Problemas diretos e inversos em química e física médica

Abstract

When we dealt with any matter related to Sciences, we always have practical situations where experiments should be observed and/or with theoretical situations where mathematical models should be developed. Both situations become routine in physical chemistry, as in the case of the deep dose deposition of ionizing radiation in biological tissues, matter of great interest inside of the Medical Physics, especially in the Physics of the Radiotherapy. Several situations appear in that context, some being resolved with techniques of direct problems and other being resolved with techniques of inverse problems, always involving advanced mathematical tools, as numeric methods, integral and differential calculation, regularizations and use of neural artificial networks. The deep dose deposition of ionizing radiation is of great interest and it can be obtained experimentally or still through simulations with numeric codes, like MCNP. In this work we develop a new way for obtaining values of PDD through techniques of inverse problems, using Tikhonov Regularization. It is shown that this sophisticated mathematical technique supplies excellent results in the resolution of this problem, and it could be used in the future in planning programs, making possible the reduction of the time of necessary processing. In the last chapter we show, in an introductory way, the theory of the quantum scatter, and it can be used in the future in the physical study of the radiotherapy techniques. This work starts a new research line inside the Chemistry Department of UFMG, using numeric methods and techniques of inverse problems inside Medical Physics.