Improved methods to determine optimal currents in electrical impedance tomography

Estimation of the electric conductivity from scalp measurements: feasibility and application to source localization

OBJECTIVES

The accuracy of electrical impedance tomography was investigated.

METHODS

The conductivities of the different compartments of the volume conductor were estimated by utilizing the boundary element method. The approach was tested for realistic head models with either 3 or 4 compartments. The impact of a geometrical error in the head model was investigated and the estimated conductivities were assigned to the compartments of the volume conductor used for the source imaging. The localization errors were quantified.

RESULTS

The method used allowed the estimation of the conductivity of the compartments. The poor conductivity of the skull decreased the precision with which the conductivity of deeper structures could be estimated. A geometrical error in the head model was compensated by the estimated conductivities. However, the estimated conductivities did not cancel the geometrical error in the head model as localization errors of the order of 10-20 mm were obtained.

CONCLUSIONS

In principle, the conductivity estimation of the distinct regions in the head is possible. The application of conductivity estimation to increase the accuracy of source localization remains questionable.

Nonlinear reconstruction constrained by image properties in electrical impedance tomography

It is proposed that image quality, for example the degree of roughness, in electrical impedance tomography is the essential measure required to regularize nonlinear reconstruction. Most previously published work has addressed efficiency, stabilization and speed of reconstruction and has overlooked the targeted image qualities. The measure of quality adopted is the mean square gradient of the logarithm of resistivity which, in combination with the chi2 statistic as a measure of the fit to the data, is minimized by iteration until convergence to a stable image is achieved. This penalty function is invariant to the scale of the resistivity and to the interchange of resistivity and conductivity. The algorithm is tested on computer simulated data and on measurements from a cylindrical tank of electrolyte. The results demonstrate the increased image definition that it would be possible to achieve as data acquisition systems are improved. The images show how a reduction in resolution can be traded for reduced noise artefacts, by selecting an appropriate target chi2.

A Kalman filter approach to track fast impedance changes in electrical impedance tomography

In electrical impedance tomography (EIT), an estimate for the cross-sectional impedance distribution is obtained from the body by using current and voltage measurements made from the boundary. All well-known reconstruction algorithms use a full set of independent current patterns for each reconstruction. In some applications, the impedance changes may be so fast that information on the time evolution of the impedance distribution is either lost or severely blurred. In this paper, we propose an algorithm for EIT reconstruction that is able to track fast changes in the impedance distribution. The method is based on the formulation of EIT as a state-estimation problem and the recursive estimation of the state with the aid of the Kalman filter. The performance of the proposed method is evaluated with a simulation of human thorax in a situation in which the impedances of the ventricles change rapidly. We show that with optimal current patterns and proper parameterization, the proposed approach yields significant enhancement of the temporal resolution over the conventional reconstruction strategy.

Anatomically constrained electrical impedance tomography for three-dimensional anisotropic bodies

As shown previously for two-dimensional geometries, anisotropy effects should not be ignored in electrical impedance tomography (EIT) and structural information is important for the reconstruction of anisotropic conductivities. Here, we will describe the static reconstruction of an anisotropic conductivity distribution for the more realistic three-dimensional (3-D) case. Boundaries between different conductivity regions are anatomically constrained using magnetic resonance imaging (MRI) data. The values of the conductivities are then determined using gradient-type algorithms in a nonlinear-indirect approach. At each iteration, the forward problem is solved by the finite element method. The approach is used to reconstruct the 3-D conductivity profile of a canine torso. Both computational performance and simulated reconstruction results are presented together with a detailed study on the sensitivity of the prediction error with respect to different parameters. In particular, the use of an intracavity catheter to better extract interior conductivities is demonstrated.

Finite element modeling of electrode-skin contact impedance in electrical impedance tomography

In electrical impedance tomography (EIT), we inject currents through and measure voltages from an array of surface electrodes. The measured voltages are sensitive to electrode-skin contact impedance because the contact impedance and the current density through this contact impedance are both high. We used large electrodes to provide a more uniform current distribution and reduce the contact impedance. A large electrode differs from a point electrode in that it has shunting and edge effects which cannot be modeled by a single resistor. We used the finite element method (FEM) to study the electric field distributions underneath an electrode, and developed three models: a FEM model, a simplified FEM model and a weighted load model. We showed that the FEM models considered both shunting and edge effects and matched closely the experimental measurements. FEM models for electrodes can be used to improve the performance of an electrical impedance tomography reconstruction algorithm.