A Boundary-Value-Free Method for Reconstructing Electrical Properties Using MRI Based on the Neumann-Type Integral Formula

Recently, magnetic resonance electrical properties tomography (MREPT) has been actively studied as a method that reconstructs the electrical properties of biological tissues from internal magnetic field data measured by using MRI. We previously proposed an explicit reconstruction method for MREPT based on a D-bar equation of the electric field. In this method, as in some other conventional methods, EP values on the boundary of the region of interest (ROI) must be given as a Dirichlet boundary condition of the D-bar equation, which is not accessible in practical situations. Therefore, in this paper, we propose a novel method for reconstructing EPs in a circular region without boundary EP values. Starting from the integral solution of the D-bar equation in a circular region with the Neumann boundary condition, we show that the PDE is solved based only on magnetic field data measured by using MRI. Numerical simulations and a phantom experiment show that the proposed method yields a good reconstruction results without giving any boundary EP values.