First-Order Induced Current Density Imaging and Electrical Properties Tomography in MRI

In this paper, we present an efficient dedicated electrical properties tomography (EPT) algorithm (called first-order current density EPT ) that exploits the particular radio frequency field structure, which is present in the midplane of a birdcage coil, to reconstruct conductivity and permittivity maps in this plane from $\hat{B}_1^+$ data. The algorithm consists of a current density and an electrical properties step. In the current density reconstruction step, the induced currents in the midplane are determined by acting with a specific first-order differentiation operator on the $\hat{B}_1^+$ data. In the electrical properties step, we first determine the electric field strength by solving a particular integral equation, and subsequently determine conductivity and permittivity maps from the constitutive relations. The performance of the algorithm is illustrated by presenting reconstructions of a human brain model based on simulated (noise corrupted) data and of a known phantom model based on experimental data. The method manages to reconstruct conductivity profiles without model related boundary artifacts and is also more robust to noise because only first-order differencing of the data is required as opposed to second-order data differencing in Helmholtz-based approaches. Moreover, reconstructions can be performed in less than a second, allowing for essentially real-time electrical properties mapping.