用三维各向异性电阻抗成像作人脑活动的研究  

3 D anisotropic electrical impedance imaging algorithm for human brain activity research

作　　者：宫莲[1,2] 张克潜[1,2] 

机构地区：[1]清华大学电机工程及应用电子技术系 [2]清华大学电子工程系

出　　处：《清华大学学报（自然科学版）》1999年第5期1-4,共4页Journal of Tsinghua University(Science and Technology)

摘　　要：为改进电阻抗成像的算法，为人脑活动的研究提供三维各向异性的不侵入检测的软件，研究了用三维各向异性电阻抗成像的算法。算法的特点：一是基于高频下人颅骨的电导纳的虚部增大，使电流易于注入脑内以实现电阻抗成像；二是用三维各向异性有限元法解正问题；三是用广义线性增量函数理论和奇异值分解法解逆问题，算法具有整体灵敏度；四是由于逆问题是一个非线性问题，先给出各元素导纳变化的起始值，解逆问题得出新的导纳增量与起始值比较，由相对误差决定是否迭代，如需迭代，用新的导纳增量直接迭代。按以上算法对一立方体作了计算机模拟，得到很好的结果。被检测的立方体离散化为４５个六面体元素，外层元素３０个模拟颅骨，内部元素１５个模拟人脑。给出７种情况的计算结果，检测了包括深部５个元素在内的１３个元素。其中包括人脑电导率的变化，以及各被检测的元素电导率的变化不同，误差小于５％。各被测元素导纳增量的起始值设为零，所需迭代次数在７～３５之间。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 dif

关 键 词：各向异性 电阻抗成像 脑活动 

分 类 号：R338[医药卫生—人体生理学] R444[医药卫生—基础医学]