Modelling heat transfer in tissues treated with thermal ablation

Thermal ablation is more and more recognized as an important alternative in cancer treatments, for which the most common procedures followed are surgery, chemotherapy, and radiotherapy. Nevertheless, these common techniques pose critical issues such as: they are too invasive for human body, they can reveal serious side effects and are expensive in terms of financial costs for the national health service. Thermal ablation of tumors, instead, is a minimally invasive treatment option for cancer, with certain advantages such as minor side effects, shorter hospital stays and consequently lower costs. It consists in focusing an energy source (commonly radiofrequency or microwave) in the target zone (the tumoral tissue) by means of a probe, that causes the tumor destruction. Generally, the complete necrosis of tissue happens instantaneously at temperatures over about 60 °C, but lower temperatures with longer exposure times can be achieved. The most common approach is a percutaneous treatment performed with the aid of imaging techniques. On the other hand, the main shortcoming of performing a thermal ablation is to not achieve the complete tissue ablation, so the risk of a tumor recurrence becomes higher. In this context, an in-depth knowledge of thermal therapy physics has a key role in modelling heat transfer in thermal therapies, in order to develop more and more accurate bioheat models for clinical applications, predicting the final necrotic tissue diameters and volumes. Moreover, the lack of experimentation in this field, makes bioheat models even more significant. The first simple bioheat model was developed in 1948 by Harry H. Pennes and it is still widely used, but it has some shortcomings that make the equation not so accurate. For this reason, over the years it has been modified and more complex models have been developed. In this thesis work, a general overview of the different employed techniques in hyperthermia treatments of biological tissues and in particular tumors is first of all introduced, together with techniques used to estimate thermal damage. Next, in the second chapter, a wide state-of-the-art of how the distinct bioheat models have been modified over the years when applied in various hyperthermia treatments of cancer, is described. In chapter three, transient bioheat equations based on different bioheat models, such as Pennes’ model, and three porous media-based model are compared, where the porosity is the volume fraction of blood in the entire tissue domain. The considered porous media-based models are the Local Thermal Non-Equilibrium equations (LTNE), the Local Thermal Equilibrium equation (LTE), and the three-energy equations model. The models are implemented to a biological tissue modelled as a sphere with liver tissue properties. The effects of thermal ablation on the living tissue are included with a spherical energy source at the sphere center. Governing equations with the appropriate boundary conditions are solved with the finite-element software COMSOL Multiphysics®. Results are presented in terms of temperature profiles in the biological tissue, to appreciate differences due to the various bioheat models, concluding that LTNE model is preferable because it is a good compromise between accuracy and complexity. Thus, in the next chapter, the LTNE model is applied to the same spherical biological model with tumoral properties, to investigate the pulsating energy source effects modeled with references to a cosine function with different frequencies, and such different heating protocols are compared at equal delivered energy, namely, different heating times at equal maximum power. The results are shown in terms of tissue temperature and percentage of necrotic tissue obtained. The most powerful result achieved using a pulsating heat source instead of a constant one is the decreasing of maximum temperature in any considered case, even reaching about 30% lower maximum temperatures. Furthermore, the evaluation of tissue damage at the end of treatment shows that pulsating heat allows to necrotize the same tumoral tissue area of the non-pulsating heat source. In addition, a more complex model is developed to study a pulsating protocols application for radiofrequency ablation (RFA) of in vivo liver tissue using a cooled electrode and three different voltage levels. Three distinct heat transfer models coupled to the electrical problem are compared: the simplest but less realistic Pennes’ equation and two porous media-based models, i.e., the LTNE and LTE models, both modified to take into account two-phase water vaporization (tissue and blood). Moreover, different blood volume fractions in liver are considered and the blood velocity is modeled to simulate a vascular network. The results in terms of coagulation transverse diameters and temperature fields at the end of the application show significant differences, especially between Pennes and the modified LTNE and LTE models at high voltage level. The new modified porous media-based models cover the ranges found in the few in vivo experimental studies in the literature and are closer to the published results with similar in vivo protocol. The same model is applied considering tumoral tissue surrounded by healthy tissue and the outcomes show relevant differences when the tumor is included in the model. Thus, the different electrical conductivity and thermal properties between the two types of tissues play a fundamental role in the outcomes. In the final chapter five, the previous LTNE modified model is applied to a spherical tumoral tissue, in order to investigate the effects of different antennas configurations in thermal ablation. Single, double, and triple antennas arrangements are modelled in order to simulate the hepatic cancer treatment, which often requires the destruction of large volume lesions. Furthermore, different blood volume fractions and blood vessels are considered. The results show that using multiple antennas instead of a single antenna offers a potential solution for creating ablation zones with larger dimensions and to allow at the same time to have lower maximum tissue temperatures in all the cases compared to the single antenna configuration.