Optimized quantification of spin relaxation times in the hybrid state

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.

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 T 1 s of the semi-solid spin pool that is much shorter than T 1 f 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 T 1 f ≈ 1.84 s and T 1 s ≈ 0.34 s in healthy white matter. Our results confirm the reports that T 1 s ≪ T 1 f 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 m 0 s ≈ 0.212 , 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.

Water diffusion and T2 quantification in transient-state MRI: the effect of RF pulse sequence

In quantitative measurement of the T 2 value of tissues, the diffusion of water molecules has been recognized as a confounder. This is most notably so for transient-state quantitative mapping techniques, which allow simultaneous estimation of T 1 and T 2 . In prior work, apparently conflicting conclusions are presented on the level of diffusion-induced bias on the T2 estimate. So far there is a lack of studies on the effect of the RF pulse angle sequence on the level of diffusion-induced bias. In this work, we show that the specific transient-state RF pulse sequence has a large effect on this level of bias. In particular, the bias level is strongly influenced by the mean value of the RF pulse angles. Also, for realistic values of the spoiling gradient area, we infer that the diffusion-induced bias is negligible for non-liquid human tissues; yet, for phantoms, the effect can be substantial (15% of the true T 2 value) for some RF pulse sequences. This should be taken into account in validation procedures.

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.

Mutual-information based optimal experimental design for hyperpolarized [Formula: see text]C-pyruvate MRI

A key parameter of interest recovered from hyperpolarized (HP) MRI measurements is the apparent pyruvate-to-lactate exchange rate, [Formula: see text], for measuring tumor metabolism. This manuscript presents an information-theory-based optimal experimental design approach that minimizes the uncertainty in the rate parameter, [Formula: see text], recovered from HP-MRI measurements. Mutual information is employed to measure the information content of the HP measurements with respect to the first-order exchange kinetics of the pyruvate conversion to lactate. Flip angles of the pulse sequence acquisition are optimized with respect to the mutual information. A time-varying flip angle scheme leads to a higher parameter optimization that can further improve the quantitative value of mutual information over a constant flip angle scheme. However, the constant flip angle scheme, 35 and 28 degrees for pyruvate and lactate measurements, leads to an accuracy and precision comparable to the variable flip angle schemes obtained from our method. Combining the comparable performance and practical implementation, optimized pyruvate and lactate flip angles of 35 and 28 degrees, respectively, are recommended.

Cartesian vs radial MR-STAT: An efficiency and robustness study

MR Spin TomogrAphy in Time-domain ("MR-STAT") is quantitative MR technique in which multiple quantitative parameters are estimated from a single short scan by solving a large-scale non-linear optimization problem. In this work we extended the MR-STAT framework to non-Cartesian gradient trajectories. Cartesian MR-STAT and radial MR-STAT were compared in terms of time-efficiency and robustness in simulations, gel phantom measurements and in vivo measurements. In simulations, we observed that both Cartesian and radial MR-STAT are highly robust against undersampling. Radial MR-STAT does have a lower spatial encoding power because the outer corners of k-space are never sampled. However, especially in T2, this is compensated by a higher dynamic encoding power that comes from sampling the k-space center with each readout. In gel phantom measurements, Cartesian MR-STAT was observed to be robust against overfitting whereas radial MR-STAT suffered from high-frequency artefacts in the parameter maps at later iterations. These artefacts are hypothesized to be related to hardware imperfections and were (partially) suppressed with image filters. The time-efficiencies were higher for Cartesian MR-STAT in all vials. In-vivo, the radial reconstruction again suffered from overfitting artefacts. The robustness of Cartesian MR-STAT over the entire range of experiments may make it preferable in a clinical setting, despite radial MR-STAT resulting in a higher T1 time-efficiency in white matter.

Mitigating undersampling errors in MR fingerprinting by sequence optimization

PURPOSE

To develop a method for MR Fingerprinting (MRF) sequence optimization that takes both the applied undersampling pattern and a realistic reference map into account.

METHODS

A predictive model for the undersampling error leveraging on perturbation theory was exploited to optimize the MRF flip angle sequence for improved robustness against undersampling artifacts. In this framework parameter maps from a previously acquired MRF scan were used as reference. Sequences were optimized for different sequence lengths, smoothness constraints and undersampling factors. Numerical simulations and in vivo measurements in eight healthy subjects were performed to assess the effect of the performed optimization. The optimized MRF sequences were compared to a conventionally shaped flip angle pattern and an optimized pattern based on the Cramér-Rao lower bound (CRB).

RESULTS

Numerical simulations and in vivo results demonstrate that the undersampling errors can be suppressed by flip angle optimization. Analysis of the in vivo results show that a sequence optimized for improved robustness against undersampling with a flip angle train of length 400 yielded significantly lower median absolute errors in T 1 : 5 . 6 % ± 2 . 9 % and T 2 : 7 . 9 % ± 2 . 3 % compared to the conventional ( T 1 : 8 . 0 % ± 1 . 9 % , T 2 : 14 . 5 % ± 2 . 6 % ) and CRB-based ( T 1 : 21 . 6 % ± 4 . 1 % , T 2 : 31 . 4 % ± 4 . 4 % ) sequences.

CONCLUSION

The proposed method is able to optimize the MRF flip angle pattern such that significant mitigation of the artifacts from strong k-space undersampling in MRF is achieved.

Quantitative MRI by nonlinear inversion of the Bloch equations

PURPOSE

Development of a generic model-based reconstruction framework for multiparametric quantitative MRI that can be used with data from different pulse sequences.

METHODS

Generic nonlinear model-based reconstruction for quantitative MRI estimates parametric maps directly from the acquired k-space by numerical optimization. This requires numerically accurate and efficient methods to solve the Bloch equations and their partial derivatives. In this work, we combine direct sensitivity analysis and pre-computed state-transition matrices into a generic framework for calibrationless model-based reconstruction that can be applied to different pulse sequences. As a proof-of-concept, the method is implemented and validated for quantitative T 1 $$ {\mathrm{T}}_1 $$ and T 2 $$ {\mathrm{T}}_2 $$ mapping with single-shot inversion-recovery (IR) FLASH and IR bSSFP sequences in simulations, phantoms, and the human brain.

RESULTS

The direct sensitivity analysis enables a highly accurate and numerically stable calculation of the derivatives. The state-transition matrices efficiently exploit repeating patterns in pulse sequences, speeding up the calculation by a factor of 10 for the examples considered in this work, while preserving the accuracy of native ordinary differential equations solvers. The generic model-based method reproduces quantitative results of previous model-based reconstructions based on the known analytical solutions for radial IR FLASH. For IR bSFFP it produces accurate T 1 $$ {\mathrm{T}}_1 $$ and T 2 $$ {\mathrm{T}}_2 $$ maps for the National Insitute of Standards and Technology (NIST) phantom in numerical simulations and experiments. Feasibility is also shown for human brain, although results are affected by magnetization transfer effects.

CONCLUSION

By developing efficient tools for numerical optimizations using the Bloch equations as forward model, this work enables generic model-based reconstruction for quantitative MRI.

Efficient performance analysis and optimization of transient-state sequences for multiparametric magnetic resonance imaging

In transient-state multiparametric MRI sequences such as Magnetic Resonance Spin TomogrAphy in Time-domain (MR-STAT), MR fingerprinting, or hybrid-state imaging, the flip angle pattern of the RF excitation varies over the sequence. This gives considerable freedom to choose an optimal pattern of flip angles. For pragmatic reasons, most optimization methodologies choose for a single-voxel approach (i.e., without taking the spatial encoding scheme into account). Particularly in MR-STAT, the context of spatial encoding is important. In the current study, we present a methodology, called BLock Analysis of a K-space-domain Jacobian (BLAKJac), which is sufficiently fast to optimize a sequence in the context of a predetermined phase-encoding pattern. Based on MR-STAT acquisitions and reconstructions, we show that sequences optimized using BLAKJac are more reliable in terms of actually achieved precision than conventional single-voxel-optimized sequences. In addition, BLAKJac provides analytical tools that give insights into the performance of the sequence in a very limited computation time. Our experiments are based on MR-STAT, but the theory is equally valid for other transient-state multiparametric methods.

Approximate B 1 + scaling of the SSFP steady state

PURPOSE

It is shown that the steady state of rapid, TR-periodic steady-state free precession (SSFP) sequences at small to moderate flip angles exhibits a universal, approximate scaling law with respect to variations of B 1 + $$ {B}_1^{+} $$ . Implications for the accuracy and precision of relaxometry experiments are discussed.

METHODS

The approximate scaling law is derived from and numerically tested against known analytical solutions. To assess the attainable estimator precision in a typical relaxometry experiment, we calculate the Cramér-Rao bound (CRB) and perform Monte Carlo (MC) simulations.

RESULTS

The approximate universal scaling holds well up to moderate flip angles. For pure steady state relaxometry, we observe a significant precision penalty for simultaneous estimation of R 1 $$ {R}_1 $$ and B 1 + $$ {B}_1^{+} $$ , whereas good R 2 $$ {R}_2 $$ estimates can be obtained without even knowing the correct actual flip angle.

CONCLUSION

Simultaneous estimation of R 1 $$ {R}_1 $$ and B 1 + $$ {B}_1^{+} $$ from a set of SSFP steady states alone is not advisable. Apart from separate B 1 + $$ {B}_1^{+} $$ measurements, the problem can be addressed by adding transient state information, but, depending on the situation, residual effects due to the scaling may still require some attention.

Artificial intelligence in cardiac magnetic resonance fingerprinting

Magnetic resonance fingerprinting (MRF) is a fast MRI-based technique that allows for multiparametric quantitative characterization of the tissues of interest in a single acquisition. In particular, it has gained attention in the field of cardiac imaging due to its ability to provide simultaneous and co-registered myocardial T₁ and T₂ mapping in a single breath-held cardiac MRF scan, in addition to other parameters. Initial results in small healthy subject groups and clinical studies have demonstrated the feasibility and potential of MRF imaging. Ongoing research is being conducted to improve the accuracy, efficiency, and robustness of cardiac MRF. However, these improvements usually increase the complexity of image reconstruction and dictionary generation and introduce the need for sequence optimization. Each of these steps increase the computational demand and processing time of MRF. The latest advances in artificial intelligence (AI), including progress in deep learning and the development of neural networks for MRI, now present an opportunity to efficiently address these issues. Artificial intelligence can be used to optimize candidate sequences and reduce the memory demand and computational time required for reconstruction and post-processing. Recently, proposed machine learning-based approaches have been shown to reduce dictionary generation and reconstruction times by several orders of magnitude. Such applications of AI should help to remove these bottlenecks and speed up cardiac MRF, improving its practical utility and allowing for its potential inclusion in clinical routine. This review aims to summarize the latest developments in artificial intelligence applied to cardiac MRF. Particularly, we focus on the application of machine learning at different steps of the MRF process, such as sequence optimization, dictionary generation and image reconstruction.

Low‐rank inversion reconstruction for through‐plane accelerated radial MR fingerprinting applied to relaxometry at 0. 35 T

Purpose

To reduce scan time, methods to accelerate phase‐encoded/non‐Cartesian MR fingerprinting (MRF) acquisitions for variable density spiral acquisitions have recently been developed. These methods are not applicable to MRF acquisitions, wherein a single k‐space spoke is acquired per frame. Therefore, we propose a low‐rank inversion method to resolve MRF contrast dynamics from through‐plane accelerated Cartesian/radial measurements applied to quantitative relaxation‐time mapping on a 0.35T system.

Methods

An algorithm was implemented to reconstruct through‐plane aliased low‐rank images describing the contrast dynamics occurring because of the transient‐state MRF acquisition. T₁ and T₂ times from accelerated acquisitions were compared with those from unaccelerated linear reconstructions in a standardized system phantom and within in vivo brain and prostate experiments on a hybrid 0.35T MRI/linear accelerator.

Results

No significant differences between T₁ and T₂ times for the accelerated reconstructions were observed compared to fully sampled acquisitions (p = 0.41 and p = 0.36, respectively). The mean absolute errors in T₁ and T₂ were 5.6% and 2.9%, respectively, between the full and accelerated acquisitions. The SDs in T₁ and T₂ decreased with the advanced accelerated reconstruction compared with the unaccelerated reconstruction (p = 0.02 and p = 0.03, respectively). The quality of the T₁ and T₂ maps generated with the proposed approach are comparable to those obtained using the unaccelerated data sets.

Conclusions

Through‐plane accelerated MRF with radial k‐space coverage was demonstrated at a low field strength of 0.35 T. This method enabled 3D T₁ and T₂ mapping at 0.35 T with a 3‐min scan.

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.

Automated design of pulse sequences for magnetic resonance fingerprinting using physics-inspired optimization

Magnetic resonance fingerprinting (MRF) is a method to extract quantitative tissue properties such as [Formula: see text] and [Formula: see text] relaxation rates from arbitrary pulse sequences using conventional MRI hardware. MRF pulse sequences have thousands of tunable parameters, which can be chosen to maximize precision and minimize scan time. Here, we perform de novo automated design of MRF pulse sequences by applying physics-inspired optimization heuristics. Our experimental data suggest that systematic errors dominate over random errors in MRF scans under clinically relevant conditions of high undersampling. Thus, in contrast to prior optimization efforts, which focused on statistical error models, we use a cost function based on explicit first-principles simulation of systematic errors arising from Fourier undersampling and phase variation. The resulting pulse sequences display features qualitatively different from previously used MRF pulse sequences and achieve fourfold shorter scan time than prior human-designed sequences of equivalent precision in [Formula: see text] and [Formula: see text] Furthermore, the optimization algorithm has discovered the existence of MRF pulse sequences with intrinsic robustness against shading artifacts due to phase variation.

Toward magnetic resonance fingerprinting for low-field MR-guided radiation therapy

PURPOSE

The acquisition of multiparametric quantitative magnetic resonance imaging (qMRI) is becoming increasingly important for functional characterization of cancer prior to- and throughout the course of radiation therapy. The feasibility of a qMRI method known as magnetic resonance fingerprinting (MRF) for rapid T₁ and T₂ mapping was assessed on a low-field MR-linac system.

METHODS

A three-dimensional MRF sequence was implemented on a 0.35T MR-guided radiotherapy system. MRF-derived measurements of T₁ and T₂ were compared to those obtained with gold standard single spin echo methods, and the impacts of the radiofrequency field homogeneity and scan times ranging between 6 and 48 min were analyzed by acquiring between 1 and 8 spokes per time point in a standard quantitative system phantom. The short-term repeatability of MRF was assessed over three measurements taken over a 10-h period. To evaluate transferability, MRF measurements were acquired on two additional MR-guided radiotherapy systems. Preliminary human volunteer studies were performed.

RESULTS

The phantom benchmarking studies showed that MRF is capable of mapping T₁ and T₂ values within 8% and 10% of gold standard measures, respectively, at 0.35T. The coefficient of variation of T₁ and T₂ estimates over three repeated scans was < 5% over a broad range of relaxation times. The T₁ and T₂ times derived using a single-spoke MRF acquisition across three scanners were near unity and mean percent errors in T₁ and T₂ estimates using the same phantom were < 3%. The mean percent differences in T₁ and T₂ as a result of truncating the scan time to 6 min over the large range of relaxation times in the system phantom were 0.65% and 4.05%, respectively.

CONCLUSIONS

The technical feasibility and accuracy of MRF on a low-field MR-guided radiation therapy device has been demonstrated. MRF can be used to measure accurate T₁ and T₂ maps in three dimensions from a brief 6-min scan, offering strong potential for efficient and reproducible qMRI for future clinical trials in functional plan adaptation and tumor/normal tissue response assessment.

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.

3D sodium (23 Na) magnetic resonance fingerprinting for time-efficient relaxometric mapping

PURPOSE

To develop a framework for 3D sodium (²³ Na) MR fingerprinting (MRF), based on irreducible spherical tensor operators with tailored flip angle (FA) pattern and time-efficient data acquisition for simultaneous quantification of T₁ , T 2 l ∗ , T 2 s ∗ , and T 2 ∗ in addition to ΔB₀ .

METHODS

²³ Na-MRF was implemented in a 3D sequence and irreducible spherical tensor operators were exploited in the simulations. Furthermore, the Cramér Rao lower bound was used to optimize the flip angle pattern. A combination of single and double echo readouts was implemented to increase the readout efficiency. A study was conducted to compare results in a multicompartment phantom acquired with MRF and reference methods. Finally, the relaxation times in the human brain were measured in four healthy volunteers.

RESULTS

Phantom experiments revealed a mean difference of 1.0% between relaxation times acquired with MRF and results determined with the reference methods. Simultaneous quantification of the longitudinal and transverse relaxation times in the human brain was possible within 32 min using 3D ²³ Na-MRF with a nominal resolution of (5 mm)³ . In vivo measurements in four volunteers yielded average relaxation times of: T_1,brain = (35.0 ± 3.2) ms, T 2 l , brain ∗ = (29.3 ± 3.8) ms and T 2 s , brain ∗ = (5.5 ± 1.3) ms in brain tissue, whereas T_1,CSF = (61.9 ± 2.8) ms and T 2 , CSF ∗ = (46.3 ± 4.5) ms was found in cerebrospinal fluid.

CONCLUSION

The feasibility of in vivo 3D relaxometric sodium mapping within roughly ½ h is demonstrated using MRF in the human brain, moving sodium relaxometric mapping toward clinically relevant measurement times.

Accelerated MR-STAT Reconstructions Using Sparse Hessian Approximations

MR-STAT is a quantitative magnetic resonance imaging framework for obtaining multi-parametric quantitative tissue parameter maps using data from single short scans. A large-scale optimization problem is solved in which spatial localization of signal and estimation of tissue parameters are performed simultaneously by directly fitting a Bloch-based volumetric signal model to measured time-domain data. In previous work, a highly parallelized, matrix-free Gauss-Newton reconstruction algorithm was presented that can solve the large-scale optimization problem for high-resolution scans. The main computational bottleneck in this matrix-free method is solving a linear system involving (an approximation to) the Hessian matrix at each iteration. In the current work, we analyze the structure of the Hessian matrix in relation to the dynamics of the spin system and derive conditions under which the (approximate) Hessian admits a sparse structure. In the case of Cartesian sampling patterns with smooth RF trains we demonstrate how exploiting this sparsity can reduce MR-STAT reconstruction times by approximately an order of magnitude.

Myelin water fraction estimation using small-tip fast recovery MRI

PURPOSE

To demonstrate the feasibility of an optimized set of small-tip fast recovery (STFR) MRI scans for rapidly estimating myelin water fraction (MWF) in the brain.

METHODS

We optimized a set of STFR scans to minimize the Cramér-Rao Lower Bound of MWF estimates. We evaluated the RMSE of MWF estimates from the optimized scans in simulation. We compared STFR-based MWF estimates (both modeling exchange and not modeling exchange) to multi-echo spin echo (MESE)-based estimates. We used the optimized scans to acquire in vivo data from which a MWF map was estimated. We computed the STFR-based MWF estimates using PERK, a recently developed kernel regression technique, and the MESE-based MWF estimates using both regularized non-negative least squares (NNLS) and PERK.

RESULTS

In simulation, the optimized STFR scans led to estimates of MWF with low RMSE across a range of tissue parameters and across white matter and gray matter. The STFR-based MWF estimates that modeled exchange compared well to MESE-based MWF estimates in simulation. When the optimized scans were tested in vivo, the MWF map that was estimated using a 3-compartment model with exchange was closer to the MESE-based MWF map.

CONCLUSIONS

The optimized STFR scans appear to be well suited for estimating MWF in simulation and in vivo when we model exchange in training. In this case, the STFR-based MWF estimates are close to the MESE-based estimates.

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.