Study on the conformal conversion in the Open Electrical Impedance Tomography

This paper presents a feasible method and validated algorithm for the Open Electrical Impedance Tomography (OEIT) problem which will reduce the computational complexity and the errors in employing the Maxwell equations and implementing the boundary conditions under test. Considering the tested area of skin could be assumed as a plate condenser. So the model like this often exists some fringe effects in practice which may lead to the Maxwell equations are no longer applicable even the divergence of data. The goal of this paper is to solve the problem by developing a way to making an open rectangle region mapped to a closed circular region based on the conformal conversion. For this purpose, a set of conformal mapping formulas has been finally worked out. In addition, the format of boundary conditions of the skin model proved to be the same in a 3D domain. Eventually a conclusion of this work can be drawn from the substantial simulations for its effectiveness under certain conditions.