This Small Business Innovation Phase I Research project will develop efficient computational algorithms that will enable accurate imaging using Electrical Impedance Tomography (EIT) for both two-dimensional (2-D) and three-dimensional (3-D) applications in medicine and industry. EIT attempts to determine the distribution of electrical conductivity inside objects by applying specified currents at their surface, and measuring the voltage induced there. In comparison to other imaging methods, if successful, EIT offers significant advantages in economy, convenience, and safety for a wide variety of clinical and industrial applications. While much progress in experimental EIT techniques and in the mathematical modeling of EIT have been made, it remains restricted to laboratory situations and imaging objects in 2-D. The chief stumbling block to extending EIT to practical situations appears to be the lack of efficient algorithms that can perform accurate inversion of data. Conventional inversion algorithms in EIT are based on either heuristic techniques that are only applicable to 2-D ring-like geometries, or on full numerical solution using Finite Elements. In the proposed research the much more computationally efficient Boundary Element Method (BEM) will be extended to EIT by using new algorithms that use dual reciprocity techniques. These algorithms will allow efficient imaging in complicated 2-D and 3-D geometries and will significantly reduce problem size, avoid cumbersome grid/mesh generation, and offer order of magnitude speed-up. Phase I research will develop the numerical algorithms and software for inverting EIT data using Dual Reciprocity BEM. The software developed will be tested on analytically generated forward problem data. Phase II will develop algorithms in the develop a prototype EIT system using and further refining the Phase I algorithm. Phase III will commercialize the developed system and software.
