Technische Universität Berlin

Institut für Mathematik

Room: MA 580

Straße des 17. Juni 136

10623 Berlin

Telephone: +49 30 314 27379

Email: macdonald@math.tu-berlin.de

 

Machine learning approaches for MR-fingerprinting  of cardiovascular flow

PIs: Kutyniok, Schäffter, Schulz-Menger

Application area: Cardiovascular

Modality: MRI

Background: Recently, there has been an increased interest in employing machine learning methods (e.g. deep neural networks) for tasks in medical imaging such as image reconstruction, denoising, or super-resolution. Although first experimental works show promising results, there is yet an unsatisfactory lack of fundamental theory and understanding of these methods. A more rigorous mathematical analysis is needed before they could be considered admissible for clinical applications.

Aim: Development of a mathematical theory of deep learning for inverse problems. A particular focus lies on inverse problems arising in medical imaging, in particular the reconstruction of MRI signals from incomplete k-space data and MR parameter mapping in the framework of MR-Fingerprinting. As a first step, the basis pursuit problem (which arises in compressed sensing) is considered.

Methods: MR-flow is a well-established quantitative technique in diagnosis of cardiovascular medicine at all stages of life. However, due to the high spatiotemporal resolution requirements, fast and accurate flow quantification remains a challenge. Sometimes the differentiation of neighbouring arteries and veins can be difficult. Magnetic Resonance Fingerprinting (MRF) is a new approach that aims to acquire parameters of interest, such as T1, T2 and proton density, within one single scan. For this, unique signal evolutions (‘fingerprints’) of each tissue type are created and measured signals are matched to a signal dictionary to reconstruct parameters. For far, MRF has been applied to measure parameter maps of spin-density, off-resonance and relaxation times (T1, T2). Recently, MRF has also been investigated for perfusion parameter mapping. An important prerequisite for MRF is the dictionary, which is determined by simulating the signal evolution of the fingerprinting sequence setup (i.e., timing, flip angles etc.) using the Bloch equations. Matching of the measured data with the dictionary is usually performed voxel-vise based on least squares correlation. However, matching algorithms are time-consuming and prone to errors if parameter sampling of the dictionary is too sparse or encoding does not allow proper classification.