A new approach for electrical properties estimation using a global integral equation and improvements using high permittivity materials.

Electrical Properties Tomography (EPT) using MRI is a technique that has been developed to provide a new contrast mechanism for in vivo imaging. Currently the most common method relies on the solution of the homogeneous Helmholtz equation, which has limitations in accurate estimation at tissue interfaces. A new method proposed in this work combines a Maxwell's integral equation representation of the problem, and the use of high permittivity materials (HPM) to control the RF field, in order to reconstruct the electrical properties image. The magnetic field is represented by an integral equation considering each point as a contrast source. This equation can be solved in an inverse method. In this study we use a reference simulation or scout scan of a uniform phantom to provide an initial estimate for the inverse solution, which allows the estimation of the complex permittivity within a single iteration. Incorporating two setups with and without the HPM improves the reconstructed result, especially with respect to the very low electric field in the center of the sample. Electromagnetic simulations of the brain were performed at 3T to generate the B1(+) field maps and reconstruct the electric properties images. The standard deviations of the relative permittivity and conductivity were within 14% and 18%, respectively for a volume consisting of white matter, gray matter and cerebellum.