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Mathematical analysis of the 1D model and reconstruction schemes for magnetic particle imaging
(2018)
Magnetic particle imaging (MPI) is a promising new in vivo medical imaging modality in which distributions of super-paramagnetic nanoparticles are tracked based on their response in an applied magnetic field. In this paper we provide a mathematical analysis of the modeled MPI operator in the univariate situation. We provide a Hilbert space setup, in which the MPI operator is decomposed into simple building blocks and in which these building blocks are analyzed with respect to their mathematical properties. In turn, we obtain an analysis of the MPI forward operator and, in particular, of its ill-posedness properties. We further get that the singular values of the MPI core operator decrease exponentially. We complement our analytic results by some numerical studies which, in particular, suggest a rapid decay of the singular values of the MPI operator.
Object
The consistency of parametric registration in multi-temporal magnetic resonance (MR) imaging studies was evaluated.
Materials and methods
Serial MRI scans of adult patients with a brain tumor (glioma) were aligned by parametric registration. The performance of low-order spatial alignment (6/9/12 degrees of freedom) of different 3D serial MR-weighted images is evaluated. A registration protocol for the alignment of all images to one reference coordinate system at baseline is presented. Registration results were evaluated for both, multimodal intra-timepoint and mono-modal multi-temporal registration. The latter case might present a challenge to automatic intensity-based registration algorithms due to ill-defined correspondences. The performance of our algorithm was assessed by testing the inverse registration consistency. Four different similarity measures were evaluated to assess consistency.
Results
Careful visual inspection suggests that images are well aligned, but their consistency may be imperfect. Sub-voxel inconsistency within the brain was found for allsimilarity measures used for parametric multi-temporal registration. T1-weighted images were most reliable for establishing spatial correspondence between different timepoints.
Conclusions
The parametric registration algorithm is feasible for use in this application. The sub-voxel resolution mean displacement error of registration transformations demonstrates that the algorithm converges to an almost identical solution for forward and reverse registration.