Projeto ótimo do tratamento de câncer de pele por termoablação sob incertezas

Abstract

This dissertation dealt with the analysis of different protocols for the thermo-ablation treatment of skin cancer, by considering optimal designs within a probabilistic approach. Heating of the tissues, including a tumor between the epidermis and papillary dermis, was promoted by a laser. Nanoparticles were supposed uniformly distributed in the epidermis and the tumor, to concentrate the thermal damage in the region of interest. Design variables were obtained with the on-dimensional coupled problem of the laser propagation and bioheat transfer win the tissues. The protocols examined here were: (i) Multiple treatment sessions, each one with one single laser pulse; (ii) One single treatment session with sequential laser pulses; (iii) One single treatment session with the functional form of the laser power modulated by sines and cosines; (iv) One single treatment session without the a priori definition of the functional form of the laser power. The optimal design problems were solved with the Markov Chain Monte Carlo method, and both the classical and a modified version of the Metropolis-Hastings algorithm with sampling by blocks were analyzed. Therefore, the posterior distributions of the design variables were estimated for each protocol examined, taking into account uncertainties in the model parameters and the desired statistical distribution of the thermal damage in the tissues.