On the Simultaneous Quantification of Flow Velocities and Relaxation Constants Through Magnetic Resonance Fingerprinting

In this thesis, the development of a novel magnetic resonance imaging (MRI) pulse sequence based on magnetic resonance fingerprinting (MRF) is presented. The proposed technique, termed “Flow-MRF”, allows time-resolved velocities and relaxation constants to be quantified simultaneously, in shorter acquisition times than conventional MR-based velocimetry. The simultaneous quantification of both sets of parameters was achieved by formulating the combined problem in the MRF framework. An MRF pattern was designed to create minimal coupling between the relaxometric and velocimetric parameter encoding. Flow-MRF was validated and tested in simulations, phantom experiments, and an in vivo study targeting the popliteal artery and the gastrocnemius muscle. In each investigation, Flow-MRF quantified relaxation constants and flow velocities in strong agreement with literature and reference measurements. Furthermore, the use of high velocity encoding moments (Δm1 = 60 mT/m·ms^2) was demonstrated while maintaining a range of correctly quantifiable velocities beyond 800 cm/s. In the volunteer study, Flow-MRF determined an average longitudinal relaxation time of (1384±75) ms and a transverse relaxation time of (26±4) ms in the gastrocnemius muscle. The average velocity deviation over all three volunteers between Flow-MRF and the reference was (-2.6±5.2) cm/s. Lastly, the potential to quantify the complete Reynolds stress tensor with Flow-MRF was investigated and shown in a stenotic flow phantom experiment. Flow‐MRF presents a novel method of quantifying velocities in up to fourfold shorter measurement times than conventional velocity mapping techniques, while simultaneously providing relaxometric maps of static tissue. These improvements can potentially be helpful in the assessment of pathologies such as arteriosclerosis

Cram\'er-Rao Bound Optimized Subspace Reconstruction in Quantitative MRI

We extend the traditional framework for estimating subspace bases that maximize the preserved signal energy to additionally preserve the Cram\'er-Rao bound (CRB) of the biophysical parameters and, ultimately, improve accuracy and precision in the quantitative maps. To this end, we introduce an \textit{approximate compressed CRB} based on orthogonalized versions of the signal's derivatives with respect to the model parameters. This approximation permits singular value decomposition (SVD)-based minimization of both the CRB and signal losses during compression. Compared to the traditional SVD approach, the proposed method better preserves the CRB across all biophysical parameters with negligible cost to the preserved signal energy, leading to reduced bias and variance of the parameter estimates in simulation. In vivo, improved accuracy and precision are observed in two quantitative neuroimaging applications, permitting the use of smaller basis sizes in subspace reconstruction and offering significant computational savings

Generalized Bloch model: a theory for pulsed magnetization transfer

Purpose: The paper introduces a classical model to describe the dynamics of large spin-1/2 ensembles associated with nuclei bound in large molecule structures, commonly referred to as the semi-solid spin pool, and their magnetization transfer (MT) to spins of nuclei in Theory and Methods: Like quantum-mechanical descriptions of spin dynamics and like the original Bloch equations, but unlike existing MT models, the proposed model is based on the algebra of angular momentum in the sense that it explicitly models the rotations induced by radio-frequency (RF) pulses. It generalizes the original Bloch model to non-exponential decays, which are, e.g., observed for semi-solid spin pools. The combination of rotations with non-exponential decays is facilitated by describing the latter as Green's functions, comprised in an integro-differential equation. Results: Our model describes the data of an inversion-recovery magnetization-transfer experiment with varying durations of the inversion pulse substantially better than established models. We made this observation for all measured data, but in particular for pulse durations small than 300$\mu$s. Furthermore, we provide a linear approximation of the generalized Bloch model that reduces the simulation time by approximately a factor 15,000, enabling simulation of the spin dynamics caused by a rectangular RF-pulse in roughly 2$\mu$s. Conclusion: The proposed theory unifies the original Bloch model, Henkelman's steady-state theory for magnetization transfer, and the commonly assumed rotation induced by hard pulses (i.e., strong and infinitesimally short applications of RF fields) and describes experimental data better than previous models

Cram\'er-Rao bound-informed training of neural networks for quantitative MRI

Neural networks are increasingly used to estimate parameters in quantitative MRI, in particular in magnetic resonance fingerprinting. Their advantages over the gold standard non-linear least square fitting are their superior speed and their immunity to the non-convexity of many fitting problems. We find, however, that in heterogeneous parameter spaces, i.e. in spaces in which the variance of the estimated parameters varies considerably, good performance is hard to achieve and requires arduous tweaking of the loss function, hyper parameters, and the distribution of the training data in parameter space. Here, we address these issues with a theoretically well-founded loss function: the Cram\'er-Rao bound (CRB) provides a theoretical lower bound for the variance of an unbiased estimator and we propose to normalize the squared error with respective CRB. With this normalization, we balance the contributions of hard-to-estimate and not-so-hard-to-estimate parameters and areas in parameter space, and avoid a dominance of the former in the overall training loss. Further, the CRB-based loss function equals one for a maximally-efficient unbiased estimator, which we consider the ideal estimator. Hence, the proposed CRB-based loss function provides an absolute evaluation metric. We compare a network trained with the CRB-based loss with a network trained with the commonly used means squared error loss and demonstrate the advantages of the former in numerical, phantom, and in vivo experiments.Comment: Xiaoxia Zhang, Quentin Duchemin, and Kangning Liu contributed equally to this wor

On multi-path longitudinal spin relaxation in brain tissue

The purpose of this paper is to confirm previous reports that identified magnetization transfer (MT) as an inherent driver of longitudinal relaxation in brain tissue by asserting a substantial difference between the $T_1$ relaxation times of the free and the semi-solid spin pools. Further, we aim to identify an avenue towards the quantification of these relaxation processes on a voxel-by-voxel basis in a clinical imaging setting, i.e. with a nominal resolution of 1mm isotropic and full brain coverage in 12min. To this end, we optimized a hybrid-state pulse sequence for mapping the parameters of an unconstrained MT model. We scanned 4 people with relapsing-remitting multiple sclerosis (MS) and 4 healthy controls with this pulse sequence and estimated $T_1^f \approx 1.90$s and $T_1^s \approx 0.327$s for the free and semi-solid spin pool of healthy WM, respectively, confirming previous reports and questioning the commonly used assumptions $T_1^s = T_1^f$ or $T_1^s = 1$s. Further, we estimated a fractional size of the semi-solid spin pool of $m_0^s \approx 0.202$, which is larger than previously assumed. An analysis of $T_1^f$ in normal appearing white matter revealed statistically significant differences between individuals with MS and controls. In conclusion, we confirm that longitudinal spin relaxation in brain tissue is dominated by MT and that the hybrid state facilitates a voxel-wise fit of the unconstrained MT model, which enables the analysis of subtle neurodegeneration

Das Bedingungslose Grundeinkommen - ein tragfähiges Konzept?

In der Schweiz betreibt eine Initiative aktuell ganz konkret einen Volksentscheid mit dem Ziel, ein bedingungsloses Grundeinkommen einzuführen. In Deutschland wird das Konzept lebhaft diskutiert. Allerdings wird seine Wirkung auf Beschäftigung, Besteuerung, Einkommensverteilung und die Bereitstellung von staatlichen Leistungen ganz unterschiedlich beurteilt.The introduction of an unconditional basic income has been discussed in Switzerland for many years. Germany, however, takes a sceptical view of this idea. The authors of this 'Zeitgespräch' express disparate opinions on how broadly the concept should be defined, but they agree on the motive behind the concept: respect for human dignity. Moreover, it may make many social policy rules obsolete. There are conflicting opinions concerning the reaction of labour supply to the unconditional basic income. Some authors fear that it will shrink substantially. But its financing will be the main problem. There are proposals to increase the value added tax rate. The economic impacts of funding it by income tax revenues are analysed using a macroeconomic model. Ultimately, the implementation of the concept will have distributional effects which are very difficult to predict

Rapid quantitative magnetization transfer imaging: utilizing the hybrid state and the generalized Bloch model

Purpose: To improve spatial resolution and scan time of quantitative magnetization transfer (qMT) imaging without constraints on model parameters. Theory and Methods: We combine two recently-proposed models in a Bloch-McConnell equation: the dynamics of the free spin pool is confined to the hybrid state and the dynamics of the semi-solid spin pool is described by the generalized Bloch model. We numerically optimize the flip angles and durations of a train of radio frequency pulses to enhance the encoding of three marked qMT parameters while accounting for an 8-parameter model. We sparsely sample each time frame along this spin dynamics with a 3D radial koosh-ball trajectory, reconstruct the data with sub-space modeling, and fit the qMT model with a neural network for computational efficiency. Results: We were able to extract qMT parameter maps of the whole brain with a nominal resolution of 1mm isotropic and high SNR from a 12.6 minute scan. In lesions of multiple sclerosis subjects, we observe a decreased size of the semi-solid spin pool and slower relaxation, consistent with previous reports. Conclusion: The encoding power of the hybrid state, combined with regularized image reconstruction, and the accuracy of the generalized Bloch model provide an excellent basis for highly efficient quantitative magnetization transfer imaging

Minimization of Eddy Current Artifacts in Sequences with Periodic Dynamics

Purpose: To minimize eddy-current artifacts in periodic pulse sequences with balanced gradient moments as, e.g., used for quantitative MRI. Theory and Methods: Eddy current artifacts in balanced sequences result from large jumps in k-space. In quantitative MRI, one often samples some spin dynamics repeatedly while acquiring different parts of k-space. We swap individual k-space lines between different repetitions in order to minimize jumps within each repetition. This reordering can be formulated as a travelling salesman problem and we tackle the discrete optimization with a simulated annealing algorithm. Results: The proposed approach is highly effective at minimizing the change of the readout direction of a 3D koosh-ball trajectory. This decreases the eddy-current induced perturbations of the magnetization and reduces artifacts in the derived parameter maps, as demonstrated in the example of a hybrid-state free precession sequence. Conclusion: Beyond this example application, we believe that the approach can be used for most k-space trajectories, other quantitative MRI methods, as well as for cine cardiac imaging.Comment: 7 pages, 5 figure

Generalized Bloch model: A theory for pulsed magnetization transfer

PurposeThe paper introduces a classical model to describe the dynamics of large spin-1/2 ensembles associated with nuclei bound in large molecule structures, commonly referred to as the semi-solid spin pool, and their magnetization transfer (MT) to spins of nuclei in water.Theory and methodsLike quantum-mechanical descriptions of spin dynamics and like the original Bloch equations, but unlike existing MT models, the proposed model is based on the algebra of angular momentum in the sense that it explicitly models the rotations induced by radiofrequency (RF) pulses. It generalizes the original Bloch model to non-exponential decays, which are, for example, observed for semi-solid spin pools. The combination of rotations with non-exponential decays is facilitated by describing the latter as Green's functions, comprised in an integro-differential equation.ResultsOur model describes the data of an inversion-recovery magnetization-transfer experiment with varying durations of the inversion pulse substantially better than established models. We made this observation for all measured data, but in particular for pulse durations smaller than 300 μs. Furthermore, we provide a linear approximation of the generalized Bloch model that reduces the simulation time by approximately a factor 15,000, enabling simulation of the spin dynamics caused by a rectangular RF-pulse in roughly 2 μs.ConclusionThe proposed theory unifies the original Bloch model, Henkelman's steady-state theory for MT, and the commonly assumed rotation induced by hard pulses (i.e., strong and infinitesimally short applications of RF-fields) and describes experimental data better than previous models