Sensitivity analysis and the inverse problem in the mathematical modelling of tumor ablation using the interstitial hyperthermia

The paper presents the mathematical modeling of the interstitial hyperthermia process caused by the action of internal applicator using electric field. As one knows, the increase of the tissue temperature causes the destruction of the cancer tissue. To estimate the degree of damage of the tumor tissue the Arrhenius scheme is used. From the point of view of the possibility of supporting thermotherapeutic techniques, it is important to examine the impact of individual parameters occurring in the mathematical model on the degree of tissue destruction. Therefore, it is necessary to estimate, based on the sensitivity analysis methods, which parameter has the greatest effect on the computations results. In the paper also the results of the inverse problem consisting in the simultaneous identification of the selected parameters controlling the process of tissue damage are also shown. The inverse problem is solved using the evolutionary algorithm. As a parameter of the fitness function for the evolutionary algorithm, the Arrhenius integral, which determines the degree of tissue destruction, is applied. The finite element method is used to solve the coupled problem related to the heating of biological tissues.