MRI based Electrical Properties Tomography: Electromagnetic inversion

In magnetic resonance imaging (MRI) the interest in electric properties tomography (EPT) is growing. In current EPT applications the reconstruction is performed based on the Helmholtz equation which relies on the assumption of a homogeneous contrast. The goal of this thesis is to present new approaches to reconstruct the electrical properties that require less assumptions on the contrast. Two fundamentally new approaches are presented, one based on first order differentiation and one on the global integral field equations using a contrast-source variable. In this thesis these methods are described alongside the existing Helmholz based approach, the contrast source inversion (CSI) - EPT approach, and a deconvolution approach. Reconstruction of both two- and three-dimensional simulations as well as the reconstruction of an in vivo measurement are performed to compare the five different methods. It can be concluded from this comparison that methods that are not based on the homogeneous contrast assumption perform much more accurate (overal) than the Helmholtz equation based method. Both CSI and the direct inversion method based on the global integral equations perform comparable, but the latter is significantly faster and offers almost the same range of flexibility regarding regularisation and preconditioning. The direct inversion method is an improvement on the deconvolution method, performing equally well regarding noise robustness, but offering better reconstructions in all cases due to the lack of an apodisation step. The first order differential method provides a surprisingly robust, accurate and extremely fast way to get insight into the data, and shows that the inversion problem in MRI is actually very well behaved as far as inversion problems go. These new methods provide new insight into the inversion problem in MRI, specifically for EPT and get us one step closer to accurate electric properties reconstruction from an MRI scan.

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Embargo date

2017-06-30

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51.998831, 4.373474

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Student theses

Document type

master thesis

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PSFuchs_MSc_Thesis.pdf

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