Andrew Seagar

The Sheffield data collection system

Because of the intrinsically low sensitivity of any surface potential measurement to resistivity changes within a volume conductor, any data collection system for impedance imaging must be sensitive to changes in the peripheral potential profile of the order of 0.1%. For example, whilst the resistivity changes associated with lung ventilation and the movement of blood during the cardiac cycle range from 3 to 100% the changes recorded at the surface are very much less than this. The Sheffield data collection system uses 16 electrodes which are addressed through 4 multiplexers. Overall system accuracy is largely determined by the front-end equivalent circuit which is considered in some detail. This equivalent circuit must take into account wiring and multiplexer capacitances. A current drive of 5 mA p-p at 5 kHz is multiplexed to adjacent pairs of electrodes and peripheral potential profiles are recorded by serially stepping around adjacent electrode pairs. The existing Sheffield system collects the 208 data points for one image in 79 ms and offers 10 image data sets per second to the microprocessor. For a homogeneous circular conductor the ratio of the maximum to minimum signals within each peripheral potential profile is 45:1. The temptation to increase the number of electrodes in order to improve resolution is great and an achievable performance for 128 electrodes is given. However, any improvement in spatial resolution can only be made at the expense of speed and sensitivity which may well be the more important factors in determining the clinical utility of APT.

Applied potential tomography: possible clinical applications

Applied potential tomography (APT) or electrical impedance imaging has received considerable attention during the past few years and some in vivo images have been produced. This paper reviews the current situation in terms of what in vivo results have been and are likely to be obtained in the near future. Both static and dynamic imaging are possible and these two areas are dealt with separately. Features of the existing in vivo imaging system are good tissue contrast, high-speed data collection, good sensitivity to resistivity changes, low spatial resolution, low cost and no known hazard. It is concluded that the most promising way forward to clinical application in the short term is to use dynamic as opposed to static imaging. An example of lung imaging is shown and the application to measuring regional ventilation and pulmonary oedema is discussed. Use of APT for the detection of intraventricular bleeding in neonates is discussed as is the proven ability to study gastric physiology by imaging resistivity distribution changes following the ingestion of conducting or insulating fluids. Other areas of possible application which are considered are blood flow measurement, cell counting, measurement of lean-fat ratios and the detection of soft tissue lesions.

Fast reconstruction of resistance images.

Resistance imaging involves the reconstruction of the distribution of electrical resistivity within a conducting object from measurements of the voltages or voltage gradients developed on the boundary of the object while current is flowing within the object. In general, the relationship between the distribution of resistivity in the object and the voltage profile on the object boundary is non-linear and attempts to reconstruct the distribution of resistivity from these profiles usually appear to involve time consuming iterative solutions. If it is assumed that the required resistivity distribution is close to a known reference distribution then it can be shown that there is an approximately linear relationship between the perturbation of the boundary voltage gradient measurements from those of the reference distribution and the logarithm of the resistivity perturbation from the reference distribution. The reconstruction problem then becomes solvable by linear methods. In particular it has proved possible to construct a single-pass back-projection method which can produce images of resistivity from a 16 electrode data collection system. Although the present implementation of this algorithm also assumes that the data is produced from a two-dimensional distribution of resistivity within a circular boundary and that the reference distribution is always uniform it seems capable of reconstructing useful images using data from three dimensional objects, including human subjects.

Theoretical limits to sensitivity and resolution in impedance imaging

In any practical impedance imaging system it is important to be able to predict the image quality which can be expected from particular measurements. It is of interest both to establish the smallest object that can be detected for a certain noise level and to determine the maximum resolution for a certain number of electrodes. In impedance imaging this is not straightforward. The reason is that the resolution and the accuracy of an image which represents a conductive region are related to the number of electrodes and to the noise on the measurements. They also vary with position in the image and depend on the particular distribution of conductivity itself. It is therefore not possible, in general, to make quantitative statements about the resolution and accuracy. It is of course possible to make qualitative statements, but they are not of much use in any particular situation. Formulations are presented here which do allow quantitative assessment of the resolution and accuracy in a certain class of conductive regions. The regions to which they apply are two-dimensional and have a circular boundary shape. The details of the approach are included, both mathematically and descriptively. The quantitative improvement in image quality which can be obtained by reducing the noise, is shown both in terms of accuracy and resolution. The limit to the improvement in quality which can be obtained by taking unlimited independent measurements (i.e. using an unlimited number of electrodes) is calculated. It is shown how to predict the smallest sized object that can just be detected by measurements with a known level of noise.

Applied Potential Tomography: A New Noninvasive Technique for Measuring Gastric Emptying

Applied potential tomography is a new, noninvasive technique that yields sequential images of the resistivity of gastric contents after subjects have ingested a liquid or semisolid meal. This study validates the technique as a means of measuring gastric emptying. Experiments in vitro showed an excellent correlation between measurements of resistivity and either the square of the radius of a glass rod or the volume of water in a spherical balloon when both were placed in an oval tank containing saline. Altering the lateral position of the rod in the tank did not alter the values obtained. Images of abdominal resistivity were also directly correlated with the volume of air in a gastric balloon. Profiles of gastric emptying of liquid meals obtained using applied potential tomography were very similar to those obtained using scintigraphy or dye dilution techniques, provided that acid secretion was inhibited by cimetidine. Profiles of emptying of a mashed potato meal using applied potential tomography were also very similar to those obtained by scintigraphy. Measurements of the emptying of a liquid meal from the stomach were reproducible if acid secretion was inhibited by cimetidine. Thus, applied potential tomography is an accurate and reproducible method of measuring gastric emptying of liquids and particulate food. It is inexpensive, well tolerated, easy to use, and ideally suited for multiple studies in patients, even those who are pregnant.

Electrical impedance imaging

Described herein is an electrical impedance scanner, comprising: a first planar plate comprising a plurality of excitation cells; a second planar plate comprising a plurality of detector cells; the first planar plate held in spaced parallel relation to the second planar plate and defining a chamber therebetween; the first and second planar plates arranged to align each excitation cell with a corresponding detector cell in a one-to-one paired relationship; and each paired excitation cell and detector cell configured for synchronized activation with an electric field communicating therebetween. Systems incorporating the scanner and methods relating to use of the scanner are also described.

Applied potential tomography: a new noninvasive technique for assessing gastric function

Applied potential tomography is a new, non-invasive technique that yields sequential images of the resistivity of gastric contents after subjects have ingested a liquid or semi-solid meal. This study validates the technique as a means of measuring gastric emptying. Experiments in vitro showed an excellent correlation between measurements of resistivity and either the square of the radius of a glass rod or the volume of water in a spherical balloon when both were placed in an oval tank containing saline. Altering the lateral position of the rod in the tank did not alter the values obtained. Images of abdominal resistivity were also directly correlated with the volume of air in a gastric balloon. Profiles of gastric emptying of liquid meals obtained using APT were very similar to those obtained using scintigraphy or dye dilution techniques provided that acid secretion was inhibited by cimetidine. Profiles of emptying of a mashed potato meal using APT were also very similar to those obtained by scintigraphy. Measurements of the emptying of a liquid meal from the stomach were reproducible if acid secretion was inhibited by cimetidine. Thus, APT is an accurate and reproducible method of measuring gastric emptying of liquids and particulate food. It is inexpensive, well tolerated, easy to use and ideally suited for multiple studies in patients, even those who are pregnant. A preliminary study is also presented that assesses the technique as a means of measuring gastric acid secretion. Comparison of resistivity changes with measured acid secretion following the injection of pentagastrin shows good correlations. APT might offer a non-invasive alternative to the use of a nasogastric tube and acid collection.

A Limitation on Systems for Imaging Electrical Conductivity Distributions

The problem of reconstructing a two-dimensional distribution of electrical conductivity from impedance measurements made on the circumference of a circle enclosing the distribution is studied. It is shown to be, in general, impossible to uniquely reconstruct such conductivity distributions when employing certain recently proposed approaches based on the concept of computed tomography which is so successful when X-rays are used. The trouble is that the current stream-lines cannot usually be forced to be straight and paralel. It is indicated how ambiguities might be resolved by making moe extensive sets of measurements.

Limitations in hardware design in impedance imaging

The collection of data suitable for impedance imaging is a well defined task. Once the number of electrodes is chosen, it is possible to specify the number of independent measurements which must be made. Having done so, a data collection system can be designed; preferably with the view to both maximising the speed of data collection and minimising the noise on the measurements. The former is desirable to eliminate aliasing when taking measurements on regions in which the conductivity varies with time, the latter to ensure maximum image quality. When designing such a system many practical problems become apparent. Some are a result of the electrical components used. In principle these can be overcome, although in practice they will always be important. Other problems arise from the nature of the measurements and the way in which they must be taken. These problems do not depend on how the hardware is implemented. They impose fundamental constraints on the quality of the measurements. The problems in the design of a data collection system are considered here. The design is analysed at the functional rather than electronic level, so the results are of general use. Factors considered include the number of measurements, speed of data collection, noise, bandwidth, isolation, common mode feedback, dynamic range, and quantisation.

Iterative Solutions for Electromagnetic Fields at Perfectly Reflective and Transmissive Interfaces Using Clifford Algebra and the Multidimensional Cauchy Integral

A technique is presented for calculating the solution of Maxwells equations using a CFIE based on the Cauchy integral and formulated in the guise of Clifford algebra. This formulation has a geometric interpretation leading to an iterative method of solution which is easily proven as convergent and correct for both perfectly reflective and perfectly transmissive interfaces. Simple test cases involving a cubic boundary and plane wave and dipole sources are used to investigate the numerical performance of the method.