Joint system relaxometry (JSR) and Crámer-Rao lower bound optimization of sequence parameters: A framework for enhanced precision of DESPOT T1 and T2 estimation

In vivo T2 measurements of the fetal brain using single-shot fast spin echo sequences

PURPOSE

We propose a quantitative framework for motion-corrected T2 fetal brain measurements in vivo and validate the single-shot fast spin echo (SS-FSE) sequence to perform these measurements.

METHODS

Stacks of two-dimensional SS-FSE slices are acquired with different echo times (TE) and motion-corrected with slice-to-volume reconstruction (SVR). The quantitative T2 maps are obtained by a fit to a dictionary of simulated signals. The sequence is selected using simulated experiments on a numerical phantom and validated on a physical phantom scanned on a 1.5T system. In vivo quantitative T2 maps are obtained for five fetuses with gestational ages (GA) 21-35 weeks on the same 1.5T system.

RESULTS

The simulated experiments suggested that a TE of 400 ms combined with the clinically utilized TEs of 80 and 180 ms were most suitable for T2 measurements in the fetal brain. The validation on the physical phantom confirmed that the SS-FSE T2 measurements match the gold standard multi-echo spin echo measurements. We measured average T2s of around 200 and 280 ms in the fetal brain grey and white matter, respectively. This was slightly higher than fetal T2* and the neonatal T2 obtained from previous studies.

CONCLUSION

The motion-corrected SS-FSE acquisitions with varying TEs offer a promising practical framework for quantitative T2 measurements of the moving fetus.

Widespread, depth-dependent cortical microstructure alterations in pediatric focal epilepsy

OBJECTIVE

Tissue abnormalities in focal epilepsy may extend beyond the presumed focus. The underlying pathophysiology of these broader changes is unclear, and it is not known whether they result from ongoing disease processes or treatment-related side effects, or whether they emerge earlier. Few studies have focused on the period of onset for most focal epilepsies, childhood. Fewer still have utilized quantitative magnetic resonance imaging (MRI), which may provide a more sensitive and interpretable measure of tissue microstructural change. Here, we aimed to determine common spatial modes of changes in cortical architecture in children with heterogeneous drug-resistant focal epilepsy and, secondarily, whether changes were related to disease severity.

METHODS

To assess cortical microstructure, quantitative T1 and T2 relaxometry (qT1 and qT2) was measured in 43 children with drug-resistant focal epilepsy (age range = 4-18 years) and 46 typically developing children (age range = 2-18 years). We assessed depth-dependent qT1 and qT2 values across the neocortex, as well as their gradient of change across cortical depths. We also determined whether global changes seen in group analyses were driven by focal pathologies in individual patients. Finally, as a proof-of-concept, we trained a classifier using qT1 and qT2 gradient maps from patients with radiologically defined abnormalities (MRI positive) and healthy controls, and tested whether this could classify patients without reported radiological abnormalities (MRI negative).

RESULTS

We uncovered depth-dependent qT1 and qT2 increases in widespread cortical areas in patients, likely representing microstructural alterations in myelin or gliosis. Changes did not correlate with disease severity measures, suggesting they may represent antecedent neurobiological alterations. Using a classifier trained with MRI-positive patients and controls, sensitivity was 71.4% at 89.4% specificity on held-out MRI-negative patients.

SIGNIFICANCE

These findings suggest the presence of a potential imaging endophenotype of focal epilepsy, detectable irrespective of radiologically identified abnormalities.

Fast and robust quantification of uncertainty in non-linear diffusion MRI models

Diffusion MRI (dMRI) allows for non-invasive investigation of brain tissue microstructure. By fitting a model to the dMRI signal, various quantitative measures can be derived from the data, such as fractional anisotropy, neurite density and axonal radii maps. We investigate the Fisher Information Matrix (FIM) and uncertainty propagation as a generally applicable method for quantifying the parameter uncertainties in linear and non-linear diffusion MRI models. In direct comparison with Markov Chain Monte Carlo (MCMC) sampling, the FIM produces similar uncertainty estimates at much lower computational cost. Using acquired and simulated data, we then list several characteristics that influence the parameter variances, including data complexity and signal-to-noise ratio. For practical purposes we investigate a possible use of uncertainty estimates in decreasing intra-group variance in group statistics by uncertainty-weighted group estimates. This has potential use cases for detection and suppression of imaging artifacts.

SIMPLEX: Multiple phase-cycled bSSFP quantitative magnetization transfer imaging with physic-guided simulation learning of neural network

Most quantitative magnetization transfer (qMT) imaging methods require acquiring additional quantitative maps (such as T1) for data fitting. A method based on multiple phase-cycled bSSFP was recently proposed to enable high-resolution 3D qMT imaging based on least square fitting without any extra acquisition, and thus has high potential for simplifying the qMT procedure. However, the quantification of qMT parameters with this method was suboptimal, limiting its potential for clinical application despite its simpler protocol and higher spatial resolution. To improve the fitting of qMT data obtained with multiple phase-cycled bSSFP, we propose SIMulation-based Physics-guided Learning of neural network for qMT parameters EXtraction, or SIMPLEX. In contrast to previous deep learning supervised approaches for quantitative MR that require the acquisition of input data and corresponding ground truth for training, we leveraged the MR signal model to generate training samples without expensive data curation. The network was trained exclusively with simulation data by predicting the simulation parameters. The same network was applied directly to in-vivo data without additional training. The approach was verified with both simulation and in-vivo data. SIMPLEX showed a decrease in fitting mean squared error for all simulation data compared to the existing least-square fitting method. The in-vivo experiment revealed that the network performed well with the real in vivo data unseen during training. For all experiments, we observed that SIMPLEX consistently improved the quantification quality of the qMT parameters whilst being more robust to noise compared to the prior technique. The proposed SIMPLEX will expedite the routine clinical application of qMT by providing qMT parameters (exchange rate, pool fraction) as well as T1, T2, and ΔB0 maps simultaneously with high spatial resolution, better reliability, and reduced processing time.

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.

Optimization of spin-lock times in T1ρ mapping of knee cartilage: Cramér-Rao bounds versus matched sampling-fitting

PURPOSE

To compare different optimization approaches for choosing the spin-lock times (TSLs), in spin-lattice relaxation time in the rotating frame (T_1ρ ) mapping.

METHODS

Optimization criteria for TSLs based on Cramér-Rao lower bounds (CRLB) are compared with matched sampling-fitting (MSF) approaches for T_1ρ mapping on synthetic data, model phantoms, and knee cartilage. The MSF approaches are optimized using robust methods for noisy cost functions. The MSF approaches assume that optimal TSLs depend on the chosen fitting method. An iterative non-linear least squares (NLS) and artificial neural networks (ANN) are tested as two possible T_1ρ fitting methods for MSF approaches.

RESULTS

All optimized criteria were better than non-optimized ones. However, we observe that a modified CRLB and an MSF based on the mean of the normalized absolute error (MNAE) were more robust optimization approaches, performing well in all tested cases. The optimized TSLs obtained the best performance with synthetic data (3.5-8.0% error), model phantoms (1.5-2.8% error), and healthy volunteers (7.7-21.1% error), showing stable and improved quality results, comparing to non-optimized approaches (4.2-13.3% error on synthetic data, 2.1-6.2% error on model phantoms, 9.8-27.8% error on healthy volunteers).

CONCLUSION

A modified CRLB and the MSF based on MNAE are robust optimization approaches for choosing TSLs in T_1ρ mapping. All optimized criteria allowed good results even using rapid scans with two TSLs when a complex-valued fitting is done with iterative NLS or ANN.

An MR fingerprinting approach for quantitative inhomogeneous magnetization transfer imaging

PURPOSE

Magnetization transfer (MT) and inhomogeneous MT (ihMT) contrasts are used in MRI to provide information about macromolecular tissue content. In particular, MT is sensitive to macromolecules, and ihMT appears to be specific to myelinated tissue. This study proposes a technique to characterize MT and ihMT properties from a single acquisition, producing both semiquantitative contrast ratios and quantitative parameter maps.

THEORY AND METHODS

Building on previous work that uses multiband RF pulses to efficiently generate ihMT contrast, we propose a cyclic steady-state approach that cycles between multiband and single-band pulses to boost the achieved contrast. Resultant time-variable signals are reminiscent of an MR fingerprinting acquisition, except that the signal fluctuations are entirely mediated by MT effects. A dictionary-based low-rank inversion method is used to reconstruct the resulting images and to produce both semiquantitative MT ratio and ihMT ratio maps, as well as quantitative parameter estimates corresponding to an ihMT tissue model.

RESULTS

Phantom and in vivo brain data acquired at 1.5 Tesla demonstrate the expected contrast trends, with ihMT ratio maps showing contrast more specific to white matter, as has been reported by others. Quantitative estimation of semisolid fraction and dipolar T₁ was also possible and yielded measurements consistent with literature values in the brain.

CONCLUSION

By cycling between multiband and single-band pulses, an entirely MT-mediated fingerprinting method was demonstrated. This proof-of-concept approach can be used to generate semiquantitative maps and quantitatively estimate some macromolecular-specific tissue parameters.

Using quantitative MRI to study brain responses to immune challenge with interferon-α

Inflammatory processes in the Central Nervous System (CNS) have been proposed to mediate the association between peripheral inflammation and the development of psychiatric disorders, but we currently lack sensitive measures of CNS inflammation for human studies in vivo. Here we used quantitative MRI (qMRI) to explore the in vivo central response to a peripheral immune challenge in healthy humans, and we assessed whether changes in quantitative relaxometry MRI parameters were associated with changes in peripheral inflammation. Quantitative relaxation times (T1 & T2) and Proton Density (PD) were measured in n ​= ​6 healthy males (mean age ​= ​30.5 ​± ​6.8 years) in two MRI assessments collected before and 24 ​hours after a subcutaneous injection of the proinflammatory cytokine and immune activator, interferon-alpha (IFN-α). Serum levels of immune markers and markers of blood-brain barrier integrity (S100B) were also measured before and after the injection. Region of interest and histogram-based analyses (optimized for the small sample size) showed a statistically significant increase of both T1 (t₍₅₎ ​= ​3.78, p ​= 0.013) and PD (t₍₅₎ ​= ​2.91, p ​= ​0.033) parameters in the bilateral hippocampus after IFN-α administration. T1 peak values in bilateral hippocampus were positively correlated with serum Tumour Necrosis Factor-alpha levels at 24 ​h after the injection, when this cytokine peaked (Spearman's rho ​= ​0.67, p ​= ​0.018) and negatively correlated with S100B levels (Spearman's rho ​= ​-0.826, p ​= ​0.001). Our data suggest that peripheral administration of IFN-α produces acute changes in brain qMRI which might indicate a brain immune response. This is supported by the association of such changes with low-grade peripheral inflammation.

Efficiency analysis for quantitative MRI of T1 and T2 relaxometry methods

This study presents a comparison of quantitative MRI methods based on an efficiency metric that quantifies their intrinsic ability to extract information about tissue parameters. Under a regime of unbiased parameter estimates, an intrinsic efficiency metricηwas derived for fully-sampled experiments which can be used to both optimize and compare sequences. Here we optimize and compare several steady-state and transient gradient-echo based qMRI methods, such as magnetic resonance fingerprinting (MRF), for jointT1andT2mapping. The impact of undersampling was also evaluated, assuming incoherent aliasing that is treated as noise by parameter estimation.In vivovalidation of the efficiency metric was also performed. Transient methods such as MRF can be up to 3.5 times more efficient than steady-state methods, when spatial undersampling is ignored. If incoherent aliasing is treated as noise during least-squares parameter estimation, the efficiency is reduced in proportion to the SNR of the data, with reduction factors of 5 often seen for practical SNR levels.In vivovalidation showed a very good agreement between the theoretical and experimentally predicted efficiency. This work presents and validates an efficiency metric to optimize and compare the performance of qMRI methods. Transient methods were found to be intrinsically more efficient than steady-state methods, however the effect of spatial undersampling can significantly erode this advantage.

Free-breathing abdominal T1 mapping using an optimized MR fingerprinting sequence

In this work, we propose a free-breathing magnetic resonance fingerprinting (MRF) method that can be used to obtain B₁⁺ -robust quantitative T₁ maps of the abdomen in a clinically acceptable time. A three-dimensional MRF sequence with a radial stack-of-stars trajectory was implemented, and its k-space acquisition ordering was adjusted to improve motion-robustness in the context of MRF. The flip angle pattern was optimized using the Cramér-Rao Lower Bound, and the encoding efficiency of sequences with 300, 600, 900 and 1800 flip angles was evaluated. To validate the sequence, a movable multicompartment phantom was developed. Reference multiparametric maps were acquired under stationary conditions using a previously validated MRF method. Periodic motion of the phantom was used to investigate the motion-robustness of the proposed sequence. The best performing sequence length (600 flip angles) was used to image the abdomen during a free-breathing volunteer scan. When using a series of 600 or more flip angles, the estimated T₁ values in the stationary phantom showed good agreement with the reference scan. Phantom experiments revealed that motion-related artifacts can appear in the quantitative maps and confirmed that a motion-robust k-space ordering is essential. The in vivo scan demonstrated that the proposed sequence can produce clean parameter maps while the subject breathes freely. Using this sequence, it is possible to generate B₁⁺ -robust quantitative maps of T₁ and B₁⁺ next to M₀ -weighted images under free-breathing conditions at a clinically usable resolution within 5 min.

MRzero - Automated discovery of MRI sequences using supervised learning

PURPOSE

A supervised learning framework is proposed to automatically generate MR sequences and corresponding reconstruction based on the target contrast of interest. Combined with a flexible, task-driven cost function this allows for an efficient exploration of novel MR sequence strategies.

METHODS

The scanning and reconstruction process is simulated end-to-end in terms of RF events, gradient moment events in x and y, and delay times, acting on the input model spin system given in terms of proton density, T 1 and T 2 , and Δ B 0 . As a proof of concept, we use both conventional MR images and T 1 maps as targets and optimize from scratch using the loss defined by data fidelity, SAR penalty, and scan time.

RESULTS

In a first attempt, MRzero learns gradient and RF events from zero, and is able to generate a target image produced by a conventional gradient echo sequence. Using a neural network within the reconstruction module allows arbitrary targets to be learned successfully. Experiments could be translated to image acquisition at the real system (3T Siemens, PRISMA) and could be verified in the measurements of phantoms and a human brain in vivo.

CONCLUSIONS

Automated MR sequence generation is possible based on differentiable Bloch equation simulations and a supervised learning approach.

Multidimensional correlation spectroscopic imaging of exponential decays: From theoretical principles to in vivo human applications

Multiexponential modeling of relaxation or diffusion MR signal decays is a popular approach for estimating and spatially mapping different microstructural tissue compartments. While this approach can be quite powerful, it is also limited by the fact that one-dimensional multiexponential modeling is an ill-posed inverse problem with substantial ambiguities. In this article, we present an overview of a recent multidimensional correlation spectroscopic imaging approach to this problem. This approach helps to alleviate ill-posedness by making advantageous use of multidimensional contrast encoding (e.g., 2D diffusion-relaxation encoding or 2D relaxation-relaxation encoding) combined with a regularized spatial-spectral estimation procedure. Theoretical calculations, simulations, and experimental results are used to illustrate the benefits of this approach relative to classical methods. In addition, we demonstrate an initial proof-of-principle application of this kind of approach to in vivo human MRI experiments.

High-resolution in vivo MR-STAT using a matrix-free and parallelized reconstruction algorithm

MR-STAT is a recently proposed framework that allows the reconstruction of multiple quantitative parameter maps from a single short scan by performing spatial localisation and parameter estimation on the time-domain data simultaneously, without relying on the fast Fourier transform (FFT). To do this at high resolution, specialized algorithms are required to solve the underlying large-scale nonlinear optimisation problem. We propose a matrix-free and parallelized inexact Gauss-Newton based reconstruction algorithm for this purpose. The proposed algorithm is implemented on a high-performance computing cluster and is demonstrated to be able to generate high-resolution (1 mm  ×  1 mm in-plane resolution) quantitative parameter maps in simulation, phantom, and in vivo brain experiments. Reconstructed T1 and T2 values for the gel phantoms are in agreement with results from gold standard measurements and, for the in vivo experiments, the quantitative values show good agreement with literature values. In all experiments, short pulse sequences with robust Cartesian sampling are used, for which MR fingerprinting reconstructions are shown to fail.

Magnetic resonance fingerprinting review part 2: Technique and directions

Magnetic resonance fingerprinting (MRF) is a general framework to quantify multiple MR-sensitive tissue properties with a single acquisition. There have been numerous advances in MRF in the years since its inception. In this work we highlight some of the recent technical developments in MRF, focusing on sequence optimization, modifications for reconstruction and pattern matching, new methods for partial volume analysis, and applications of machine and deep learning. Level of Evidence: 2 Technical Efficacy: Stage 2 J. Magn. Reson. Imaging 2020;51:993-1007.

Initial assessment of 3D magnetic resonance fingerprinting (MRF) towards quantitative brain imaging for radiation therapy

PURPOSE

Magnetic resonance fingerprinting (MRF) provides quantitative T1/T2 maps, enabling applications in clinical radiotherapy such as large-scale, multi-center clinical trials for longitudinal assessment of therapy response. We evaluated the feasibility of a quantitative three-dimensional-MRF (3D-MRF) towards its radiotherapy applications of primary brain tumors.

METHODS

A fast whole-brain 3D-MRF sequence initially developed for diagnostic radiology was optimized using flexible body coils, which is the typical MR imaging setup for radiotherapy treatment planning and for MR imaging (MRI)-guided treatment delivery. Optimization criteria included the accuracy and the precision of T1/T2 quantifications of polyvinylpyrrolidone (PVP) solutions, compared to those from the 3D-MRF using a 32-channel head coil. The accuracy of T1/T2 quantifications from the optimized MRF was first examined in healthy volunteers with two different coil setups. The intra- and inter-scanner variations of image intensity from the optimized sequence were quantified by longitudinal scans of the PVP solutions on two 3T scanners. Using a 3D-printed MRI geometry phantom, susceptibility-induced distortion with the optimized 3D-MRF was quantified as the Dice coefficient of phantom contours, compared to those from CT images. By introducing intentional head motion during 10% of the scan, the robustness of the optimized 3D-MRF towards motion was evaluated through visual inspection of motion artifacts and through quantitative analysis of image sharpness in brain MRF maps.

RESULTS

The optimized sequence acquired whole-brain T1, T2 and proton density maps and with a resolution of 1.2 × 1.2 × 3 mm³ in 10 min, similar to the total acquisition time of 3D T1- and T2-weighted images of the same resolution. In vivo T1 and T2 values of the white and gray matter were consistent with literature. The intra- and inter-scanner variability of the intensity-normalized MRF T1 was 1.0% ± 0.7% and 2.3% ± 1.0% respectively, in contrast to 5.3% ± 3.8% and 3.2% ± 1.6% from the normalized T1-weighted MRI. Repeatability and reproducibility of MRF T1 were independent of intensity normalization. Both phantom and human data demonstrated that the optimized 3D-MRF is more robust to subject motion and artifacts from subject-specific susceptibility difference. Compared to CT contours, the Dice coefficient of phantom contours from 3D-MRF was 0.93, improved from 0.87 from the T1-weighted MRI.

CONCLUSION

Compared to conventional MRI, the optimized 3D-MRF demonstrated improved repeatability across time points and reproducibility across scanners for better tissue quantification, as well as improved robustness to subject-specific susceptibility and motion artifacts under a typical MR imaging setup for radiotherapy. More importantly, quantitative MRF T1/T2 measurements lead to promising potentials towards longitudinal quantitative assessment of treatment response for better adaptive therapy and for large-scale, multi-center clinical trials.

Controlled saturation magnetization transfer for reproducible multivendor variable flip angle T1 and T2 mapping

Purpose

The widespread clinical application of quantitative MRI has been hindered by a lack of reproducibility across sites and vendors. Previous work has attributed this to incorrect B₁ mapping or insufficient spoiling conditions. We recently proposed the controlled saturation magnetization transfer (CSMT) framework and hypothesized that the lack of reproducibility can also be attributed to magnetization transfer effects. This work seeks to validate this hypothesis and demonstrate that reproducible multivendor single‐pool relaxometry can be achieved with the CSMT approach.

Methods

Three healthy volunteers were scanned on scanners from 3 vendors (GE Healthcare, Philips, Siemens). An extensive set of images necessary for joint T₁ and T₂ estimation were acquired with (1) each vendor default RF pulses and spoiling conditions; (2) harmonized RF spoiling; and (3) harmonized RF spoiling and CSMT pulses. Different subsets of images were used to generate 6 different T₁ and T₂ maps for each subject’s data from each vendor. Cross‐protocol, cross‐vendor, and test/retest variability were estimated.

Results

Harmonized RF spoiling conditions are insufficient to ensure good cross‐vendor reproducibility. Controlled saturation magnetization transfer allows cross‐protocol variability to be reduced from 18.3% to 4.0%. Whole‐brain variability using the same protocol was reduced from a maximum of 19% to 4.5% across sites. Both CSMT and native vendor RF conditions have a reported variability of less than 5% for repeat measures on the same vendor.

Conclusion

Magnetization transfer effects are a major contributor to intersite/intrasite variability of T₁ and T₂ estimation. Controlled saturation magnetization transfer stabilizes these effects, paving the way for the use of single‐pool T₁ and T₂ as a reliable source for clinical diagnosis across sites.

Impact of (k,t) sampling on DCE MRI tracer kinetic parameter estimation in digital reference objects

Purpose

To evaluate the impact of (k,t) data sampling on the variance of tracer‐kinetic parameter (TK) estimation in high‐resolution whole‐brain dynamic contrast enhanced magnetic resonance imaging (DCE‐MRI) using digital reference objects. We study this in the context of TK model constraints, and in the absence of other constraints.

Methods

Three anatomically and physiologically realistic brain‐tumor digital reference objects were generated. Data sampling strategies included uniform and variable density; zone‐based, lattice, pseudo‐random, and pseudo‐radial; with 50‐time frames and 4‐fold to 25‐fold undersampling. In all cases, we assume a fully sampled first time frame, and prior knowledge of the arterial input function. TK parameters were estimated by indirect estimation (i.e., image‐time‐series reconstruction followed by model fitting), and direct estimation from the under‐sampled data. We evaluated methods based on the Cramér‐Rao bound and Monte‐Carlo simulations, over the range of signal‐to‐noise ratio (SNR) seen in clinical brain DCE‐MRI.

Results

Lattice‐based sampling provided the lowest SDs, followed by pseudo‐random, pseudo‐radial, and zone‐based. This ranking was consistent for the Patlak and extended Tofts model. Pseudo‐random sampling resulted in 19% higher averaged SD compared to lattice‐based sampling. Zone‐based sampling resulted in substantially higher SD at undersampling factors above 10. CRB analysis showed only a small difference between uniform and variable density for both lattice‐based and pseudo‐random sampling up to undersampling factors of 25.

Conclusion

Lattice sampling provided the lowest SDs, although the differences between sampling schemes were not substantial at low undersampling factors. The differences between lattice‐based and pseudo‐random sampling strategies with both uniform and variable density were within the range of error induced by other sources, at up to 25‐fold undersampling.

Flexible and efficient optimization of quantitative sequences using automatic differentiation of Bloch simulations

PURPOSE

To investigate a computationally efficient method for optimizing the Cramér-Rao Lower Bound (CRLB) of quantitative sequences without using approximations or an analytical expression of the signal.

METHODS

Automatic differentiation was applied to Bloch simulations and used to optimize several quantitative sequences without the need for approximations or an analytical expression. The results were validated with in vivo measurements and comparisons to prior art. Multi-echo spin echo and DESPO T 1 were used as benchmarks to verify the CRLB implementation. The CRLB of the Magnetic Resonance Fingerprinting (MRF) sequence, which has a complicated analytical formulation, was also optimized using automatic differentiation.

RESULTS

The sequence parameters obtained for multi-echo spin echo and DESPO T 1 matched results obtained using conventional methods. In vivo, MRF scans demonstrate that the CRLB optimization obtained with automatic differentiation can improve performance in presence of white noise. For MRF, the CRLB optimization converges in 1.1 CPU hours for N TR = 400 and has O ( N TR ) asymptotic runtime scaling for the calculation of the CRLB objective and gradient.

CONCLUSIONS

Automatic differentiation can be used to optimize the CRLB of quantitative sequences without using approximations or analytical expressions. For MRF, the runtime is computationally efficient and can be used to investigate confounding factors as well as MRF sequences with a greater number of repetitions.

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 T 1 -encoding, T 2 -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 T 1 - and T 2 -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 T 1 and T 2 in the hybrid state are substantially more efficient than sequential encoding techniques.

Designing contrasts for rapid, simultaneous parameter quantification and flow visualization with quantitative transient-state imaging

Magnetic resonance imaging (MRI) has evolved into an outstandingly versatile diagnostic modality, as it has the ability to non-invasively produce detailed information on a tissue's structure and function. Complementary data is normally obtained in separate measurements, either as contrast-weighted images, which are fast and simple to acquire, or as quantitative parametric maps, which offer an absolute quantification of underlying biophysical effects, such as relaxation times or flow. Here, we demonstrate how to acquire and reconstruct data in a transient-state with a dual purpose: 1 - to generate contrast-weighted images that can be adjusted to emphasise clinically relevant image biomarkers; exemplified with signal modulation according to flow to obtain angiography information, and 2 - to simultaneously infer multiple quantitative parameters with a single, highly accelerated acquisition. This is achieved by introducing three novel elements: a model that accounts for flowing blood, a method for sequence design using smooth flip angle excitation patterns that incorporates both parameter encoding and signal contrast, and the reconstruction of temporally resolved contrast-weighted images. From these images we simultaneously obtain angiography projections and multiple quantitative maps. By doing so, we increase the amount of clinically relevant data without adding measurement time, creating new dimensions for biomarker exploration and adding value to MR examinations for patients and clinicians alike.

Optimal Experiment Design for Magnetic Resonance Fingerprinting: Cramér-Rao Bound Meets Spin Dynamics

Magnetic resonance (MR) fingerprinting is a new quantitative imaging paradigm, which simultaneously acquires multiple MR tissue parameter maps in a single experiment. In this paper, we present an estimation-theoretic framework to perform experiment design for MR fingerprinting. Specifically, we describe a discrete-time dynamic system to model spin dynamics, and derive an estimation-theoretic bound, i.e., the Cramér-Rao bound, to characterize the signal-to-noise ratio (SNR) efficiency of an MR fingerprinting experiment. We then formulate an optimal experiment design problem, which determines a sequence of acquisition parameters to encode MR tissue parameters with the maximal SNR efficiency, while respecting the physical constraints and other constraints from the image decoding/reconstruction process. We evaluate the performance of the proposed approach with numerical simulations, phantom experiments, and in vivo experiments. We demonstrate that the optimized experiments substantially reduce data acquisition time and/or improve parameter estimation. For example, the optimized experiments achieve about a factor of two improvement in the accuracy of T2 maps, while keeping similar or slightly better accuracy of T1 maps. Finally, as a remarkable observation, we find that the sequence of optimized acquisition parameters appears to be highly structured rather than randomly/pseudo-randomly varying as is prescribed in the conventional MR fingerprinting experiments.

NOVIFAST: A Fast Algorithm for Accurate and Precise VFA MRI Mapping

In quantitative magnetic resonance mapping, the variable flip angle (VFA) steady state spoiled gradient recalled echo (SPGR) imaging technique is popular as it provides a series of high resolution weighted images in a clinically feasible time. Fast, linear methods that estimate maps from these weighted images have been proposed, such as DESPOT1 and iterative re-weighted linear least squares. More accurate, non-linear least squares (NLLS) estimators are in play, but these are generally much slower and require careful initialization. In this paper, we present NOVIFAST, a novel NLLS-based algorithm specifically tailored to VFA SPGR mapping. By exploiting the particular structure of the SPGR model, a computationally efficient, yet accurate and precise map estimator is derived. Simulation and in vivo human brain experiments demonstrate a twenty-fold speed gain of NOVIFAST compared with conventional gradient-based NLLS estimators while maintaining a high precision and accuracy. Moreover, NOVIFAST is eight times faster than the efficient implementations of the variable projection (VARPRO) method. Furthermore, NOVIFAST is shown to be robust against initialization.

Integrated and efficient diffusion-relaxometry using ZEBRA

The emergence of multiparametric diffusion models combining diffusion and relaxometry measurements provides powerful new ways to explore tissue microstructure, with the potential to provide new insights into tissue structure and function. However, their ability to provide rich analyses and the potential for clinical translation critically depends on the availability of efficient, integrated, multi-dimensional acquisitions. We propose a fully integrated sequence simultaneously sampling the acquisition parameter spaces required for T1 and T2* relaxometry and diffusion MRI. Slice-level interleaved diffusion encoding, multiple spin/gradient echoes and slice-shuffling are combined for higher efficiency, sampling flexibility and enhanced internal consistency. In-vivo data was successfully acquired on healthy adult brains. Obtained parametric maps as well as clustering results demonstrate the potential of the technique to provide eloquent data with an acceleration of roughly 20 compared to conventionally used approaches. The proposed integrated acquisition, which we call ZEBRA, offers significant acceleration and flexibility compared to existing diffusion-relaxometry studies, and thus facilitates wider use of these techniques both for research-driven and clinical applications.

Fast quantitative MRI using controlled saturation magnetization transfer

Purpose

This study demonstrates magnetization transfer (MT) effects directly affect relaxometry measurements and develops a framework that allows single‐pool models to be valid in 2‐pool MT systems.

Methods

A theoretical framework is developed in which a 2‐pool MT system effectively behaves as a single‐pool if the RMS RF magnetic field (B1rms{\text{B}}_{1}^{{{\text{rms}}}}) is kept fixed across all measurements. A practical method for achieving controlled saturation magnetization transfer (CSMT) using multiband RF pulses is proposed. Numerical, Phantom, and in vivo validations were performed directly comparing steady state (SS) estimation approaches that under correct single‐pool assumptions would be expected to vary in precision but not accuracy.

Results

Numerical simulations predict single‐pool estimates obtained from MT model generated data are not consistent for different SS estimation methods, and a systematic underestimation of T₂ is expected. Neither effect occurs under the proposed CSMT approach. Both phantom and in vivo experiments corroborate the numerical predictions. Experimental data highlights that even when using the same relaxometry method, different estimates are obtained depending on which combination of flip angles (FAs) and TRs are used if the CSMT approach is not used. Using CSMT, stable measurements of both T₁ and T₂ are obtained. The measured T₁(T1CSMT)) depends on B1rms{\text{B}}_{1}^{{{\text{rms}}}}, which is therefore an important parameter to specify.

Conclusion

This work demonstrates that conventional single pool relaxometry, which is highly efficient for human studies, results in unreliable parameter estimates in biological tissues because of MT effects. The proposed CSMT framework is shown to allow single‐pool assumptions to be valid, enabling reliable and efficient quantitative imaging to be performed.

Imaging structural and functional brain development in early childhood

In humans, the period from term birth to ∼2 years of age is characterized by rapid and dynamic brain development and plays an important role in cognitive development and risk of disorders such as autism and schizophrenia. Recent imaging studies have begun to delineate the growth trajectories of brain structure and function in the first years after birth and their relationship to cognition and risk of neuropsychiatric disorders. This Review discusses the development of grey and white matter and structural and functional networks, as well as genetic and environmental influences on early-childhood brain development. We also discuss initial evidence regarding the usefulness of early imaging biomarkers for predicting cognitive outcomes and risk of neuropsychiatric disorders.

Inferring brain tissue composition and microstructure via MR relaxometry

MRI relaxometry is sensitive to a variety of tissue characteristics in a complex manner, which makes it both attractive and challenging for characterizing tissue. This article reviews the most common water proton relaxometry measures, T₁, T₂, and T₂^*, and reports on their development and current potential to probe the composition and microstructure of brain tissue. The development of these relaxometry measures is challenged by the need for suitably accurate tissue models, as well as robust acquisition and analysis methodologies. MRI relaxometry has been established as a tool for characterizing neural tissue, particular with respect to myelination, and the potential for further development exists.

Modified dixon-based renal dynamic contrast-enhanced MRI facilitates automated registration and perfusion analysis

Purpose

Renal dynamic contrast‐enhanced (DCE) MRI provides information on renal perfusion and filtration. However, clinical implementation is hampered by challenges in postprocessing as a result of misalignment of the kidneys due to respiration. We propose to perform automated image registration using the fat‐only images derived from a modified Dixon reconstruction of a dual‐echo acquisition because these provide consistent contrast over the dynamic series.

Methods

DCE data of 10 hypertensive patients was used. Dual‐echo images were acquired at 1.5 T with temporal resolution of 3.9 s during contrast agent injection. Dixon fat, water, and in‐phase and opposed‐phase (OP) images were reconstructed. Postprocessing was automated. Registration was performed both to fat images and OP images for comparison. Perfusion and filtration values were extracted from a two‐compartment model fit.

Results

Automatic registration to fat images performed better than automatic registration to OP images with visible contrast enhancement. Median vertical misalignment of the kidneys was 14 mm prior to registration, compared to 3 mm and 5 mm with registration to fat images and OP images, respectively (P = 0.03). Mean perfusion values and MR‐based glomerular filtration rates (GFR) were 233 ± 64 mL/100 mL/min and 60 ± 36 mL/minute, respectively, based on fat‐registered images. MR‐based GFR correlated with creatinine‐based GFR (P = 0.04) for fat‐registered images. For unregistered and OP‐registered images, this correlation was not significant.

Conclusion

Absence of contrast changes on Dixon fat images improves registration in renal DCE MRI and enables automated postprocessing, resulting in a more accurate estimation of GFR. Magn Reson Med 80:66–76, 2018. © 2017 The Authors Magnetic Resonance in Medicine published by Wiley Periodicals, Inc. on behalf of International Society for Magnetic Resonance in Medicine. This is an open access article under the terms of the Creative Commons Attribution NonCommercial License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited and is not used for commercial purposes.

Propagation of error from parameter constraints in quantitative MRI: Example application of multiple spin echo T2 mapping

PURPOSE

Quantitative MRI may require correcting for nuisance parameters which can or must be constrained to independently measured or assumed values. The noise and/or bias in these constraints propagate to fitted parameters. For example, the case of refocusing pulse flip angle constraint in multiple spin echo T₂ mapping is explored.

METHODS

An analytical expression for the mean-squared error of a parameter of interest was derived as a function of the accuracy and precision of an independent estimate of a nuisance parameter. The expression was validated by simulations and then used to evaluate the effects of flip angle (θ) constraint on the accuracy and precision of T⁁2 for a variety of multi-echo T₂ mapping protocols.

RESULTS

Constraining θ improved T⁁2 precision when the θ-map signal-to-noise ratio was greater than approximately one-half that of the first spin echo image. For many practical scenarios, constrained fitting was calculated to reduce not just the variance but the full mean-squared error of T⁁2, for bias in θ⁁≲6%.

CONCLUSION

The analytical expression derived in this work can be applied to inform experimental design in quantitative MRI. The example application to T₂ mapping provided specific cases, depending on θ⁁ accuracy and precision, in which θ⁁ measurement and constraint would be beneficial to T⁁2 variance or mean-squared error. Magn Reson Med 79:673-682, 2018. © 2017 International Society for Magnetic Resonance in Medicine.