Contrast Source Inversion Electrical Property Tomography

Abstract

Electrical property tomography (EPT) reconstructs the human body’s conductivity and relative permittivity using the radio frequency field from a magnetic resonance machine. Since conductivity and relative permittivity can be biomarkers for many illnesses, it is necessary to reconstruct them accurately. To this end, this thesis focuses on the two-dimensional tranceive phase corrected contrast source inversion algorithm (2D-CSI).

This 2D-CSI algorithm is significantly faster than its three-dimensional (3D) counterpart. However, reconstruction artefacts may appear since the 2D field description is not always applicable. In this thesis, these artefacts are identified and it is investigated if the 2D-CSI algorithm can be improved to handle them. In particular, the proposed updates are, first, implementing the early stopping principle, then adding a positivity constraint to the conductivity and relative permittivity, and lastly, initialising with Helmholtz electrical property tomography (HEPT). The first two enhancements create a more robust algorithm, while the third update could be useful only in specific cases (with no fine structures and low noise levels).

After achieving a more robust algorithm, the 2D-CSI algorithm is applied to the realistic 3D dataset ”A Database for MR-based Electrical Properties Tomography” (ADEPT). The first and foremost challenge is accurately simulating the incident field, as the reconstructions depend a lot on the incident fields. If the incident fields do not match perfectly, the algorithm can only produce satisfactory reconstruction results in a part of the reconstruction domain. The reconstructions are only partly accurate because the reconstructed electric fields converge to a line creating line artefacts. It is shown that small changes in the incident fields produce small changes in the position of the artefacts. Based on this observation, a reconstruction strategy has been developed in which a reconstruction without artefacts is produced by combining reconstruction results of multiple incident fields. Integrating all modifications of the 2D-CSI
algorithm in one single framework shows that the conductivity and relative permittivity of the brain in the middle of the birdcage coil can be reconstructed accurately