Simulation of current flow in piecewise constant media.

A boundary method is presented and is used to calculate the electric potential throughout two-dimensional regions which represent cross-sections of the human body. The method differs from the usual boundary element method by representing both the boundaries and the voltages supported on them as smooth (i.e. infinitely differentiable). Examples are given which show the flow of current through the chest due to electrodes placed on its surface, and that throughout the brain due to a dipole source within the grey matter.

Leg blood flow during total hip replacement under spinal or general anaesthesia.

Calf blood flow was studied using venous occlusion impedance plethysmography during 122 total hip arthroplasties. Patients were randomly allocated to receive spinal or general anaesthesia. Blood flow was measured nine times perioperatively. In the non-surgical leg, mean blood flow rose by over 50% in both groups following anaesthetic induction, remaining significantly elevated with spinal but falling back gradually to baseline with general anaesthesia. In the surgical leg, surgical manipulations produced marked falls in flow in many patients, particularly with femoral component insertion. If this occurred, hyperaemia was commonly seen with spinal anaesthesia but rarely with general anaesthesia once the joint was relocated. Venous outflow resistance rose slightly during anaesthesia in both groups, more so with general anaesthesia. In the surgical leg, marked rises occurred with surgical manipulations, but resistance fell abruptly once the joint was relocated. No clear relationship between these observations and the occurrence of deep vein thrombosis postoperatively was established.

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.

Applied potential tomography: a new non-invasive 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.

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.

Localisation of cardiac related impedance changes in the thorax.

The existence of variations of normal human thoracic impedance, during the cardiac cycle to high frequency electrical current is well known. Since the impedance variations within the thorax are synchronous with the electrocardiogram (ECG), they are attributed to cardiac activity. They can arise from the change of either the rate of blood flow or the blood volume in the heart chambers, the great blood vessels and the lungs. However, their relative contribution is not known. Many investigators have worked on the non-invasive determination of some cardiac parameters using surface electrode impedance measurements on the thorax. Since the relationships between the measurement results and the pulsatile circulation of blood in various organs inside the chest are not well known, the information determined by surface impedance measurements is not as accurate as the results of invasive techniques. Recent advances in the clinical use of applied potential tomography (APT), or electrical impedance imaging, showed that the APT system gives a good soft-tissue contrast and has good sensitivity to resistivity changes. It is therefore concluded that the origin of thoracic impedance changes related to cardiac activity can be deduced from APT images. Our initial studies of ECG gated dynamic APT images of the thorax show that cardiac related thoracic impedance variations originating from different organs can be separated. Sequential APT images of the thorax during the cardiac cycle are presented. The movement of blood from the ventricles to the lungs and vascular system and back to the ventricles is observable in these images.(ABSTRACT TRUNCATED AT 250 WORDS)

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.

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.

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.