1. Introduction
Cancer is considered to be one of the leading causes of death, hindering the possibility of a global increase in life expectancy [
1]. Lung cancer is a malignant tumor with the highest morbidity and mortality rate in the world, which seriously threatens the life and health of human beings [
2]. At present, microwave ablation is widely used as an emerging treatment method for parenchymal tumors of the liver, kidney, lung, thyroid, etc., which has the advantages of less trauma, precise positioning, and rapid and efficient inactivation of tumor cells compared with surgery and chemotherapy [
3,
4]. The principle of microwave ablation is to insert the microwave antenna into the tumor under the guidance of CT or MRI [
5]. The microwave antenna focuses the microwave energy on the tumor, and the tumor tissue will reach a high temperature of 60 °C–150 °C in a short time, enabling a complete necrosis to achieve the goal of treatment of tumors [
6,
7]. The key to microwave ablation is to destroy the tumor tissue while minimizing the damage caused to the surrounding healthy tissues. More importantly, tumor and normal tissue properties differ greatly, which may have an impact on therapeutic ablation. In this case, a biological heat transfer model close to the clinical effect was constructed for microwave ablation to evaluate the influence of tumor and normal tissue heterogeneity on the efficacy and analyze the temperature distribution and thermal injury volume. It is very important to predict the final ablation area and volume according to the tumor size, which is beneficial to the accurate treatment of microwave ablation of lung tumors.
For this reason, various biological heat transfer models have been developed over the years, starting with the Pennes equation. Pennes biological heat transfer equation is the simplest biological heat equation and is widely used for modeling heat transfer in biological tissues during thermotherapy [
8]. However, the Pennes heat transfer equation has the disadvantage of neglecting the direction of blood flow and the reverse flow arrangement of the arteries and veins. This equation assumes thermal equilibrium between venous blood and tissue and assumes a constant arterial temperature of 37 °C [
9,
10]. This is unrealistic in thermal ablation. Biological tissues are complex structures composed of cells of different sizes and microvascular beds. According to the porous medium theory, it can be divided into different phases coexisting in the same domain, namely the “tissue phase” and the “blood phase”. The former consists of cells and intercellular spaces, while the latter represents the vasculature that permeates the entire tissue [
11,
12]. During microwave ablation, the more blood vessels there are, the more heat is carried away by blood flow [
13]. Therefore, the higher the degree of vascularization of biological tissues, the more it is necessary to use them as porous media in the model, for example, for the liver and lung [
14]. At the same time, the heat transfer model using a porous media theory is established with fewer assumptions, so the porous theory is gradually applied to the biological heat transfer model, and a porous media heat transfer model is established. Alzahrani et al. [
15] used the eigenvalue technique to study the effects of weak, normal, and strong thermal conductivity on displacement, temperature, stress, and volume fraction fields in two-dimensional porous media. Su et al. [
16] established a theoretical model of porous media in an intermittent microwave heating process and considered the changes in electromagnetic energy, phase transition, and large deformation. Chaichanyut et al. [
17] developed the porous liver model, including a solid tumor, based on the porous medium model and the generalized two-phase lag (DPL) model. Zhang et al. [
18] analyzed the thermoelastic response of skin tissue during laser irradiation. However, few studies have considered the lung as a porous medium and investigated whether differences in lung tumors have an impact on the results of microwave ablation.
There is a lack of basic reference data for microwave ablation of lung tumors, and the selection of treatment parameters (ablation time and power) that are only based on experience is prone to inadequate or excessive ablation. Therefore, it is necessary to establish a model which is closer to the actual situation of lung tissue, and the results of this model can provide help for obtaining more accurate ablation parameters.
In this study, microwave ablation of a spherical tumor surrounded by healthy lung tissue was simulated, and heat transfer in porous media was modeled, based on the local thermal equilibrium equation. The maximum temperature obtained by Pennes heat transfer equation and the porous medium heat transfer equation are compared. At the same time, the effects of different tumor diameters, different tumor porosities, and different microwave ablation powers on the therapeutic effect of microwave ablation of lung tumors were analyzed from three aspects: the highest temperature of the tissue, the volume of ablation, and the size of the ablation area. The final ablation area and volume can be predicted more accurately by using the porous heat transfer model, and thus the ablation parameters can be determined, which is beneficial to the accurate treatment of microwave ablation of lung tumors.
4. Discussion
In order to ensure that the tumor tissue is completely destroyed and to minimize the damage to the surrounding healthy tissues, a model that more closely fits the actual lung tissue is needed. Pennes biological heat transfer equation does not take into account the porous characteristics of lung tissue and ignores the influence of blood flow [
9]. The difference between the lung tissue temperature obtained using the Pennes heat transfer equation and the temperature achieved in the actual ablation in the simulation is large, which will have a certain impact on the ablation efficacy. Therefore, it is important to establish a heat transfer model based on porous lung tissue in microwave ablation.
In this paper, a biological heat transfer model based on porous lung tissue was established, and microwave ablation of lung tissue containing tumor tissue was simulated using the finite element method. The effects of tumor diameter, tumor porosity, and microwave ablation power on the ablation effect of porous lung tissue were investigated in terms of tissue temperature distribution, ablation zone, and ablation volume. The results showed that as the tumor diameter increased, the tissue temperature and the longitudinal diameter of the ablation zone decreased, while the ablation volume did not change significantly. The greater the porosity of tumor tissue, the lower the tissue temperature, and the lower the ablation area and ablation volume. The tissue temperature, ablation area, and ablation volume will increase with the increase of ablation power. Therefore, increasing the ablation power can ensure a certain degree of complete ablation of the tumor.
The larger the diameter of the tumor, the more abundant the blood vessels deep inside it, the more heat is taken away by the blood flow in the vessels, and the temperature reached by the tumor tissue is subsequently reduced. Since the coaxial single-slot antenna mainly transfers energy along the direction of antenna insertion, it is not conducive to the ablation of large-size tumors in the lateral direction, and the transverse diameter of the ablation zone is consequently reduced, so the treatment difficulty increases. Tehrani et al. [
29] showed that in smaller tumors, the cell death process occurs faster; the percentage of dead cancer cells also decreases by 20% when the tumor diameter increases, and the treatment of large tumors are more difficult than that of small tumors, in agreement with the findings of our study. One of the most important properties of biological porous tissue is the blood volume fraction, i.e., porosity; the greater the tumor porosity, the more blood vessels in the tissue, the more heat is taken away by blood flow, and the lower the temperature reached by the tissue, which further affects the size of the ablation zone and ablation volume. Andreozz et al. [
25] showed that the tissue temperature and ablation zone were much lower at a tumor porosity of 0.23 than at a porosity of 0.07, which also indicates that tumor porosity affects ablation efficacy. In our study, when the ablation power was increased from 10 W to 30 W, the maximum temperature reached by the tissue increased from 87.3 °C to 142.0 °C, and the ablation volume increased from 2.28 cm
3 to 4.06 cm
3, and the possibility of complete ablation of the tumor increased, so we believe that the risk of tumor recurrence can be reduced to some extent by appropriately increasing the ablation power.
Meanwhile, the porosity changes from the central to the marginal regions of the tumor [
29]. However, in the present study, we considered the tumor tissue porosity as a constant value to simplify the study, which is one of the limitations of our study. Also, the variation of electrical properties as well as thermal properties of lung and tumor tissues with temperature was not considered in the numerical simulation. Although the porous model in this paper considers the vascular distribution and blood flow inside the lung tissue, it adopts the local thermal equilibrium equation to study, ignoring the temperature difference between the lung tissue and the blood and the heat exchange existing between them during the actual ablation process. Therefore, in the subsequent study of the porous heat transfer model, the local thermal non-equilibrium equation should be used to consider the heat transfer process of lung tissue, which will be closer to the actual microwave ablation.
To ensure that the tumor tissue is ablated and the risk of recurrence is reduced, in subsequent studies, we will consider the safety boundary of the ablation area in the simulation and will consider the difference in tumor porosity in the clinical application to better provide surgical planning.