基于伽辽金有限元法的磁感应断层成像正问题仿真

Forward Problem Simulation in Magnetic Induction Tomography Based on Galerkin Finite Element Method

磁感应断层成像(MIT)的正问题计算为系统建模和研究提供了重要依据,由于MIT中涡流场微分方程的非正定性,增加了MIT正问题计算的复杂度。本研究提出一种基于伽辽金有限元法的正问题求解方法,该方法对微分算子无特殊要求,解决了涡流场微分方程非正定性的问题,利用该方法对成像区域内的磁场分布、涡流强度以及检测线圈的相位差等参数进行了分析。计算结果表明,成像区域内磁感应强度的幅值主要由实部决定,而虚部对场域内电导率的变化较为敏感,因此,可以用磁感应强度的虚部进行图像重建。同时,与目标导体的位置越近、激励线圈的位置越远,检测线圈中的相位差值越大;同一位置的目标导体,检测线圈的相位差与电导率大小成线性关系。经理论推导与仿真实验的验证,所采用的伽辽金有限元法能够有效求解MIT正问题,进而为MIT硬件系统的测量及重建算法的研究提供实验参考和理论依据。

Forward problem solution in magnetic induction tomography（MIT） can provide significant basis to system modeling,because MIT differential equation is non-positive-definite,which increases calculative complexity.The paper designed a method based on Galerkin Finite Element（GFE） that had no special requirement about differential operator.The GFE solved the non-positive-definite problem of eddy current field,the method was used to analyze accurately the magnetic field distribution,eddy current intensity and phase shift in detecting coils.The result demonstrated that magnetic flux density amplitude was mainly decided by real part and imaginary was sensitive to conductivity change,thus the imaginary of magnetic flux density could be used to reconstruct image.At the same time,the phase shift in the detecting coil was investigated.The result showed that the phase shift of detecting coil increased as it closed to object or was far away from exciting coil.To the same position of the object,the phase shift in detecting coil was linear to the conductivity.The theoretical derivation and the simulated experiment verified that the GFE method used in the paper was effective to solve the MIT forward problem,and further more it could provide the experiment reference and theoretical verification to MIT hardware system measurement and reconstruction algorithm study.