Research On The Boundary Element Method In Eie Forward Problem

In electrical impedance endotomography (EIE), electrodes or probes are placed at the centre of the interest region of the human body. When the current is switched on, voltage is measured to help to rebuild the electrical characteristics of the internal organizations in human body. Due to this reason, EIE is more suitable for measuring relatively small organs or organs in a deeper position inside of the body. As a result, some researchers use EIE to help with the cardiac research, all of which is of great significance to clinical application.In the thesis, the current researches are reviewed firstly, the imaging principle of EIE is introduced, the numerical computation methods of EIE forward problem are analyzed, and the boundary element method (BEM) is studied in detail. Based on the theoretical study of boundary element method, the author derives the boundary integral equations and discrete integral form about boundary element method of the EIE forward problem. In the second part, simulation experiments are carried out on three-dimensional cylindrical model of uniform medium. The result shows that the boundary element method has achieved the desired goal and approved the correctness and effectiveness of the algorithm in EIE forward problem. Furthermore, the BEM for multilayer homogeneous mediums is deduced. The cardiac model is constructed. The simulation results prove the correctness of the theoretical analysis. Finally, the calculation formulas of finite element method are derived in the 3-D field, both the homogeneous media model and heterogeneous media model are calculated. The result shows that the solutions are consistent with the theoretical results.