Magnetic Resonance-Based Electric Properties Tomography via Green’s Integral Identity

A new approach to Magnetic Resonance-based Electric Properties Tomography (EPT) is presented. The method applies Green's integral identity to the equation that regulates the EPT problem. The resultant integral equations are used to impose the consistency of the measured values of the radiofrequency field. This is achieved by seeking dielectric properties values that allow satisfying the identity within suitable kernels of voxels. In each kernel, an overdetermined system of equations is written, and the corresponding problem is solved in the least squares sense, providing an index of trustworthiness of the solution. Both the complete formulation and its phase-based approximation are presented. The application of a filter, which post-processes the raw results based on the index of trustworthiness, is also discussed. The performance of the method is evaluated on synthetic data and experimental measurements acquired on a heterogeneous brain phantom and on four human volunteers. The reconstructions are compared to those produced through a Helmholtz-EPT with adaptive kernel. The new EPT method performs well in all tests.