3 D anisotropic electrical impedance imaging algorithm for human brain activity research
GONG Lian, ZHANG Keqian Department of Electrical Engineering, Tsinghua University, Beijing 100084, China
An algorithm of 3 D anisotropic electrical impedance imaging was presented. The aim of this research is to improve the software of the electrical impedance imaging to be a 3 D anisotropic one to provide a nondestructive detection of tha activity of the human brain. In the proposed algorithm, firstly, based on the fact that the imaginary part of the electric admittance of the skull can be high enough at high frequency to ease the injection of electric current to do the electrical impedance imaging. Secondly, the forward problem of the proposed algorithm was solved by 3 D anisotropic finite element method. Thirdly, the inverse problem was solved by the generalized linear incremental function theory, for it has the high global sensitivity, and the singular value decomposition. To save the memory, 1 D storage was applied. Fourthly, because the inverse problem is a nonlinear one, the initial values of the conductivity variations of the detected elements were given, then the new conductivity variations of the detected elements are the solution of the inverse problem. The differences between the initial values and the new values were compared and the iterations were determined by the relative errors of them. When iteration is needed, the new conductivity variations are applied directly to do the iteration. According to the above algorithm, a computer simulation to a cube was carried out and good results are obtained. The detected cube was discretised into 45 prism elements, 30 outer layer elements simulate the skull and 15 inner layer elements simulate the brain. The electric parameters of elements, for instance, conductivities and relative permittivities are from the typical values of human biological data. One pair of injection electrodes was used and rotated 5 times to give five folds information of boundary measurements. Threeten elements including 5 elements which are located in the deep part of the cube were detected. Results of 7 cases are given where the electric conductivity variations of elements are different from each other. The results show that the relative errors are less than 5% and the number of iteration is between 7￣35, whereas the initial values of the conductivity variations of the detected elements are set to be zero.
【CateGory Index】： TM934