Fast Multipole Boundary Element Method Research On Three-dimensional Forward Problem Of Electrical Impedance Endotomography

Electrical impedance endotomography(EIE) is a new developing technology based on electrical impedance tomography(EIT) image reconstruction. In EIE, the probe with electrodes is inserted into the body, the internal potentials of the target group are measured directly, and the impedance distribution is reconstructed. It has important significance and application prospect in internal body tissue imaging such as cardiac imaging.EIE forward problem with boundary element method(BEM) is studied in this thesis. Firstly, the boundary integral equation and its discrete form are derived. Then, a three-dimensional cylindrical model is established to simulate the cardiac cavity, and forward problems of single boundary and multiple boundaries are solved. The results show that the method used can solve forward problem correctly, and can reflect the electrode potential value changes with the changes of conductivity. The results can be used as the basis of inverse problem of reconstruction. Finally, to enhance the efficiency of forward problem calculation, the fast multipole boundary element method(FMBEM) is studied. And the method and implementation steps of FMBEM to solve 2D and 3D models are analyzed in detail, and forward problems of cylindrical probe and heart model are solved with the increasing of the freedom degrees. Compared with the conventional BEM, the fast multipole boundary element method can significantly improve the efficiency of calculation of EIE forward problem under the premise of accuracy, and the more degrees of freedom the model has, the faster it calculates.