Quantification in multifrequency tomography

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Abstract
The time domain change in human body impedance, in short intervals, usually falls into the approximation Delta Z<0 ( Delta Z: impedance change, Z0: base impedance). This makes it possible to obtain both an image and an estimate of the log-conductivity change for the considered section using backprojection algorithms. In multifrequency tomography, however, the impedance change can be very large, depending on the applied frequencies. In this situation it is possible to obtain images using the methods applied in dynamic impedance imaging, but the estimate of the impedance change becomes highly non-linear. We have developed an algorithm based on the analytical solution of the linearized Poisson equation in a curvilinear space formed by the current lines and the equipotential lines. In order to set the correct boundary conditions, the current profile under the electrodes has been numerically computed. The behaviour of the algorithm has been assessed using the voltages obtained by analytically solving the direct problem in a circular region with small circular centred and non-centred perturbations of different size. The results are compared with those obtained using a backprojection algorithm. Although the developed algorithm displays higher linearity than a backprojection algorithm, it still shows a dependence on the perturbation size and position. This algorithm has been applied to the reconstruction of a series of measurements from 8 kHz to 500 kHz made in a sample of porcine liver immersed in a saline tank. A Cole-Cole model is fitted to the data. The parameters of this model are compared with those calculated from a 4-wire measurements using a commercial impedance analyser.