Physics-based reconstruction methods for magnetic resonance imaging

Accelerated model-based T1, T2* and proton density mapping using a Bayesian approach with automatic hyperparameter estimation

PURPOSE

To achieve automatic hyperparameter estimation for the model-based recovery of quantitative MR maps from undersampled data, we propose a Bayesian formulation that incorporates the signal model and sparse priors among multiple image contrasts.

THEORY

We introduce a novel approximate message passing framework "AMP-PE" that enables the automatic and simultaneous recovery of hyperparameters and quantitative maps.

METHODS

We employed the variable-flip-angle method to acquire multi-echo measurements using gradient echo sequence. We explored undersampling schemes to incorporate complementary sampling patterns across different flip angles and echo times. We further compared AMP-PE with conventional compressed sensing approaches such as thel 1 $$ {l}_1 $$ -norm minimization, PICS and other model-based approaches such as GraSP, MOBA.

RESULTS

Compared to conventional compressed sensing approaches such as thel 1 $$ {l}_1 $$ -norm minimization and PICS, AMP-PE achieved superior reconstruction performance with lower errors inT 2 ∗ $$ {\mathrm{T}}_2^{\ast } $$ mapping and comparable performance inT 1 $$ {\mathrm{T}}_1 $$ and proton density mappings. When compared to other model-based approaches including GraSP and MOBA, AMP-PE exhibited greater robustness and outperformed GraSP in reconstruction error. AMP-PE offers faster speed than MOBA. AMP-PE performed better than MOBA at higher sampling rates and worse than MOBA at a lower sampling rate. Notably, AMP-PE eliminates the need for hyperparameter tuning, which is a requisite for all the other approaches.

CONCLUSION

AMP-PE offers the benefits of model-based recovery with the additional key advantage of automatic hyperparameter estimation. It works adeptly in situations where ground-truth is difficult to obtain and in clinical environments where it is desirable to automatically adapt hyperparameters to individual protocol, scanner and patient.

Fundamental effects of array density and modulation frequency on image quality of diffuse optical tomography

BACKGROUND

Diffuse optical tomography (DOT) provides three-dimensional image reconstruction of chromophore perturbations within a turbid volume. Two leading strategies to optimize DOT image quality include, (i) arrays of regular, interlacing, high-density (HD) grids of sources and detectors with closest spacing less than 15 mm, or (ii) source modulated light of order ∼100 MHz.

PURPOSE

However, the general principles for how these crucial design parameters of array density and modulation frequency may interact to provide an optimal system design have yet to be elucidated.

METHODS

Herein, we systematically evaluated how these design parameters effect image quality via multiple key metrics. Specifically, we simulated 32 system designs with realistic measurement noise and quantified localization error, spatial resolution, signal-to-noise, and localization depth of field for each of ∼85 000 point spread functions in each model.

RESULTS

We found that array density had a far stronger effect on image quality metrics than modulation frequency. Additionally, model fits for image quality metrics revealed that potential improvements diminish with regular arrays denser than 9 mm closest spacing. Further, for a given array density, 300 MHz source modulation provided the deepest reliable imaging compared to other frequencies.

CONCLUSIONS

Our results indicate that both array density and modulation frequency affect the spatial sampling of tissue, which asymptotically saturates due to photon diffusivity within a turbid volume. In summary, our results provide comprehensive perspectives for optimizing future DOT system designs in applications from wearable functional brain imaging to breast tumor detection.

Color-map recommendation for MR relaxometry maps

PURPOSE

To harmonize the use of color for MR relaxometry maps and therefore recommend the use of specific color-maps for representingT 1 $$ {\mathrm{T}}_1 $$ ,T 2 $$ {\mathrm{T}}_2 $$ , andT 2 * $$ {\mathrm{T}}_2^{\ast } $$ maps and their inverses.

METHODS

Perceptually linearized color-maps were chosen to have similar color settings as those proposed by Griswold et al. in 2018. A Delphi process, polling the opinion of a panel of 81 experts, was used to generate consensus on the suitability of these maps.

RESULTS

Consensus was reached on the suitability of the logarithm-processed Lipari color-map forT 1 $$ {\mathrm{T}}_1 $$ and the logarithm-processed Navia color-map forT 2 $$ {\mathrm{T}}_2 $$ andT 2 * $$ {\mathrm{T}}_2^{\ast } $$ . There was consensus on color bars being mandatory and on the use of a specific value indicating "invalidity." There was no consensus on whether the ranges should be fixed per anatomy.

CONCLUSION

The authors recommend the use of the logarithm-processed Lipari color-map for displaying quantitativeT 1 $$ {\mathrm{T}}_1 $$ maps andR 1 $$ {\mathrm{R}}_1 $$ maps; likewise, the authors recommend the logarithm-processed Navia color-map for displayingT 2 $$ {\mathrm{T}}_2 $$ ,T 2 * $$ {\mathrm{T}}_2^{\ast } $$ ,R 2 $$ {\mathrm{R}}_2 $$ , andR 2 * $$ {\mathrm{R}}_2^{\ast } $$ maps. This work originated with the Quantitative MR Study Group of the International Society of Magnetic Resonance in Medicine (ISMRM); it has the approval of the Publication Committee and of the Board of the ISMRM.

QRAGE-Simultaneous multiparametric quantitative MRI of water content, T1, T2*, and magnetic susceptibility at ultrahigh field strength

PURPOSE

To introduce quantitative rapid gradient-echo (QRAGE), a novel approach for the simultaneous mapping of multiple quantitative MRI parameters, including water content, T1, T2*, and magnetic susceptibility at ultrahigh field strength.

METHODS

QRAGE leverages a newly developed multi-echo MPnRAGE sequence, facilitating the acquisition of 171 distinct contrast images across a range of TI and TE points. To maintain a short acquisition time, we introduce MIRAGE2, a novel model-based reconstruction method that exploits prior knowledge of temporal signal evolution, represented as damped complex exponentials. MIRAGE2 minimizes local Block-Hankel and Casorati matrices. Parameter maps are derived from the reconstructed contrast images through postprocessing steps. We validate QRAGE through extensive simulations, phantom studies, and in vivo experiments, demonstrating its capability for high-precision imaging.

RESULTS

In vivo brain measurements show the promising performance of QRAGE, with test-retest SDs and deviations from reference methods of < 0.8% for water content, < 17 ms for T1, and < 0.7 ms for T2*. QRAGE achieves whole-brain coverage at a 1-mm isotropic resolution in just 7 min and 15 s, comparable to the acquisition time of an MP2RAGE scan. In addition, QRAGE generates a contrast image akin to the UNI image produced by MP2RAGE.

CONCLUSION

QRAGE is a new, successful approach for simultaneously mapping multiple MR parameters at ultrahigh field.

Efficient standardization of clinical T2-weighted images: Phase-conjugacy e-CAMP with projected gradient descent

PURPOSE

To standardize T  2 $$ {}_2 $$ -weighted images from clinical Turbo Spin Echo (TSE) scans by generating corresponding T  2 $$ {}_2 $$ maps with the goal of removing scanner- and/or protocol-specific heterogeneity.

METHODS

The T  2 $$ {}_2 $$ map is estimated by minimizing an objective function containing a data fidelity term in a Virtual Conjugate Coils (VCC) framework, where the signal evolution model is expressed as a linear constraint. The objective function is minimized by Projected Gradient Descent (PGD).

RESULTS

The algorithm achieves accuracy comparable to methods with customized sampling schemes for accelerated T  2 $$ {}_2 $$ mapping. The results are insensitive to the tunable parameters, and the relaxed background phase prior produces better T  2 $$ {}_2 $$ maps compared to the strict real-value enforcement. It is worth noting that the algorithm works well with challenging T  2 $$ {}_2 $$ w-TSE data using typical clinical parameters. The observed normalized root mean square error ranges from 6.8% to 12.3% over grey and white matter, a clinically common level of quantitative map error.

CONCLUSION

The novel methodological development creates an efficient algorithm that allows for T  2 $$ {}_2 $$ map generated from TSE data with typical clinical parameters, such as high resolution, long echo train length, and low echo spacing. Reconstruction of T  2 $$ {}_2 $$ maps from TSE data with typical clinical parameters has not been previously reported.

Self-supervised learning for improved calibrationless radial MRI with NLINV-Net

PURPOSE

To develop a neural network architecture for improved calibrationless reconstruction of radial data when no ground truth is available for training.

METHODS

NLINV-Net is a model-based neural network architecture that directly estimates images and coil sensitivities from (radial) k-space data via nonlinear inversion (NLINV). Combined with a training strategy using self-supervision via data undersampling (SSDU), it can be used for imaging problems where no ground truth reconstructions are available. We validated the method for (1) real-time cardiac imaging and (2) single-shot subspace-based quantitative T1 mapping. Furthermore, region-optimized virtual (ROVir) coils were used to suppress artifacts stemming from outside the field of view and to focus the k-space-based SSDU loss on the region of interest. NLINV-Net-based reconstructions were compared with conventional NLINV and PI-CS (parallel imaging + compressed sensing) reconstruction and the effect of the region-optimized virtual coils and the type of training loss was evaluated qualitatively.

RESULTS

NLINV-Net-based reconstructions contain significantly less noise than the NLINV-based counterpart. ROVir coils effectively suppress streakings which are not suppressed by the neural networks while the ROVir-based focused loss leads to visually sharper time series for the movement of the myocardial wall in cardiac real-time imaging. For quantitative imaging, T1-maps reconstructed using NLINV-Net show similar quality as PI-CS reconstructions, but NLINV-Net does not require slice-specific tuning of the regularization parameter.

CONCLUSION

NLINV-Net is a versatile tool for calibrationless imaging which can be used in challenging imaging scenarios where a ground truth is not available.

Accelerated 3D multi-echo spin-echo sequence with a subspace constrained reconstruction for whole mouse brain T 2 mapping

PURPOSE

To accelerate whole-brain quantitativeT 2 $$ {\mathrm{T}}_2 $$ mapping in preclinical imaging setting.

METHODS

A three-dimensional (3D) multi-echo spin echo sequence was highly undersampled with a variable density Poisson distribution to reduce the acquisition time. Advanced iterative reconstruction based on linear subspace constraints was employed to recover high-quality raw images. Different subspaces, generated using exponential or extended-phase graph (EPG) simulations or from low-resolution calibration images, were compared. The subspace dimension was investigated in terms ofT 2 $$ {\mathrm{T}}_2 $$ precision. The method was validated on a phantom containing a wide range ofT 2 $$ {\mathrm{T}}_2 $$ and was then applied to monitor metastasis growth in the mouse brain at 4.7T. Image quality andT 2 $$ {\mathrm{T}}_2 $$ estimation were assessed for 3 acceleration factors (6/8/10).

RESULTS

The EPG-based dictionary gave robust estimations of a large range ofT 2 $$ {\mathrm{T}}_2 $$ . A subspace dimension of 6 was the best compromise betweenT 2 $$ {\mathrm{T}}_2 $$ precision and image quality. Combining the subspace constrained reconstruction with a highly undersampled dataset enabled the acquisition of whole-brainT 2 $$ {\mathrm{T}}_2 $$ maps, the detection and the monitoring of metastasis growth of less than 500μ m 3 $$ \mu {\mathrm{m}}^3 $$ .

CONCLUSION

Subspace-based reconstruction is suitable for 3DT 2 $$ {\mathrm{T}}_2 $$ mapping. This method can be used to reach an acceleration factor up to 8, corresponding to an acquisition time of 25 min for an isotropic 3D acquisition of 156μ $$ \mu $$ m on the mouse brain, used here for monitoring metastases growth.

Open-source magnetic resonance imaging: Improving access, science, and education through global collaboration

Open-source practices and resources in magnetic resonance imaging (MRI) have increased substantially in recent years. This trend started with software and data being published open-source and, more recently, open-source hardware designs have become increasingly available. These developments towards a culture of sharing and establishing nonexclusive global collaborations have already improved the reproducibility and reusability of code and designs, while providing a more inclusive approach, especially for low-income settings. Community-driven standardization and documentation efforts are further strengthening and expanding these milestones. The future of open-source MRI is bright and we have just started to discover its full collaborative potential. In this review we will give an overview of open-source software and open-source hardware projects in human MRI research.

T1 mapping of myocardium in rats using self-gated golden-angle acquisition

PURPOSE

The aim of this study is to design a method of myocardial T1 quantification in small laboratory animals and to investigate the effects of spatiotemporal regularization and the needed acquisition duration.

METHODS

We propose a compressed-sensing approach to T1 quantification based on self-gated inversion-recovery radial two/three-dimensional (2D/3D) golden-angle stack-of-stars acquisition with image reconstruction performed using total-variation spatiotemporal regularization. The method was tested on a phantom and on a healthy rat, as well as on rats in a small myocardium-remodeling study.

RESULTS

The results showed a good match of the T1 estimates with the results obtained using the ground-truth method on a phantom and with the literature values for rats myocardium. The proposed 2D and 3D methods showed significant differences between normal and remodeling myocardium groups for acquisition lengths down to approximately 5 and 15 min, respectively.

CONCLUSIONS

A new 2D and 3D method for quantification of myocardial T1 in rats was proposed. We have shown the capability of both techniques to distinguish between normal and remodeling myocardial tissue. We have shown the effects of image-reconstruction regularization weights and acquisition length on the T1 estimates.

AI in MRI: Computational Frameworks for a Faster, Optimized, and Automated Imaging Workflow

Over the last decade, artificial intelligence (AI) has made an enormous impact on a wide range of fields, including science, engineering, informatics, finance, and transportation [...].

Free-breathing myocardial T1 mapping using inversion-recovery radial FLASH and motion-resolved model-based reconstruction

PURPOSE

To develop a free-breathing myocardialT 1 $$ {\mathrm{T}}_1 $$ mapping technique using inversion-recovery (IR) radial fast low-angle shot (FLASH) and calibrationless motion-resolved model-based reconstruction.

METHODS

Free-running (free-breathing, retrospective cardiac gating) IR radial FLASH is used for data acquisition at 3T. First, to reduce the waiting time between inversions, an analytical formula is derived that takes the incompleteT 1 $$ {\mathrm{T}}_1 $$ recovery into account for an accurateT 1 $$ {\mathrm{T}}_1 $$ calculation. Second, the respiratory motion signal is estimated from the k-space center of the contrast varying acquisition using an adapted singular spectrum analysis (SSA-FARY) technique. Third, a motion-resolved model-based reconstruction is used to estimate both parameter and coil sensitivity maps directly from the sorted k-space data. Thus, spatiotemporal total variation, in addition to the spatial sparsity constraints, can be directly applied to the parameter maps. Validations are performed on an experimental phantom, 11 human subjects, and a young landrace pig with myocardial infarction.

RESULTS

In comparison to an IR spin-echo reference, phantom results confirm goodT 1 $$ {\mathrm{T}}_1 $$ accuracy, when reducing the waiting time from 5 s to 1 s using the new correction. The motion-resolved model-based reconstruction further improvesT 1 $$ {\mathrm{T}}_1 $$ precision compared to the spatial regularization-only reconstruction. Aside from showing that a reliable respiratory motion signal can be estimated using modified SSA-FARY, in vivo studies demonstrate that dynamic myocardialT 1 $$ {\mathrm{T}}_1 $$ maps can be obtained within 2 min with good precision and repeatability.

CONCLUSION

Motion-resolved myocardialT 1 $$ {\mathrm{T}}_1 $$ mapping during free-breathing with good accuracy, precision and repeatability can be achieved by combining inversion-recovery radial FLASH, self-gating and a calibrationless motion-resolved model-based reconstruction.

Deep Learning Initialized Compressed Sensing (Deli-CS) in Volumetric Spatio-Temporal Subspace Reconstruction

Introduction

Spatio-temporal MRI methods enable whole-brain multi-parametric mapping at ultra-fast acquisition times through efficient k-space encoding, but can have very long reconstruction times, which limit their integration into clinical practice. Deep learning (DL) is a promising approach to accelerate reconstruction, but can be computationally intensive to train and deploy due to the large dimensionality of spatio-temporal MRI. DL methods also need large training data sets and can produce results that don't match the acquired data if data consistency is not enforced. The aim of this project is to reduce reconstruction time using DL whilst simultaneously limiting the risk of deep learning induced hallucinations, all with modest hardware requirements.

Methods

Deep Learning Initialized Compressed Sensing (Deli-CS) is proposed to reduce the reconstruction time of iterative reconstructions by "kick-starting" the iterative reconstruction with a DL generated starting point. The proposed framework is applied to volumetric multi-axis spiral projection MRF that achieves whole-brain T1 and T2 mapping at 1-mm isotropic resolution for a 2-minute acquisition. First, the traditional reconstruction is optimized from over two hours to less than 40 minutes while using more than 90% less RAM and only 4.7 GB GPU memory, by using a memory-efficient GPU implementation. The Deli-CS framework is then implemented and evaluated against the above reconstruction.

Results

Deli-CS achieves comparable reconstruction quality with 50% fewer iterations bringing the full reconstruction time to 20 minutes.

Conclusion

Deli-CS reduces the reconstruction time of subspace reconstruction of volumetric spatio-temporal acquisitions by providing a warm start to the iterative reconstruction algorithm.

Model-based reconstructions for intravoxel incoherent motion and diffusion tensor imaging parameter map estimations

Intravoxel incoherent motion (IVIM) imaging and diffusion tensor imaging (DTI) facilitate noninvasive quantification of tissue perfusion and diffusion. Both are promising biomarkers in various diseases and a combined acquisition is therefore desirable. This comes with challenges, including noisy parameter maps and long scan times, especially for the perfusion fraction f and pseudo-diffusion coefficient D*. A model-based reconstruction has the potential to overcome these challenges. As a first step, our goal was to develop a model-based reconstruction framework for IVIM and combined IVIM-DTI parameter estimation. The IVIM and IVIM-DTI models were implemented in the PyQMRI model-based reconstruction framework and validated with simulations and in vivo data. Commonly used voxel-wise nonlinear least-squares fitting was used as the reference. Simulations with the IVIM and IVIM-DTI models were performed with 100 noise realizations to assess accuracy and precision. Diffusion-weighted data were acquired for IVIM reconstruction in the liver (n = 5), as well as for IVIM-DTI in the kidneys (n = 5) and lower-leg muscles (n = 6) of healthy volunteers. The median and interquartile range (IQR) values of the IVIM and IVIM-DTI parameters were compared to assess bias and precision. With model-based reconstruction, the parameter maps exhibited less noise, which was most pronounced in the f and D* maps, both in the simulations and in vivo. The bias values in the simulations were comparable between model-based reconstruction and the reference method. The IQR was lower with model-based reconstruction compared with the reference for all parameters. In conclusion, model-based reconstruction is feasible for IVIM and IVIM-DTI and improves the precision of the parameter estimates, particularly for f and D* maps.

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.

Application of the Model of Spots for Inverse Problems

This article proposes the application of a new mathematical model of spots for solving inverse problems using a learning method, which is similar to using deep learning. In general, the spots represent vague figures in abstract "information spaces" or crisp figures with a lack of information about their shapes. However, crisp figures are regarded as a special and limiting case of spots. A basic mathematical apparatus, based on L4 numbers, has been developed for the representation and processing of qualitative information of elementary spatial relations between spots. Moreover, we defined L4 vectors, L4 matrices, and mathematical operations on them. The developed apparatus can be used in Artificial Intelligence, in particular, for knowledge representation and for modeling qualitative reasoning and learning. Another application area is the solution of inverse problems by learning. For example, this can be applied to image reconstruction using ultrasound, X-ray, magnetic resonance, or radar scan data. The introduced apparatus was verified by solving problems of reconstruction of images, utilizing only qualitative data of its elementary relations with some scanning figures. This article also demonstrates the application of a spot-based inverse Radon algorithm for binary image reconstruction. In both cases, the spot-based algorithms have demonstrated an effective denoising property.

Synergistic tomographic image reconstruction: part 1

This special issue focuses on synergistic tomographic image reconstruction in a range of contributions in multiple disciplines and various application areas. The topic of image reconstruction covers substantial inverse problems (Mathematics) which are tackled with various methods including statistical approaches (e.g. Bayesian methods, Monte Carlo) and computational approaches (e.g. machine learning, computational modelling, simulations). The issue is separated in two volumes. This volume focuses mainly on algorithms and methods. Some of the articles will demonstrate their utility on real-world challenges, either medical applications (e.g. cardiovascular diseases, proton therapy planning) or applications in material sciences (e.g. material decomposition and characterization). One of the desired outcomes of the special issue is to bring together different scientific communities which do not usually interact as they do not share the same platforms (such as journals and conferences). This article is part of the theme issue 'Synergistic tomographic image reconstruction: part 1'.