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 also 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 saving 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. For a given cross-sectional boundary, the ratios of the gradients calculated for both 2-D and 3-D homogeneous objects are formed. The actual measurements from the 3-D object are multiplied by these ratios and thereafter the tomographic image is obtained by the 2-D iterative equipotential lines method. The algorithm is applied to data collected from phantoms, and the errors incurred from the several assumptions of the method are investigated. The method is also applied to humans and satisfactory images are obtained. It is argued that the method finds an “equivalent” translationally uniform object, the calculated gradients for which are the same as the actual measurements collected. In the absence of any other information about the translational variation of conductance this method is especially suitable for body parts with some translational uniformity.