The convection-reaction partial differential equation (PDE) based algorithm for Magnetic Resonance Electrical Properties Tomograpy, cr-MREPT, does not suffer from internal boundary artifacts but has the Low Convective Field (LCF) artifact. The cr-MREPT PDE is rearranged such that H1+ is the unknown variable and the coefficients depend on the EPs. The EPs are iteratively adjusted to minimize the difference between calculated and measured H1+. The method can be applied to a Region-of-Interest without considering the whole object. Conductivity reconstructions for simulation objects and also for an agar phantom demonstrate that the proposed method does not suffer from boundary and LCF artifacts.