Computational and Mathematical Methods in Medicine

Volume 2014, Article ID 485353, 8 pages

http://dx.doi.org/10.1155/2014/485353

## Mathematical Modeling of Radiofrequency Ablation for Varicose Veins

^{1}Department of Radiology and Medical Research Institute, School of Medicine, Ewha Womans University, 1071 Anyangcheon-ro, Yangcheon-gu, Seoul 158-710, Republic of Korea^{2}Department of Radiology, College of Medicine, Chung-Ang University, 102 Heukseok-ro, Dongjak-gu, Seoul 156-755, Republic of Korea^{3}Department of Mechanical and Automotive Engineering, Andong National University, 388 Songchun-dong, Andong 760-749, Republic of Korea

Received 22 August 2014; Revised 8 October 2014; Accepted 1 December 2014; Published 18 December 2014

Academic Editor: Reinoud Maex

Copyright © 2014 Sun Young Choi et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

We present a three-dimensional mathematical model for the study of radiofrequency ablation (RFA) with blood flow for varicose vein. The model designed to analyze temperature distribution heated by radiofrequency energy and cooled by blood flow includes a cylindrically symmetric blood vessel with a homogeneous vein wall. The simulated blood velocity conditions are *U* = 0, 1, 2.5, 5, 10, 20, and 40 mm/s. The lower the blood velocity, the higher the temperature in the vein wall and the greater the tissue damage. The region that is influenced by temperature in the case of the stagnant flow occupies approximately 28.5% of the whole geometry, while the region that is influenced by temperature in the case of continuously moving electrode against the flow direction is about 50%. The generated RF energy induces a temperature rise of the blood in the lumen and leads to an occlusion of the blood vessel. The result of the study demonstrated that higher blood velocity led to smaller thermal region and lower ablation efficiency. Since the peak temperature along the venous wall depends on the blood velocity and pullback velocity, the temperature distribution in the model influences ablation efficiency. The vein wall absorbs more energy in the low pullback velocity than in the high one.

#### 1. Introduction

Contraction of limb muscles forces up venous blood to the heart while walking. Venous leaflet valves prevent the blood from refluxing against gravity. If the elasticity of vein decreases and the leaflet valves work improperly, the blood will then flow backward and the veins will enlarge. This disease is called venous insufficiency. “Varicose veins” are used when the venous insufficiency occurs in the superficial veins of the legs, that is, the great saphenous veins (GSV) and small saphenous veins (SSV) in the lower limbs [1–3]. The varicose veins are fairly easy to identify because they protrude or bulge from under the skin.

The conventional surgical treatments for varicose veins include surgical ligation and stripping of the great saphenous veins. Endovenous laser ablation (EVLA) and radiofrequency ablation (RFA) have been developed as alternatives to surgery because they are minimally invasive. Both endovenous laser ablation and radiofrequency ablation use thermal energy in the form of either laser or radiofrequency energy for closure of blood vessel. Endovenous laser ablation and radiofrequency ablation are designed to ablate varicose veins by introducing heat-induced catheter. Both methods are better than the traditional vein stripping because their success rate is much higher. The clinical results [4–6] have reported that radiofrequency ablation and endovascular laser ablation had no difference in occlusion rate. However, the thermal damage to normal tissue from radiofrequency was less likely than that from the laser light for endovascular laser ablation. Radiofrequency ablation had advantage in that radiofrequency ablation produced less bruising after operation than that of endovascular laser ablation [4].

Besides endovenous ablation of varicose vein, radiofrequency ablation has been used in thermal ablation of liver or kidney tumors, as well as ventricular tachycardia. In various applications of radiofrequency ablation, simulation of thermal effects has been performed by mathematical modeling. Computer models for radiofrequency ablation of endocardium for ventricular tachycardia have been developed with thermal damage function to analyze the extent of the lesion [9–12]. In hepatic tumor ablation, Barauskas et al. [13] presented the character of ablation processes with high frequency electrical current and developed a mathematical model of radiofrequency ablation in liver tissues. Panescu et al. [11] studied the effects of tissue-electrode angle on temperature distribution and of blood flow on current density distribution during radiofrequency ablation. They found that the insulating coating layer over the junction with catheter body decreases the chance of charring and coagulation. Tungjitkusolmun et al. [12] conducted computer simulation to calculate the temperature distribution during radiofrequency ablation in cardiac tissue using ANSYS [14].

Radiofrequency ablation uses the heat generated from high frequency alternating current in the range from 350 to 500 kHz [13]. In endovenous radiofrequency ablation, radiofrequency catheter is inserted into the vein under ultrasound guidance. At an electrode of the catheter, the heat ablates surrounding abnormal vein. If vessel wall temperature is raised above 323 K, cell damage cannot be recovered and coagulation around electrode can occur [7, 15].

Mathematical model for varicose vein may be a useful tool to evaluate the effects of blood flow rates, thermal energy generated from radiofrequency wave, and the occlusion of vein [12, 16]. However, the mathematical modeling of radiofrequency ablation in varicose vein has not been proposed to date. Thus, our aim in this study will be to examine the impact of radiofrequency heat generated in the electrode on blood and vessel wall. Computer simulations for radiofrequency ablation will be conducted to quantify the effect of the heat generated from the electrode and to calculate the temperature profiles in lumen and vessel wall.

#### 2. Formulation of the Problem

##### 2.1. Geometric Model

For the simplification of the geometric model, we ignored the valve leaflets in vein. As shown in Figure 1 the geometry of the vein and electrode has been simplified for half of the vein and tissue. In the study the geometric domains are composed of the lumen and the vessel wall. The lumen is 3 mm in diameter with 60 mm length, while the vein wall is 0.4 mm in thickness with the tunica intima at the interface between blood and vessel wall and tunica adventitia. The electrode is 0.4 mm in diameter with 10 mm length, which is a unitary transformation for 0.4064 mm. The electrode is positioned in the middle of lumen and 20 mm apart from inlet region as shown in Figure 1. In the geometry we assumed that the RF power was supplied to the electrode to conduct the radiofrequency ablation until there is an increase in uncontrolled impedance. In the simulation we assumed that the electrode moves continuously with a constant pullback velocity against the blood flow direction.