Electrical impedance tomography of conductivity and permittivity distributions in arbitrary geometries using regularized algorithms

Electrical impedance tomography is used to image electrical properties inside the body. Since these properties vary among different tissues and tumors, images of their distributions inside a body can give useful information about the functioning of different organs. The research work presented in this thesis demonstrates the importance of accurate boundary representation and regularization techniques to reconstruct the conductivity and permittivity distributions inside a body.; Since the reconstruction algorithm is based on minimizing the error between the measured and predicted voltages, accurate prediction of voltages is needed to reconstruct the true distributions of the electrical properties. A finite element model is used to predict the boundary voltages by solving the forward problem. Meshes with different number of boundary nodes and the degree of refinement are considered. A mesh with 6017 nodes predicted the voltages with a maximum error of 0.05 percent. The reconstructed images for an off-centered inhomogeneity showed a 35 percent improvement in both the conductivity and permittivity contrast from that observed with only one iteration. Regularization techniques based on the penalty methods are used to reconstruct a more realistic conductivity distribution with lungs and heart. The reconstructed images improved by using the penalty terms based on the prior information about the conductivity distribution.; A significant improvement in the images is achieved by accurately modeling the boundary shape. The images are distorted by assuming a circular boundary and the amount of distortion increases significantly as the boundary shape becomes more elliptical. For a homogeneous distribution in an elliptical body with axis-ratio of 0.64, an image reconstructed assuming the boundary to be circular has an artifact at the center of the image with an error of 37 percent. A reconstruction algorithm which assumed the correct boundary shape reduced the error in the conductivity values to within 0.5 percent of the actual values. In the case of a typical thorax boundary the error spread out in the larger regions of the image. Although the present algorithm does not model the shunting effects of the current flow above and below the plane of electrodes, reasonably accurate images are obtained using the experimental data from the chest of a human subject.