In electrical impedance tomography an approximation for the internal resistivity distribution is computed based on the knowledge of the injected currents and measured voltages on the surface of the body. It is often assumed that the injected currents are confined to the two-dimensional (2-D) electrode plane and the reconstruction is based on 2-D assumptions. However, the currents spread out in three dimensions and, therefore, off-plane structures have significant effect on the reconstructed images. In this paper we propose a finite element-based method for the reconstruction of three-dimensional resistivity distributions. The proposed method is based on the so-called complete electrode model that takes into account the presence of the electrodes and the contact impedances. Both the forward and the inverse problems are discussed and results from static and dynamic (difference) reconstructions with real measurement data are given. It is shown that in phantom experiments with accurate finite element computations it is possible to obtain static images that are comparable with difference images that are reconstructed from the same object with the empty (saline filled) tank as a reference.

The EIDORS (electrical impedance and diffuse optical reconstruction software) project aims to produce a software system for reconstructing images from electrical or diffuse optical data. MATLAB is a software that is used in the EIDORS project for rapid prototyping, graphical user interface construction and image display. We have written a MATLAB package (http://venda.uku.fi/ vauhkon/) which can be used for two-dimensional mesh generation, solving the forward problem and reconstructing and displaying the reconstructed images (resistivity or admittivity). In this paper we briefly describe the mathematical theory on which the codes are based on and also give some examples of the capabilities of the package.

In this paper we consider the reconstruction of rapidly varying objects in process tomography. The evolution of the physical parameters can often be approximated with stochastic convection-diffusion and fluid dynamics models. We use the state estimation approach to obtain the tomographic reconstructions and show how these flow models can be exploited with the actual observation models that by themselves induce ill-posed problems. The state estimation problem can be stated in different ways based on the available temporal information. We concentrate on such cases in which continuous monitoring is essential but a small delay for the reconstructions is allowable. The state estimation problem is solved with the fixed-lag Kalman smoother algorithm. As the boundary observations we use the voltage data of electrical impedance tomography. We also give a numerical illustration of the approach in a case in which we track a bolus that moves rapidly through a pipeline.

In electrical impedance tomography (EIT) currents are applied through the electrodes attached on the surface of the object and the resulting voltages are measured using the same or additional electrodes. The internal admittivity distribution is estimated based on the current and voltage data. When the voltages are measured on the current carrying electrodes the contact impedance that exists in the electrode–surface interface causes a voltage drop. In some cases this effect of the electrodes is known. However, this is not always the case and the contact impedance has to be taken into account in the image reconstruction. In this paper we propose an approach for estimating the contact impedance of the electrodes simultaneously with the estimation of the admittivity of the object. The complete electrode model (CEM) is used in the estimation procedure. We compare the proposed approach to a simple method which is based on the well known definition of the sample resistivity. The proposed approach is tested with real measurements by estimating the admittivity of isotonic saline solution in a cylindrical test cell and with simulations in a three-dimensional cylindrical domain. The CEM-based approach is shown to produce results that are similar to the results obtained with the simple approach in the test cell case. The advantage of the CEM-based approach over the simple approach is that the complete electrode model does not have any geometrical constraints, which makes it possible to utilize it in EIT studies. The results show that the CEM-based approach works well and can be used in practical contact impedance estimation with real measurements. This will be further studied in part II of this paper.

In electrical impedance tomography, an approximation for the internal resistivity distribution is computed based on the knowledge of the voltages and currents on the surface of the body. Usually, it is assumed that the injected currents stay at the two‐dimensional (2D) electrode plane and the reconstruction is based on 2D assumptions. However, the currents spread out in three dimensions (3D) and therefore the structures out of the current injection plane may have significant effect on the reconstructed images. We have studied possibilities of a finite element‐based method to reconstruct static 3D images from real measurements made on a saline‐filled tank. We show that the 3D static images obtained from simple experiments are better than the 2D difference images obtained from the same object. We further show that the static images obtained with 2D calculations are much worse than the images obtained with 3D calculations. We also discuss the effects of the boundary shape error on the reconstructed static 3D images.