Finite element based three-dimensional forward and inverse solvers for electrical impedance tomography

Electrical impedance tomography (EIT) has been successfully employed to a wide range of problems including chemical process engineering, biomedical and environmental applications. In many cases information of a qualitative nature is satisfactory and to fulfil these aims techniques such as those based on backprojection methods have been used. In some cases quantitative information is needed, for example changes in true resistivity from some baseline case, rather than a 'greyscale' change. Two-dimensional (2D) methods have been used in a number of such cases although, since applications are rarely of a 2D nature, these studies cannot be classified as truly quantitative. In all cases the resultant tomogram reflects some change in electrical property, such as resistivity, but the scale of these changes cannot be quantified. Only with fully three-dimensional (3D) forward and inverse models can a true quantitative image be produced. 3D modelling also permits more accurate treatment of the true shape of the body of the region under investigation. 3D analysis, however, is clearly much more computationally demanding than a 2D alternative. In addition, increasing the parameter dimension to accommodate 3D inversion demands larger measured datasets (and hence increased data acquisition time). The authors describe here a fully 3D EIT forward and inverse modelling procedure based on finite elements techniques that has been successfully employed for a number of applications. The authors' analysis refers specifically to resistive EIT in which the objective is to determine the 3D distribution of resistivity within the body of interest from a series of boundary measurements of resistance under different current injection configurations.