Sensitivity of unconstrained quantitative magnetization transfer MRI to Amyloid burden in preclinical Alzheimer's disease.

Introduction: Magnetization transfer MRI is sensitive to semi-solid macromolecules, including amyloid beta, and has been used to discriminate Alzheimer's disease (AD) patients from controls. Here, we utilize an unconstrained 2-pool quantitative MT (qMT) approach that quantifies the longitudinal relaxation rates of free water and semi-solids separately, and investigate its sensitivity to amyloid accumulation in preclinical subjects. Methods: We recruited 15 cognitively normal subjects, of which nine were amyloid positive by [ 18 F]Florbetaben PET. A 12 min qMT scan was used to estimate the unconstrained 2-pool qMT parameters. Group comparisons and correlations were analyzed at the lobar level. Results: The exchange rate and semi-solid pool's were sensitive to the amyloid concentration. The former finding is consistent with previous reports in clinical AD, but the latter is novel as its value is typically constrained. Discussion: qMT MRI may be a promising surrogate marker of amyloid beta without the need for contrast agents or radiotracers.

Bias-reduced neural networks for parameter estimation in quantitative MRI.

PURPOSE: To develop neural network (NN)-based quantitative MRI parameter estimators with minimal bias and a variance close to the Cramér-Rao bound. THEORY AND METHODS: We generalize the mean squared error loss to control the bias and variance of the NN's estimates, which involves averaging over multiple noise realizations of the same measurements during training. Bias and variance properties of the resulting NNs are studied for two neuroimaging applications. RESULTS: In simulations, the proposed strategy reduces the estimates' bias throughout parameter space and achieves a variance close to the Cramér-Rao bound. In vivo, we observe good concordance between parameter maps estimated with the proposed NNs and traditional estimators, such as nonlinear least-squares fitting, while state-of-the-art NNs show larger deviations. CONCLUSION: The proposed NNs have greatly reduced bias compared to those trained using the mean squared error and offer significantly improved computational efficiency over traditional estimators with comparable or better accuracy.

Bias-Reduced Neural Networks for Parameter Estimation in Quantitative MRI.

Purpose: To develop neural network (NN)-based quantitative MRI parameter estimators with minimal bias and a variance close to the Cramér-Rao bound. Theory and Methods: We generalize the mean squared error loss to control the bias and variance of the NN's estimates, which involves averaging over multiple noise realizations of the same measurements during training. Bias and variance properties of the resulting NNs are studied for two neuroimaging applications. Results: In simulations, the proposed strategy reduces the estimates' bias throughout parameter space and achieves a variance close to the Cramér-Rao bound. In vivo, we observe good concordance between parameter maps estimated with the proposed NNs and traditional estimators, such as non-linear least-squares fitting, while state-of-the-art NNs show larger deviations. Conclusion: The proposed NNs have greatly reduced bias compared to those trained using the mean squared error and offer significantly improved computational efficiency over traditional estimators with comparable or better accuracy.

Unconstrained quantitative magnetization transfer imaging: disentangling T1 of the free and semi-solid spin pools.

Since the inception of magnetization transfer (MT) imaging, it has been widely assumed that Henkelman's two spin pools have similar longitudinal relaxation times, which motivated many researchers to constrain them to each other. However, several recent publications reported a T1s of the semi-solid spin pool that is much shorter than T1f of the free pool. While these studies tailored experiments for robust proofs-of-concept, we here aim to quantify the disentangled relaxation processes on a voxel-by-voxel basis in a clinical imaging setting, i.e., with an effective resolution of 1.24mm 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 four people with relapsing-remitting multiple sclerosis (MS) and four healthy controls with this pulse sequence and estimated T1f≈1.84s and T1s≈0.34s in healthy white matter. Our results confirm the reports that T1s≪T1f and we argue that this finding identifies MT as an inherent driver of longitudinal relaxation in brain tissue. Moreover, we estimated a fractional size of the semi-solid spin pool of m0s≈0.212, which is larger than previously assumed. An analysis of T1f in normal-appearing white matter revealed statistically significant differences between individuals with MS and controls.

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

PURPOSE: To explore efficient encoding schemes for quantitative magnetization transfer (qMT) imaging with few 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 are confined to the hybrid state, and the dynamics of the semi-solid spin pool are 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 qMT parameters while accounting for all eight parameters of the two-pool model. We sparsely sample each time frame along this spin dynamics with a three-dimensional radial koosh-ball trajectory, reconstruct the data with subspace modeling, and fit the qMT model with a neural network for computational efficiency. RESULTS: We extracted qMT parameter maps of the whole brain with an effective resolution of 1.24 mm from a 12.6-min scan. In lesions of multiple sclerosis subjects, we observe a decreased size of the semi-solid spin pool and longer relaxation times, 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 efficient quantitative magnetization transfer imaging with few constraints on model parameters.

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, for example, 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 in temporal succession without changing the overall trajectory. This reordering can be formulated as a traveling salesman problem and we tackle the discrete optimization with a simulated annealing algorithm. RESULTS: Compared to the default ordering, we observe a substantial reduction of artifacts in the reconstructed images and the derived quantitative parameter maps. Comparing two variants of our algorithm, one that resembles the pairing approach originally proposed by Bieri et al., and one that minimizes all k-space jumps equally, we observe slightly lower artifact levels in the latter. CONCLUSION: The proposed reordering scheme effectively reduces eddy current artifacts in sequences with balanced gradient moments. In contrast to previous approaches, we capitalize on the periodicity of the sampled signal dynamics, enabling both efficient k-space sampling and minimizing artifacts caused by eddy currents.

Cramér-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 Cramér-Rao bound (CRB) of the biophysical parameters and, ultimately, improve accuracy and precision in the quantitative maps. To this end, we introduce an 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.

Cramér-Rao bound-informed training of neural networks for quantitative MRI.

PURPOSE: 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: A theoretically well-founded loss function is proposed that normalizes the squared error of each estimate with respective Cramér-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: 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: 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: 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 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. CONCLUSION: 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.

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.

Optimized quantification of spin relaxation times in the hybrid state.

PURPOSE: 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: Numerical optimizations were performed to find spin ensemble trajectories that minimize the Cramér-Rao bound for T1 -encoding, T2 -encoding, and their weighted sum, respectively, followed by a comparison between the Cramér-Rao bounds obtained with our optimized spin-trajectories, Look-Locker sequences, and multi-spin-echo methods. Finally, we experimentally tested our optimized spin trajectories with in vivo scans of the human brain. RESULTS: After a nonrecurring inversion segment on the southern half of the Bloch sphere, all optimized spin trajectories pursue repetitive loops on the northern hemisphere in which the beginning of the first and the end of the last loop deviate from the others. The numerical results obtained in this work align well with intuitive insights gleaned directly from the governing equation. Our results suggest that hybrid-state sequences outperform traditional methods. Moreover, hybrid-state sequences that balance T1 - and T2 -encoding still result in near optimal signal-to-noise efficiency for each relaxation time. Thus, the second parameter can be encoded at virtually no extra cost. CONCLUSIONS: We provided new insights into the optimal encoding processes of spin relaxation times in order to guide the design of robust and efficient pulse sequences. We found that joint acquisitions of T1 and T2 in the hybrid state are substantially more efficient than sequential encoding techniques.

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: To introduce a novel technique to measure T1 and T2 along radial sections of the hip for accurate and reproducible multiparametric quantitative cartilage assessment in a clinically feasible scan time. STUDY TYPE: Reproducibility, technical validation. SUBJECTS/PHANTOM: A seven-compartment phantom and three healthy volunteers. FIELD STRENGTH/SEQUENCE: A novel MR pulse sequence that simultaneously measures proton density (PD), T1 , and T2 at 3 T was developed. Automatic positioning and semiautomatic cartilage segmentation were implemented to improve consistency and simplify workflow. ASSESSMENT: Intra- and interscanner variability of our technique was assessed over multiple scans on three different MR scanners. STATISTICAL TESTS: For each scan, the median of cartilage T1 and T2 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: The estimation error for T1 and T2 with respect to reference standard measurements was less than 3% on average for the phantom. The average interscanner coefficient of variation was 1.5% (1.2-1.9%) and 0.9% (0.0-3.7%) for T1 and T2 , respectively, in the seven compartments of the phantom. Total scan time in vivo was 7:13 minutes to obtain PD, T1 , and T2 maps along six radial hip sections at 0.6 × 0.6 × 4.0 mm3 voxel resolution. Interscanner variability for the in vivo study was 1.99% and 5.46% for T1 and T2 , respectively. in vivo intrascanner variability was 1.15% for T1 and 3.24% for T2 . DATA CONCLUSION: 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: 1 Technical Efficacy: Stage 1 J. Magn. Reson. Imaging 2019;50:810-815.

Exploring the sensitivity of magnetic resonance fingerprinting to motion.

PURPOSE: 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: Morphological structures were well preserved in multi-parametric maps despite subject motion. Although the bulk T1 values were not significantly affected by motion, fine structures were blurred when in-plane motion was present during the first part of the scan. On the other hand, T2 values showed a considerable deviation from the motion-free results, especially when through-plane motion was present in the middle of the scan (-44% on average). Explicitly removing the motion-corrupted data from the scan partially restored the T2 values (-10% on average). CONCLUSION: 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-𝓁1-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.

Application of spin echoes in the regime of weak dephasing to T1 -mapping of the lung.

PURPOSE: This work presents an approach to mapping the entire lung's proton density and T1 within a single breath-hold and analyzes the apparent T1 when exciting with a spin echo generating pulse in comparison to a standard gradient echo acquisition. METHODS: An inversion-recovery SNAPSHOT-FLASH sequence with a stack-of-stars k-space readout with a golden angle increment was modified to use a spin echo generating radiofrequency-pulse for excitation. Data of five volunteers were acquired on a 3T scanner and image reconstruction was performed by an iterative algorithm adopted from MR-Fingerprinting. RESULTS: The feasibility of acquiring quantitative maps of the entire lung with a resolution of 5 × 5 × 10 mm within 7.5 s is demonstrated. It is shown that the proposed spin echo forming radiofrequency-pulse increases the apparent proton density compared to a rectangular pulse. Further, the apparent T1 is reduced in the spin echo case compared to the gradient echo sequence. CONCLUSION: The proposed spin echo based method results in T1 maps that are comparable to the ones that were acquired with ultra-short echo time sequences elsewhere. The T1 shortening is believed to originate from increased signal contributions of the extra vascular compartment, which has a short T2∗ and T1 . Magn Reson Med 79:960-967, 2018. © 2017 International Society for Magnetic Resonance in Medicine.

Low rank alternating direction method of multipliers reconstruction for MR fingerprinting.

PURPOSE: The proposed reconstruction framework addresses the reconstruction accuracy, noise propagation and computation time for magnetic resonance fingerprinting. METHODS: Based on a singular value decomposition of the signal evolution, magnetic resonance fingerprinting is formulated as a low rank (LR) inverse problem in which one image is reconstructed for each singular value under consideration. This LR approximation of the signal evolution reduces the computational burden by reducing the number of Fourier transformations. Also, the LR approximation improves the conditioning of the problem, which is further improved by extending the LR inverse problem to an augmented Lagrangian that is solved by the alternating direction method of multipliers. The root mean square error and the noise propagation are analyzed in simulations. For verification, in vivo examples are provided. RESULTS: The proposed LR alternating direction method of multipliers approach shows a reduced root mean square error compared to the original fingerprinting reconstruction, to a LR approximation alone and to an alternating direction method of multipliers approach without a LR approximation. Incorporating sensitivity encoding allows for further artifact reduction. CONCLUSION: The proposed reconstruction provides robust convergence, reduced computational burden and improved image quality compared to other magnetic resonance fingerprinting reconstruction approaches evaluated in this study. Magn Reson Med 79:83-96, 2018. © 2017 International Society for Magnetic Resonance in Medicine.

Phase unwinding for dictionary compression with multiple channel transmission in magnetic resonance fingerprinting.

PURPOSE: 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: Our method reduces the dimensions of the dictionary atoms and enables to implement any fingerprint compression strategy in the case of multiple transmit channels.

Pseudo Steady-State Free Precession for MR-Fingerprinting.

PURPOSE: This article discusses the signal behavior in the case the flip angle in steady-state free precession sequences is continuously varied as suggested for MR-fingerprinting sequences. Flip angle variations prevent the establishment of a steady state and introduce instabilities regarding to magnetic field inhomogeneities and intravoxel dephasing. We show how a pseudo steady state can be achieved, which restores the spin echo nature of steady-state free precession. METHODS: Based on geometrical considerations, relationships between the flip angle, repetition and echo time are derived that suffice to the establishment of a pseudo steady state. The theory is tested with Bloch simulations as well as phantom and in vivo experiments. RESULTS: A typical steady-state free precession passband can be restored with the proposed conditions. The stability of the pseudo steady state is demonstrated by comparing the evolution of the signal of a single isochromat to one resulting from a spin ensemble. As confirmed by experiments, magnetization in a pseudo steady state can be described with fewer degrees of freedom compared to the original fingerprinting and the pseudo steady state results in more reliable parameter maps. CONCLUSION: The proposed conditions restore the spin-echo-like signal behavior typical for steady-state free precession in fingerprinting sequences, making this approach more robust to B0 variations. Magn Reson Med 77:1151-1161, 2017. © 2016 International Society for Magnetic Resonance in Medicine.

Spin echoes in the regime of weak dephasing.

PURPOSE: This article analyzes possibilities and limits of spin echoes beyond Hahn's theory. The regime of weak dephasing is explored with the purpose of combining the enhanced signal and reduced artifacts of spin echoes with the speed and flexibility of the fast low angle shot sequence. METHODS: In the regime of weak dephasing, an upper boundary of the echo time is derived analytically. This limit is verified with optimal control pulses, which are also used to heuristically examine the transition to Hahn's regime of complete dephasing. The potential of the proposed pulses is demonstrated in proof-of-concept spin echo fast low angle shot images of a volunteer's lung and head. RESULTS: It was found that the time between the end of the pulse and the spin echo can exceed the duration of the composite radio frequency-pulse, which stands in contrast to Hahn echoes where those measures are at most equal. The maximum echo time was found to mainly depend on the total amount of dephasing. In vivo spin echo fast low angle shot images show an increased pulmonary signal as well as reduced artifacts in areas affected by susceptibility differences. CONCLUSION: The spin dynamics in the regime of weak dephasing was investigated and the feasibility of spin echo fast low angle shot imaging was demonstrated in vivo.