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Four aspects of probing with low frequency electric currents are considered. Applications of probing with electric currents in geophysics and medicine are reviewed. The theory of conservative fields is reviewed, and is discussed in relation to low frequency electric currents and other physical phenomena to which it applies. The resolution with which a conductivity distribution can be reconstructed from electrical measurements is examined. Relationships are derived which relate the accuracy of the measurements to both the spatial resolution and conductivity resolution of the distribution. These relationships are obtained for conductivity distributions within both circular and half plane regions. It is found that the spatial resolution and conductivity resolution at any point depend on both the location and the conductivity of that point. It is experimentally verified that the best theoretical value of spatial resolution, for measurements having a particular accuracy, can be closely approached in practice. The relationship between two-dimensional circularly symmetric conductivity distributions and electrical probing measurements performed on them is studied. Two approaches are employed. One treats these distributions as smooth and the other treats them as piecewise constant. Two techniques are developed for reconstructing the conductivity distributions from the measurements. One technique is iterative whereas the other is direct. Examples are given in which these techniques are applied to a variety of simulated and experimental measurements. These examples show how well conductivity distributions, reconstructed by these techniques, can be expected to represent the actual conductivity distributions. The relationship between electrical probing measurements and general two-dimensional conductivity distributions is examined. These distributions are represented both as being smooth and piecewise continuous. Equations are developed relating the measurements on the boundary of a region to the conductivity distribution therein. The conditions on such measurements, for them to fully characterise the electrical response of the region, are established. The circumstances are identified under which coupling between different portions of the region can be neglected. These circumstances are experimentally verified. A direct technique is developed for interpreting measurements in terms of a particular type of conductivity distribution. This technique is applied successfully to both experimental and simulated measurements. A model is developed to interpret changes in limb volume measured during venous occlusion plethysmography. The parameters of the model are chosen to represent, as closely as possible, physiological variables of the limb. Experiments are reported in which these changes in volume are infer from measurements of the electrical resistance of limbs. It is shown that the model can accurately mimic such changes in volume. An experiment is described which demonstrates how changes in the model parameters can be USE to monitor changes in the circulatory system within the limb. The model used to show that significant changes in the limb circulation can occur during surgery. Such changes have particular relevance to the formation c peri-operative venous thrombosis. |
