Finite element method and reconstruction algorithms in electrical impedance tomography

In electrical impedance tomography (EIT), we inject current patterns into a subject and measure boundary voltages to reconstruct a cross-sectional image of resistivity distribution. Static EIT image reconstruction requires a computer model of a subject, an efficient data collection method, and robust and fast reconstruction algorithms. As the computer model, we used the finite element method (FEM) including an interactive graphical mesh generator and fast algorithms for solving linear systems of equations using sparse matrix/vector techniques. We developed various models of irregularly shaped subjects using mesh design tools including automatic mesh generation and optimization using the Delaunay algorithm.; In order to achieve the best signal-to-noise ratio (SNR) in the measurement of boundary voltages, we inject optimal current patterns. However, this requires many independent current sources with high-accuracy amplitude resolution. We developed a data collection method using spatial Walsh functions. By using the complete set of Walsh functions as the injection current patterns, we can use the simplicity of pulse type injection and yield the optimal distinguishability or SNR of sinusoidal injection. We developed a new method of measuring skin impedance using both simple and compound electrodes. We found that the real part of the skin impedance at 50 kHz is small (less than 80 {dollar}Omega{dollar}).; We developed a robust iterative image reconstruction algorithm using Hachtel's augmented matrix method. This improved Newton-Raphson method produced more accurate images by reducing the undesirable effects of the ill-conditioned Hessian matrix. We demonstrated that our system could produce two-dimensional static images from a physical phantom with 7% spatial resolution at the center and 5% at the periphery.; Static EIT image reconstruction requires a large amount of computation. In order to overcome the limitations for reducing the computation time by algorithmic approaches, we implemented the improved Newton-Raphson algorithm on a parallel computer system and showed that the parallel computation could reduce the computation time from hours to minutes.; Among the many potential clinical applications of EIT, we proposed the use of EIT static imaging technique in apnea monitoring and showed the feasibility of this technique.