Probabilidade de controle tumoral: modelos e estatísticas

Abstract

Radiobiological modeling allows one to predict the ecacy of radiotherapeutic treatments, specifying protocols and strategies to treat patients with cancer. Many mathematical models have been proposed to evaluate the Tumor Control Probability (TCP). In this thesis we rst present a study in colaboration with researchers at the University of Alberta [1], Canada, in which we compare the TCPs obtained by Monte Carlo simulations and from the Poissonian, Zaider-Minerbo (ZM) and Dawson-Hillen (DH) models. Results show that, for low proliferation tumors, the use of the Poissonian model for indicating the treatment protocol is as eective as the Monte Carlo method or more sosticated models (ZM and DH). in the second part of the thesis, we propose a statistical test [2] based on Monte Carlo simulations of the DH TCP model to determine the prediction capacity of tumor eradication (cure). We obtain the ROC curve of the test from the probability distributions of the remaining tumor cells for conditions of cure and non-cure. Results show that the method can also be applied to clinical data suggesting that the evaluation of the tumor size at the beginning of the radiotherapy leads to a short-term prognosis of the treatment. In the third part of the thesis, we study the surviving fraction (FS) of tumor cells as function of the radiation dose to which they are subjected. In the literature, this surviving fraction has been formulated by the Linear-Quadratic (LQ) model and, more recently, from the Tsallis non-extensive statistics [3]. We evaluate the behaviour of both formulations in terms of the FS ttings to experimental data in the ix x literature (related to cells cultivated in vitro for several tumoral tissues) so that we extend previous studies in the literature. The FS parameters for both formulations are obtained and the quality of the FS ttings to experimental data is compared using the reduced chi-square. Results show that in general both formulations lead to very good FS-curve ttings. Furthermore, we use the Tsallis non-extensive statistics to obtain the ZM TCP as function of the dose, expressing it analitically in terms of the Gamma function (for a dose prole typical of external beam radiation) and the Hipergeometric function (for a dose prole typical of brachitherapy). Finally, the curves of the corresponding TCPs are plotted using experimental data and then compared with TCPs obtained from the LQ model.