In vivo validation of Magnetic Resonance Spin Tomography in Time-domain

Magnetic Resonance Spin Tomography in Time-domain (MR-STAT) is a novel MRI technique that enables the quantification of multiple tissue properties based on a single scan. In contrast to traditional two-step quantitative MRI methods, MR-STAT does not generate contrast images. Instead, the spatial localization and quantification of tissue properties are performed at the same time. The reconstruction process in MR-STAT involves solving a large-scale, nonlinear optimization problem in all voxels simultaneously, posing challenges in terms of computation times and computer memory requirements. This thesis further develops the MR-STAT technique in terms of acquisition protocols and reconstruction algorithms.

Chapter 2 describes the underlying theory of MR-STAT and demonstrates its potential through simulation and low-resolution in vivo experiments.
Chapter 3 introduces a generic, Gauss-Newton-based reconstruction algorithm for MR-STAT. A parallel, matrix-free implementation of the algorithm is proposed and it is validated on high-resolution, two-dimensional MR-STAT data. In principle, the reconstruction can be used in three-dimensional and non-Cartesian settings. However, reconstruction times for this implementation pose a challenge for the clinical adoption of MR-STAT.

In Chapter 4, we argue that the Gauss-Newton matrix used in Chapter 3 admits a sequence-dependent structure. A theoretical foundation is provided based on which we predict that for Cartesian sequences with smoothly varying flip angles, the Gauss-Newton matrix admits a sparse structure. The sparse structure is leveraged to reduce reconstruction times from hours to approximately fifteen minutes on a CPU cluster.

Chapter 5 focuses on developing a GPU implementation of the MR-STAT reconstruction algorithm using the relatively new Julia programming language. In addition, an adjustment to the reconstruction algorithm is proposed. Rather than a fully matrix-free algorithm, the computationally most demanding subset of the model matrices are stored in (GPU) memory, resulting in a partially matrix-free Gauss-Newton technique. With this modification, two-dimensional MR-STAT reconstructions can be performed in the order of minutes on a single GPU card. The Julia code developed in Chapter 5 to perform Bloch simulations is released as a standalone Julia software package named BlochSimulators.jl.

Chapter 6 explores non-Cartesian readout strategies for MR-STAT. More specifically, a comparison between Cartesian and radial MR-STAT is conducted in terms of efficiency and robustness. Simulation experiments predict higher efficiencies with the radial readout strategy. However, in phantom and in vivo experiments the radial readout strategy suffers from reliability issues that likely originate from a higher sensitivity to scanner hardware imperfections. Drawing conclusions about scan efficiency is in clinical settings is therefore less straightforward and the robustness of Cartesian readout strategies may be preferred.

Based on the work presented in this thesis, full brain multi-two-dimensional MR-STAT acquisitions of five minutes are possible based on which quantitative images of T1, T2, and proton density can be reconstructed. The reconstruction times are in the order of minutes per slice on a single GPU card. An initial clinical demonstration has been conducted successfully on 30 patients with various symptoms. At the time of this writing, a second clinical demonstrator study is being performed on a large group of patients suffering from Parkinson's disease.