Analytic solution of the forward problem for induced current electrical impedance tomography systems

An analytic method of solving the forward problem for a single target in a two-dimensional induced-current electrical impedance tomography (EIT) system is presented. The solution, derived for a single circular target anywhere within a circular region, takes account of both conductivity and permittivity discontinuities between target and background, and yields quadrature components of peripheral potential differences. The solution is used to explore the effects that the position and size of the target and its conductivity and permittivity have on the peripheral potential differences and the required instrumentation sensitivity to detect the target. It is shown that the effects of a change in target conductivity and permittivity are almost indistinguishable from those of a change in target area. It is also shown how the induced-current analytic solution may be modified to simulate an injected-current EIT system