Numerical Modeling of Tissue Irradiation in Cylindrical Coordinates Using the Fuzzy Finite Pointset Method

This study focuses on the numerical analysis of heat transfer in biological tissue. The proposed model is formulated using the Pennes equation for a two-dimensional cylindrical domain. The tissue undergoes laser irradiation, where internal heat sources are determined based on the Beer–Lambert law. Moreover, key parameters—such as the perfusion rate and effective scattering coefficient—are modeled as functions dependent on tissue damage. In addition, a fuzzy heat source associated with magnetic nanoparticles is also incorporated into the model to account for magnetothermal effects. A novel aspect of this work is the introduction of uncertainty in selected model parameters by representing them as triangular fuzzy numbers. Consequently, the entire Finite Pointset Method (FPM) framework is extended to operate with fuzzy-valued quantities, which—to the best of our knowledge—has not been previously applied in two-dimensional thermal modeling of biological tissues. The numerical computations are carried out using the fuzzy-adapted FPM approach. All calculations are performed due to the fuzzy arithmetic rules with the application of α-cuts. This fuzzy formulation inherently captures the variability of uncertain parameters, effectively replacing the need for a traditional sensitivity analysis. As a result, the need for multiple simulations over a wide range of input values is eliminated. The findings, discussed in the final Section, demonstrate that this extended FPM formulation is a viable and effective tool for analyzing heat transfer processes under uncertainty, with an evaluation of α-cut widths and the influence of the degree of fuzziness on the results also carried out.