GPU-accelerated Bloch simulations and MR-STAT reconstructions using the Julia programming language.

PURPOSE: MR-STAT is a relatively new multiparametric quantitative MRI technique in which quantitative paramater maps are obtained by solving a large-scale nonlinear optimization problem. Managing reconstruction times is one of the main challenges of MR-STAT. In this work we leverage GPU hardware to reduce MR-STAT reconstruction times. A highly optimized, GPU-compatible Bloch simulation toolbox is developed as part of this work that can be utilized for other quantitative MRI techniques as well. METHODS: The Julia programming language was used to develop a flexible yet highly performant and GPU-compatible Bloch simulation toolbox called BlochSimulators.jl. The runtime performance of the toolbox is benchmarked against other Bloch simulation toolboxes. Furthermore, a (partially matrix-free) modification of a previously presented (matrix-free) MR-STAT reconstruction algorithm is proposed and implemented using the Julia language on GPU hardware. The proposed algorithm is combined with BlochSimulators.jl and the resulting MR-STAT reconstruction times on GPU hardware are compared to previously presented MR-STAT reconstruction times. RESULTS: The BlochSimulators.jl package demonstrates superior runtime performance on both CPU and GPU hardware when compared to other existing Bloch simulation toolboxes. The GPU-accelerated partially matrix-free MR-STAT reconstruction algorithm, which relies on BlochSimulators.jl, allows for reconstructions of 68 seconds per two-dimensional (2D slice). CONCLUSION: By combining the proposed Bloch simulation toolbox and the partially matrix-free reconstruction algorithm, 2D MR-STAT reconstructions can be performed in the order of one minute on a modern GPU card. The Bloch simulation toolbox can be utilized for other quantitative MRI techniques as well, for example for online dictionary generation for MR Fingerprinting.

High SNR full brain relaxometry at 7T by accelerated MR-STAT.

PURPOSE: To demonstrate the feasibility and robustness of the Magnetic Resonance Spin TomogrAphy in Time-domain (MR-STAT) framework for fast, high SNR relaxometry at 7T. METHODS: To deploy MR-STAT on 7T-systems, we designed optimized flip-angles using the BLAKJac-framework that incorporates the SAR-constraints. Transmit RF-inhomogeneities were mitigated by including a measured B 1 + $$ {B}_1^{+} $$ -map in the reconstruction. Experiments were performed on a gel-phantom and on five volunteers to explore the robustness of the sequence and its sensitivity to B 1 + $$ {B}_1^{+} $$ inhomogeneities. The SNR-gain at 7T was explored by comparing phantom and in vivo results to MR-STAT at 3T in terms of SNR-efficiency. RESULTS: The higher SNR at 7T enabled two-fold acceleration with respect to current 2D MR-STAT protocols at lower field strengths. The resulting scan had whole-brain coverage, with 1 x 1 x 3 mm3 resolution (1.5 mm slice-gap) and was acquired within 3 min including the B 1 + $$ {B}_1^{+} $$ -mapping. After B 1 + $$ {B}_1^{+} $$ -correction, the estimated T1 and T2 in a phantom showed a mean relative error of, respectively, 1.7% and 4.4%. In vivo, the estimated T1 and T2 in gray and white matter corresponded to the range of values reported in literature with a variation over the subjects of 1.0%-2.1% (WM-GM) for T1 and 4.3%-5.3% (WM-GM) for T2. We measured a higher SNR-efficiency at 7T (R = 2) than at 3T for both T1 and T2 with, respectively, a 4.1 and 2.3 times increase in SNR-efficiency. CONCLUSION: We presented an accelerated version of MR-STAT tailored to high field (7T) MRI using a low-SAR flip-angle train and showed high quality parameter maps with an increased SNR-efficiency compared to MR-STAT at 3T.

A three-dimensional Magnetic Resonance Spin Tomography in Time-domain protocol for high-resolution multiparametric quantitative magnetic resonance imaging.

Magnetic Resonance Spin TomogrAphy in Time-domain (MR-STAT) is a multiparametric quantitative MR framework, which allows for simultaneously acquiring quantitative tissue parameters such as T1, T2, and proton density from one single short scan. A typical two-dimensional (2D) MR-STAT acquisition uses a gradient-spoiled, gradient-echo sequence with a slowly varying RF flip-angle train and Cartesian readouts, and the quantitative tissue maps are reconstructed by an iterative, model-based optimization algorithm. In this work, we design a three-dimensional (3D) MR-STAT framework based on previous 2D work, in order to achieve better image signal-to-noise ratio, higher though-plane resolution, and better tissue characterization. Specifically, we design a 7-min, high-resolution 3D MR-STAT sequence, and the corresponding two-step reconstruction algorithm for the large-scale dataset. To reduce the long acquisition time, Cartesian undersampling strategies such as SENSE are adopted in our transient-state quantitative framework. To reduce the computational burden, a data-splitting scheme is designed for decoupling the 3D reconstruction problem into independent 2D reconstructions. The proposed 3D framework is validated by numerical simulations, phantom experiments, and in vivo experiments. High-quality knee quantitative maps with 0.8 × 0.8 × 1.5 mm3 resolution and bilateral lower leg maps with 1.6 mm isotropic resolution can be acquired using the proposed 7-min acquisition sequence and the 3-min-per-slice decoupled reconstruction algorithm. The proposed 3D MR-STAT framework could have wide clinical applications in the future.

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.

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.

Synthetic MRI with Magnetic Resonance Spin TomogrAphy in Time-Domain (MR-STAT): Results from a Prospective Cross-Sectional Clinical Trial.

BACKGROUND: Magnetic Resonance Spin TomogrAphy in Time-domain (MR-STAT) can reconstruct whole-brain multi-parametric quantitative maps (eg, T1 , T2 ) from a 5-minute MR acquisition. These quantitative maps can be leveraged for synthetization of clinical image contrasts. PURPOSE: The objective was to assess image quality and overall diagnostic accuracy of synthetic MR-STAT contrasts compared to conventional contrast-weighted images. STUDY TYPE: Prospective cross-sectional clinical trial. POPULATION: Fifty participants with a median age of 45 years (range: 21-79 years) consisting of 10 healthy participants and 40 patients with neurological diseases (brain tumor, epilepsy, multiple sclerosis or stroke). FIELD STRENGTH/SEQUENCE: 3T/Conventional contrast-weighted imaging (T1 /T2 weighted, proton density [PD] weighted, and fluid-attenuated inversion recovery [FLAIR]) and a MR-STAT acquisition (2D Cartesian spoiled gradient echo with varying flip angle preceded by a non-selective inversion pulse). ASSESSMENT: Quantitative T1 , T2 , and PD maps were computed from the MR-STAT acquisition, from which synthetic contrasts were generated. Three neuroradiologists blinded for image type and disease randomly and independently evaluated synthetic and conventional datasets for image quality and diagnostic accuracy, which was assessed by comparison with the clinically confirmed diagnosis. STATISTICAL TESTS: Image quality and consequent acceptability for diagnostic use was assessed with a McNemar's test (one-sided α = 0.025). Wilcoxon signed rank test with a one-sided α = 0.025 and a margin of Δ = 0.5 on the 5-level Likert scale was used to assess non-inferiority. RESULTS: All data sets were similar in acceptability for diagnostic use (≥3 Likert-scale) between techniques (T1 w:P = 0.105, PDw:P = 1.000, FLAIR:P = 0.564). However, only the synthetic MR-STAT T2 weighted images were significantly non-inferior to their conventional counterpart; all other synthetic datasets were inferior (T1 w:P = 0.260, PDw:P = 1.000, FLAIR:P = 1.000). Moreover, true positive/negative rates were similar between techniques (conventional: 88%, MR-STAT: 84%). DATA CONCLUSION: MR-STAT is a quantitative technique that may provide radiologists with clinically useful synthetic contrast images within substantially reduced scan time. EVIDENCE LEVEL: 1 Technical Efficacy: Stage 2.

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.

Acceleration Strategies for MR-STAT: Achieving High-Resolution Reconstructions on a Desktop PC Within 3 Minutes.

MR-STAT is an emerging quantitative magnetic resonance imaging technique which aims at obtaining multi-parametric tissue parameter maps from single short scans. It describes the relationship between the spatial-domain tissue parameters and the time-domain measured signal by using a comprehensive, volumetric forward model. The MR-STAT reconstruction solves a large-scale nonlinear problem, thus is very computationally challenging. In previous work, MR-STAT reconstruction using Cartesian readout data was accelerated by approximating the Hessian matrix with sparse, banded blocks, and can be done on high performance CPU clusters with tens of minutes. In the current work, we propose an accelerated Cartesian MR-STAT algorithm incorporating two different strategies: firstly, a neural network is trained as a fast surrogate to learn the magnetization signal not only in the full time-domain but also in the compressed low-rank domain; secondly, based on the surrogate model, the Cartesian MR-STAT problem is re-formulated and split into smaller sub-problems by the alternating direction method of multipliers. The proposed method substantially reduces the computational requirements for runtime and memory. Simulated and in-vivo balanced MR-STAT experiments show similar reconstruction results using the proposed algorithm compared to the previous sparse Hessian method, and the reconstruction times are at least 40 times shorter. Incorporating sensitivity encoding and regularization terms is straightforward, and allows for better image quality with a negligible increase in reconstruction time. The proposed algorithm could reconstruct both balanced and gradient-spoiled in-vivo data within 3 minutes on a desktop PC, and could thereby facilitate the translation of MR-STAT in clinical settings.

Feasibility of cardiac-synchronized quantitative T1 and T2 mapping on a hybrid 1.5 Tesla magnetic resonance imaging and linear accelerator system.

Background and Purpose: The heart is important in radiotherapy either as target or organ at risk. Quantitative T1 and T2 cardiac magnetic resonance imaging (qMRI) may aid in target definition for cardiac radioablation, and imaging biomarker for cardiotoxicity assessment. Hybrid MR-linac devices could facilitate daily cardiac qMRI of the heart in radiotherapy. The aim of this work was therefore to enable cardiac-synchronized T1 and T2 mapping on a 1.5 T MR-linac and test the reproducibility of these sequences on phantoms and in vivo between the MR-linac and a diagnostic 1.5 T MRI scanner. Materials and methods: Cardiac-synchronized MRI was performed on the MR-linac using a wireless peripheral pulse-oximeter unit. Diagnostically used T1 and T2 mapping sequences were acquired twice on the MR-linac and on a 1.5 T MR-simulator for a gel phantom and 5 healthy volunteers in breath-hold. Phantom T1 and T2 values were compared to gold-standard measurements and percentage errors (PE) were computed, where negative/positive PE indicate underestimations/overestimations. Manually selected regions-of-interest were used for in vivo intra/inter scanner evaluation. Results: Cardiac-synchronized T1 and T2 qMRI was enabled after successful hardware installation on the MR-linac. From the phantom experiments, the measured T1/T2 relaxation times had a maximum percentage error (PE) of -4.4%/-8.8% on the MR-simulator and a maximum PE of -3.2%/+8.6% on the MR-linac. Mean T1/T2 of the myocardium were 1012 ± 34/51 ± 2 ms on the MR-simulator and 1034 ± 42/51 ± 1 ms on the MR-linac. Conclusions: Accurate cardiac-synchronized T1 and T2 mapping is feasible on a 1.5 T MR-linac and might enable novel plan adaptation workflows and cardiotoxicity assessments.

Fast and accurate modeling of transient-state, gradient-spoiled sequences by recurrent neural networks.

Fast and accurate modeling of MR signal responses are typically required for various quantitative MRI applications, such as MR fingerprinting. This work uses a new extended phase graph (EPG)-Bloch model for accurate simulation of transient-state, gradient-spoiled MR sequences, and proposes a recurrent neural network (RNN) as a fast surrogate of the EPG-Bloch model for computing large-scale MR signals and derivatives. The computational efficiency of the RNN model is demonstrated by comparisons with other existing models, showing one to three orders of acceleration compared with the latest GPU-accelerated, open-source EPG package. By using numerical and in vivo brain data, two used cases, namely, MRF dictionary generation and optimal experimental design, are also provided. Results show that the RNN surrogate model can be efficiently used for computing large-scale dictionaries of transient-state signals and derivatives within tens of seconds, resulting in several orders of magnitude acceleration with respect to state-of-the-art implementations. The practical application of transient-state quantitative techniques can therefore be substantially facilitated.

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.

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

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