Nonlinear Difference Imaging Approach to Three-Dimensional Electrical Impedance Tomography in the Presence of Geometric Modeling Errors
Objective: To evaluate the recently proposed nonlinear difference imaging approach to electrical impedance tomography (EIT) in realistic 3-D geometries. Methods: In this paper, the feasibility of nonlinear difference approach-based EIT is tested using simulation studies in 3-D geometries of thorax and larynx, and with an experimental study of a thorax-shaped water tank. All test cases exhibit severe modeling errors due to uncertainty in the boundary shape of the body. Results: In all test cases, the conductivity change reconstructed with nonlinear difference imaging outperforms the conventional reconstructions qualitatively and quantitatively. Conclusion: The results demonstrate that the nonlinear difference reconstructions tolerate geometrical modeling errors at least to the same extent as the conventional linear approach and produce quantitatively more accurate information on the conductivity change. Significance: Physiological processes that produce changes in the electrical conductivity of the body can be monitored with difference imaging based on EIT. The wide popularity of linearized difference imaging in EIT is mainly based on its good tolerance for the ubiquitous modeling errors, which are predominantly caused by inexact knowledge of the body geometry. However, the linearized difference imaging produces only qualitative information on the conductivity change, and the feasibility of the estimates also depends on the selection of the linearization point which ideally should be equal to the conductivity of the initial state. Based on the findings of this paper, these problems can be avoided by nonlinear difference imaging, and potentially the approach can enable quantitative imaging of conductivity change in medical applications.