MRI Fingerprinting with Philips
Supervisors
Dr. Manuel Baumann (Philips Research), JunProf. Jan Heiland FMA
Wanted
A highly motivated Masters’ student of mathematics or statistics that feels comfortable with the problem below and that, at best, has good command of a programming language.
Problem Statement
MR Fingerprinting is a new, quantitative imaging technique in Magnetic Resonance Imaging (MRI)^{1}. In short,

MR Fingerprinting relies on the simulation of the Bloch equation, a parameterdependent ODE for the magnetization $M$ of the form
$$\dot{M}(t) = f(M(t), B(t), T_1, T_2),$$where the magnetic field $B$ is determined by the parameters of the acquisition.

Variation of the relaxation times $T_1$ and $T_2$ yield a series of trajectories forming a socalled dictionary.

Fingerprinting means the matching of the acquired undersampled data with the dictionary entries for querying the relevant tissuespecific parameters.
The development and implementation opens a number of options for a Master’s project:

System Theory: Reformulation of the MRF dictionary computation as an inputstateoutput system and model order reduction of the underlying Bloch equation. While the reformulation enables the matching by established system identification routines, a reduced order model can be used for aposteriori checks of the selected parameters or for enriching the dictionary in the relevant parameter range.

Statistics: The estimation of parameters based on data is a common task in statistics. Apart from implementing and testing relevant routines for Fingerprinting, the inclusion of tailored statistical approaches for the particular problem of Fingerprinting can be useful for improving the dictionary in general and for providing confidence estimates for the selection obtained from classical matching.

Optimization: Fingerprinting seeks for the best match of collected data with the precomputed dictionary entries. Tools from mathematical optimization will be used to improve the reliability of the selected optimum and to enhance both the data aquisition and the dictionary through optimal design.
How to apply
Please see the job advertisement and apply by June 30.

See here for a scientific paper on MR Fingerprinting: https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3602925/ ↩︎