Estratégia para a solução numérica do problema inverso da identificação de inclusões em domínio condutor

Abstract

The images reconstruction of the conductivity distribution inside a conductive body based on electrical current injection and potential measurements on the outer boundary of this body is a technique known as electrical impedance tomography. This is an inverse problem that has been studied in biomedical applications, industrial process monitoring and geophysics investigation. In some cases, it is possible to take into account in the reconstruction process, informations about the body, leading to the problem of identifying inclusions, that is the problem actually treated in this work. This inverse problem can be solved by the minimization of a function, defined as the difference between the measured potentials and the computed ones for a given conductivity distribution. The present work describes a strategy to solve this problem based on the parametrization of the inclusions boundary, whose shape and size is intended to be determined. The minimization problem is solved via Levenberg-Marquardt Method and the forward one is solved via Boundary Elements Method. In order to evaluate the performance of the proposed strategy, numerical experiments with inclusions of boundaries defined by splines, problems with noisy data, current injection and potential measurement protocols and an application of the strategy to the cardiac function monitoring are presented.