Forward problem solution for electrical conductivity imaging via contactless measurements

The forward problem of a new medical imaging system is analysed in this study. This system uses magnetic excitation to induce currents inside a conductive body and measures the magnetic fields of the induced currents. The forward problem, that is determining induced currents in the conductive body and their magnetic fields, is formulated. For a general solution of the forward problem, the finite element method (FEM) is employed to evaluate the scalar potential distribution. Thus, inhomogeneity and anisotropy of conductivity is taken into account for the FEM solutions. An analytical solution for the scalar potential is derived for homogeneous conductive spherical objects in order to test FEM solutions. It is observed that the peak error in FEM solutions is less than 2%. The numerical system is used to reveal the characteristics of the measurement system via simulations. Currents are induced in a 9x9x5 cm body of conductivity 0.2 S m(-1) by circular coils driven sinusoidally. It is found that a 1 cm shift in the perturbation depth reduces the field magnitudes to approximately one-tenth. In addition, the distance between extrema increases. Further simulations carried out using different coil configurations revealed the performance of the method and provided a design perspective for a possible data acquisition system.