Electrical properties based B 1 + prediction for electrical properties tomography reconstruction evaluation

In MR electrical properties tomography (EPT), conductivity and permittivity are reconstructed from MR measurements. However, depending on the reconstruction method, reconstructed electrical properties (EPs) show large variability in vivo, reducing confidence in the reconstructed values for clinical application in practice. To overcome this problem we present a method to evaluate the reconstructed EPs using a physics-based $B_1^{+}$ estimation model.

A physics-based method using a finite difference based recurrent relation is used to estimate the $B_1^{+}$ field from a set of given EPs and the boundary of the measured $B_1^{+}$ field. Reconstructed EPs can be evaluated by comparing the estimated $B_1^{+}$ field with the measured $B_1^{+}$ field. The method was first validated in simulations and afterward tested using MRI data from phantoms and in vivo.

The simulation experiments show that the $B_1^{+}$ field can be accurately estimated, within 90 s for a typical brain at 1 mm³ isotropic resolution, when correct EPs are used as input. When incorrect EPs are used as input the estimated $B_1^{+}$ fields shows differences with the measured $B_1^{+}$ fields. These differences directly correspond to the errors in the underlying EPs, enabling detection of errors in the reconstructions. The results obtained in MRI experiments using phantoms and in vivo show the applicability of the method in practice.

With the proposed method, $B_1^{+}$ fields can be accurately estimated from EPs. This approach can be used to evaluate EPT reconstructions and consequently gain more confidence in reconstructed EPs values in vivo.