Estimativa de estado e de parâmetros em modelagem do tratamento de tumor prostático via radioterapia e hormonioterapia

Abstract

The present work presents an adaptation of a mathematical model from the literature formulated for the treatment of prostate cancer through radiotherapy in order to incorporate the joint action of radiotherapy and hormone therapy. The adapted model is formed by a system of four coupled differential equations and takes into account the interactions between normal (N), immunological (I) , tumor (T ) cells and the action of the hormone therapy agent (Q). The modeling of the growth of the populations considered, made in a simulated way, considers a high-risk prostate tumor (5+5=10) on the Gleason scale. Due to the lack of real data for model validation, the Prostate Specific Antigen (PSA) was not considered, but the number of cells of the cell populations involved. In the simulations carried out to evaluate the combined effect of radiotherapy and hormone therapy we used the Matlab R2019b software and for the solution of the direct problem we used the ode15s subroutine. Simulations were performed from the standard oncology treatment protocols that show that the parameters that regulate tumor growth are important for understanding the phenomenon studied. As this work is in the scope of Inverse Problems, the inverse analysis was done through a Bayesian filter. This filter works with the combined estimation of state variables and model parameters and was proposed (LIU; WEST, 2001). To assess the goodness of fit of state variables and parameters, we used the mean squared error (MSE). The results obtained were quite satisfactory, since the model is able to capture the dynamics of the populations involved in tumor growth. Furthermore, the estimates obtained when compared to the simulated data show a good agreement.