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A new method for solving the magnetic induction tomography forward problem is presented. It is based on the combination of an OcTree type multi-level adaptive orthogonal mesh generation algorithm with a conformal finite integration technique-like formulation. The results obtained were compared with both analytical solutions and the response from a previously validated method. The presented method was proven to be capable of dealing with both complex electrical conductivity and magnetic permeability, giving a response with a low relative error, even when fairly coarse grids are used, thus reducing the overall system size and consequently the time for the attainment of the solution. This method is shown to be sensitive enough to be useful for image reconstruction in biological applications, where very small conductivities and relative permeabilities are usually found.