Magnetic resonance electrical properties tomography is a type of quantitative magnetic resonance imaging that aims to reconstruct the conductivity and permittivity of biological tissue. These electrical properties of the tissue can be used to compute the specific absorption rate, to differentiate tumours from healthy tissue and for hyperthermia treatment planning. Several methods to reconstruct these electrical properties exist with different degrees of success. Combining analytical reconstruction methods with deep learning methods is left relatively unexplored in the field of magnetic resonance electrical properties tomography. Hence, this work explores such hybrid methods in which deep learning is embedded in an analytical reconstruction method. A recurrent inference machine is integrated into the iterative reconstruction scheme called Contrast Source Inversion, in an attempt to decrease its high computational load. Additionally, a U-net is trained to correct reconstructed conductivity maps using discrepancies in measured- and reconstructed phase data, which is based on the relation between conductivity and phase in the Helmholtz equation. The recurrent inference machine embedded version of contrast source inversion failed to achieve a desirable reconstruction quality with its current implementation. However, the large amount of potential improvements to its implementation motivates further research into its application before discarding it. The conductivity correction U-net is able to correct conductivity errors as small as 0.13 S/m when used iteratively or 0.05 S/m when used a single time when noiseless data is used. Further research in its capabilities of handling noisy data is required to assess practical usage.

Electrical properties tomography is the quantification of the conductivity and permittivity of different materials. In an MRI setting this can be used to map the electrical properties of tissue. These values can be used as a different contrast mechanism, for hyperthermia treatment or the improvement of antenna design for specific applications. There are different methods used to obtain these electrical properties, however these often use differential operators on measured data. This leads to reconstructions corrupted by noise, thus in this thesis the work on contrast source inversion based electrical properties tomography is continued. This method uses an integral approach and is therefore more robust with respect to noise. The work presented continues from the two-dimensional Matlab based simulations and extends these to a more realistic measurement setup. The RF-shield is numerically implemented and an extension is made to the existing algorithm to handle the transceive phase based on Maxwell's equations. This is done by implementing a forward problem into the inverse problem of getting the contrast from the measured radiofrequency field. After this the algorithm was tested with three-dimensional FDTD simulations and finally a phantom study was done to test with an MRI scanner. From the results of the two-dimensional simulations it was seen that this method is indeed very robust when it comes to a realistic measurement setup. In the three-dimensional simulations it was observed that the electrical properties are underestimated. Nonetheless CSI-EPT is more precise than the standard Helmholtz based methods. Plus the improvement made to the algorithm makes it possible to map all the RF fields inside the scanner which has not been done before. The same underestimation was seen with the reconstruction of the measured data from the phantom study.