3-D MRI-based electrical properties tomography using the volume integral equation method

MRI-based electrical properties tomography, a noninvasive technique for characterizing electrical conductivity and permittivity of human tissues, has been developed for the diagnosis of cancer and specific absorption rate quantification since 1991, based on the distortion of radio frequency magnetic field in MRI. For high-contrast tissues, the volume integral equation (VIE) method is appropriate to reconstruct the electrical properties because of its flexibility in handling complex high-contrast inhomogeneous scatterers without approximations. In this paper, the variational Born iterative method is used to solve the nonlinear inverse problem of the reconstruction of dielectric contrast function. To improve the computation efficiency, the stabilized biconjugate-gradient fast Fourier transform method and the conjugate-gradient fast Fourier transform method are incorporated in the forward and inverse problems of the VIE, respectively. The numerical results have demonstrated that the inversion method based on the positive rotating magnetic field of MRI is capable of reconstructing high-spatial-resolution electrical properties mapping of inhomogeneous human tissues.