A new local method for magnetic resonance electrical properties tomography (EPT), dubbed transverse-EPT (T-EPT), is introduced. This approach iteratively optimizes the dielectric properties (conductivity and permittivity) and the z-component of the electric field strength, exploiting the locally E-polarized field structure typically present in the midplane of a birdcage radiofrequency (RF) coil. In contrast to conventional Helmholtz-based EPT, T-EPT does not impose homogeneity assumptions on the object and requires only first order differentiation operators, which makes the method more accurate near tissue boundaries and more noise robust. Additionally, in contrast to integral equation-based approaches, estimation of the incident fields is not required. The EPT approach is derived from Maxwell’s equations and evaluated on simulated data of a realistic tuned RF coil model to demonstrate its potential.

The main objective of electrical-property tomography (EPT) is to retrieve dielectric tissue parameters from B ₁ ⁺ data as measured by a magnetic-resonance (MR) scanner. This is a so-called hybrid inverse problem in which data are defined inside the reconstruction domain of interest. In this paper, we discuss recent and new developments in EPT based on the contrast-source inversion (CSI) method. After a short review of the basics of this method, two- and three-dimensional implementations of CSI-EPT are presented along with a very efficient variant of 2D CSI-EPT called first-order induced current EPT (foIC-EPT). Practical implementation issues that arise when applying the method to measured data are addressed as well, and the limitations of a two-dimensional approach are extensively discussed. Tissue-parameter reconstructions of an anatomically correct male head model illustrate the performance of two- and three-dimensional CSI-EPT. We show that 2D implementation only produces reliable reconstructions under very special circumstances, while accurate reconstructions can be obtained with 3D CSI-EPT.

Magnetic resonance electrical properties tomography (MR-EPT) is a technique used to estimate the conductivity and permittivity of tissues from MR measurements of the transmit magnetic field. Different reconstruction methods are available; however, all these methods present several limitations, which hamper the clinical applicability. Standard Helmholtz-based MR-EPT methods are severely affected by noise. Iterative reconstruction methods such as contrast source inversion electrical properties tomography (CSI-EPT) are typically time-consuming and are dependent on their initialization. Deep learning (DL) based methods require a large amount of training data before sufficient generalization can be achieved. Here, we investigate the benefits achievable using a hybrid approach, that is, using MR-EPT or DL-EPT as initialization guesses for standard 3D CSI-EPT. Using realistic electromagnetic simulations at 3 and 7 T, the accuracy and precision of hybrid CSI reconstructions are compared with those of standard 3D CSI-EPT reconstructions. Our results indicate that a hybrid method consisting of an initial DL-EPT reconstruction followed by a 3D CSI-EPT reconstruction would be beneficial. DL-EPT combined with standard 3D CSI-EPT exploits the power of data-driven DL-based EPT reconstructions, while the subsequent CSI-EPT facilitates a better generalization by providing data consistency.

Contrast source inversion – electrical properties tomography (CSI-EPT) is an iterative reconstruction method to retrieve the electrical properties (EPs) of tissues from MR data. The method is based on integral representations of the electromagnetic (EM) field and has been shown to allow EP reconstructions of small structures as well as tissue boundaries with compelling accuracy. However, to date CSI-EPT has been implemented for two-dimensional (2D) configurations only which limits its applicability. In this paper, a full three-dimensional (3D) extension of the CSI-EPT method is presented, to enable CSI-EPT to be applied to realistic 3D scenarios. Here, we demonstrate a proof-of-principle of 3D CSI-EPT and present reconstructions of a 3D abdominal body section and a 3D head model using different settings of the transmit coil. Numerical results show that the full 3D approach yields accurate reconstructions of the EPs, even at tissue boundaries and is most accurate in regions where the absolute value of the electric field is highest.