John C. Goble

NOSER: An algorithm for solving the inverse conductivity problem

The inverse conductivity problem is the mathematical problem that must be solved in order for electrical impedance tomography systems to be able to make images. Here we show how this inverse conductivity problem is related to a number of other inverse problem. We then explain the workings of an algorithm that we have used to make images from electrical impedance data measured on the boundary of a circle in two dimensions. This algorithm is based on the method of least squares. It takes one step of a Newtons method, using a constant conductivity as an initial guess. Most of the calculations can therefore be done analytically. The resulting code is named NOSER, for Newtons One‐Step Error Reconstructor. It provides a reconstruction with 496 degrees of freedom. The code does not reproduce the conductivity accurately (unless it differs very little from a constant), but it yields useful images. This is illustrated by images reconstructed from numerical and experimental data, including data from a human chest.

ACT3: a high-speed, high-precision electrical impedance tomograph

Presents the design, implementation, and performance of Rensselaers third-generation adaptive current tomograph, ACT3. This system uses 32 current sources and 32 phase-sensitive voltmeters to make a 32-electrode system that is capable of applying arbitrary spatial patterns of current. The instrumentation provides 16 b precision on both the current values and the real and reactive voltage readings and can collect the data for a single image in 133 ms. Additionally, the instrument is able to automatically calibrate its voltmeters and current sources and adjust the current source output impedance under computer control. The major system components are discussed in detail and performance results are given. Images obtained using stationary agar targets and a moving pendulum in a phantom as well as in vivo resistivity profiles showing human respiration are shown.<<ETX>>

A Phase Sensitive Voltmeter For A High-speed, High-precision Electrical Impedance Tomograph

Many potential applications for Electrical Impedance Tomography (EIT) have been investigated, many of which are particularly suited to real-time imaging [I]. The ill-posedness of the inverse problem of reconstructing the interior impedance distribution from boundary measurements requires that the boundary data be measured with great precision. As speed and precision are in general conflicting requirements, the construction of an instrument having both has proven to be a challenge. We describe here the phase-sensitive voltmeter to be used in ACT 111, Rensselaers third generation impedance tomograph [2],[3].

Thoracic Impedance Images During Ventilation

Static and dynamic impedance images of a human chest at various stages in its respiratory cycle are presented. These images were made by an adaptive current tomography (ACT) system that applied 31 trigonometric patterns of currents to 32 electrodes and measured the voltages that resulted on those same electrodes. A video tape showing a sequence of these images will be presented.

Optimal current patterns for three-dimensional electric current computed tomography

Basic investigations of the detectability of small targets in a three-dimensional cylindrical saline phantom are described. Distinguishability, a measure of target detectability, is defined, and the effects of electrode geometry, target volume and target height on distinguishability are reported. An algorithm that computes current patterns that maximize distinguishability in a three-dimensional electrode array is described and tested. The results show that the algorithm greatly increases distinguishability for small, off-center targets and converges quickly to optimal current patterns.<<ETX>>

Analog Electronics For A High-speed High-precision Electrical Impedance Tomograph

Electronic components for each electrode of Rensselaers ACT 111 impedance imaging system occupy two circuit boards. One is devoted to digital and timing circuits and the other to analog and interface circuits. The analog board includes the sinusoid generator, the current source and its compensator, the voltmeter buffers and some switching and calibration components. Some details on the design considerations and implementation of this portion of the system will be presented here.

A distributed architecture for medical instrumentation: an electric current computed tomograph

Advances in electric-current computed tomography (ECCT) have resulted in reconstruction algorithms that far exceed the capabilities of the minicomputer-based architectures historically used in medical imaging devices. Further, computers optimized for reconstruction and software development tasks are not well suited to the real-time hardware control required in ECCT. The authors report their efforts to overcome these conflicting computational requirements through the use of a distributed medical-instrument architecture.<<ETX>>

Impedance images of the chest

This paper reports the results of electrical impedance imaging of the thorax of normal human subjects. The data collection and reconstruction algorithms used permit an assessment of the absolute value of the resistivities reported as well as changes in those resistivities.

Current Sources For Impedance Imaging Systems

It can be seen from the calculations in (l) that impedance imaging systems that apply currents and measure voltages are less sensitive to errors than systems which apply voltages and measure currents. For some system designs (2), it is possible to use a single floating current source with an appropriate switching system to sequentially address all electrodes in pairs. Other system designs require an individual source for each electrode, with consequent increased costs (3). For in-vivo systems which operate above 10 kHz, high resolution images require a high internal impedance for the current sources in the presence of cables from the instrument to the electrodes. This paper explores some of the circuits available for such current sources, and indicates their disadvantages along with an approach to a circuit configuration that resolves most of the problems.

Images from an adaptive current tomograph

The authors have designed, built, and tested an electric current tomograph suitable for applying the adaptive current algorithm described by D. Isaacson et al. (1988). Usable images can be obtained by a relatively primitive reconstruction algorithm. Demonstrable improvement in these images is obtained when optimal current patterns are used.<<ETX>>