Adaptive Reconstruction for Electrical Impedance Tomography with a Piecewise Constant Conductivity

In this work we propose and analyze a numerical method for electrical impedance tomography of recovering a piecewise constant conductivity from boundary voltage measurements. It is based on standard Tikhonov regularization with a Modica-Mortola penalty functional and adaptive mesh refinement using suitable a posteriori error estimators of residual type that involve the state, adjoint and variational inequality in the necessary optimality condition and a separate marking strategy. We prove the convergence of the adaptive algorithm in the following sense: the sequence of discrete solutions contains a subsequence convergent to a solution of the continuous necessary optimality system. Several numerical examples are presented to illustrate the convergence behavior of the algorithm.Comment: 26 pages, 12 figure

Comparing D-Bar and Common Regularization-Based Methods for Electrical Impedance Tomography

Objective: To compare D-bar difference reconstruction with regularized linear reconstruction in electrical impedance tomography. Approach: A standard regularized linear approach using a Laplacian penalty and the GREIT method for comparison to the D-bar difference images. Simulated data was generated using a circular phantom with small objects, as well as a \u27Pac-Man\u27 shaped conductivity target. An L-curve method was used for parameter selection in both D-bar and the regularized methods. Main results: We found that the D-bar method had a more position independent point spread function, was less sensitive to errors in electrode position and behaved differently with respect to additive noise than the regularized methods. Significance: The results allow a novel pathway between traditional and D-bar algorithm comparison

EIT Reconstruction Algorithms: Pitfalls, Challenges and Recent Developments

We review developments, issues and challenges in Electrical Impedance Tomography (EIT), for the 4th Workshop on Biomedical Applications of EIT, Manchester 2003. We focus on the necessity for three dimensional data collection and reconstruction, efficient solution of the forward problem and present and future reconstruction algorithms. We also suggest common pitfalls or ``inverse crimes'' to avoid.Comment: A review paper for the 4th Workshop on Biomedical Applications of EIT, Manchester, UK, 200

EIT-MESHER – Segmented FEM Mesh Generation and Refinement

EIT-MESHER (https://github.com/EIT-team/Mesher) is C++ software, based on the CGAL library, which generates high quality Finite Element Model tetrahedral meshes from binary masks of 3D volume segmentations. Originally developed for biomedical applications in Electrical Impedance Tomography (EIT) to address the need for custom, non-linear refinement in certain areas (e.g. around electrodes), EIT-MESHER can also be used in other fields where custom FEM refinement is required, such as Diffuse Optical Tomography (DOT)

Evaluation of 3D current injection patterns for human lung monitoring in electrical impedance tomography

Electrical impedance tomography (EIT) is a non-invasive imaging technique for monitoring the lungs continuously. During EIT Measurements, currents propagate intrinsically in 3D, since electrical current propagates diffusely in the human tissues, so a 2D EIT remains not sufficient to study the out-of-electrodes plane effects on the images. Until now, not enough effort has been made to evaluate the performance of 3D measurement patterns for lung monitoring. In this paper, to investigate 3D current injection patterns for 3D EIT, a 3D model mimicking the geometrical and electrical characteristics of the human thorax has been developed based on Finite Element Method (FEM) along with the Complete Electrode Model (CEM). Simulations have been performed with aligned (“planar,” “zigzag”, “square”, “zigzag opposite”, and “planar opposite”), and offset (“planar offset”, and “zigzag offset”) current injection patterns. Analysis shows the greatest current density diffusion results using the “zigzag opposite” current injection pattern

A boundary integral equation method for the complete electrode model in electrical impedance tomography with tests on real-world data

We develop a boundary integral equation-based numerical method to solve for the electrostatic potential in two dimensions, inside a medium with piecewise constant conductivity, where the boundary condition is given by the complete electrode model (CEM). The CEM is seen as the most accurate model of the physical setting where electrodes are placed on the surface of an electrically conductive body, and currents are injected through the electrodes and the resulting voltages are measured again on these same electrodes. The integral equation formulation is based on expressing the electrostatic potential as the solution to a finite number of Laplace equations which are coupled through boundary matching conditions. This allows us to re-express the solution in terms of single layer potentials; the problem is thus re-cast as a system of integral equations on a finite number of smooth curves. We discuss an adaptive method for the solution of the resulting system of mildly singular integral equations. This solver is both fast and accurate. We then present a numerical inverse solver for electrical impedance tomography (EIT) which uses our forward solver at its core. To demonstrate the applicability of our results we test our numerical methods on an open electrical impedance tomography data set provided by the Finnish Inverse Problems Society.Comment: 27 pages, 14 figure

Thorax measurement and analysis using electrical impedance tomography

The article deals with a novel method of visualizing interior of an object based on the measurements made on the boundary. Although an electrical impedance tomography is well established in areas where reference measurement can be easily made (difference method), it is still rather a theoretical approach for areas where reference cannot be taken (mainly in medicine). We have made a thorax measurement using difference method. The results show that electrical impedance tomography can provide valuable information for thorax visualization