Electrical impedance tomography of translationally uniform cylindrical objects with general cross-sectional boundaries

An algorithm is developed for electrical impedance tomography (EIT) of finite cylinders with general cross-sectional boundaries and translationally uniform conductivity distributions. The electrodes for data collection are assumed to be placed around a cross-sectional plane; therefore, the axial variation of the boundary conditions and the potential field are expanded in Fourier series. For each Fourier component a two-dimensional (2-D) partial differential equation is derived. Thus the 3-D forward problem is solved as a succession of 2-D problems, and it is shown that the Fourier series can be truncated to provide substantial savings in computation time. The finite element method is adopted and the accuracy of the boundary potential differences (gradients) thus calculated is assessed by comparison to results obtained using cylindrical harmonic expansions for circular cylinders. A 1016-element and 541-node mesh is found to be optimal. The algorithm is applied to data collected from phantoms, and the errors incurred from the several assumptions of the method are investigated.