Partial differential equations for the inverse of admittivity for magnetic resonance electrical property tomography

Magnetic resonance electrical property tomography (MREPT) has attracted considerable attention for application to the estimation of the electric conductivity and permittivity inside the human body by measuring the transverse magnetic field component of the applied RF field at the Larmor frequency with an MRI scanner. However, conventional methods assume that these electrical properties are homogeneous inside the human body, which leads to a reconstruction error. In this paper, we present a linear, first-order partial differential equation (PDE) for the inverse of the admittivity, while the conventional PDE for the admittivity is nonlinear. This allows well-established methods for solving linear first-order PDEs to be used in MREPT.