CSI-EPT: A Contrast Source Inversion Approach for Improved MRI-Based Electric Properties Tomography

Electric properties tomography (EPT) is an imaging modality to reconstruct the electric conductivity and permittivity inside the human body based on B₁⁺ maps acquired by a magnetic resonance imaging (MRI) system. Current implementations of EPT are based on the local Maxwell equations and assume piecewise constant media. The accuracy of the reconstructed maps may therefore be sensitive to noise and reconstruction errors occur near tissue boundaries. In this paper, we introduce a multiplicative regularized CSI-EPT method (contrast source inversion - electric properties tomography) where the electric tissue properties are retrieved in an iterative fashion based on a contrast source inversion approach. The method takes the integral representations for the electromagnetic field as a starting point and the tissue parameters are obtained by iteratively minimizing an objective function which measures the discrepancy between measured and modeled data and the discrepancy in satisfying a consistency equation known as the object equation. Furthermore, the objective function consists of a multiplicative Total Variation factor for noise suppression during the reconstruction process. Finally, the presented implementation is able to simultaneously include more than one B₁⁺ data set acquired by complementary RF excitation settings. We have performed in vivo simulations using a female pelvis model to compute the B₁⁺ fields. Three different RF excitation settings were used to acquire complementary B₁⁺ fields for an improved overall reconstruction. Numerical results illustrate the improved reconstruction near tissue boundaries and the ability of CSI-EPT to reconstruct small tissue structures.