Mathematical models for the tumour control probability (TCP) are used to estimate the expected success of radiation treatment protocols of cancer. There are several TCP models in the literature, from the simplest (Poissonian TCP) to the well-advanced stochastic birth-death processes. Simple and complex models often make the same predictions. Hence, here, we present a systematic study where we compare six of these TCP models: the Poisson TCP, the Zaider-Minerbo TCP, a Monte Carlo TCP and their corresponding cell cycle (two-compartment) models. Several clinical non-uniform treatment protocols for prostate cancer are employed to evaluate these models. These include fractionated external beam radiotherapies, and high and low dose rate brachytherapies. We find that in realistic treatment scenarios, all one-compartment models and all two-compartment models give basically the same results. A difference occurs between one-compartment and two-compartment models due to reduced radiosensitivity of quiescent cells.We find that care must be taken for the right choice of parameters, such as the radiosensitivities α and β and the hazard function h. Typically, different hazard functions are used for fractionated treatment (fractionated survival fraction) and for brachytherapies (Lea-Catcheside protraction factor). We were able to combine these two approaches into one 'effective' hazard function. Based on our results, we can recommend the use of the Poissonian TCP for everyday treatment planning. More complicated models should only be used when absolutely necessary.

SANTOS, M. M. dos,. Study of a well-type ionization chamber by Monte Carlo simulation. 2009. 71p. Thesis (Master)

Several mathematical models have been proposed to describe the dynamics of irradiated cancer cells and to evaluate the tumour control probability (TCP). In this article, we propose a TCP model-based statistical test for predicting the outcome of a radiation treatment. We determine the foresight capability of prostate tumour erradication (cure) from Monte Carlo simulations of the Dawson-Hillen TCP model. We construct the receiver operating characteristic (ROC) curves of the test from the probability distributions of the fraction of remaining tumour cells for simulated experiments that evolve either to cure or non-cure. Simulations show that a similar procedure may be applicable to clinical data. Results suggest that the evaluation of tumour sizes after the treatment has started may be used for short-term prognosis.

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.