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.
CramÃ©r-Rao bound-informed training of neural networks for quantitative MRI
PURPOSE/OBJECTIVE:To improve the performance of neural networks for parameter estimation in quantitative MRI, in particular when the noise propagation varies throughout the space of biophysical parameters. THEORY AND METHODS/METHODS:A theoretically well-founded loss function is proposed that normalizes the squared error of each estimate with respective CramÃ©r-Rao bound (CRB)-a theoretical lower bound for the variance of an unbiased estimator. This avoids a dominance of hard-to-estimate parameters and areas in parameter space, which are often of little interest. The normalization with corresponding CRB balances the large errors of fundamentally more noisy estimates and the small errors of fundamentally less noisy estimates, allowing the network to better learn to estimate the latter. Further, proposed loss function provides an absolute evaluation metric for performance: A network has an average loss of 1 if it is a maximally efficient unbiased estimator, which can be considered the ideal performance. The performance gain with proposed loss function is demonstrated at the example of an eight-parameter magnetization transfer model that is fitted to phantom and in vivo data. RESULTS:Networks trained with proposed loss function perform close to optimal, that is, their loss converges to approximately 1, and their performance is superior to networks trained with the standard mean-squared error (MSE). The proposed loss function reduces the bias of the estimates compared to the MSE loss, and improves the match of the noise variance to the CRB. This performance gain translates to in vivo maps that align better with the literature. CONCLUSION/CONCLUSIONS:Normalizing the squared error with the CRB during the training of neural networks improves their performance in estimating biophysical parameters.
Generalized Bloch model: A theory for pulsed magnetization transfer
PURPOSE/OBJECTIVE: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 water. THEORY AND METHODS/UNASSIGNED: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 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. 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 smaller than 300Â Î¼s. 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 2Â Î¼s. CONCLUSION/CONCLUSIONS:The 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.
A Perspective on MR Fingerprinting
This article reviews the basic concept of MR fingerprinting (MRF) with the goal of highlighting MRF's key contributions, putting them in the context of other quantitative MRI literature, and refining MRF's terminology. The article discusses the robustness and flexibility of MRF's signature dictionary-matching reconstruction along with more advanced MRF reconstructions. A key feature of MRF is the lack of assumptions about the signal evolution, which gives scientists the flexibility to tailor sequences for their needs. The article argues that the concept of unique fingerprints does not capture the requirements for successful parameter mapping and that an analysis of the signal's derivatives with respect to biophysical parameters, such as relaxation times, is more informative, as it allows one to evaluate the efficiency of a pulse sequence. The article points at the source of MRF's efficiency, namely, flip angle variations at the time scale of the relaxation times, and reveals that MRF's advantages are strongest at long scan times, as required for 3D imaging. Further, it outlines how MRF's flexibility can be used to design mutually tailored pulse sequences and biophysical models with the goal of improving the reproducibility of parameter mapping biological tissue. LEVEL OF EVIDENCE: 5 TECHNICAL EFFICACY STAGE: 1.
Optimized quantification of spin relaxation times in the hybrid state
PURPOSE/OBJECTIVE:The optimization and analysis of spin ensemble trajectories in the hybrid state-a state in which the direction of the magnetization adiabatically follows the steady state while the magnitude remains in a transient state. METHODS: RESULTS: CONCLUSIONS:
Rapid Radial T1 and T2 Mapping of the Hip Articular Cartilage With Magnetic Resonance Fingerprinting
BACKGROUND:Quantitative MRI can detect early changes in cartilage biochemical components, but its routine clinical implementation is challenging. PURPOSE/OBJECTIVE:along radial sections of the hip for accurate and reproducible multiparametric quantitative cartilage assessment in a clinically feasible scan time. STUDY TYPE/METHODS:Reproducibility, technical validation. SUBJECTS/PHANTOM/UNASSIGNED:A seven-compartment phantom and three healthy volunteers. FIELD STRENGTH/SEQUENCE/UNASSIGNED:at 3 T was developed. Automatic positioning and semiautomatic cartilage segmentation were implemented to improve consistency and simplify workflow. ASSESSMENT/RESULTS:Intra- and interscanner variability of our technique was assessed over multiple scans on three different MR scanners. STATISTICAL TESTS/UNASSIGNED:over six radial slices was calculated. Restricted maximum likelihood estimation of variance components was used to estimate intrasubject variances reflecting variation between results from the two scans using the same scanner (intrascanner variance) and variation among results from the three scanners (interscanner variance). RESULTS:. DATA CONCLUSION/UNASSIGNED:Our method, which includes slice positioning, model-based parameter estimation, and cartilage segmentation, is highly reproducible. It could enable employing quantitative hip cartilage evaluation for longitudinal and multicenter studies. LEVEL OF EVIDENCE/METHODS:1 Technical Efficacy: Stage 1 J. Magn. Reson. Imaging 2018.
Hybrid-state free precession in nuclear magnetic resonance
The dynamics of large spin-1/2 ensembles are commonly described by the Bloch equation, which is characterized by the magnetization's non-linear response to the driving magnetic field. Consequently, most magnetic field variations result in non-intuitive spin dynamics, which are sensitive to small calibration errors. Although simplistic field variations result in robust spin dynamics, they do not explore the richness of the system's phase space. Here, we identify adiabaticity conditions that span a large experiment design space with tractable dynamics. All dynamics are trapped in a one-dimensional subspace, namely in the magnetization's absolute value, which is in a transient state, while its direction adiabatically follows the steady state. In this hybrid state, the polar angle is the effective drive of the spin dynamics. As an example, we optimize this drive for robust and efficient quantification of spin relaxation times and utilize it for magnetic resonance imaging of the human brain.
Exploring the sensitivity of magnetic resonance fingerprinting to motion
PURPOSE/OBJECTIVE:To explore the motion sensitivity of magnetic resonance fingerprinting (MRF), we performed experiments with different types of motion at various time intervals during multiple scans. Additionally, we investigated the possibility to correct the motion artifacts based on redundancy in MRF data. METHODS:A radial version of the FISP-MRF sequence was used to acquire one transverse slice through the brain. Three subjects were instructed to move in different patterns (in-plane rotation, through-plane wiggle, complex movements, adjust head position, and pretend itch) during different time intervals. The potential to correct motion artifacts in MRF by removing motion-corrupted data points from the fingerprints and dictionary was evaluated. RESULTS:values (-10% on average). CONCLUSION/CONCLUSIONS:Our experimental results showed that different kinds of motion have distinct effects on the precision and effective resolution of the parametric maps measured with MRF. Although MRF-based acquisitions can be relatively robust to motion effects occurring at the beginning or end of the sequence, relying on redundancy in the data alone is not sufficient to assure the accuracy of the multi-parametric maps in all cases.
Multicompartment Magnetic Resonance Fingerprinting
Magnetic resonance fingerprinting (MRF) is a technique for quantitative estimation of spin- relaxation parameters from magnetic-resonance data. Most current MRF approaches assume that only one tissue is present in each voxel, which neglects intravoxel structure, and may lead to artifacts in the recovered parameter maps at boundaries between tissues. In this work, we propose a multicompartment MRF model that accounts for the presence of multiple tissues per voxel. The model is fit to the data by iteratively solving a sparse linear inverse problem at each voxel, in order to express the measured magnetization signal as a linear combination of a few elements in a precomputed fingerprint dictionary. Thresholding-based methods commonly used for sparse recovery and compressed sensing do not perform well in this setting due to the high local coherence of the dictionary. Instead, we solve this challenging sparse-recovery problem by applying reweighted-ð“1-norm regularization, implemented using an efficient interior-point method. The proposed approach is validated with simulated data at different noise levels and undersampling factors, as well as with a controlled phantom-imaging experiment on a clinical magnetic-resonance system.
Phase unwinding for dictionary compression with multiple channel transmission in magnetic resonance fingerprinting
PURPOSE/OBJECTIVE:Magnetic Resonance Fingerprinting reconstructions can become computationally intractable with multiple transmit channels, if the B1+ phases are included in the dictionary. We describe a general method that allows to omit the transmit phases. We show that this enables straightforward implementation of dictionary compression to further reduce the problem dimensionality. METHODS:We merged the raw data of each RF source into a single k-space dataset, extracted the transceiver phases from the corresponding reconstructed images and used them to unwind the phase in each time frame. All phase-unwound time frames were combined in a single set before performing SVD-based compression. We conducted synthetic, phantom and in-vivo experiments to demonstrate the feasibility of SVD-based compression in the case of two-channel transmission. RESULTS:Unwinding the phases before SVD-based compression yielded artifact-free parameter maps. For fully sampled acquisitions, parameters were accurate with as few as 6 compressed time frames. SVD-based compression performed well in-vivo with highly under-sampled acquisitions using 16 compressed time frames, which reduced reconstruction time from 750 to 25min. CONCLUSION/CONCLUSIONS:Our method reduces the dimensions of the dictionary atoms and enables to implement any fingerprint compression strategy in the case of multiple transmit channels.