Analysis of Heat Transfer in Biological Tissue Using the Finite Difference Method

Cancer remains one of the main causes of death worldwide. Conventional treatments such as surgery, chemotherapy, and radiotherapy are widely employed, but often have significant side effects and limitations, highlighting the need for new and less invasive therapies. Among emerging approaches, Laser Ablation is a promising thermal therapy that induces controlled heating of the targeted tumor tissue, offering high precision and minimal invasive impact. Optimized treatments require accurate control of the temperature, which is still a challenge. A proposed solution is to use fiber optic sensors, particularly FBG sensors, to measure temperature in real time. However, further research is still required to develop a reliable method for reconstructing the temperature distribution in the entire tumor mass. This master’s thesis aims to analyze the thermal evolution in a biological tissue, developing a model designed to reproduce the resulting temperature distribution evolution following a laser heat pulse within the tissue, offering valuable insights into how thermal energy propagates and accumulates during treatment. The temperature distribution in biological tissue can be obtained either through an analytical solution, derived from the bioheat transfer equation, or using the Finite Difference Method. The analytical approach provides an instantaneous result but is limited to homogeneous and infinite media. In contrast, FDM offers higher accuracy, as it can handle heterogeneous and finite domains, though it requires longer computation times. To combine their advantages, the results obtained from the FDM simulations are then fitted to the analytical solution derived from the bioheat transfer equation in the simplified case of a homogeneous medium. Through this fitting process, equivalent thermal parameters can be determined, which are then used by the analytical model to improve its predictive accuracy. Several simulation cases of biological tissue are analyzed, including prostate, liver, and osteosarcoma, with the goal of assessing both the model capabilities and the impact of some sources of errors, such as: •??the finite dimension of the medium, to evaluate the distance from the heat source at which the effect of external air convection is no longer negligible; •??the properties of healthy and tumor tissues, to study if temperature distribution can be used as an additional discriminant; •?? the effect in the temperature estimation of glass capillaries used to protect FBG temperature sensors; •?? the temperature map distortion due to an important blood vessel close to the heat source; •?? the differences arising from considering or neglecting blood perfusion in highly vascularized tissue, such as that of the liver. From all these cases, it can be observed that applying the equivalent parameters is useful for predicting the temperature evolution in regions not easily accessible to direct measurement, although the associated errors tend to increase with tissue inhomogeneity. Therefore, FDM is the model which better describes the thermal response of real biological tissue, since it can be applied to inhomogeneous and finite media, differently from the analytical one. Experimental validations using dedicated mock-ups are currently in progress, and this thesis has laid the foundation for future developments aimed at improving model accuracy and extending its applicability to more complex biological scenarios.