. G. Webster, “Finite element analyses of uniform current density electrodes for radiofrequency cardiac ablation”, IEEE Trans. Biomed. Eng., vol. 47, pp. 32–40, 2000.

134

Probe

Vessel

Figure 1. Model geometry.

135

J (10-3·A/m2) 0 0.4 0.8 1.2 1.6 2.0 2.4 2.8 3.2 3.6 4.0

Figure 2. Current density distribution in plane 1. Hot spots are located at the sharp tip, and at the transition between conductive and insulated part of the probe. The dark gray block represents the insulated probe portion, the light gray area represents the conducting probe portion. The black line represents the vessel wall.

136 T (°C) 20 50 53 55 58 60 63 65 68 70 73 75 78 80

Figure 3. Temperature distribution in plane 1. Hot spots are located at the sharp tip, and at the transition between conductive and insulated part of the probe. The dark gray block represents the insulated probe portion, the light gray area represents the conducting probe portion. The black line represents the vessel wall. The outermost gray border marks the 50 °C margin.

137 T (°C) 20 50 53 55 58 60 63 65 68 70 73 75 78 80

Figure 4. Temperature distribution in plane 2. The small circle represents the probe, the large arc represents the vessel wall. The outermost gray border marks the 50 °C margin.

138

Chapter VIII

Assessment of Heat Dissipation in Radio-Frequency Ablation: A Finite Element Study

139 Abstract Cardiac radio-frequency (RF) abla tion is an important minimally- invasive treatment modality for cardiac arrhythmias. The Finite Element Method (FEM) and the Finite Difference Method (FDM) have been used for evaluation of device performance. Typically, the result of the models is the temperature distribution at the end of treatment. Sometimes it is of interest to determine where significant heat dissipation is generated by RF ablation, without considering thermal conduction effects. Researchers have previously used current density or electric field strength to quantify where significant heat dissipation occurs within the material. We created an axisymmetric FEM model of cardiac RF ablation. We examined current density, electric field strength, power density, and initial rate of temperature rise in terms of their performance and limitations to determine where significant heat dissipation arises. Current density and electric field strength are limited because they must be squared to yield dissipated power. Rate of initial temperature change sho wed the best performance. It also takes material density and heat capacity into account, and further allows a quantitative appreciation of where significant heating occurs due to the unit of °C/s. Initial rate of temperature rise can be easily calculated from the bioheat equation after simplification. We show a simple implementation of how to determine initial rate of temperature rise in the FEM model.

140

1. Introduction Radio- frequency (RF) ablation is a minimally invasive technique which has been very successful in treating cardiac arrhythmias. It is now the treatment of choice for supraventricular tachycardias [1]. RF ablation creates a lesion in cardiac tissue by resistive heating. A catheter is introduced into the heart and placed at the treatment location. Current is passed through the catheter for 30 s to 60 s and heats up the tissue next to the catheter electrode. Above 50 °C, denaturation of proteins and cell destruction occurs [2]. In RF ablation, different modeling modalities such as the Finite Element Method (FEM) and the Finite Difference Method (FDM) are commonly used to evaluate device performance [3] [4] [5] [6]. Typically, the result of the model simulation is the temperature distribution in the volume of interest. The temperature distribution is the result of effects from both heat dissipation caused by the electric current, and thermal conduction. Since RF ablation relies for a large part on thermal conduction, it is sometimes desirable to directly determine where heat is dissipated. Some researchers used current density maps [3] [4] to assess where significant power dissipation is present, others used electric field strength [5]. We examined both these variables, and further examined how they compare to two other variables: power density and initial rate of temperature rise.

141 2. Methods

A. Bioheat Equation Joule heating arises when an electric current passes through a conductor. Electromagnetic energy is converted into heat. The heating of tissue during RF ablation is governed by the bioheat equation, which was first introduced by Pennes in 1948 [11]:

∂T = ∇ ⋅ k∇T + J ⋅ E − hbl (T − Tbl ) − Qm ∂t hbl = ρ blc bl wbl ρc

(1)

where ρ is the density (kg/m3), c is the specific heat (J/(kg⋅K)), and k is the thermal conductivity (W/(m⋅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/(kg⋅K)), and wbl is the blood perfusion (L/s). hbl is 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 terms [9].

B. Finite element method We created FEM models of a cardiac ablation catheter placed in cardiac tissue. Figure 1 shows the probe geometry, and figure 2 shows the model geometry that has been used previously for other studies [6]. Due to the symmetry, we created an axisymmetric model. We used the material properties from the literature [6] [7] [8]. Table 1 shows the values of material properties we used in our model. We set the initial temperature of the liver tissue

142 and temperature at the boundary of the model to 37 ºC. We set the model boundary to ground potential, and the electrode to the value of the applied voltage (Vcc). In temperaturecontrolled RF ablation, the applied voltage has to be changed during the procedure to keep the tip temperature constant. Since the results of our analyses are stationary values, we had to use a constant voltage in the model. We used the average value of the voltage applied during temperature-controlled RF ablation of previous experiments [6]. The FEM models consisted of ~10.000 tetrahedral elements. We used a nonuniform mesh; mesh size was 0.2 mm close to the probe where we see large temperature and current gradients, and 5 mm at the model boundaries. We used PATRAN Version 2000 (The MacNeal-Schwendler Co., Los Angeles, CA) to generate the geometric models, assign material properties, assign boundary conditions and perform meshing. After creating the model, PATRAN generates an input file for the ABAQUS/Standard 5.8 (Hibbitt, Karlsson & Sorensen, Inc., Pawtucket, RI) solver. A coupled thermo-electrical analysis was performed by ABAQUS. For postprocessing we used the built- in module ABAQUS/POST to generate profiles of temperature and electric field intensity. All analysis was performed on a HP-C180 workstation equipped with 1.1 GB of RAM and 34 GB of hard disk space.

3. Results Figure 3 shows the current density distribution. Figure 4 shows the electric field gradient. Figure 5 shows the power density of dissipated power. Figure 6 shows the initial rate of temperature rise.

143 4. Discussion Usually for cardiac RF ablation, a temperature-controlled catheter is used. The catheter has a thermistor or a thermocouple embedded in the tip, which is thermally insulated from the surrounding electrode. We created a model of common catheter geometry, embedded in cardiac tissue and surrounded by blood (see Figure 2). This catheter creates lesions of up to 10 mm in depth and width [6]. However, the region where heat is actually generated due to resistive heating is much smaller. We used the FEM solver to solve the electric field problem, and to determine initial rise of temperature within the model. We evaluate these four variables on their effectiveness to determine where heat is dissipated. In all figures 3, 4, 5 and 6 we observe so-called “hot-spots” at locations of discontinuity in the catheter, most notably at the interface between the electrode and the catheter. However, there are substantial differences between the figures. Both the electric current density (Figure 4) and the power density (Figure 5) show a discontinuity at the interface between blood and tissue due to the difference in electrical conductivity (see Figure 2). This discontinuity is not seen in the electric field strength (Figure 3), which therefore gives a skewed representation of heat dissipation. Both electric current density and electric field strength show a common problem, which is that they must be squared to yield power density. The dissipated power density is given by the second term on the right side of equation 1, i.e. power density is given by: p = JE

(2)

144 The relationship between conductivity, current density (J) and electric field (E) is given by the local version of Ohm’s law: J = Eσ

(3)

By combining equations 2 and 3, we obtain the square relationship between power density, and electric field and current density: p = J2 /σ = E2 σ

(4)

This becomes also evident when comparing electric field strength (Figure 3) and electric current density (Figure 4) to power density (Figure 5). In both figures 3 and 4, the zone where we apparently obtain significant direct resistive heating extends much further than what is apparent from figure 5. Electric field strength and electric current density therefore give a distorted image of where significant power dissipation occurs. How much the material (tissue and blood in our case) really heats up does however not only depend on dissipated power, but also on the density and heat capacity of the material (see equation 1). We propose that an even better appreciation than looking at power density is given by examination of the initial rate of temperature rise (?T/?t|t=0+, where we apply voltage to the electrode starting at t = 0). Now we consider the bioheat equation (equation 1), where we neglect the metabolic heat since it is small compared to the other terms [9]:

ρc

∂T = ∇ ⋅ k∇T + J ⋅ E − hbl (T − Tbl ) ∂t

(5)

We can make a few simplifications, if we want to acquire initial rate of temperature rise. Initially, the whole model (tissue, blood, etc.) is at the same temperature (37 °C). Therefore,

145 the thermal conduction term (first term on the right- hand side of equation 5) is equal to zero. Furthermore, since blood also is at 37 °C, the perfusion term (2nd term on right-hand side of equation 5) is also equal to zero. We obtain for the initial rate of temperature rise in the model:

J t = 0+ ⋅ E t = 0+ ∂T + = ∂t t =0 ρ⋅c

(6)

Figure 6 shows the map of initial rate of temperature increase for our model. This image can be considered a “thermal activation map”, since it determines where the material is initially heated up. Compared to the power density (Figure 5), we notice that tissue heats up more than blood as would suggested from the power density distribution figure 5. This is due to the higher heat capacity of blood, compared to tissue (see Table 1). In the end we would like to know where we obtain significant heating in our model. So one question that remains so far with all of the methods described in this paper is: How do we determine where we obtain significant heating? The answer to this question is: the initial rate of temperature rise has a great advantage compared to the other variables. It has the unit of °C/s, which gives us an appreciation of how much the material heats up, which we don’t get with the other variables. If we take the typical treatment time for cardiac RF ablation of 30 s to 60 s into account, we conclude that we won’t get any significant heating for regions where the initial rate of temperature rise is below 0.5 °C/s. If we imagine a material without thermal conduction, we would get a total rise of temperature during RF application within the tissue of: 30 s × 0.5 °C/s = 15 °C; i.e. the final temperature would be 52 °C at locations with

146 temperature rise rate of 0.5 °C/s. This temperature is just above the temperature of 50 °C, which is necessary to destroy tissue. To obtain the initial rate of temperature rise within the FEM model, we would have to use a very small step size to obtain the accurate slope for the temperature rise curve. However, there is a much simpler way of obtaining the initial rate of temperature rise. We just have to set the thermal conductivity within the model to zero, and not include perfusion in the model. Then the conductive term (first term on right side of equation 5) and the perfusion term (third term on right side of equation 5) are both equal to zero. We run the simulation for one second, and the result we get for the temperature distribution is equal to the initial rate of temperature rise in the original model.

5. Conclusion We compared four different ways of estimating where significant heat dissipation occurs during resistive heating, using the example of a model of cardiac radio-frequency ablation. Both current density and electric field strength are limited, because they must be squared to yield dissipated power. Power density gives a better picture of where significant heat is produced, but does not take material density and heat capacity into account. These material properties are taken into account when observing initial rate of temperature rise. Further, initial rate of temperature rise gives a quantitative appreciation of where significant heating occurs, since it has the unit of ºC/s. We found initial rate of temperature rise the best indicator of where significant heating occurs. We further showed a simple implementation of how to obtain this variable in a FEM model.

147

6. References [1] S. K. S. Huang and D. J. Wilber, Eds., Radiofrequency Catheter Ablation of Cardiac Arrhythmias: Basic Concepts and Clinical Applications, 2nd ed. Armonk, NY: Futura, 2000. [2] S. Nath, C. Lynch III, J. G. Whayne, D. E. Haines, “Cellular electrophysiological effects of hyperthermia on isolated Guinea pig papillary muscle: Implications for catheter ablation”, Circulation, vol. 88, pp. 1826–1831, 1993. [3] E. J. Woo, S. Tungjitkusolmun, H. Cao, J. Tsai, J. G. Webster, V. R. Vorperian, J. A. Will, “A new catheter design using needle electrode for subendocardial RF ablation of ventricular muscles: finite element analysis and in- vitro experiments”, IEEE Trans. Biomed. Eng., vol. 47, pp. 23–31, 2000. [4] S. Tungjitkusolmun, E. J. Woo, H. Cao, J.-Z. Tsai, V. R. Vorperian, J. G. Webster, “Finite element analyses of uniform current density electrodes for radiofrequency cardiac ablation”, IEEE Trans. Biomed. Eng., vol. 47, pp. 32–40, 2000. [5] D. Haemmerich, S. T. Staelin, S. Tungjitkusolmun, F. T. Lee Jr., D. M. Mahvi, J. G. Webster, “Hepatic bipolar radio- frequency ablation between separated multiprong electrodes”, IEEE Trans. Biomed. Eng., vol. 48, pp. 1145–1152, 2001. [6] S. Tungjitkusolmun, E. J. Woo, H. Cao, J.- Z. Tsai, V. R. Vorperian, and J. G. Webster, “Thermal-electrical finite element modeling for radio- frequency cardiac ablation: effects of changes in myocardial properties,” Med. Biol. Eng. Comput., vol. 38, pp. 562–568, 2000. [7] D. Panescu, “Intraventricular electrogram mapping and radio-frequency cardiac ablation for ventricular tachycardia”, Physiol. Meas., vol. 18, pp. 1–38, 1997.

148 [8] N. Bhavaraju, J. W. Valvano, “Thermophysical properties of swine myocardium”, Int. J. Thermophys., vol. 20, pp. 665–676, 1999. [9] R. K. Jain, “Temperature distribution in normal and neoplastic tissues during normothermia and hyperthermia”, in Thermal characteristics of tumors: applications in detection and treatment . Jain, R. K., Gullino, P. M. (eds.), Ann. N. Y. Acad. Sci., vol. 335, pp. 48–62, 1980. [10] S. D. Edwards, R. A. Stern, “Electrode and associated systems using thermally insulated temperature sensing elements”, US Patent: 5,688,266, 1997. [11] H. H. Pennes, “Analysis of tissue and arterial blood temperatures in resting forearm,” J. Appl. Phys., vol. 1, pp. 93–122, 1948.

149 Table 1. Material properties.

Material Blood Catheter body (Polyurethane) Potting material Thermistor (Metal oxide) Thermal insulation Electrode (Pt-Ir) Air Cardiac tissue

Electrical conductivity [S/m] 0.667

Thermal conductivity [W/(m⋅K)] 0.543

Specific heat [J/(kg⋅K)]

Density 3 [kg/m ]

4180

1000

-5

0.026

1045

70

-5

0.038

835

32

-5

71

835

32

-5

0.038

835

32

4 * 10

6

71

132

21500

∞ 0.5

1005 0.531

0.0261 3200

1.18 1060

1 * 10 1 * 10 1 * 10 1 * 10

150

0.25 0.25 0.5 1.5

Catheter Body Potting Thermal Insulation

2.0

Electrode

Air 2.0

Thermistor 0.08

0.22

Rotation Axis

0.8

0.5

Figure 1. Probe geometry.

151

8 mm

2 mm Interstitial Fluid Catheter Heart Chamber Cardiac muscle

Figure 2. Model geometry.

152 E (V/cm) 17 15.6 14.2 12.8 11.3 9.9 8.5 7.1 5.7 4.3 2.8 1.4 0 Figure 3. Electric field strength (E).

153

J (A/cm2 ) 1.1 1.08 9.81 8.83 7.85 6.87 5.89 4.90 3.92 2.94 1.96 0.98 0 Figure 4. Electric current density.

154

P (W/cm3 ) 1.05 0.37 0.33 0.3 0.27 0.23 0.2 0.17 0.13 0.1 0.67 0.33 0

Figure 5. Density of dissipated power.

155 dT/dt (°C/s) 24.1 22 20 18 16 14 12 10 8 6 4 2 0

Figure 6. Initial rate of temperature rise.

156

Chapter IX

Ablation at Audio Frequencies Preferentially Targets Tumor: A Finite Element Study

157

1. Introduction Radio- 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 mortality of 1,000,000 people [1]. 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 necessary [2]. In RF ablation, RF current is delivered to the tissue via electrodes inserted percutaneously or during surgery. The electromagnetic energy is converted to heat by ionic agitation. Temperatures above 45 ºC to 50 ºC have been shown to cause denaturation of intracellular proteins and destruction of membranes of tumor cells, eventually resulting in cell necrosis [3]. One of the major limitations of this technique is the extent of induced necrosis. When tumo rs greater than 2 cm are treated, multiple applications are necessary to obtain complete tumor necrosis. Often tumor cells survive, which leads to high recurrence rates [4], [5], [6], [7]. Several methods have been investigated for increasing lesion size and improving efficacy. Internally cooled probes have been used [8], [9]. Pulsed techniques have been used to further increase necrosis diameter created by internally cooled probes [10]. Interstitial saline infusion creates larger lesions by cooling and inc reasing effective electrode area [11], [12], [13]. The cooling effects of large blood vessels and vascular perfusion can be minimized by the Pringle maneuver, in which vascular inflow occlusion is performed by clamping the hepatic artery and portal vein [14]. However, the Pringle requires a major surgical procedure, which negates one of the major advantages of RF ablation—the use in a minimally invasive fashion

158 (percutaneous or laporoscopic). Vasoactive pharmacologic agents have also been used to reduce blood flow to the liver [15] to reduce the blood cooling effect. Hepatic tumor exhibit significantly different conductivity characteristics compared to normal liver tissue. Especially at low frequencies, there is a marked difference between electrical conduc tivity of normal and tumor tissue. Tumors exhibit around two times higher conductivity at frequencies below around 20 kHz compared to normal tissue for human lung cancer [16] as well in animal tumor models [17] [18] [19]. Our initial results of in-vivo measurements show the same relationship between human normal liver tissue and hepatocellular carcinoma. Interstitial saline infusion creates larger lesions, partially due to a zone of higher conductivity created around the probe [11] [12] [13]. We see a similar situation when we examine conductivity at frequencies below 20 kHz—tumor with high conductivity is surrounded by normal liver with lower conductivity. We evaluated if ablation carried out at lower frequencies than the typical frequency of around 500 kHz increases efficacy. We created FEM models of different geometric configurations, where a RITA model-30 probe (RITA Medical, Irvine, CA) is surrounded by tumors of 20 mm diameter and 40 mm diameter. We used the models to compare lesions created at frequencies of 500 kHz and 20 kHz.

159 2. Materials and Methods

A. Bioheat Equation Joule heating arises when an electric current passes through a conductor. Electromagnetic energy is converted into heat. The heating of tissue during RF ablation is governed by the bioheat equation, which was first introduced by Pennes in 1948 [20]:

∂T = ∇ ⋅ k∇T + J ⋅ E − hbl (T − Tbl ) − Qm ∂t hbl = ρ blc bl wbl ρc

where ρ is the density (kg/m3), c is the specific heat (J/(kg⋅K)), and k is the thermal conductivity (W/(m⋅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/(kg⋅K)), and wbl is the blood perfusion (L/s). hbl is 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 terms.

B. Finite element method We created FEM models of the RITA model-30, 15-gauge probe (RITA Medical Systems, Mountainview, CA). We used the same model geometry as in chapter II [22] [23]. We placed the probe in a spherical tumor, surrounded by normal liver tissue. We created models with two different tumor sizes. In case 1, we created a tumor with 40 mm diameter, where the probe is completely submerged in the tumor (see Figure 1). In case 2, the tumor was 20 mm

160 in diameter (see Figure 2), and part of the probe tines where extending outside the tumor into normal liver tissue. For both cases, the probes and tumor were placed within a cylinder (140 mm diame ter, 105 mm long) of liver tissue. Due to the symmetry of the arrangement, we could reduce computing time by only modeling a quarter of the cylinder. We used the same material properties as in chapter II, except for electrical conductivity of tissues where we used the initial results of our human study. Tumor had a conductivity of 0.4 S/m both at 20 kHz and at 500 kHz, normal liver tissue had a conductivity of 0.2 S/m at 20 kHz, and 0.4 S/m at 500 kHz. For each case we created two models, where we simulated RF ablation at 500 kHz and at 20 kHz; the only difference between these two models was difference in electrical conductivity of tumor, and normal liver tissue (see Table 1). We set the initial temperature of the model and temperature at the boundary of the model to 37 ºC. Blood perfusion was modeled according to the Pennes model [20]. The blood perfusion wbl used in this model is 6.4·10–3 1/s [21]. We assumed the same perfusion both in tumor and liver tissue. We simulated ablation for 12 min. The maximum temperature of hepatic tissue was kept at 95 ºC by varying the voltage applied to the electrodes. The lesion size was determined using the 50 ºC margin (i.e. tissue above 50 ºC is considered destroyed). The models consisted of ~63,000 tetrahedral elements and ~12,000 nodes. We used PATRAN Version 9.0 (The MacNeal-Schwendler Co., Los Angeles, CA) to generate the geometric models, assign material properties, assign boundary conditions and perform meshing. After creating the model, PATRAN generates an input file for the ABAQUS/Standard 5.8 (Hibbitt, Karlsson & Sorensen, Inc., Pawtucket, RI) solver. A

161 coupled thermo-electrical analysis was performed by ABAQUS. For postprocessing we used the built- in module ABAQUS/POST to generate profiles of temperature and electric field intensity. All analysis was performed on a HP-C180 workstation equipped with 1.1 GB of RAM and 34 GB of hard disk space.

C. Limitations Properties in both tumor and normal liver tissue are considered homogenous. Also perfusion is considered to be homogenous. In reality however, the liver is a very complex organ with regard to its electrical and thermal characteristics. Three types of blood vessels are present (hepatic veins, hepatic arteries, portal veins) with different diameters and flow velocities. Liver parenchyma, hepatic tumors, bile ducts and stroma all have unique electrical and thermal properties. We simplified the geometry due to the limitation of computing resources. In the FEM model we used temperature independent tissue properties for both thermal and electrical properties due to lack of data. In reality there is a marked dependence of tissue properties on temperature. We also considered blood perfusion to be constant whereas in reality there is a significant dependence of perfusion on temperature. Blood perfusion drops as coagulation occurs at high temperatures. Perfusion is also different between different types of tumors, and between tumor and normal liver tissue. We did not consider the impact of large blood vessels close to the ablation site. These inaccuracies in the FEM may lead to different results in the model, than would be seen in reality.

162 3. Results We determined temperature distribution at the end of the simulation. We show the temperature distribution, and current density distribution in a plane going through the probe axis, and through the center of the tines. Figure 3 shows the temperature distribution for case 1 (40 mm-diameter tumor), for ablation at frequencies of 500 kHz and 20 kHz. Figure 4 shows the current distribut ion for case 1 (40 mm-diameter tumor), for ablation at frequencies of 500 kHz and 20 kHz. Figures 3 and 5 show the temperature distribution for case 2 (20 mm-diameter tumor), for ablation at frequencies of 500 kHz and 20 kHz, respectively. Figures 4 and 6 show the current distribution for case 2 (20 mm-diameter tumor), for ablation at frequencies of 500 kHz and 20 kHz, respectively. Figure 7 shows the differential image of lesion dimension for case 2, between ablation at 500 kHz and 20 kHz (the dark area represents the additional lesion obtained at 20 kHz).

4. Discussion In-vivo measurements of electrical conductivity of human hepatocellular carcinoma have shown that there is a pronounced difference at lower frequencies. Tumor has about two times higher cond uctivity at 20 kHz compared to normal liver tissue, whereas they both exhibit similar conductivity at 500 kHz. Moreover, tumor has similar conductivity at 20 kHz and at 500 kHz. The differences seen in electrical conductivity are probably due to tumor necrosis [18]. RF ablation is carried out at frequencies of around 500 kHz. We evaluated with FEM models, if RF ablation carried out at lower frequencies preferentially targets tumor tissue. Firstly we examine case 1, where the ablation probe is centered within a tumor of 40 mm diameter (see Figure 1). In this case, the probe is completely surrounded by tumor. As

163 noted earlier, tumor shows similar electrical conductivity at 20 kHz and at 500 kHz. Since the probe is completely surrounded by tumor, we find similar electric conductivity in the vicinity of the probe, at both 20 kHz and 500 kHz. Heat dissipation occurs only very close to the ablation probe (see Figure 4), and is dependent on current density and electrical conductivity. We see the same current density distribution for 20 kHz frequency and for 500 kHz frequency (Figure 4). Since conductivity is also identical for both frequencies, also the heat dissipation is equal in both cases, which ultimately results in the same temperature distribution (Figure 3) and lesion size. For case 1 (tumor of 40 mm diameter), there is no advantage to using 20 kHz frequency. Now we examine case 2 where the ablation probe is centered within a tumor of 20 mm diameter (see Figure 2). In this case, a segment of the probe tines extends beyond the tumor boundary. At 500 kHz frequency both tumor and normal tissue show similar electrical conductivity. Therefore the situation is similar to the case 1, and we expect to see similar temperature distribution and lesion dimensions. We actua lly see the same current density distribution as before (Figure 4), resulting in identical temperature distribution (Figure 3). However, at 20 kHz frequency the electrical conductivity of normal liver tissue is only around half of what it is at 500 kHz, whereas tumor electrical conductivity is same at both frequencies. We see a spherical zone of higher conductivity in the vicinity of the probe, surrounded by a zone of lower conductivity. This results in a significant difference in current density distribution at 20 kHz (Figure 6) compared to 500 kHz (Figure 4) at the different segments of the probe. The current density at the conducting parts of the probe within the tumor is notably larger at the probe–tissue interface within the tumor, compared to outside of

164 the tumor. We get preferential heat deposition within the tumor, while less heat is dissipated next to the tines in normal liver tissue. Compared to ablation carried out at 500 kHz (Figure 3), the temperature achieved within the tumor is higher compared to the temperature within liver tissue. Now we reach a temperature of 80 to 85 °C next to the probe shaft, whereas we reached a temperature of only 70 to 75 °C at a frequency of 500 kHz. The end result is that more tumor tissue is destroyed, while liver tissue is preserved. Ablation carried out at 20 kHz is advantageous in that it preferentially targets tumor tissue, and preserves normal liver tissue (see Figure 7). In the probe type we used, temperature sensors are located in the probe tips, which report the temperature back to the RF generator for temperature-controlled ablation. However as described above, we now reach higher temperature within the tumor next to the probe shaft compared to when we used 500 kHz frequency. Depending on the probe geometry, we might even reach higher temperatures than at the probe tip, which may lead to charring and desiccation. Therefore a redesign of the probe may be necessary for ablation at lower frequencies.

5. Conclusion Ablation carried out at lower frequencies brings no advantage in a configuration where the probe is completely submerged in the tumor. When part of the conductive portion of the probe is with in the tumor, and part is within normal liver tissue, we see an advantage in using lower electric current frequenc y. Electric current density in tumor is higher compared to liver tissue. This results in preferential ablation of tumor tissue, whereas liver tissue is partially preserved. The difference in electric conductivity between tumor tissue and normal liver tissue increases with decreasing frequency, so the targeting of tumor tissue could be

165 enhanced by usage of even lower frequencies than 20 kHz. However, note that use of frequencies below 20 kHz for RF ablation could result in excitation of nerve tissue and muscle tissue (e.g. cardiac tissue), and therefore it has to be evaluated if such excitation can result before usage of lower frequencies for clinical application.

166

6. References [1] M. C. Kew, “The development of hepatocellular carcinoma in humans,” Cancer Surv., vol. 5, pp. 719–739, 1985. [2] S. A. Curley, B. S. Davidson, R. Y. Fleming, F. Izzo, L. C. Stephens, P. Tinkey, D. Cromeens, “Laparoscopically guided bipolar radiofrequency ablation of areas of porcine liver”, Surg. Endosc., pp. 729–733, 1997. [3] W. Lounsberry, V. Goldschmidt, C. Linke, “The early histologic changes following electrocoagulation,” Gastrointest. Endosc., vol. 41, pp. 68–70, 1995. [4] S. Rossi, M. Di Stasi, E. Buscarini, P. Quaretti, F. Garbagnati, L. Squassante, C. T. Paties, D. E. Silverman, L. Buscarini, “Percutaneous RF interstitial thermal ablation in the treatment of hepatic cancer,” Am. J. Roentgenol., vol. 167, pp. 759–768, 1996. [5] L. R. Jiao, P. D. Hansen, R. Havlik, R. R. Mitry, M. Pignatelli, N. Habib, “Clinical shortterm results of radiofrequency ablation in primary and secondary liver tumors,” Am. J. Surgery, vol. 177, pp. 303–306, 1999. [6] L. Solbiati, T. Ierace, S. N. Goldberg, S. Sironi, T. Livraghi, R. Fiocca, G. Servadio, G. Rizzatto, P. R. Mueller, A. Del Maschio, G. S. Gazelle, “Percutaneous US- guided radiofrequency tissue ablation of liver metastases: treatment and follow- up in 16 patients,” Radiology, vol. 202, pp. 195–203, 1997. [7] S. A. Curley, F. Izzo, P. Delrio, L. M. Ellis, J. Granchi, P. Vallone, F. Fiore, S. Pignata, B. Daniele, F. Cremona, “Radiofrequency ablation of unresectable primary and metastatic hepatic malignancies,” Ann. Surg., vol. 230, pp. 1–8, 1999.

167 [8] S. N. Goldberg, G. S. Gazelle, L. Solbiati, W. J. Rittman, P. R. Mueller, “Radiofrequency tissue ablation: increased lesion diameter with a perfusion electrode,” Acad. Radiol., vol. 3, pp. 636–644, 1996. [9] T. A. Lorentzen, “A cooled needle electrode for radio-frequency tissue ablation: thermodynamic aspects of improved performance compared with conventional needle design,” Acad. Radiol., vol. 3, pp. 556–563, 1996. [10] S. N. Goldberg, M. C. Stein, G. S. Gazelle, R. G. Sheiman, J. B. Kruskal, M. E. Clouse, “Percutaneous radiofrequency tissue ablation: Optimization of pulsed-radiofrequency technique to increase coagulation necrosis”, J. Vasc. Interv. Radiol, vol.10, pp. 907–916, 1999. [11] Y. Miao, Y. Ni, S. Mulier, K. Wang, M. F. Hoez, P. Mulier, F. Penninckx, J. Yu, I. De Scheerder, A. L. Baert, G. Marchal, “Ex vivo experiment on radiofrequency liver ablation with saline infusion through a screw-tip cannulated electrode,” J. Surg. Res., vol. 71, pp. 18– 26, 1997. [12] R. S. Mittleman, S. K. Huang, W. T. De Guzman, H. Cuenoud, A. B. Wagshal, L. A. Pires, “Use of saline infusion electrode catheter for improved energy delivery and increased lesion size in radiofrequency catheter ablation,” PACE, vol. 18, pp. 1022–1027, 1995. [13] F. Burdio, Guemes A, Burdio JM, Castiella T, De Gregorio MA, Lozano R, Livraghi T, “Hepatic lesion ablation with bipolar saline-enhanced radiofrequency in the audible spectrum”, Acad. Radiol., vol. 6, pp. 680–686, 1999. [14] E. Delva, Y. Camus, B. Nordlinger, “Vascular occlusions for liver resections,” Ann. Surg., vol. 209, pp. 297–304, 1989.

168 [15] S. N. Goldberg, P. F. Hahn, E. F. Halpern, R. M. Fogle, G. S. Gazelle, “Radiofrequency tissue ablation: effect of pharmacologic modulation of blood flow on coagulation diameter,” Radiology, vol. 209, pp. 761–767, 1998. [16] T. Morimoto, S. Kimura, Y. Konishi, K. Komaki, T. Uyama, Y. Monden, “A study of the electrical bio-impedance of tumors”, J Invest Surg, vol. 6, pp. 25-32, 1993. [17] J. D. Goodrich, R. A. Rinaldi, “Electrical resistivity of a tumor”, Oncology, vol. 42, pp. 338-339, 1985. [18] D. Haemmerich, O. Ozkan, J.-Z. Tsai, T. S. Staelin, S. Tungjitkusolmun, J. G. Webster, "Electrical resistivity of K12/TRb tumors versus normal liver tissue", World Congress on Biomedical Engineering, Chicago, 2000. [19] S. R. Smith, K. R. Foster, G. L. Wolf. “Dielectric properties of VX-2 carcinoma versus normal liver tissue”, IEEE Trans Biomed Eng, Vol. 33, p. 522-524, 1986. [20] H. H. Pennes, “Analysis of tissue and arterial blood temperatures in resting forearm,” J. Appl. Phys., vol. 1, pp. 93–122, 1948. [21] E. S. Ebbini, S.-I. Umemura, M. Ibbini, C. A. Cain, “A cylindrical-section ultrasound phased-array applicator for hyperthermia cancer therapy,” IEEE Trans. Biomed. Eng., vol. 35, pp. 561–572, 1988. [22] D. Panescu, J. G. Whayne, S. D. Fleischman, M. S. Mirotznik, D. K. Swanson J. G. Webster, “Three-dimensional finite element analysis of current density and temperature distributions during radio-frequency ablation,” IEEE Trans. Biomed. Eng., vol. 42, pp. 879– 890, 1995.

169 [23] J. W. Valvano, J. R. Cochran, K. R. Diller, “Thermal conductivity and diffusivity of biomaterials measured with self- heating thermistors”, Int. J. Thermophys., vol. 6, pp. 301– 311, 1985.

170

Figure 1. Case 1: Probe is surrounded by tumor (black) of 40 mm diameter.

Figure 2. Case 2: Probe is submerged in tumor (black) of 20 mm diameter. Part of the probe tines extend beyond the tumor boundary, into normal liver tissue (white).

T (°C)

171

37 50 55 60 65 70 75 80 85 90 95

Figure 3. Temperature distribution for case 1, current frequencies of 500 kHz and 20 kHz and for case 2, current frequenc y 500 kHz. The outermost gray margin represents the 50 °C isotherm, which is considered lesion boundary. J (A / cm2) 0 0.05 0.11 0.16 0.21 0.27 0.32 0.37 0.43 0.48 0.53

Figure 4. Current distribution for case 1, current frequencies of 500 kHz and 20 kHz and for case 2, current frequency 500 kHz.

172 T (°C) 37 50 55 60 65 70 75 80 85 90 95

Figure 5. Temperature distribution for case 2, current frequency of 20 kHz. The outermost gray margin represents the 50 °C isotherm, which is considered lesion boundary. J (A / m2) 0 0.05 0.11 0.16 0.21 0.27 0.32 0.37 0.43 0.48 0.53

Figure 6. Current distribution for case 2, current frequency of 20 kHz. The dark circle represents the tumor boundary.

173

Figure 7. Additional lesion produced for case 2, at frequency of 20 kHz compared to 500 kHz. The circle represents the tumor boundary.

174

Appendix How to create model input-files for ABAQUS FEM Solver, using PATRAN Software

175 We used Patran 2000 to create model geometry. Patran then creates a so-called input file to submit to the FEM software Abaqus. However, Patran only supports modeling of thermal models, so we have to make a few changes for it to become a thermo-electrical model. In Patran, for the electrical boundary conditions we create thermal boundary conditions instead and change the input file manually.

Following are the changes we have to make in the input file (.inp), after we create the file with Patran. Open the file with any text editor.

1) We have to change the element type to one, that supports electrical boundary conditions:

BEFORE: *ELEMENT, TYPE=DCAX3, ELSET=THERMIST

AFTER: *ELEMENT, TYPE=DCAX3E, ELSET=THERMIST

We have to add an “E” at the end of the type. We have to do that for all lines of this type (basically for each section with a different material). If we search for “ELSET”, we find the lines where changes are necessary.

176 2) We have to add the material properties. It’s easiest, if we open a previous file and copy & paste the properties: BEFORE:

AFTER:

** ** metal_ox ** Date: 14-Aug-01 ** *MATERIAL, NAME=METAL_OX ** *DENSITY 1., ** *CONDUCTIVITY, TYPE=ISO 1., ** *SPECIFIC HEAT 1.,

** metal_oxide ** Date: 12-Aug-98 ** *MATERIAL, NAME=METAL_OX ** *DENSITY 3.2E-5, ** *CONDUCTIVITY, TYPE=ISO 0.071, ** *SPECIFIC HEAT 0.835, ** *ELECTRICAL CONDUCTIVITY 1.00E-8,

We have to add the properties for all materials used in our model. Search for “MATERIAL” to find the section in the input file, where the properties are located. Also make sure, that the material name used for the different sections (NAME=METAL_OX) is the same as in the material definition, e.g. for the thermistor made of metal oxide we have: ** ** thermistor ** *SOLID SECTION, ELSET=THERMIST, MATERIAL=METAL_OX 1.,

177 3) We have to change the step definition that defines what kind of analysis we perform, and for how long. Search for “STEP” to find the section, and exchange it with the following. BEFORE: ** Step 1, Default Static Step ** LoadCase, Default ** *STEP, AMPLITUDE=RAMP, PERTURBATION Linear Static Analysis ** This load case is the default load case that always appears ** *STATIC

AFTER: *STEP, AMPLITUDE=STEP, INC=100 *COUPLED THERMAL-ELECTRICAL, DELTMX=5., END=PERIOD 0.05, 5.

Abaqus divides the step into increments (i.e time discretization). The initial increment size for the case above is 0.05. The model will run for 5 s.

DELTMX=5 … max. temperature change allowed within an increment. If the maximum temperature change is exceeded within an increment, Abaqus will reduce the increment size and try again.

178 4) Go to the end of the input file. ** ** border_tmp ** *BOUNDARY, OP=NEW BORDER_T, 11, 11, 37. ** ** conv ** *FILM, OP=NEW ** CONV_1, F3, 37., 2000. CONV, F2, 37., 2000. ** ** vcc ** *CFLUX, OP=NEW VCC, 11, 10. ** ** gnd ** *CFLUX, OP=NEW GND, 11, 0.1 ** *DFLUX, OP=NEW CARDIAC_, BFNU, 1. ** ** *NODE PRINT, FREQ=1 U, *NODE FILE, FREQ=1 U, ** *EL PRINT, POS=INTEG, FREQ=1 S, E, *EL FILE, DIR=YES, POS=INTEG, FREQ=1 S, E, ** *EL PRINT, POS=NODES, FREQ=0 ** *EL FILE, DIR=YES, POS=NODES, FREQ=0 ** *EL PRINT, POS=CENTR, FREQ=0 ** *EL FILE, DIR=YES, POS=CENTR, FREQ=0 ** *EL PRINT, POS=AVERAGE, FREQ=0 ** *EL FILE, POS=AVERAGE, FREQ=0 ** *MODAL PRINT, FREQ=99999 ** *MODAL FILE, FREQ=99999 ** *PRINT, FREQ=1 ** *END STEP

This lines set the temperature at the outer model boundary to 37 C (no changes here) If you have no convection defined, you can remove FILM, OP=NEW and following 3 lines.

I defined the voltage using “HEAT SOURCE” in Patran. Now I have to change it into a voltage source: ** ** vcc ** *BOUNDARY, OP=NEW VCC, 9, 9, 10. ** ** gnd ** *BOUNDARY, OP=NEW VCC, 9, 9, 0.

To include tissue perfusion, you have to insert these two lines. CARDIAC_ is the name of the element set of the tissue, i.e. you will have the following line in the first section of the file: *ELEMENT, TYPE=DCAX3E, ELSET=CARDIAC_

You can remove the remaining part starting from this line, and replace it with: *ENERGY PRINT, FREQ=10000 *ENERGY FILE, FREQ=10000 *NODE PRINT, FREQ=10000 NT, EPOT *NODE FILE, FREQ=10000 NT, EPOT ** *RESTART, WRITE, FREQ=10000 ** ** *END STEP

These lines print result data in the ascii file (job.dat). Check the abaqus manual for further information.

179 5) Create a text file “flux.f”, which looks like the following: SUBROUTINE DFLUX(FLUX,SOL,JSTEP,JINC,TIME,NOEL,NPT,COORDS,JLTYP, 1 TEMP,PRESS) C INCLUDE 'ABA_PARAM.INC' C DIMENSION COORDS(3),FLUX(2),TIME(2) FLUX(1)=-2.675E-5*(SOL-37.) FLUX(2)=-2.675E-5 RETURN END

This is a FORTRAN- file defining perfusion. In this case, the perfusion coefficient is hbl = 2.675E-5. 6) To start abaqus with the input-file, type: “abaqus job=jobname.inp user=flux.f inter”