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

Efficient pulse sequence design framework for high-dimensional MR fingerprinting scans using systematic error index

PURPOSE

For effective optimization of MR fingerprinting (MRF) pulse sequences, estimating and minimizing errors from actual scan conditions are crucial. Although virtual-scan simulations offer an approximation to these errors, their computational demands become expensive for high-dimensional MRF frameworks, where interactions between more than two tissue properties are considered. This complexity makes sequence optimization impractical. We introduce a new mathematical model, the systematic error index (SEI), to address the scalability challenges for high-dimensional MRF sequence design.

METHODS

By eliminating the need to perform dictionary matching, the SEI model approximates quantification errors with low computational costs. The SEI model was validated in comparison with virtual-scan simulations. The SEI model was further applied to optimize three high-dimensional MRF sequences that quantify two to four tissue properties. The optimized scans were examined in simulations and healthy subjects.

RESULTS

The proposed SEI model closely approximated the virtual-scan simulation outcomes while achieving hundred- to thousand-times acceleration in the computational speed. In both simulation and in vivo experiments, the optimized MRF sequences yield higher measurement accuracy with fewer undersampling artifacts at shorter scan times than the heuristically designed sequences.

CONCLUSION

We developed an efficient method for estimating real-world errors in MRF scans with high computational efficiency. Our results illustrate that the SEI model could approximate errors both qualitatively and quantitatively. We also proved the practicality of the SEI model of optimizing sequences for high-dimensional MRF frameworks with manageable computational power. The optimized high-dimensional MRF scans exhibited enhanced robustness against undersampling and system imperfections with faster scan times.

A genetic optimisation and iterative reconstruction framework for sparse multi-dimensional diffusion-relaxation correlation MRI

Multi-dimensional diffusion-relaxation correlation (DRC) magnetic resonance imaging (MRI) techniques have recently been developed to investigate tissue microstructures. Sub-voxel tissue heterogeneity is resolved from the local correlation distributions of relaxation time and molecular diffusivity. However, the implementation of these techniques considerably increases the total acquisition time, and simply reducing the scan time may be at the expense of detailed structural resolution. To overcome these limitations, an optimised framework was proposed for acquiring microstructural maps of the human brain on a clinically feasible timescale. First, the acquisition parameters of the multi-dimensional DRC MRI method were sparsely optimised using a genetic algorithm with a fitness function according to the spectral resolution of the correlation map, hardware requirements, and total scan time. Next, the acquired DRC MRI data were processed using a proposed numerical algorithm based on the dynamic inverse Laplace transform (ILT). Prior knowledge from one-dimensional data was then utilised in the iterative procedure to improve the spectral resolution. Finally, the proposed framework was validated using Monte Carlo simulations and experimental data acquired from healthy participants on an MRI scanner. The results demonstrated that the suggested approach is feasible for offering high-resolution DRC maps that correspond to distinct microstructures with a limited amount of optimised acquisition data from two-dimensional DRC sampling space. By significantly reducing scan time while retaining structural resolution, this approach may enable multi-dimensional DRC MRI to be more widely used for quantitative evaluation in biological and medical settings.

High-resolution myelin-water fraction and quantitative relaxation mapping using 3D ViSTa-MR fingerprinting

PURPOSE

This study aims to develop a high-resolution whole-brain multi-parametric quantitative MRI approach for simultaneous mapping of myelin-water fraction (MWF), T1, T2, and proton-density (PD), all within a clinically feasible scan time.

METHODS

We developed 3D visualization of short transverse relaxation time component (ViSTa)-MRF, which combined ViSTa technique with MR fingerprinting (MRF), to achieve high-fidelity whole-brain MWF and T1/T2/PD mapping on a clinical 3T scanner. To achieve fast acquisition and memory-efficient reconstruction, the ViSTa-MRF sequence leverages an optimized 3D tiny-golden-angle-shuffling spiral-projection acquisition and joint spatial-temporal subspace reconstruction with optimized preconditioning algorithm. With the proposed ViSTa-MRF approach, high-fidelity direct MWF mapping was achieved without a need for multicompartment fitting that could introduce bias and/or noise from additional assumptions or priors.

RESULTS

The in vivo results demonstrate the effectiveness of the proposed acquisition and reconstruction framework to provide fast multi-parametric mapping with high SNR and good quality. The in vivo results of 1 mm- and 0.66 mm-isotropic resolution datasets indicate that the MWF values measured by the proposed method are consistent with standard ViSTa results that are 30× slower with lower SNR. Furthermore, we applied the proposed method to enable 5-min whole-brain 1 mm-iso assessment of MWF and T1/T2/PD mappings for infant brain development and for post-mortem brain samples.

CONCLUSIONS

In this work, we have developed a 3D ViSTa-MRF technique that enables the acquisition of whole-brain MWF, quantitative T1, T2, and PD maps at 1 and 0.66 mm isotropic resolution in 5 and 15 min, respectively. This advancement allows for quantitative investigations of myelination changes in the brain.

Deep image prior cine MR fingerprinting with B1 + spin history correction

PURPOSE

To develop a deep image prior (DIP) reconstruction for B1 + -corrected 2D cine MR fingerprinting (MRF).

METHODS

The proposed method combines low-rank (LR) modeling with a DIP to generate cardiac phase-resolved parameter maps without motion correction, employing self-supervised training to enforce consistency with undersampled spiral k-space data. Two implementations were tested: one approach (DIP) for cine T1 , T2 , and M0 mapping, and a second approach (DIP with effective B1 + estimation [DIP-B1]) that also generated an effective B1 + map to correct for errors due to RF transmit inhomogeneities, through-plane motion, and blood flow. Cine MRF data were acquired in 14 healthy subjects and four reconstructions were compared: LR, low-rank motion-corrected (LRMC), DIP, and DIP-B1. Results were compared to diastolic ECG-triggered MRF, MOLLI, and T2 -prep bSSFP. Additionally, bright-blood and dark-blood images calculated from cine MRF maps were used to quantify ventricular function and compared to reference cine measurements.

RESULTS

DIP and DIP-B1 outperformed other cine MRF reconstructions with improved noise suppression and delineation of high-resolution details. Within-segment variability in the myocardium (reported as the coefficient of variation for T1 /T2 ) was lowest for DIP-B1 (2.3/8.3%) followed by DIP (2.7/8.7%), LRMC (3.5/10.5%), and LR (15.3/39.6%). Spatial homogeneity improved with DIP-B1 having the lowest intersegment variability (2.6/4.1%). The mean bias in ejection fraction was -1.1% compared to reference cine scans.

CONCLUSION

A DIP reconstruction for 2D cine MRF enabled cardiac phase-resolved mapping of T1 , T2 , M0 , and the effective B1 + with improved noise suppression and precision compared to LR and LRMC.

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.

Deep learning-assisted preclinical MR fingerprinting for sub-millimeter T1 and T2 mapping of entire macaque brain

PURPOSE

Preclinical MR fingerprinting (MRF) suffers from long acquisition time for organ-level coverage due to demanding image resolution and limited undersampling capacity. This study aims to develop a deep learning-assisted fast MRF framework for sub-millimeter T1 and T2 mapping of entire macaque brain on a preclinical 9.4 T MR system.

METHODS

Three dimensional MRF images were reconstructed by singular value decomposition (SVD) compressed reconstruction. T1 and T2 mapping for each axial slice exploited a self-attention assisted residual U-Net to suppress aliasing-induced quantification errors, and the transmit-field (B1 + ) measurements for robustness against B1 + inhomogeneity. Supervised network training used MRF images simulated via virtual parametric maps and a desired undersampling scheme. This strategy bypassed the difficulties of acquiring fully sampled preclinical MRF data to guide network training. The proposed fast MRF framework was tested on experimental data acquired from ex vivo and in vivo macaque brains.

RESULTS

The trained network showed reasonable adaptability to experimental MRF images, enabling robust delineation of various T1 and T2 distributions in the brain tissues. Further, the proposed MRF framework outperformed several existing fast MRF methods in handling the aliasing artifacts and capturing detailed cerebral structures in the mapping results. Parametric mapping of entire macaque brain at nominal resolution of 0.35× $$ \times $$ 0.35× $$ \times $$ 1 mm3 can be realized via a 20-min 3D MRF scan, which was sixfold faster than the baseline protocol.

CONCLUSION

Introducing deep learning to MRF framework paves the way for efficient organ-level high-resolution quantitative MRI in preclinical applications.

Emerging Trends in Magnetic Resonance Fingerprinting for Quantitative Biomedical Imaging Applications: A Review

Magnetic resonance imaging (MRI) stands as a vital medical imaging technique, renowned for its ability to offer high-resolution images of the human body with remarkable soft-tissue contrast. This enables healthcare professionals to gain valuable insights into various aspects of the human body, including morphology, structural integrity, and physiological processes. Quantitative imaging provides compositional measurements of the human body, but, currently, either it takes a long scan time or is limited to low spatial resolutions. Undersampled k-space data acquisitions have significantly helped to reduce MRI scan time, while compressed sensing (CS) and deep learning (DL) reconstructions have mitigated the associated undersampling artifacts. Alternatively, magnetic resonance fingerprinting (MRF) provides an efficient and versatile framework to acquire and quantify multiple tissue properties simultaneously from a single fast MRI scan. The MRF framework involves four key aspects: (1) pulse sequence design; (2) rapid (undersampled) data acquisition; (3) encoding of tissue properties in MR signal evolutions or fingerprints; and (4) simultaneous recovery of multiple quantitative spatial maps. This paper provides an extensive literature review of the MRF framework, addressing the trends associated with these four key aspects. There are specific challenges in MRF for all ranges of magnetic field strengths and all body parts, which can present opportunities for further investigation. We aim to review the best practices in each key aspect of MRF, as well as for different applications, such as cardiac, brain, and musculoskeletal imaging, among others. A comprehensive review of these applications will enable us to assess future trends and their implications for the translation of MRF into these biomedical imaging applications.

Fast deep learning reconstruction techniques for preclinical magnetic resonance fingerprinting

We propose a deep learning (DL) model and a hyperparameter optimization strategy to reconstruct T1 and T2 maps acquired with the magnetic resonance fingerprinting (MRF) methodology. We applied two different MRF sequence routines to acquire images of ex vivo rat brain phantoms using a 7-T preclinical scanner. Subsequently, the DL model was trained using experimental data, completely excluding the use of any theoretical MRI signal simulator. The best combination of the DL parameters was implemented by an automatic hyperparameter optimization strategy, whose key aspect is to include all the parameters to the fit, allowing the simultaneous optimization of the neural network architecture, the structure of the DL model, and the supervised learning algorithm. By comparing the reconstruction performances of the DL technique with those achieved from the traditional dictionary-based method on an independent dataset, the DL approach was shown to reduce the mean percentage relative error by a factor of 3 for T1 and by a factor of 2 for T2 , and to improve the computational time by at least a factor of 37. Furthermore, the proposed DL method enables maintaining comparable reconstruction performance, even with a lower number of MRF images and a reduced k-space sampling percentage, with respect to the dictionary-based method. Our results suggest that the proposed DL methodology may offer an improvement in reconstruction accuracy, as well as speeding up MRF for preclinical, and in prospective clinical, investigations.

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.

High-resolution myelin-water fraction and quantitative relaxation mapping using 3D ViSTa-MR fingerprinting

Purpose

This study aims to develop a high-resolution whole-brain multi-parametric quantitative MRI approach for simultaneous mapping of myelin-water fraction (MWF), T1, T2, and proton-density (PD), all within a clinically feasible scan time.

Methods

We developed 3D ViSTa-MRF, which combined Visualization of Short Transverse relaxation time component (ViSTa) technique with MR Fingerprinting (MRF), to achieve high-fidelity whole-brain MWF and T1/T2/PD mapping on a clinical 3T scanner. To achieve fast acquisition and memory-efficient reconstruction, the ViSTa-MRF sequence leverages an optimized 3D tiny-golden-angle-shuffling spiral-projection acquisition and joint spatial-temporal subspace reconstruction with optimized preconditioning algorithm. With the proposed ViSTa-MRF approach, high-fidelity direct MWF mapping was achieved without a need for multi-compartment fitting that could introduce bias and/or noise from additional assumptions or priors.

Results

The in-vivo results demonstrate the effectiveness of the proposed acquisition and reconstruction framework to provide fast multi-parametric mapping with high SNR and good quality. The in-vivo results of 1mm- and 0.66mm-iso datasets indicate that the MWF values measured by the proposed method are consistent with standard ViSTa results that are 30x slower with lower SNR. Furthermore, we applied the proposed method to enable 5-minute whole-brain 1mm-iso assessment of MWF and T1/T2/PD mappings for infant brain development and for post-mortem brain samples.

Conclusions

In this work, we have developed a 3D ViSTa-MRF technique that enables the acquisition of whole-brain MWF, quantitative T1, T2, and PD maps at 1mm and 0.66mm isotropic resolution in 5 and 15 minutes, respectively. This advancement allows for quantitative investigations of myelination changes in the brain.

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.

Global deep learning optimization of chemical exchange saturation transfer magnetic resonance fingerprinting acquisition schedule

Chemical exchange saturation transfer (CEST) MRI is a promising molecular imaging technique but suffers from long scan times and complicated processing. CEST was recently combined with magnetic resonance fingerprinting (MRF) to address these shortcomings. However, the CEST-MRF signal depends on multiple acquisition and tissue parameters so selecting an optimal acquisition schedule is challenging. In this work, we propose a novel dual-network deep learning framework to optimize the CEST-MRF acquisition schedule. The quality of the optimized schedule was assessed in a digital brain phantom and compared with alternate deep learning optimization approaches. The effect of schedule length on the reconstruction error was also investigated. A healthy subject was scanned with optimized and random schedules and with a conventional CEST sequence for comparison. The optimized schedule was also tested in a subject with metastatic renal cell carcinoma. Reproducibility was assessed via test-retest experiments and the concordance correlation coefficient calculated for white matter (WM) and grey matter (GM). The optimized schedule was 12% shorter but yielded equal or lower normalized root mean square error for all parameters. The proposed optimization also provided a lower error compared with alternate methodologies. Longer schedules generally yielded lower error. In vivo maps obtained with the optimized schedule showed reduced noise and improved delineation of GM and WM. CEST curves synthesized from the optimized parameters were highly correlated (r = 0.99) with measured conventional CEST. The mean concordance correlation coefficient in WM/GM for all tissue parameters was 0.990/0.978 for the optimized schedule but only 0.979/0.975 for the random schedule. The proposed schedule optimization is widely applicable to MRF pulse sequences and provides accurate and reproducible tissue maps with reduced noise at a shorter scan time than a randomly generated schedule.

Only-train-once MR fingerprinting for B0 and B1 inhomogeneity correction in quantitative magnetization-transfer contrast

PURPOSE

To develop a fast, deep-learning approach for quantitative magnetization-transfer contrast (MTC)-MR fingerprinting (MRF) that simultaneously estimates multiple tissue parameters and corrects the effects of B0 and B1 variations.

METHODS

An only-train-once recurrent neural network was designed to perform the fast tissue-parameter quantification for a large range of different MRF acquisition schedules. It enabled a dynamic scan-wise linear calibration of the scan parameters using the measured B0 and B1 maps, which allowed accurate, multiple-tissue parameter mapping. MRF images were acquired from 8 healthy volunteers at 3 T. Estimated parameter maps from the MRF images were used to synthesize the MTC reference signal (Zref ) through Bloch equations at multiple saturation power levels.

RESULTS

The B0 and B1 errors in MR fingerprints, if not corrected, would impair the tissue quantification and subsequently corrupt the synthesized MTC reference images. Bloch equation-based numerical phantom studies and synthetic MRI analysis demonstrated that the proposed approach could correctly estimate water and semisolid macromolecule parameters, even with severe B0 and B1 inhomogeneities.

CONCLUSION

The only-train-once deep-learning framework can improve the reconstruction accuracy of brain-tissue parameter maps and be further combined with any conventional MRF or CEST-MRF method.

3D magnetic resonance fingerprinting on a low-field 50 mT point-of-care system prototype: evaluation of muscle and lipid relaxation time mapping and comparison with standard techniques

OBJECTIVE

To implement magnetic resonance fingerprinting (MRF) on a permanent magnet 50 mT low-field system deployable as a future point-of-care (POC) unit and explore the quality of the parameter maps.

MATERIALS AND METHODS

3D MRF was implemented on a custom-built Halbach array using a slab-selective spoiled steady-state free precession sequence with 3D Cartesian readout. Undersampled scans were acquired with different MRF flip angle patterns and reconstructed using matrix completion and matched to the simulated dictionary, taking excitation profile and coil ringing into account. MRF relaxation times were compared to that of inversion recovery (IR) and multi-echo spin echo (MESE) experiments in phantom and in vivo. Furthermore, B₀ inhomogeneities were encoded in the MRF sequence using an alternating TE pattern, and the estimated map was used to correct for image distortions in the MRF images using a model-based reconstruction.

RESULTS

Phantom relaxation times measured with an optimized MRF sequence for low field were in better agreement with reference techniques than for a standard MRF sequence. In vivo muscle relaxation times measured with MRF were longer than those obtained with an IR sequence (T₁: 182 ± 21.5 vs 168 ± 9.89 ms) and with an MESE sequence (T₂: 69.8 ± 19.7 vs 46.1 ± 9.65 ms). In vivo lipid MRF relaxation times were also longer compared with IR (T₁: 165 ± 15.1 ms vs 127 ± 8.28 ms) and with MESE (T₂: 160 ± 15.0 ms vs 124 ± 4.27 ms). Integrated ΔB₀ estimation and correction resulted in parameter maps with reduced distortions.

DISCUSSION

It is possible to measure volumetric relaxation times with MRF at 2.5 × 2.5 × 3.0 mm³ resolution in a 13 min scan time on a 50 mT permanent magnet system. The measured MRF relaxation times are longer compared to those measured with reference techniques, especially for T₂. This discrepancy can potentially be addressed by hardware, reconstruction and sequence design, but long-term reproducibility needs to be further improved.

Adaptive model-based Magnetic Resonance

PURPOSE

Conventional sequences are static in nature, fixing measurement parameters in advance in anticipation of a wide range of expected tissue parameter values. We set out to design and benchmark a new, personalized approach-termed adaptive MR-in which incoming subject data is used to update and fine-tune the pulse sequence parameters in real time.

METHODS

We implemented an adaptive, real-time multi-echo (MTE) experiment for estimating T₂ s. Our approach combined a Bayesian framework with model-based reconstruction. It maintained and continuously updated a prior distribution of the desired tissue parameters, including T₂ , which was used to guide the selection of sequence parameters in real time.

RESULTS

Computer simulations predicted accelerations between 1.7- and 3.3-fold for adaptive multi-echo sequences relative to static ones. These predictions were corroborated in phantom experiments. In healthy volunteers, our adaptive framework accelerated the measurement of T₂ for n-acetyl-aspartate by a factor of 2.5.

CONCLUSION

Adaptive pulse sequences that alter their excitations in real time could provide substantial reductions in acquisition times. Given the generality of our proposed framework, our results motivate further research into other adaptive model-based approaches to MRI and MRS.

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.

A fast MR fingerprinting simulator for direct error estimation and sequence optimization

Magnetic resonance fingerprinting (MRF) is a novel quantitative MR technique that simultaneously provides multiple tissue property maps. When optimizing MRF scans, modeling undersampling errors and field imperfections in cost functions for direct measurement of quantitative errors will make the optimization results more practical and robust. However, optimizing such cost function is computationally expensive and impractical for MRF optimization with tens of thousands of iterations. Here, we introduce a fast MRF simulator to simulate aliased images from actual scan scenarios including undersampling and system imperfections, which substantially reduces computational time and allows for direct error estimation of the quantitative maps and efficient sequence optimization. We evaluate the performance and computational speed of the proposed approach by simulations and in vivo experiments. The simulations from the proposed method closely approximate the signals and MRF maps from in vivo scans, with 158 times shorter processing time than the conventional simulation method using Non-uniform Fourier transform. We also demonstrate the power of applying the fast MRF simulator in MRF sequence optimization. The optimized sequences are validated with in vivo scans to assess the image quality and accuracy. The optimized sequences produce artifact-free T1 and T2 maps in 2D and 3D scans with equivalent mapping accuracy as the human-designed sequence but at shorter scan times. Incorporating the proposed simulator in the MRF optimization framework makes direct estimation of undersampling errors during the optimization process feasible, and provide optimized MRF sequences that are robust against undersampling artifacts and field inhomogeneity.

Optimized three-dimensional ultrashort echo time: Magnetic resonance fingerprinting for myelin tissue fraction mapping

Quantitative assessment of brain myelination has gained attention for both research and diagnosis of neurological diseases. However, conventional pulse sequences cannot directly acquire the myelin-proton signals due to its extremely short T2 and T2* values. To obtain the myelin-proton signals, dedicated short T2 acquisition techniques, such as ultrashort echo time (UTE) imaging, have been introduced. However, it remains challenging to isolate the myelin-proton signals from tissues with longer T2. In this article, we extended our previous two-dimensional ultrashort echo time magnetic resonance fingerprinting (UTE-MRF) with dual-echo acquisition to three dimensional (3D). Given a relatively low proton density (PD) of myelin-proton, we utilized Cramér-Rao Lower Bound to encode myelin-proton with the maximal SNR efficiency for optimizing the MR fingerprinting design, in order to improve the sensitivity of the sequence to myelin-proton. In addition, with a second echo of approximately 3 ms, myelin-water component can be also captured. A myelin-tissue (myelin-proton and myelin-water) fraction mapping can be thus calculated. The optimized 3D UTE-MRF with dual-echo acquisition is tested in simulations, physical phantom and in vivo studies of both healthy subjects and multiple sclerosis patients. The results suggest that the rapidly decayed myelin-proton and myelin-water signal can be depicted with UTE signals of our method at clinically relevant resolution (1.8 mm isotropic) in 15 min. With its good sensitivity to myelin loss in multiple sclerosis patients demonstrated, our method for the whole brain myelin-tissue fraction mapping in clinical friendly scan time has the potential for routine clinical imaging.

Three-dimensional multi-parameter brain mapping using MR fingerprinting

The purpose of this study was to develop and test a 3D multi-parameter MR fingerprinting (MRF) method for brain imaging applications. The subject cohort included 5 healthy volunteers, repeatability tests done on 2 healthy volunteers and tested on two multiple sclerosis (MS) patients. A 3D-MRF imaging technique capable of quantifying T1, T2 and T1ρ was used. The imaging sequence was tested in standardized phantoms and 3D-MRF brain imaging with multiple shots (1, 2 and 4) in healthy human volunteers and MS patients. Quantitative parametric maps for T1, T2, T1ρ, were generated. Mean gray matter (GM) and white matter (WM) ROIs were compared for each mapping technique, Bland-Altman plots and intra-class correlation coefficient (ICC) were used to assess repeatability and Student T-tests were used to compare results in MS patients. Standardized phantom studies demonstrated excellent agreement with reference T1/T2/T1ρ mapping techniques. This study demonstrates that the 3D-MRF technique is able to simultaneously quantify T1, T2 and T1ρ for tissue property characterization in a clinically feasible scan time. This multi-parametric approach offers increased potential to detect and differentiate brain lesions and to better test imaging biomarker hypotheses for several neurological diseases, including MS.

On Ambiguity in Linear Inverse Problems: Entrywise Bounds on Nearly Data-Consistent Solutions and Entrywise Condition Numbers

Ill-posed linear inverse problems appear frequently in various signal processing applications. It can be very useful to have theoretical characterizations that quantify the level of ill-posedness for a given inverse problem and the degree of ambiguity that may exist about its solution. Traditional measures of ill-posedness, such as the condition number of a matrix, provide characterizations that are global in nature. While such characterizations can be powerful, they can also fail to provide full insight into situations where certain entries of the solution vector are more or less ambiguous than others. In this work, we derive novel theoretical lower- and upper-bounds that apply to individual entries of the solution vector, and are valid for all potential solution vectors that are nearly data-consistent. These bounds are agnostic to the noise statistics and the specific method used to solve the inverse problem, and are also shown to be tight. In addition, our results also lead us to introduce an entrywise version of the traditional condition number, which provides a substantially more nuanced characterization of scenarios where certain elements of the solution vector are less sensitive to perturbations than others. Our results are illustrated in an application to magnetic resonance imaging reconstruction, and we include discussions of practical computation methods for large-scale inverse problems, connections between our new theory and the traditional Cramér-Rao bound under statistical modeling assumptions, and potential extensions to cases involving constraints beyond just data-consistency.

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.

The future is 2D: spectral-temporal fitting of dynamic MRS data provides exponential gains in precision over conventional approaches

PURPOSE

Many MRS paradigms produce 2D spectral-temporal datasets, including diffusion-weighted, functional, and hyperpolarized and enriched (carbon-13, deuterium) experiments. Conventionally, temporal parameters-such as T₂ , T₁ , or diffusion constants-are assessed by first fitting each spectrum independently and subsequently fitting a temporal model (1D fitting). We investigated whether simultaneously fitting the entire dataset using a single spectral-temporal model (2D fitting) would improve the precision of the relevant temporal parameter.

METHODS

We derived a Cramer Rao lower bound for the temporal parameters for both 1D and 2D approaches for 2 experiments: a multi-echo experiment designed to estimate metabolite T₂ s, and a functional MRS experiment designed to estimate fractional change ( δ $$ \delta $$ ) in metabolite concentrations. We investigated the dependence of the relative standard deviation (SD) of T₂ in multi-echo and δ $$ \delta $$ in functional MRS.

RESULTS

When peaks were spectrally distant, 2D fitting improved precision by approximately 20% relative to 1D fitting, regardless of the experiment and other parameter values. These gains increased exponentially as peaks drew closer. Dependence on temporal model parameters was weak to negligible.

CONCLUSION

Our results strongly support a 2D approach to MRS fitting where applicable, and particularly in nuclei such as hydrogen and deuterium, which exhibit substantial spectral overlap.

CEST MR fingerprinting (CEST-MRF) for brain tumor quantification using EPI readout and deep learning reconstruction

PURPOSE

To develop a clinical CEST MR fingerprinting (CEST-MRF) method for brain tumor quantification using EPI acquisition and deep learning reconstruction.

METHODS

A CEST-MRF pulse sequence originally designed for animal imaging was modified to conform to hardware limits on clinical scanners while keeping scan time under 2 min. Quantitative MRF reconstruction was performed using a deep reconstruction network (DRONE) to yield the water relaxation and chemical exchange parameters. The feasibility of the six parameter DRONE reconstruction was tested in simulations using a digital brain phantom. A healthy subject was scanned with the CEST-MRF sequence, conventional MRF and CEST sequences for comparison. Reproducibility was assessed via test-retest experiments and the concordance correlation coefficient calculated for white matter and gray matter. The clinical utility of CEST-MRF was demonstrated on four patients with brain metastases in comparison to standard clinical imaging sequences. Tumors were segmented into edema, solid core, and necrotic core regions and the CEST-MRF values compared to the contra-lateral side.

RESULTS

DRONE reconstruction of the digital phantom yielded a normalized RMS error of ≤7% for all parameters. The CEST-MRF parameters were in good agreement with those from conventional MRF and CEST sequences and previous studies. The mean concordance correlation coefficient for all six parameters was 0.98 ± 0.01 in white matter and 0.98 ± 0.02 in gray matter. The CEST-MRF values in nearly all tumor regions were significantly different (P = 0.05) from each other and the contra-lateral side.

CONCLUSION

Combination of EPI readout and deep learning reconstruction enabled fast, accurate and reproducible CEST-MRF in brain tumors.

MR Fingerprinting for Liver Tissue Characterization: A Histopathologic Correlation Study

Background Liver MR fingerprinting (MRF) enables simultaneous quantification of T1, T2, T2*, and proton density fat fraction (PDFF) maps in single breath-hold acquisitions. Histopathologic correlation studies are desired for its clinical use. Purpose To compare liver MRF-derived metrics with separate reference quantitative MRI in participants with diffuse liver disease, evaluate scan-rescan repeatability of liver MRF, and validate MRF-derived measurements for histologic grading of liver biopsies. Materials and Methods This prospective study included participants with diffuse liver disease undergoing MRI from July 2021 to January 2022. Participants underwent two-dimensional single-section liver MRF and separate reference quantitative MRI. Linear regression, Bland-Altman plots, and coefficients of variation were used to assess the bias and repeatability of liver MRF measurements. For participants undergoing liver biopsy, the association between mapping and histologic grading was evaluated by using the Spearman correlation coefficient. Results Fifty-six participants (mean age, 59 years ± 15 [SD]; 32 women) were included to compare mapping techniques and 23 participants were evaluated with liver biopsy (mean age, 52.7 years ± 12.7; 14 women). The linearity of MRF with reference measurements in participants with diffuse liver disease (R² value) for T1, T2, T2*, and PDFF maps was 0.86, 0.88, 0.54, and 0.99, respectively. The overall coefficients of variation for repeatability in the liver were 3.2%, 5.5%, 7.1%, and 4.6% for T1, T2, T2*, and PDFF maps, respectively. MRF-derived metrics showed high diagnostic performance in differentiating moderate or severe changes from mild or no changes (area under the receiver operating characteristic curve for fibrosis, inflammation, steatosis, and siderosis: 0.62 [95% CI: 0.52, 0.62], 0.92 [95% CI: 0.88, 0.92], 0.97 [95% CI: 0.96, 0.97], and 0.74 [95% CI: 0.57, 0.74], respectively). Conclusion Liver MR fingerprinting provided repeatable T1, T2, T2*, and proton density fat fraction maps in high agreement with reference quantitative mapping and may correlate with pathologic grades in participants with diffuse liver disease. © RSNA, 2022 Online supplemental material is available for this article.

Multicomponent MR fingerprinting reconstruction using joint-sparsity and low-rank constraints

PURPOSE

To develop an efficient algorithm for multicomponent MR fingerprinting (MC-MRF) reconstructions directly from highly undersampled data without making prior assumptions about tissue relaxation times and expected number of tissues.

METHODS

The proposed method reconstructs MC-MRF maps from highly undersampled data by iteratively applying a joint-sparsity constraint to the estimated tissue components. Intermediate component maps are obtained by a low-rank multicomponent alternating direction method of multipliers (MC-ADMM) including the non-negativity of tissue weights as an extra regularization term. Over iterations, the used dictionary compression is adjusted. The proposed method (k-SPIJN) is compared with a two-step approach in which image reconstruction and multicomponent estimations are performed sequentially and tested in numerical simulations and in vivo by applying different undersampling factors in eight healthy volunteers. In the latter case, fully sampled data serves as the reference.

RESULTS

The proposed method shows improved precision and accuracy in simulations compared with a state-of-art sequential approach. Obtained in vivo magnetization fraction maps for different tissue types show reduced systematic errors and reduced noise-like effects. Root mean square errors in estimated magnetization fraction maps significantly reduce from 13.0% <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:semantics><mml:mrow><mml:mo>±</mml:mo></mml:mrow> <mml:annotation>$$ \pm $$</mml:annotation></mml:semantics> </mml:math> 5.8% with the conventional, two-step approach to 9.6% <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:semantics><mml:mrow><mml:mo>±</mml:mo></mml:mrow> <mml:annotation>$$ \pm $$</mml:annotation></mml:semantics> </mml:math> 3.9% and 9.6% <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:semantics><mml:mrow><mml:mo>±</mml:mo></mml:mrow> <mml:annotation>$$ \pm $$</mml:annotation></mml:semantics> </mml:math> 3.2% with the proposed MC-ADMM and k-SPIJN methods, respectively. Mean standard deviation in homogeneous white matter regions reduced significantly from 8.6% to 2.9% (two step vs. k-SPIJN).

CONCLUSION

The proposed MC-ADMM and k-SPIJN reconstruction methods estimate MC-MRF maps from highly undersampled data resulting in improved image quality compared with the existing method.

Optimisation of data acquisition towards continuous cardiac Magnetic Resonance Fingerprinting applications

PURPOSE

Assess and optimise acquisition parameters for continuous cardiac Magnetic Resonance Fingerprinting (MRF).

METHODS

Different acquisition schemes (flip angle amplitude, lobe size, T2-preparation pulses) for cardiac MRF were assessed in simulations and phantom and demonstrated in one healthy volunteer. Three different experimental designs were evaluated using central composite and fractional factorial designs. Relative errors for T1 and T2 were calculated for a wide range of realistic T1 and T2 value combinations. The effect of different designs on the accuracy of T1 and T2 was assessed using response surface modelling and Cohen's f calculations.

RESULTS

Larger flip angle amplitudes lead to an improvement of T2 accuracy and precision for simulations and phantom experiments. Similar effects could also be shown qualitatively in in-vivo scans. Accuracy and precision of T1 were robust to different design parameters with improved values for faster flip angle variation. Cohen's f showed that T2-preparation pulses influence the accuracy of T2. The number of pulses used is the most important parameter. Without T2-preparation pulses, RMSE were 3.0 ± 8.09 % for T1 and 16.24 ± 14.47 % for T2. Using those pulses reduced the RMSE to 2.3 ± 8.4 % for T1 and 14.11 ± 13.46 % for T2. Nonetheless, even if the improvement is significant, RMSE are still too high for reliable quantification.

CONCLUSION

In contrast to previous study using triggered MRF sequences using < 30° flip angles, large flip angle amplitudes led to better results for continuous cardiac MRF sequences. T2-preparation pulse can improve the accuracy of T2 estimation but lead to longer scan times.

3D magnetic resonance fingerprinting for rapid simultaneous T1, T2, and T1ρ volumetric mapping of human articular cartilage at 3 T

Quantitative MRI can detect early biochemical changes in cartilage; however, the conventional techniques only measure one parameter (e.g., T1 , T2 , and T1ρ ) at a time while also being comparatively slow. We implemented a 3D magnetic resonance fingerprinting (3D-MRF) technique for simultaneous, volumetric mapping of T1 , T2 , and T1ρ in knee articular cartilage in under 9 min. It is evaluated on 11 healthy volunteers (mean age: 53 ± 9 years), five mild knee osteoarthritis (OA) patients (Kellgren-Lawrence (KL) score: 2, mean age: 60 ± 4 years), and the National Institute of Standards and Technology (NIST)/International Society for Magnetic Resonance in Medicine (ISMRM) system phantom. Proton density image, and T1 , T2, T1ρ relaxation times, and B1 + were estimated in the NIST/ISMRM system phantom as well as in the human knee medial and lateral femur, medial and lateral tibia, and patellar cartilage. The repeatability and reproducibility of the proposed technique were assessed in the phantom using analysis of the Bland-Altman plots. The intrasubject repeatability was assessed with the coefficient of variation (CV) and root mean square CV (rmsCV). The Mann-Whitney U test was used to assess the difference between healthy subjects and mild knee OA patients. The Bland-Altman plots in the NIST/ISMRM phantom demonstrated an average difference of 0.001% ± 015%, 1.2% ± 7.1%, and 0.47% ± 3% between two scans from the same 3-T scanner (repeatability), and 0.002% ± 015%, 0.62% ± 10.5%, and 0.97% ± 14% between the scans acquired on two different 3-T scanners (reproducibility) for T1 , T2 , and T1ρ , respectively. The in vivo knee study showed excellent repeatability with rmsCV less than 1%, 2%, and 1% for T1 , T2 , and T1ρ , respectively. T1ρ relaxation time in the mild knee OA patients was significantly higher (p < 0.05) than in healthy subjects. The proposed 3D-MRF sequence is fast, reproducible, robust to B1 + inhomogeneity, and can simultaneously measure the T1 , T2 , T1ρ , and B1 + volumetric maps of the knee joint in a single scan within a clinically feasible scan time.

MR Fingerprinting with b-Tensor Encoding for Simultaneous Quantification of Relaxation and Diffusion in a Single Scan

PURPOSE

Although both relaxation and diffusion imaging are sensitive to tissue microstructure, studies have reported limited sensitivity and robustness of using relaxation or conventional diffusion alone to characterize tissue microstructure. Recently, it has been shown that tensor-valued diffusion encoding and joint relaxation-diffusion quantification enable more reliable quantification of compartment-specific microstructural properties. However, scan times to acquire such data can be prohibitive. Here, we aim to simultaneously quantify relaxation and diffusion using MR fingerprinting (MRF) and b-tensor encoding in a clinically feasible time.

METHODS

We developed multidimensional MRF scans (mdMRF) with linear and spherical b-tensor encoding (LTE and STE) to simultaneously quantify T1, T2, and ADC maps from a single scan. The image quality, accuracy, and scan efficiency were compared between the mdMRF using LTE and STE. Moreover, we investigated the robustness of different sequence designs to signal errors and their impact on the maps.

RESULTS

T1 and T2 maps derived from the mdMRF scans have consistently high image quality, while ADC maps are sensitive to different sequence designs. Notably, the fast imaging steady state precession (FISP)-based mdMRF scan with peripheral pulse gating provides the best ADC maps that are free of image distortion and shading artifacts.

CONCLUSION

We demonstrated the feasibility of quantifying T1, T2, and ADC maps simultaneously from a single mdMRF scan in around 24 s/slice. The map quality and quantitative values are consistent with the reference scans.

Single-shot multi-parametric mapping based on multiple overlapping-echo detachment (MOLED) imaging

Multi-parametric quantitative magnetic resonance imaging (mqMRI) allows the characterization of multiple tissue properties non-invasively and has shown great potential to enhance the sensitivity of MRI measurements. However, real-time mqMRI during dynamic physiological processes or general motions remains challenging. To overcome this bottleneck, we propose a novel mqMRI technique based on multiple overlapping-echo detachment (MOLED) imaging, termed MQMOLED, to enable mqMRI in a single shot. In the data acquisition of MQMOLED, multiple MR echo signals with different multi-parametric weightings and phase modulations are generated and acquired in the same k-space. The k-space data is Fourier transformed and fed into a well-trained neural network for the reconstruction of multi-parametric maps. We demonstrated the accuracy and repeatability of MQMOLED in simultaneous mapping apparent proton density (APD) and any two parameters among T₂, T₂*, and apparent diffusion coefficient (ADC) in 130-170 ms. The abundant information delivered by the multiple overlapping-echo signals in MQMOLED makes the technique potentially robust to system imperfections, such as inhomogeneity of static magnetic field or radiofrequency field. Benefitting from the single-shot feature, MQMOLED exhibits a strong motion tolerance to the continuous movements of subjects. For the first time, it captured the synchronous changes of ADC, T₂, and T₁-weighted APD in contrast-enhanced perfusion imaging on patients with brain tumors, providing additional information about vascular density to the hemodynamic parametric maps. We expect that MQMOLED would promote the development of mqMRI technology and greatly benefit the applications of mqMRI, including therapeutics and analysis of metabolic/functional processes.

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.

Improved Balanced Steady-State Free Precession Based MR Fingerprinting with Deep Autoencoders

Magnetic Resonance (MR) Fingerprinting is an emerging transient-state imaging paradigm, which enables the quantization of multiple MR tissue parameters in a single experiment. Balanced steady-state free precession (bSSFP)-based MR Fingerprinting has excellent signal-to-noise characteristics and also allows for acquiring both tissue parameter maps and field inhomogeneity maps. However, field inhomogeneity often results in complex magnetization evolutions in bSSFP-based MR Fingerprinting, which creates significant challenges in image reconstruction. In this paper, we introduce a new method to address the image reconstruction problem. The proposed method incorporates a low-dimensional nonlinear manifold learned from an ensemble of magnetization evolutions using a deep autoencoder. It provides much better representation power than a low-dimensional linear subspace in capturing complex magnetization evolutions. We formulate the image reconstruction problem with this nonlinear model and solve the resulting optimization problem using an algorithm based on variable splitting and the alternating direction method of multipliers. We evaluate the performance of the proposed method using numerical experiments and demonstrate that it significantly outperforms the state-of-art method using a linear subspace model.

Active Sampling for Accelerated MRI with Low-Rank Tensors

Magnetic resonance imaging (MRI) is a powerful imaging modality that revolutionizes medicine and biology. The imaging speed of high -dimensional MRI is often limited, which constrains its practical utility. Recently, low-rank tensor models have been exploited to enable fast MR imaging with sparse sampling. Most existing methods use some pre-defined sampling design, and active sensing has not been explored for low-rank tensor imaging. In this paper, we introduce an active low-rank tensor model for fast MR imaging. We propose an active sampling method based on a Query-by-Committee model, making use of the benefits of low-rank tensor structure. Numerical experiments on a 3-D MRI data set with Cartesian sampling designs demonstrate the effectiveness of the proposed method.

Learning-based optimization of acquisition schedule for magnetization transfer contrast MR fingerprinting

Magnetization transfer contrast MR fingerprinting (MTC-MRF) is a novel quantitative imaging method that simultaneously quantifies free bulk water and semisolid macromolecule parameters using pseudo-randomized scan parameters. To improve acquisition efficiency and reconstruction accuracy, the optimization of MRF sequence design has been of recent interest in the MRF field, but has been challenging due to the large number of degrees of freedom to be optimized in the sequence. Herein, we propose a framework for learning-based optimization of the acquisition schedule (LOAS), which optimizes RF saturation-encoded MRF acquisitions with a minimal number of scan parameters for tissue parameter determination. In a supervised learning framework, scan parameters were subsequently updated to minimize a predefined loss function that can directly represent tissue quantification errors. We evaluated the performance of the proposed approach with a numerical phantom and in in vivo experiments. For validation, MRF images were synthesized using the tissue parameters estimated from a fully connected neural network framework and compared with references. Our results showed that LOAS outperformed existing indirect optimization methods with regard to quantification accuracy and acquisition efficiency. The proposed LOAS method could be a powerful optimization tool in the design of MRF pulse sequences.

Simultaneous 3D acquisition of 1 H MRF and 23 Na MRI

PURPOSE

To develop a 3D MR technique to simultaneously acquire proton multiparametric maps (T₁ , T₂ , and proton density) and sodium density weighted images over the whole brain.

METHODS

We implemented a 3D stack-of-stars MR pulse sequence which consists of interleaved proton (¹ H) and sodium (²³ Na) excitations, tailored slice encoding gradients that can encode the same slice for both nuclei, and simultaneous readout with different radial trajectories (¹ H, full-radial; ²³ Na, center-out radial). The receive chain of our 7T scanner was modified to enable simultaneous acquisition of ¹ H and ²³ Na signal. A heuristically optimized flip angle train was implemented for proton MR fingerprinting (MRF). The SNR and the accuracy of proton T₁ and T₂ were evaluated in phantoms. Finally, in vivo application of the method was demonstrated in five healthy subjects.

RESULTS

The SNR for the simultaneous measurement was almost identical to that for the single-nucleus measurements (<2% change). The proton T₁ and T₂ maps remained similar to the results from a reference 2D MRF technique (normalized RMS error in T₁ ≈ 4.2% and T₂ ≈ 11.3%). Measurements in healthy subjects corroborated these results and demonstrated the feasibility of our method for in vivo application. The in vivo T₁ values measured using our method were lower than the results measured by other conventional techniques.

CONCLUSIONS

With the 3D simultaneous implementation, we were able to acquire sodium and proton density weighted images in addition to proton T₁ , T₂ , and B1+ from ¹ H MRF that covers the whole brain volume within 21 min.

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.

Fast Quantitative Low-Field Magnetic Resonance Imaging With OPTIMUM-Optimized Magnetic Resonance Fingerprinting Using a Stationary Steady-State Cartesian Approach and Accelerated Acquisition Schedules

OBJECTIVE

The aim of the proposed work is to develop model-based, fast multiparametric magnetic resonance imaging (MRI) in field regimes where signal-to-noise ratio is poor, such as encountered at low-field and in low γ nuclei.

MATERIALS AND METHODS

A custom, optimized MRI pipeline was developed at low field (0.1 T) that relies on the magnetic resonance fingerprinting framework, called OPTIMUM. An optimization algorithm was used to select a short acquisition schedule (n = 18 images) that favors maximal discrimination across varying magnetic properties (T1, T2) and off-resonance effects while maintaining high transverse magnetization at the steady state. In the presented study, a stationary balanced steady-state approach was investigated that allows for Cartesian (used here) and non-Cartesian acquisition schemes. Images were collected in calibrated samples containing different concentrations of manganese(II) chloride (MnCl2) in deionized water and compared with gold standard techniques (ie, inversion recovery for T1, Carr-Purcell-Meiboom-Gill for T2). Images were then collected in vivo in the human hand and wrist.

RESULTS

OPTIMUM successfully provided sets of quantified maps (T1, T2, T2*, M0, ΔB0, B1+) in calibrated samples and in vivo in the human hand and wrist in 3 dimensions, in ~8.5 minutes, with a voxel resolution of [1.5 ×1.5 × 6.5] mm3. Relaxation parameters (T1, T2) scale linearly with [MnCl2] and are in good agreement with the calibrations performed for T1, with a consistent trend to underestimate T2.

CONCLUSION

We show that low-field MRI can benefit from innovative multiparametric approaches to gain speed and become realistic in clinical environments. For the first time, we report simultaneous, multiparametric imaging (6 quantitative maps) in 3 dimensions, in vivo in the human hand and wrist, obtained in just 8.5 minutes. It is sometimes overlooked that low magnetic fields provide higher dispersion of nuclear spin relaxation rates. Rapid quantification such as offered by OPTIMUM could be an enabling technology to explore new metrics and contrasts in point-of-care MRI diagnosis, making it an important step toward broad democratization.

3D MR fingerprinting using Seiffert spirals

PURPOSE

Seiffert spirals were recently explored as an efficient way to traverse 3D k-space compared to traditional 3D techniques. Several studies have shown the ability of 3D MR fingerprinting (MRF) techniques to acquire T₁ and T₂ relaxation maps in a short period of time. However, these sequences do not sample across a large region of 3D k-space every TR, especially in the way that Seiffert trajectories can.

METHODS

A 3D MRF sequence was designed using 8 Seiffert spirals rotated in 3D k-space, with flip angle modulation for T₁ and T₂ sensitivity. The sequence was compared to an MRF sequence using a 2D spiral rotated in 3D k-space using the tiny golden angle acquisition with similar resolution/readout duration. Both sequences were evaluated using simulations, phantom validation, and in vivo imaging.

RESULTS

In all experiments, the Seiffert spiral MRF sequence performed similar to if not better than the multi-axis 2D spiral MRF sequence. Strong intraclass correlation coefficients (> 0.9) were found between conventional and MRF sequences in phantoms, whereas the in vivo results showed slightly less aliasing artifact with the Seiffert trajectory.

CONCLUSION

In this study, Seiffert spirals were used within the MRF framework to acquire high-resolution T₁ and T₂ relaxation time maps in less than 2.5 min. The reduced aliasing artifacts seen with the Seiffert sequence suggests that sampling over 3D k-space evenly each TR can improve quantification or shorten scan times.

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.

A Multicomponent Temporal Coherence Model for 3-D Phase Unwrapping in Time-Series InSAR of Seasonal Deformation Areas

3-D phase unwrapping (PU) methods based on the 2-D linear temporal coherencemodel have been widely used in time-series interferometric synthetic aperture radar (TS-InSAR) for measuring topography and monitoring subtle deformation. However, the linear temporal coherencemodel can not characterize the coherence of highly coherent pixels accurately in seasonal deformation areas, where nonlinear deformation is deterministic and nonnegligible. Especially, for urban areas with groundwater or thermal dilation seasonal changes or permafrost regions, the nonlinear deformation is usually associated with periodic temperature changes. In this work, a general multi-component temporal coherence model, which considers multiple components including the seasonal deformation, is proposed for 3-D PU of seasonal deformation areas. Moreover, the uncertainty evaluation criterion, based on Cramér–Rao bound (CRB), is derived for TS-InSAR. The experimental results, obtained by applying the multi-component temporal coherence model to a data set acquired from January 2012 to February 2016 over the Beijing Capital International Airport area, confirm the effectiveness of the proposed method. High phase consistency, accurate corrected digital elevation model (DEM) and deformation information monitoring with high-density and high-coverage PS pixels are achieved. Under the same iterations and TS-InSAR procedure, the enhanced performance by the proposed model is illustrated by comparing with that of linear model in terms of phase consistency of 3-D phase unwrapping, PSCs selection at each step, and final results evaluation. In summary, the number of phase-consistency edges after 3-D PU is increased by about 15%, the number of final PS pixels selected with the same coherence threshold constraint is increased by about 10%, and more PS pixels provide a low uncertainty in residual topography, mean deformation velocity and seasonal amplitude estimation.

MR fingerprinting for semisolid magnetization transfer and chemical exchange saturation transfer quantification

Chemical exchange saturation transfer (CEST) MRI has positioned itself as a promising contrast mechanism, capable of providing molecular information at sufficient resolution and amplified sensitivity. However, it has not yet become a routinely employed clinical technique, due to a variety of confounding factors affecting its contrast-weighted image interpretation and the inherently long scan time. CEST MR fingerprinting (MRF) is a novel approach for addressing these challenges, allowing simultaneous quantitation of several proton exchange parameters using rapid acquisition schemes. Recently, a number of deep-learning algorithms have been developed to further boost the performance and speed of CEST and semi-solid macromolecule magnetization transfer (MT) MRF. This review article describes the fundamental theory behind semisolid MT/CEST-MRF and its main applications. It then details supervised and unsupervised learning approaches for MRF image reconstruction and describes artificial intelligence (AI)-based pipelines for protocol optimization. Finally, practical considerations are discussed, and future perspectives are given, accompanied by basic demonstration code and data.

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.

Combined diffusion-relaxometry microstructure imaging: Current status and future prospects

Microstructure imaging seeks to noninvasively measure and map microscopic tissue features by pairing mathematical modeling with tailored MRI protocols. This article reviews an emerging paradigm that has the potential to provide a more detailed assessment of tissue microstructure-combined diffusion-relaxometry imaging. Combined diffusion-relaxometry acquisitions vary multiple MR contrast encodings-such as b-value, gradient direction, inversion time, and echo time-in a multidimensional acquisition space. When paired with suitable analysis techniques, this enables quantification of correlations and coupling between multiple MR parameters-such as diffusivity, T 1 , T 2 , and T 2 ∗ . This opens the possibility of disentangling multiple tissue compartments (within voxels) that are indistinguishable with single-contrast scans, enabling a new generation of microstructural maps with improved biological sensitivity and specificity.

Encoding capability prediction of acquisition schedules in CEST MR fingerprinting for pH quantification

PURPOSE

To identify a reliable metric for predicting the encoding capability of CEST MR fingerprinting acquisition schedules for pH quantification, which may facilitate CEST MR fingerprinting protocol optimization.

METHODS

Numerical simulations and Cr phantom MRI experiments were conducted at 3 Tesla under representative CEST MR fingerprinting sampling scenarios, including the pseudorandomization of imaging parameters (e.g., saturation power B₁ , saturation frequency offset, saturation time, and relaxation time), and variation of the maximum saturation power B_1max , B₁ number, and sampling pattern. The CEST effect at 2 ppm was measured using asymmetry analysis and matched to a predefined dictionary to determine the pH. The pH quantification error was assessed using RMSE. Three metrics, namely the Cramer-Rao bound, dot product, and Euclidean distance, were calculated for each sampling scenario, and their relationships with the pH RMSE were investigated to examine their effectiveness for predicting the encoding capability of sampling schedules for pH quantification.

RESULTS

Both simulation and phantom studies revealed that the Cramer-Rao bound metric consistently exhibited superior performance for predicting the pH quantification error. Although dot product exhibited good encoding capability prediction in most sampling scenarios, it failed in the scenario with varied B₁ numbers. In contrast, Euclidean distance exhibited the worst performance among the 3 metrics in all scenarios.

CONCLUSION

Superior over dot product and Euclidean distance, the Cramer-Rao bound metric may reliably predicting the encoding capability of CEST MR fingerprinting sampling strategies and may be useful for guiding CEST MRI protocol optimization.

Stochastic neighbor embedding as a tool for visualizing the encoding capability of magnetic resonance fingerprinting dictionaries

Objective

To visualize the encoding capability of magnetic resonance fingerprinting (MRF) dictionaries.

Materials and methods

High-dimensional MRF dictionaries were simulated and embedded into a lower-dimensional space using t-distributed stochastic neighbor embedding (t-SNE). The embeddings were visualized via colors as a surrogate for location in low-dimensional space. First, we illustrate this technique on three different MRF sequences. We then compare the resulting embeddings and the color-coded dictionary maps to these obtained with a singular value decomposition (SVD) dimensionality reduction technique. We validate the t-SNE approach with measures based on existing quantitative measures of encoding capability using the Euclidean distance. Finally, we use t-SNE to visualize MRF sequences resulting from an MRF sequence optimization algorithm.

Results

t-SNE was able to show clear differences between the color-coded dictionary maps of three MRF sequences. SVD showed smaller differences between different sequences. These findings were confirmed by quantitative measures of encoding. t-SNE was also able to visualize differences in encoding capability between subsequent iterations of an MRF sequence optimization algorithm.

Discussion

This visualization approach enables comparison of the encoding capability of different MRF sequences. This technique can be used as a confirmation tool in MRF sequence optimization.

Supplementary Information

The online version contains supplementary material available at 10.1007/s10334-021-00963-8.

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.

Generalized low-rank nonrigid motion-corrected reconstruction for MR fingerprinting

PURPOSE

Develop a novel low-rank motion-corrected (LRMC) reconstruction for nonrigid motion-corrected MR fingerprinting (MRF).

METHODS

Generalized motion-corrected (MC) reconstructions have been developed for steady-state imaging. Here we extend this framework to enable nonrigid MC for transient imaging applications with varying contrast, such as MRF. This is achieved by integrating low-rank dictionary-based compression into the generalized MC model to reconstruct MC singular images, reducing motion artifacts in the resulting parametric maps. The proposed LRMC reconstruction was applied for cardiac motion correction in 2D myocardial MRF (T₁ and T₂ ) with extended cardiac acquisition window (~450 ms) and for respiratory MC in free-breathing 3D myocardial and 3D liver MRF. Experiments were performed in phantom and 22 healthy subjects. The proposed approach was compared with reference spin echo (phantom) and with 2D electrocardiogram-triggered/breath-hold MOLLI and T₂ gradient-and-spin echo conventional maps (in vivo 2D and 3D myocardial MRF).

RESULTS

Phantom results were in general agreement with reference spin-echo measurements, presenting relative errors of approximately 5.4% and 5.5% for T₁ and short T₂ (<100 ms), respectively. The proposed LRMC MRF reduced residual blurring artifacts with respect to no MC for cardiac or respiratory motion in all cases (2D and 3D myocardial, 3D abdominal). In 2D myocardial MRF, left-ventricle T₁ values were 1150 ± 41 ms for LRMC MRF and 1010 ± 56 ms for MOLLI; T₂ values were 43.8 ± 2.3 ms for LRMC MRF and 49.5 ± 4.5 ms for T₂ gradient and spin echo. Corresponding measurements for 3D myocardial MRF were 1085 ± 30 ms and 1062 ± 29 ms for T₁ , and 43.5 ± 1.9 ms and 51.7 ± 1.7 ms for T₂ . For 3D liver, LRMC MRF measured liver T₁ at 565 ± 44 ms and liver T₂ at 35.4 ± 2.4 ms.

CONCLUSION

The proposed LRMC reconstruction enabled generalized (nonrigid) MC for 2D and 3D MRF, both for cardiac and respiratory motion. The proposed approach reduced motion artifacts in the MRF maps with respect to no motion compensation and achieved good agreement with reference measurements.

Fast data-driven learning of parallel MRI sampling patterns for large scale problems

In this study, a fast data-driven optimization approach, named bias-accelerated subset selection (BASS), is proposed for learning efficacious sampling patterns (SPs) with the purpose of reducing scan time in large-dimensional parallel MRI. BASS is applicable when Cartesian fully-sampled k-space measurements of specific anatomy are available for training and the reconstruction method for undersampled measurements is specified; such information is used to define the efficacy of any SP for recovering the values at the non-sampled k-space points. BASS produces a sequence of SPs with the aim of finding one of a specified size with (near) optimal efficacy. BASS was tested with five reconstruction methods for parallel MRI based on low-rankness and sparsity that allow a free choice of the SP. Three datasets were used for testing, two of high-resolution brain images ([Formula: see text]-weighted images and, respectively, [Formula: see text]-weighted images) and another of knee images for quantitative mapping of the cartilage. The proposed approach has low computational cost and fast convergence; in the tested cases it obtained SPs up to 50 times faster than the currently best greedy approach. Reconstruction quality increased by up to 45% over that provided by variable density and Poisson disk SPs, for the same scan time. Optionally, the scan time can be nearly halved without loss of reconstruction quality. Quantitative MRI and prospective accelerated MRI results show improvements. Compared with greedy approaches, BASS rapidly learns effective SPs for various reconstruction methods, using larger SPs and larger datasets; enabling better selection of sampling-reconstruction pairs for specific MRI problems.