Boundary value estimation for electrical properties tomography based on Helmholtz decomposition for the electric and magnetic fields

Motivation: The conventional methods for electrical properties (EPs) tomography without the local homogeneity assumption requires the EP values on the ROI boundary, which are not available in practical situations. Goal(s): Our goal was to develop a method that can compute the boundary EP values from the measured B1 field. Approach: We derived an integral equation for the boundary EP values based on the Helmholtz decomposition for the electric and magnetic fields. Results: The proposed method was verified numerically and experimentally with a phantom, showing that it can reconstruct the EP contrast more accurately than the conventional integral-equation-based method that assumes incorrect boundary values. Impact: The estimated boundary EP values can be used in the conventional partial-differential-equation-based and integral-equation based methods for reconstructing non-homogeneous EPs in the ROI, which eliminates the necessity of assuming the boundary EPs.