Convection-Reaction Equation Based Low-Frequency Conductivity Imaging Using Readout Gradient Induced Eddy Currents

Omer Faruk Oran¹, Fatih Suleyman Hafalir¹, Necip Gurler¹, Yusuf Ziya Ider¹

Imaging electrical conductivity provides both anatomical and pathological information about the tissues. Eddy-currents, which are induced in the object due to the ramp of readout gradient field, generate a secondary magnetic flux density which may be measured using MRI. In this study, we derive the key equation which relates conductivity and induced current to this measured magnetic flux density and which is in the form of the convection-reaction equation. We propose and demonstrate a low-frequency conductivity imaging algorithm which is based on the solution of this equation. We also propose and demonstrate a method for reconstructing the induced current density.