An iterative Newton-Raphson method to solve the inverse admittivity problem.

By applying electrical currents to the exterior of a body using electrodes and measuring the voltages developed on these electrodes, it is possible to reconstruct the electrical properties inside the body. This technique is known as electrical impedance tomography. The problem is nonlinear and ill conditioned meaning that a large perturbation in the electrical properties far away from the electrodes produces a small voltage change on the boundary of the body. This paper describes an iterative reconstruction algorithm that yields approximate solutions of the inverse admittivity problem in two dimensions. By performing multiple iterations, errors in the conductivity and permittivity reconstructions that result from a linearized solution to the problem are decreased. A finite-element forward-solver, which predicts voltages on the boundary of the body given knowledge of the applied current on the boundary and the electrical properties within the body, is required at each step of the reconstruction algorithm. Reconstructions generated from numerical data are presented that demonstrate the capabilities of this algorithm.

Effect of electrode size on impedance images of two- and three-dimensional objects.

The sensitivity of an impedance imaging system to small cylindrical inhomogeneities in two-dimensional (2-D) and three-dimensional (3-D) saline tanks was studied for different height electrodes and different height targets. Experimental results were compared with analytical models. Inhomogeneities in the 3-D tank having limited vertical extent were detected by electrodes of vertical size comparable to that of the inhomogeneity. Taller electrodes had increased sensitivity to short targets to only a limited extent. When the electrode height was more than twice that of the target, sensitivity decreased or remained the same with further increases in electrode height. The system was less sensitive to inhomogeneities in the 3-D tank than to those in the 2-D tank. The distinguishability of conductors was greater than that of insulators in the 3-D tank, and the opposite was true in the 2-D tank, consistent with an analytical result.

Electrical impedance tomography of complex conductivity distributions with noncircular boundary.

Electrical impedance tomography (EIT) uses low-frequency current and voltage measurements made on the boundary of a body to compute the conductivity distribution within the body. Since the permittivity distribution inside the body also contributes significantly to the measured voltages, the present reconstruction algorithm images complex conductivity distributions. A finite element model (FEM) is used to solve the forward problem, using a 6017-node mesh for a piecewise-linear potential distribution. The finite element solution using this mesh is compared with the analytical solution for a homogeneous field and a maximum error of 0.05% is observed in the voltage distribution. The boundary element method (BEM) is also used to generate the voltage data for inhomogeneous conductivity distributions inside regions with noncircular boundaries. An iterative reconstruction algorithm is described for approximating both the conductivity and permittivity distributions from this data. The results for an off-centered inhomogeneity showed a 35% improvement in contrast from that seen with only one iteration, for both the conductivity and the permittivity values. It is also shown that a significant improvement in images results from accurately modeling a noncircular boundary. Both static and difference images are distorted by assuming a circular boundary and the amount of distortion increases significantly as the boundary shape becomes more elliptical. For a homogeneous field in an elliptical body with axis ratio of 0.73, an image reconstructed assuming the boundary to be circular has an artifact at the center of the image with an error of 20%. This error increased to 37% when the axis ratio was 0.64. A reconstruction algorithm which used a mesh with the same axis ratio as the elliptical boundary reduced the error in the conductivity values to within 0.5% of the actual values.

Assessment of acute pulmonary edema in dogs by electrical impedance imaging.

Acute pulmonary edema was assessed quantitatively in 12 experiments on six anesthetized dogs. Thirty-two copper foil electrodes were placed around each animal's thorax at the level of the third intercostal space. A real-time electrical impedance tomograph was used to form images of the electrical admittivity of the thorax in and near the plane of these electrodes. The lungs were identified by studying the change in admittivity associated with inspiration. Mean admittivity in these lung regions was assessed at 40-min intervals for the next 3-6 hours. In six control experiments, each having a duration of 200 min, the initial admittivity of the lung regions was 102 +/- 16(SD) mS/m. Lung admittivity usually increased during the first 80 min, and then remained within 2 mS/m of its value at 80 min for the remaining 120 min. In six experiments with pulmonary edema, an initial period of change followed by stability was observed. When stability had been attained, 0.07 ml/kg of oleic acid was injected slowly into a central venous site. Five animals received oleic acid, the sixth received a sham injection of saline. In the five receiving oleic acid, lung admittivity rose steadily for the remainder of the experiment. The increase in lung admittivity in these five animals was between 4 and 16 mS/m. In the sham injected experiment, the lung admittivity changed by 1 mS/m. We conclude that impedance imaging can provide semiquantitative assessment of the development of acute pulmonary edema.

A real-time electrical impedance tomograph.

Electrical properties of tissues in the human body can be imaged using a technology known as Electrical Impedance Tomography. In this modality, sinusoidal electrical currents are applied to the body using electrodes attached to the skin, and voltages that are developed on the electrodes are measured. Using these data, a reconstruction algorithm computes the conductivity and permittivity distributions within the body. This paper describes the reconstruction algorithm, image display algorithm, and hardware of a real-time Electrical Impedance Tomograph known as the Real-Time Imaging System. The reconstruction algorithm, executed by a commercially available coprocessor board that resides in a 386-based personal computer, is a modification of the Newton's One Step Error Reconstructor (NOSER) that minimizes algorithm execution time by precomputing many quantities. The image display algorithm, also executed by the coprocessor board, maps the output of the reconstruction algorithm into an image which is displayed using a video graphics board. The architecture of the system and execution times of algorithms implemented by the system are discussed. Using the continuous data acquisition mode of the Real-Time Imaging System, data from the thorax of a normal human subject were collected. Admittivity changes in the chest, as a result of respiration and the cardiac cycle, are presented. Data that were collected from the leg of a normal subject are shown which demonstrate capabilities of the triggered data acquisition mode of the system, allowing data acquisition synchronization with an electrocardiogram.