Modelos computacionais para simulações de tomografia por impedância elétrica e sua aplicação no problema de determinação da fração de ejeção cardíaca

Abstract

The Electrical Impedance Tomography (EIT) consists in a technique where images are constructed from the measurements of the electrical potential in some points on the external boundary of some specific domain, caused by the injection of an electrical current in such domain. This way, knowing or estimating the electrical conductivity of some regions inside the domain, geometric aspects of the composition of that domain can be inferred. Works in literature apply this technique to the context of obtaining images from the human thorax, with the objective of estimating the geometry of some cardiac cavities of a specific patient. The final goal of this work, inside the context of the obtention of cardiac cavities, is to propose a methodology for estimating the Cardiac Ejection Fraction, orsimplyEjectionFraction(EF),whichconsistsinmeasuringthepercentualofthevolume of blood expelled from the ventricles at the end of a heart beat cicle. This work intends to evolute previous works, that models the above mentioned problem as an inverse problem, an optimization problem, where the intention is to minimize the difference between the values of measured electrical potentials and the values obtained through simulation using computational models. This evolution occurs in different levels. In the first level, is performedanimprovementoverthepre-existentoptimizationtechniquesforthesolutionof theinverseproblem,inatwodimensionalversion. Forthis,isproposedametaheuristicthat assistssearchmethodstowardstheobtentionofmoreaccuratedvalues. Suchmetaheuristic is presented in sequential and parallel versions. Computational results for performed tests for this level are presented. In a second level, a three dimensional modeling of the same approaches found in literature is done. Those approaches, for the specific application of determining the EF, are so far limited to two dimensional models. Therefore, the whole problem is reviewed in order to propose a new model, which includes the creation of three dimensional geometric models for the regions of interest of the problem. As the main contribution of this work in that second level, there is a parameterization schema of the polygon meshes that model heart ventricles, so that it provides a compact way of representing such meshes, and, at the same time, a way of reducing the computational cost of the optimization method by means of a drastic reduction of the number of variables of the problem. Finally, a preliminary study of the sensibility of the technique to the presence of noise in the input data is also performed.