Static Three‐Dimensional Electrical Impedance Tomography

Abstract

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.

EIT reconstruction algorithms: pitfalls, challenges and recent developments

“…As we are interested in non-homogeneous conductivity distributions on irregular domains Finite Element Method (FEM) is the natural choice [81,11,70,73,74,56,55,52] , although finite difference [54] and finite volume methods [23,84]have also been employed. Where the conductivity is known and homogeneous in some sub domain, especially a neighbourhood of the boundary, and attractive proposition is to use a hybrid boundary element and finite element method [36].…”

“…However it is known that data measured on a three dimensional body cannot be fitted accurately to any two dimensional conductivity distribution [41]. Moreover attempts to fit a two dimensional model result in errors of position and shape of anomalies [29,74]. Another factor in the choice of two dimensional reconstruction methods was the cost of fast processors and memory required to perform three-dimensional forward modelling and reconstruction, which in the 1980s and early 1990s were prohibitive.…”

“…In practice the assembly of the FEM system matrix, at least for simple linear tetrahedral elements, is easily implemented and the step from two to three dimensions requires only the calculations of integrals of products of shape functions over faces under electrodes [74,56]. The steps which involve considerably more time and care are mesh generation and the efficient solution of the linear system.…”

“…There are also a posteriori error estimates based on calculated solutions [3] which have not yet been widely used in EIT. Although there is some work using higher order elements [74] the best choice of element for EIT remains an open problem, and the possibility of using vector elements [10] to calculate electric fields and current densities accurately in the interior is largely unexplored for our problem. The use of infinite elements to model unbounded regions, or at least regions which while bounded have a substantial part where we have no surface data, is an interesting possibility [75].…”

Detecção da contração muscular através da tomografia de impedância elétrica.

“…2.6, α ∈ R and β ∈ R are regularization parameters, ρ ∈ R m is the resistivity vector,ρ ∈ R m is the mean It is possible to show [33], [54] that taking the derivative of Eq. 2.15 with respect to ρ, making it equal to zero and then linearizing the resulting equation, one can find the following recursion formula for Newton-Raphson algorithm (Eq.…”