Model-based MR parameter mapping with sparsity constraints: parameter estimation and performance bounds

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.

Ultrafast T2 and T2* mapping using single-shot spatiotemporally encoded MRI with reduced field of view and spiral out-in-out-in trajectory

BACKGROUND

T2 and T2* mapping are crucial components of quantitative magnetic resonance imaging, offering valuable insights into tissue characteristics and pathology. Single-shot methods can achieve ultrafast T2 or T2* mapping by acquiring multiple readout echo trains. However, the extended echo trains pose challenges, such as compromised image quality and diminished quantification accuracy.

PURPOSE

In this study, we develop a single-shot method for ultrafast T2 and T2* mapping with reduced echo train length.

METHODS

The proposed method is based on ultrafast single-shot spatiotemporally encoded (SPEN) MRI combined with reduced field of view (FOV) and spiral out-in-out-in (OIOI) trajectory. Specifically, a biaxial SPEN excitation scheme was employed to excite the spin signal into the spatiotemporal encoding domain. The OIOI trajectory with high acquisition efficiency was employed to acquire signals within targeted reduced FOV. Through non-Cartesian super-resolved (SR) reconstruction, 12 aliasing-free images with different echo times were obtained within 150 ms. These images were subsequently fitted to generate T2 or T2* mapping simultaneously using a derived model.

RESULTS

Accurate and co-registered T2 and T2* maps were generated, closely resembling the reference maps. Numerical simulations demonstrated substantial consistency (R2 > 0.99) with the ground truth values. A mean difference of 0.6% and 1.7% was observed in T2 and T2*, respectively, in in vivo rat brain experiments compared to the reference. Moreover, the proposed method successfully obtained T2 and T2* mappings of rat kidney in free-breathing mode, demonstrating its superiority over multishot methods lacking respiratory navigation.

CONCLUSIONS

The results suggest that the proposed method can achieve ultrafast and accurate T2 and T2* mapping, potentially facilitating the application of T2 and T2* mapping in scenarios requiring high temporal resolution.

MR-based electrical property tomography using a physics-informed network at 3 and 7 T

Magnetic resonance electrical propert tomography promises to retrieve electrical properties (EPs) quantitatively and non-invasively in vivo, providing valuable information for tissue characterization and pathology diagnosis. However, its clinical implementation has been hindered by, for example, B1 measurement accuracy, reconstruction artifacts resulting from inaccuracies in underlying models, and stringent hardware/software requirements. To address these challenges, we present a novel approach aimed at accurate and high-resolution EPs reconstruction based on water content maps by using a physics-informed network (PIN-wEPT). The proposed method utilizes standard clinical protocols and conventional multi-channel receive arrays that have been routinely equipped in clinical settings, thus eliminating the need for specialized RF sequence/coil configurations. Compared with the original wEPT method, the network generates accurate water content maps that effectively eliminate the influence ofB → 1 + andB → 1 - by incorporating data mismatch with electrodynamic constraints derived from the Helmholtz equation. Subsequent regression analysis develops a broad relationship between water content and EPs across various types of brain tissue. A series of numerical simulations was conducted at 7 T to assess the feasibility and performance of the method, which encompassed four normal head models and models with tumorous tissues incorporated, and the results showed normalized mean square error below 1.0% in water content, below 11.7% in conductivity, and below 1.1% in permittivity reconstructions for normal brain tissues. Moreover, in vivo validations conducted over five healthy subjects at both 3 and 7 T showed reasonably good consistency with empirical EPs values across the white matter, gray matter, and cerebrospinal fluid. The PIN-wEPT method, with its demonstrated efficacy, flexibility, and compatibility with current MRI scanners, holds promising potential for future clinical application.

Highly accelerated parameter mapping using model-based alternating reconstruction coupling fitting

Objective.A model-based alternating reconstruction coupling fitting, termed Model-based Alternating Reconstruction COupling fitting (MARCO), is proposed for accurate and fast magnetic resonance parameter mapping.Approach.MARCO utilizes the signal model as a regularization by minimizing the bias between the image series and the signal produced by the suitable signal model based on iteratively updated parameter maps when reconstructing. The technique can incorporate prior knowledge of both image series and parameters by adding sparsity constraints. The optimization problem is decomposed into three subproblems and solved through three alternating steps involving reconstruction and nonlinear least-square fitting, which can produce both contrast-weighted images and parameter maps simultaneously.Main results.The algorithm is applied toT2mapping with extended phase graph algorithm integrated and validated on undersampled multi-echo spin-echo data from both phantom and in vivo sources. Compared with traditional compressed sensing and model-based methods, the proposed approach yields more accurateT2maps with more details at high acceleration factors.Significance.The proposed method provides a basic framework for quantitative MR relaxometry, theoretically applicable to all quantitative MR relaxometry. It has the potential to improve the diagnostic utility of quantitative imaging techniques.

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.

Joint MAPLE: Accelerated joint T1 and T 2 * $$ {{\mathrm{T}}_2}^{\ast } $$ mapping with scan-specific self-supervised networks

PURPOSE

Quantitative MRI finds important applications in clinical and research studies. However, it is encoding intensive and may suffer from prohibitively long scan times. Accelerated MR parameter mapping techniques have been developed to help address these challenges. Here, an accelerated joint T1,T 2 * $$ {{\mathrm{T}}_2}^{\ast } $$ , frequency and proton density mapping technique with scan-specific self-supervised network reconstruction is proposed to synergistically combine parallel imaging, model-based, and deep learning approaches to speed up parameter mapping.

METHODS

Proposed framework, Joint MAPLE, includes parallel imaging, signal modeling, and data consistency blocks which are optimized jointly in a combined loss function. A scan-specific self-supervised reconstruction is embedded into the framework, which takes advantage of multi-contrast data from a multi-echo, multi-flip angle, gradient echo acquisition.

RESULTS

In comparison with parallel reconstruction techniques powered by low-rank methods, emerging scan specific networks, and model-basedT 2 * $$ {{\mathrm{T}}_2}^{\ast } $$ estimation approaches, the proposed framework reduces the reconstruction error in parameter maps by approximately two-fold on average at acceleration rates as high as R = 16 with uniform sampling. It can outperform evaluated parallel reconstruction techniques up to four-fold on average in the presence of challenging sub-sampling masks. It is observed that Joint MAPLE performs well at extreme acceleration rates of R = 25 and R = 36 with error values less than 20%.

CONCLUSION

Joint MAPLE enables higher fidelity parameter estimation at high acceleration rates by synergistically combining parallel imaging and model-based parameter mapping and exploiting multi-echo, multi-flip angle datasets. Utilizing a scan-specific self-supervised reconstruction obviates the need for large data sets for training while improving the parameter estimation ability.

Quantitative MR Image Reconstruction Using Parameter-Specific Dictionary Learning With Adaptive Dictionary-Size and Sparsity-Level Choice

OBJECTIVE

We propose a method for the reconstruction of parameter-maps in Quantitative Magnetic Resonance Imaging (QMRI).

METHODS

Because different quantitative parameter-maps differ from each other in terms of local features, we propose a method where the employed dictionary learning (DL) and sparse coding (SC) algorithms automatically estimate the optimal dictionary-size and sparsity level separately for each parameter-map. We evaluated the method on a T1-mapping QMRI problem in the brain using the BrainWeb data as well as in-vivo brain images acquired on an ultra-high field 7 T scanner. We compared it to a model-based acceleration for parameter mapping (MAP) approach, other sparsity-based methods using total variation (TV), Wavelets (Wl), and Shearlets (Sh) to a method which uses DL and SC to reconstruct qualitative images, followed by a non-linear (DL+Fit).

RESULTS

Our algorithm surpasses MAP, TV, Wl, and Sh in terms of RMSE and PSNR. It yields better or comparable results to DL+Fit by additionally significantly accelerating the reconstruction by a factor of approximately seven.

CONCLUSION

The proposed method outperforms the reported methods of comparison and yields accurate T1-maps. Although presented for T1-mapping in the brain, our method's structure is general and thus most probably also applicable for the the reconstruction of other quantitative parameters in other organs.

SIGNIFICANCE

From a clinical perspective, the obtained T1-maps could be utilized to differentiate between healthy subjects and patients with Alzheimer's disease. From a technical perspective, the proposed unsupervised method could be employed to obtain ground-truth data for the development of data-driven methods based on supervised learning.

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.

Single-shot T2 mapping via multi-echo-train multiple overlapping-echo detachment planar imaging and multitask deep learning

BACKGROUND

Quantitative magnetic resonance imaging provides robust biomarkers in clinics. Nevertheless, the lengthy scan time reduces imaging throughput and increases the susceptibility of imaging results to motion. In this context, a single-shot T₂ mapping method based on multiple overlapping-echo detachment (MOLED) planar imaging was presented, but the relatively small echo time range limits its accuracy, especially in tissues with large T₂ .

PURPOSE

In this work we proposed a novel single-shot method, Multi-Echo-Train Multiple OverLapping-Echo Detachment (METMOLED) planar imaging, to accommodate a large range of T₂ quantification without additional measurements to rectify signal degeneration arisen from refocusing pulse imperfection.

METHODS

Multiple echo-train techniques were integrated into the MOLED sequence to capture larger TE information. Maps of T₂ , B₁ , and spin density were reconstructed synchronously from acquired METMOLED data via multitask deep learning. A typical U-Net was trained with 3000/600 synthetic data with geometric/brain patterns to learn the mapping relationship between METMOLED signals and quantitative maps. The refocusing pulse imperfection was settled through the inherent information of METMOLED data and auxiliary tasks.

RESULTS

Experimental results on the digital brain (structural similarity (SSIM) index = 0.975/0.991/0.988 for MOLED/METMOLED-2/METMOLED-3, hyphenated number denotes the number of echo-trains), physical phantom (the slope of linear fitting with reference T₂ map = 1.047/1.017/1.006 for MOLED/METMOLED-2/METMOLED-3), and human brain (Pearson's correlation coefficient (PCC) = 0.9581/0.9760/0.9900 for MOLED/METMOLED-2/METMOLED-3) demonstrated that the METMOLED improved the quantitative accuracy and the tissue details in contrast to the MOLED. These improvements were more pronounced in tissues with large T₂ and in application scenarios with high temporal resolution (PCC = 0.8692/0.9465/0.9743 for MOLED/METMOLED-2/METMOLED-3). Moreover, the METMOLED could rectify the signal deviations induced by the non-ideal slice profiles of refocusing pulses without additional measurements. A preliminary measurement also demonstrated that the METMOLED is highly repeatable (mean coefficient of variation (CV) = 1.65%).

CONCLUSIONS

METMOLED breaks the restriction of echo-train length to TE and implements unbiased T₂ estimates in an extensive range. Furthermore, it corrects the effect of refocusing pulse inaccuracy without additional measurements or signal post-processing, thus retaining its single-shot characteristic. This technique would be beneficial for accurate T₂ quantification.

A probabilistic Bayesian approach to recover R2*$$ {R}_{2\ast } $$ map and phase images for quantitative susceptibility mapping

PURPOSE

Undersampling is used to reduce the scan time for high-resolution three-dimensional magnetic resonance imaging. In order to achieve better image quality and avoid manual parameter tuning, we propose a probabilistic Bayesian approach to recover R 2 ∗ $$ {R}_2^{\ast } $$ map and phase images for quantitative susceptibility mapping (QSM), while allowing automatic parameter estimation from undersampled data.

THEORY

Sparse prior on the wavelet coefficients of images is interpreted from a Bayesian perspective as sparsity-promoting distribution. A novel nonlinear approximate message passing (AMP) framework that incorporates a mono-exponential decay model is proposed. The parameters are treated as unknown variables and jointly estimated with image wavelet coefficients.

METHODS

Undersampling takes place in the y-z plane of k-space according to the Poisson-disk pattern. Retrospective undersampling is performed to evaluate the performances of different reconstruction approaches, prospective undersampling is performed to demonstrate the feasibility of undersampling in practice.

RESULTS

The proposed AMP with parameter estimation (AMP-PE) approach successfully recovers R 2 ∗ $$ {R}_2^{\ast } $$ maps and phase images for QSM across various undersampling rates. It is more computationally efficient, and performs better than the state-of-the-art l 1 $$ {l}_1 $$ -norm regularization (L1) approach in general, except a few cases where the L1 approach performs as well as AMP-PE.

CONCLUSION

AMP-PE achieves better performance by drawing information from both the sparse prior and the mono-exponential decay model. It does not require parameter tuning, and works with a clinical, prospective undersampling scheme where parameter tuning is often impossible or difficult due to the lack of ground-truth image.

Dynamic Imaging Using Deep Bi-Linear Unsupervised Representation (DEBLUR)

Bilinear models such as low-rank and dictionary methods, which decompose dynamic data to spatial and temporal factor matrices are powerful and memory-efficient tools for the recovery of dynamic MRI data. Current bilinear methods rely on sparsity and energy compaction priors on the factor matrices to regularize the recovery. Motivated by deep image prior, we introduce a novel bilinear model, whose factor matrices are generated using convolutional neural networks (CNNs). The CNN parameters, and equivalently the factors, are learned from the undersampled data of the specific subject. Unlike current unrolled deep learning methods that require the storage of all the time frames in the dataset, the proposed approach only requires the storage of the factors or compressed representation; this approach allows the direct use of this scheme to large-scale dynamic applications, including free breathing cardiac MRI considered in this work. To reduce the run time and to improve performance, we initialize the CNN parameters using existing factor methods. We use sparsity regularization of the network parameters to minimize the overfitting of the network to measurement noise. Our experiments on free-breathing and ungated cardiac cine data acquired using a navigated golden-angle gradient-echo radial sequence show the ability of our method to provide reduced spatial blurring as compared to classical bilinear methods as well as a recent unsupervised deep-learning approach.

Accelerated MRI Reconstruction With Separable and Enhanced Low-Rank Hankel Regularization

Magnetic resonance imaging serves as an essential tool for clinical diagnosis, however, suffers from a long acquisition time. Sparse sampling effectively saves this time but images need to be faithfully reconstructed from undersampled data. Among the existing reconstruction methods, the structured low-rank methods have advantages in robustness to the sampling patterns and lower error. However, the structured low-rank methods use the 2D or higher dimension k-space data to build a huge block Hankel matrix, leading to considerable time and memory consumption. To reduce the size of the Hankel matrix, we proposed to separably construct multiple small Hankel matrices from rows and columns of the k-space and then constrain the low-rankness on these small matrices. This separable model can significantly reduce the computational time but ignores the correlation existed in inter- and intra-row or column, resulting in increased reconstruction error. To improve the reconstructed image without obviously increasing the computation, we further introduced the self-consistency of k-space and virtual coil prior. Besides, the proposed separable model can be extended into other imaging scenarios which hold exponential characteristics in the parameter dimension. The in vivo experimental results demonstrated that the proposed method permits the lowest reconstruction error with a fast reconstruction. The proposed approach requires only 4% of the state-of-the-art STDLR-SPIRiT runtime for parallel imaging reconstruction, and achieves the fastest computational speed in parameter imaging reconstruction.

Accelerating MR Parameter Mapping Using Nonlinear Compressive Manifold Learning and Regularized Pre-Imaging

In this study, we presented a novel method to reconstruct the MR parametric maps from highly undersampled k-space data. Specifically, we utilized a nonlinear model to sparsely represent the unknown MR parameter-weighted images in high-dimensional feature space. Each image at a specific time point is assumed to belong to a low-dimensional manifold which is learned from training images created based on the parametric model. The final reconstruction is carried out by venturing the sparse representation of the images in the feature space back to the input space, using the pre-imaging technique. Particularly, among an infinite number of solutions that satisfy the data consistency, the one that is closest to the manifold is selected as the desired solution. The underlying optimization problem is solved using kernel trick, sparse coding, and split Bregman iteration algorithm. In addition, both spatial and temporal regularizations were utilized to further improve the reconstruction quality. The proposed method was validated on both phantom and in vivo human brain T2 mapping data. Results showed the proposed method was superior to the conventional linear model-based reconstruction methods, in terms of artifact removal and quantitative estimate accuracy. The proposed method could be potentially beneficial for quantitative MR applications.

Joint total variation-based reconstruction of multiparametric magnetic resonance images for mapping tissue types

Multispectral analysis of coregistered multiparametric magnetic resonance (MR) images provides a powerful method for tissue phenotyping and segmentation. Acquisition of a sufficiently varied set of multicontrast MR images and parameter maps to objectively define multiple normal and pathologic tissue types can require long scan times. Accelerated MRI on clinical scanners with multichannel receivers exploits techniques such as parallel imaging, while accelerated preclinical MRI scanning must rely on alternate approaches. In this work, tumor-bearing mice were imaged at 7 T to acquire k-space data corresponding to a series of images with varying T1-, T2- and T2*-weighting. A joint reconstruction framework is proposed to reconstruct a series of T1-weighted images and corresponding T1 maps simultaneously from undersampled Cartesian k-space data. The ambiguity introduced by undersampling was resolved by using model-based constraints and structural information from a reference fully sampled image as the joint total variation prior. This process was repeated to reconstruct T2-weighted and T2*-weighted images and corresponding maps of T2 and T2* from undersampled Cartesian k-space data. Validation of the reconstructed images and parameter maps was carried out by computing tissue-type maps, as well as maps of the proton density fat fraction (PDFF), proton density water fraction (PDwF), fat relaxation rate ( R 2 f * ) and water relaxation rate ( R 2 w * ) from the reconstructed data, and comparing them with ground truth (GT) equivalents. Tissue-type maps computed using 18% k-space data were visually similar to GT tissue-type maps, with dice coefficients ranging from 0.43 to 0.73 for tumor, fluid adipose and muscle tissue types. The mean T1 and T2 values within each tissue type computed using only 18% k-space data were within 8%-10% of the GT values from fully sampled data. The PDFF and PDwF maps computed using 27% k-space data were within 3%-15% of GT values and showed good agreement with the expected values for the four tissue types.

Model-based multi-parameter mapping

Quantitative MR imaging is increasingly favoured for its richer information content and standardised measures. However, computing quantitative parameter maps, such as those encoding longitudinal relaxation rate (R1), apparent transverse relaxation rate (R2*) or magnetisation-transfer saturation (MTsat), involves inverting a highly non-linear function. Many methods for deriving parameter maps assume perfect measurements and do not consider how noise is propagated through the estimation procedure, resulting in needlessly noisy maps. Instead, we propose a probabilistic generative (forward) model of the entire dataset, which is formulated and inverted to jointly recover (log) parameter maps with a well-defined probabilistic interpretation (e.g., maximum likelihood or maximum a posteriori). The second order optimisation we propose for model fitting achieves rapid and stable convergence thanks to a novel approximate Hessian. We demonstrate the utility of our flexible framework in the context of recovering more accurate maps from data acquired using the popular multi-parameter mapping protocol. We also show how to incorporate a joint total variation prior to further decrease the noise in the maps, noting that the probabilistic formulation allows the uncertainty on the recovered parameter maps to be estimated. Our implementation uses a PyTorch backend and benefits from GPU acceleration. It is available at https://github.com/balbasty/nitorch.

Synergistic multi-contrast cardiac magnetic resonance image reconstruction

Cardiac magnetic resonance imaging (CMR) is an important tool for the non-invasive diagnosis of a variety of cardiovascular diseases. Parametric mapping with multi-contrast CMR is able to quantify tissue alterations in myocardial disease and promises to improve patient care. However, magnetic resonance imaging is an inherently slow imaging modality, resulting in long acquisition times for parametric mapping which acquires a series of cardiac images with different contrasts for signal fitting or dictionary matching. Furthermore, extra efforts to deal with respiratory and cardiac motion by triggering and gating further increase the scan time. Several techniques have been developed to speed up CMR acquisitions, which usually acquire less data than that required by the Nyquist-Shannon sampling theorem, followed by regularized reconstruction to mitigate undersampling artefacts. Recent advances in CMR parametric mapping speed up CMR by synergistically exploiting spatial-temporal and contrast redundancies. In this article, we will review the recent developments in multi-contrast CMR image reconstruction for parametric mapping with special focus on low-rank and model-based reconstructions. Deep learning-based multi-contrast reconstruction has recently been proposed in other magnetic resonance applications. These developments will be covered to introduce the general methodology. Current technical limitations and potential future directions are discussed. This article is part of the theme issue 'Synergistic tomographic image reconstruction: part 1'.

Physics-based reconstruction methods for magnetic resonance imaging

Conventional magnetic resonance imaging (MRI) is hampered by long scan times and only qualitative image contrasts that prohibit a direct comparison between different systems. To address these limitations, model-based reconstructions explicitly model the physical laws that govern the MRI signal generation. By formulating image reconstruction as an inverse problem, quantitative maps of the underlying physical parameters can then be extracted directly from efficiently acquired k-space signals without intermediate image reconstruction-addressing both shortcomings of conventional MRI at the same time. This review will discuss basic concepts of model-based reconstructions and report on our experience in developing several model-based methods over the last decade using selected examples that are provided complete with data and code. This article is part of the theme issue 'Synergistic tomographic image reconstruction: part 1'.

Deep learning-enhanced T1 mapping with spatial-temporal and physical constraint

PURPOSE

To propose a reconstruction framework to generate accurate T₁ maps for a fast MR T₁ mapping sequence.

METHODS

A deep learning-enhanced T₁ mapping method with spatial-temporal and physical constraint (DAINTY) was proposed. This method explicitly imposed low-rank and sparsity constraints on the multiframe T₁ -weighted images to exploit the spatial-temporal correlation. A deep neural network was used to efficiently perform T₁ mapping as well as denoise and reduce undersampling artifacts. Additionally, the physical constraint was used to build a bridge between low-rank and sparsity constraint and deep learning prior, so the benefits of constrained reconstruction and deep learning can be both available. The DAINTY method was trained on simulated brain data sets, but tested on real acquired phantom, 6 healthy volunteers, and 7 atherosclerosis patients, compared with the narrow-band k-space-weighted image contrast filter conjugate-gradient SENSE (NK-CS) method, kt-sparse-SENSE (kt-SS) method, and low-rank plus sparsity (L+S) method with least-squares T₁ fitting and direct deep learning mapping.

RESULTS

The DAINTY method can generate more accurate T₁ maps and higher-quality T₁ -weighted images compared with other methods. For atherosclerosis patients, the intraplaque hemorrhage can be successfully detected. The computation speed of DAINTY was 10 times faster than traditional methods. Meanwhile, DAINTY can reconstruct images with comparable quality using only 50% of k-space data.

CONCLUSION

The proposed method can provide accurate T₁ maps and good-quality T₁ -weighted images with high efficiency.

Model-based reconstruction for simultaneous multi-slice T1 mapping using single-shot inversion-recovery radial FLASH

PURPOSE

To develop a single-shot multi-slice T 1 mapping method by combing simultaneous multi-slice (SMS) excitations, single-shot inversion-recovery (IR) radial fast low-angle shot (FLASH), and a nonlinear model-based reconstruction method.

METHODS

SMS excitations are combined with a single-shot IR radial FLASH sequence for data acquisition. A previously developed single-slice calibrationless model-based reconstruction is extended to SMS, formulating the estimation of parameter maps and coil sensitivities from all slices as a single nonlinear inverse problem. Joint-sparsity constraints are further applied to the parameter maps to improve T 1 precision. Validations of the proposed method are performed for a phantom and for the human brain and liver in 6 healthy adult subjects.

RESULTS

Phantom results confirm good T 1 accuracy and precision of the simultaneously acquired multi-slice T 1 maps in comparison to single-slice references. In vivo human brain studies demonstrate the better performance of SMS acquisitions compared to the conventional spoke-interleaved multi-slice acquisition using model-based reconstruction. Aside from good accuracy and precision, the results of 6 healthy subjects in both brain and abdominal studies confirm good repeatability between scan and re-scans. The proposed method can simultaneously acquire T 1 maps for 5 slices of a human brain ( 0.75 × 0.75 × 5 mm 3 ) or 3 slices of the abdomen ( 1.25 × 1.25 × 6 mm 3 ) within 4 seconds.

CONCLUSIONS

The IR SMS radial FLASH acquisition together with a nonlinear model-based reconstruction enable rapid high-resolution multi-slice T 1 mapping with good accuracy, precision, and repeatability.

Improving subspace constrained radial fast spin echo MRI using block matching driven non-local low rank regularization

Subspace-constrained reconstruction methods restrict the relaxation signals (of size M) in the scene to a pre-determined subspace (of size K≪M) and allow multi-contrast imaging and parameter mapping from accelerated acquisitions. However, these constraints yield poor image quality at some imaging contrasts, which can impact the parameter mapping performance. Additional regularization such as the use of joint-sparse (JS) or locally-low-rank (LLR) constraints can help improve the recovery of these images but are not sufficient when operating at high acceleration rates. We propose a method, non-local rank 3D (NLR3D), that is built on block matching and transform domain low rank constraints to allow high quality recovery of subspace-coefficient images (SCI) and subsequent multi-contrast imaging and parameter mapping. The performance of NLR3D was evaluated using Monte-Carlo (MC) simulations and compared against the JS and LLR methods. In vivo T 2 mapping results are presented on brain and knee datasets. MC results demonstrate improved bias, variance, and MSE behavior in both the multi-contrast images and parameter maps when compared to the JS and LLR methods. In vivo brain and knee results at moderate and high acceleration rates demonstrate improved recovery of high SNR early TE images as well as parameter maps. No significant difference was found in the T2 values measured in ROIs between the NLR3D reconstructions and the reference images (Wilcoxon signed rank test). The proposed method, NLR3D, enables recovery of high-quality SCI and, consequently, the associated multi-contrast images and parameter maps.

Fast multicomponent 3D-T1ρ relaxometry

NMR relaxometry can provide information about the relaxation of the magnetization in different tissues, increasing our understanding of molecular dynamics and biochemical composition in biological systems. In general, tissues have complex and heterogeneous structures composed of multiple pools. As a result, bulk magnetization returns to its original state with different relaxation times, in a multicomponent relaxation. Recovering the distribution of relaxation times in each voxel is a difficult inverse problem; it is usually unstable and requires long acquisition time, especially on clinical scanners. MRI can also be viewed as an inverse problem, especially when compressed sensing (CS) is used. The solution of these two inverse problems, CS and relaxometry, can be obtained very efficiently in a synergistically combined manner, leading to a more stable multicomponent relaxometry obtained with short scan times. In this paper, we will discuss the details of this technique from the viewpoint of inverse problems.

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.

A multi-scale residual network for accelerated radial MR parameter mapping

A deep learning MR parameter mapping framework which combines accelerated radial data acquisition with a multi-scale residual network (MS-ResNet) for image reconstruction is proposed. The proposed supervised learning strategy uses input image patches from multi-contrast images with radial undersampling artifacts and target image patches from artifact-free multi-contrast images. Subspace filtering is used during pre-processing to denoise input patches. For each anatomy and relaxation parameter, an individual network is trained. in vivo T1 mapping results are obtained on brain and abdomen datasets and in vivo T2 mapping results are obtained on brain and knee datasets. Quantitative results for the T2 mapping of the knee show that MS-ResNet trained using either fully sampled or undersampled data outperforms conventional model-based compressed sensing methods. This is significant because obtaining fully sampled training data is not possible in many applications. in vivo brain and abdomen results for T1 mapping and in vivo brain results for T2 mapping demonstrate that MS-ResNet yields contrast-weighted images and parameter maps that are comparable to those achieved by model-based iterative methods while offering two orders of magnitude reduction in reconstruction times. The proposed approach enables recovery of high-quality contrast-weighted images and parameter maps from highly accelerated radial data acquisitions. The rapid image reconstructions enabled by the proposed approach makes it a good candidate for routine clinical use.

Three Dimensional Reconstruction Models for Medical Modalities: A Comprehensive Investigation and Analysis

BACKGROUND

Image reconstruction is the mathematical process which converts the signals obtained from the scanning machine into an image. The reconstructed image plays a fundamental role in the planning of surgery and research in the medical field.

DISCUSSION

This paper introduces the first comprehensive survey of the literature about medical image reconstruction related to diseases, presenting a categorical study about the techniques and analyzing advantages and disadvantages of each technique. The images obtained by various imaging modalities like MRI, CT, CTA, Stereo radiography and Light field microscopy are included. A comparison on the basis of the reconstruction technique, Imaging Modality and Visualization, Disease, Metrics for 3D reconstruction accuracy, Dataset and Execution time, Evaluation of the technique is also performed.

CONCLUSION

The survey makes an assessment of the suitable reconstruction technique for an organ, draws general conclusions and discusses the future directions.

Further Development of Subspace Imaging to Magnetic Resonance Fingerprinting: A Low-rank Tensor Approach

Magnetic resonance fingerprinting is a recent quantitative MRI technique that simultaneously acquires multiple tissue parameter maps (e.g., T1, T2, and spin density) in a single imaging experiment. In our early work, we demonstrated that the low-rank/subspace reconstruction significantly improves the accuracy of tissue parameter maps over the conventional MR fingerprinting reconstruction that utilizes simple pattern matching. In this paper, we generalize the low-rank/subspace reconstruction by introducing a multilinear low-dimensional image model (i.e., a low-rank tensor model). With this model, we further estimate the subspace associated with magnetization evolutions to simplify the image reconstruction problem. The proposed formulation results in a nonconvex optimization problem which we solve by an alternating minimization algorithm. We evaluate the performance of the proposed method with numerical experiments, and demonstrate that the proposed method improves the conventional reconstruction method and the state-of-the-art low-rank reconstruction method.

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.

Computational MRI with Physics-based Constraints: Application to Multi-contrast and Quantitative Imaging

Compressed sensing takes advantage of low-dimensional signal structure to reduce sampling requirements far below the Nyquist rate. In magnetic resonance imaging (MRI), this often takes the form of sparsity through wavelet transform, finite differences, and low rank extensions. Though powerful, these image priors are phenomenological in nature and do not account for the mechanism behind the image formation. On the other hand, MRI signal dynamics are governed by physical laws, which can be explicitly modeled and used as priors for reconstruction. These explicit and implicit signal priors can be synergistically combined in an inverse problem framework to recover sharp, multi-contrast images from highly accelerated scans. Furthermore, the physics-based constraints provide a recipe for recovering quantitative, bio-physical parameters from the data. This article introduces physics-based modeling constraints in MRI and shows how they can be used in conjunction with compressed sensing for image reconstruction and quantitative imaging. We describe model-based quantitative MRI, as well as its linear subspace approximation. We also discuss approaches to selecting user-controllable scan parameters given knowledge of the physical model. We present several MRI applications that take advantage of this framework for the purpose of multi-contrast imaging and quantitative mapping.

Improvement of Fast Model-Based Acceleration of Parameter Look-Locker T1 Mapping

Quantitative mapping is desirable in many scientific and clinical magneric resonance imaging (MRI) applications. Recent inverse recovery-look locker sequence enables single-shot T₁ mapping with a time of a few seconds but the main computational load is directed into offline reconstruction, which can take from several minutes up to few hours. In this study we proposed improvement of model-based approach for T₁-mapping by introduction of two steps fitting procedure. We provided analysis of further reduction of k-space data, which lead us to decrease of computational time and perform simulation of multi-slice development. The region of interest (ROI) analysis of human brain measurements with two different initial models shows that the differences between mean values with respect to a reference approach are in white matter-0.3% and 1.1%, grey matter-0.4% and 1.78% and cerebrospinal fluid-2.8% and 11.1% respectively. With further improvements we were able to decrease the time of computational of single slice to 6.5 min and 23.5 min for different initial models, which has been already not achieved by any other algorithm. In result we obtained an accelerated novel method of model-based image reconstruction in which single iteration can be performed within few seconds on home computer.

Bio-SCOPE: fast biexponential T1ρ mapping of the brain using signal-compensated low-rank plus sparse matrix decomposition

PURPOSE

To develop and evaluate a fast imaging method based on signal-compensated low-rank plus sparse matrix decomposition to accelerate data acquisition for biexponential brain T_1ρ mapping (Bio-SCOPE).

METHODS

Two novel strategies were proposed to improve reconstruction performance. A variable-rate undersampling scheme was used with a varied acceleration factor for each k-space along the spin-lock time direction, and a modified nonlinear thresholding scheme combined with a feature descriptor was used for Bio-SCOPE reconstruction. In vivo brain T_1ρ mappings were acquired from 4 volunteers. The fully sampled k-space data acquired from 3 volunteers were retrospectively undersampled by net acceleration rates (R) of 4.6 and 6.1. Reference values were obtained from the fully sampled data. The agreement between the accelerated T_1ρ measurements and reference values was assessed with Bland-Altman analyses. Prospectively undersampled data with R = 4.6 and R = 6.1 were acquired from 1 volunteer.

RESULTS

T_1ρ -weighted images were successfully reconstructed using Bio-SCOPE for R = 4.6 and 6.1 with signal-to-noise ratio variations <1 dB and normalized root mean square errors <4%. Accelerated and reference T_1ρ measurements were in good agreement for R = 4.6 (T_{1ρ s} : 18.6651 ± 1.7786 ms; T_{1ρ l} : 88.9603 ± 1.7331 ms) and R = 6.1 (T_{1ρ s} : 17.8403 ± 3.3302 ms; T_{1ρ l} : 88.0275 ± 4.9606 ms) in the Bland-Altman analyses. T_1ρ parameter maps from prospectively undersampled data also show reasonable image quality using the Bio-SCOPE method.

CONCLUSION

Bio-SCOPE achieves a high net acceleration rate for biexponential T_1ρ mapping and improves reconstruction quality by using a variable-rate undersampling data acquisition scheme and a modified soft-thresholding algorithm in image reconstruction.

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

Purpose

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

Methods

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

Results

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

Conclusion

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

Model-based myocardial T1 mapping with sparsity constraints using single-shot inversion-recovery radial FLASH cardiovascular magnetic resonance

BACKGROUND

This study develops a model-based myocardial T1 mapping technique with sparsity constraints which employs a single-shot inversion-recovery (IR) radial fast low angle shot (FLASH) cardiovascular magnetic resonance (CMR) acquisition. The method should offer high resolution, accuracy, precision and reproducibility.

METHODS

The proposed reconstruction estimates myocardial parameter maps directly from undersampled k-space which is continuously measured by IR radial FLASH with a 4 s breathhold and retrospectively sorted based on a cardiac trigger signal. Joint sparsity constraints are imposed on the parameter maps to further improve T1 precision. Validations involved studies of an experimental phantom and 8 healthy adult subjects.

RESULTS

In comparison to an IR spin-echo reference method, phantom experiments with T1 values ranging from 300 to 1500 ms revealed good accuracy and precision at simulated heart rates between 40 and 100 bpm. In vivo T1 maps achieved better precision and qualitatively better preservation of image features for the proposed method than a real-time CMR approach followed by pixelwise fitting. Apart from good inter-observer reproducibility (0.6% of the mean), in vivo results confirmed good intra-subject reproducibility (1.05% of the mean for intra-scan and 1.17, 1.51% of the means for the two inter-scans, respectively) of the proposed method.

CONCLUSION

Model-based reconstructions with sparsity constraints allow for single-shot myocardial T1 maps with high spatial resolution, accuracy, precision and reproducibility within a 4 s breathhold. Clinical trials are warranted.

Robust Single-Shot T2 Mapping via Multiple Overlapping-Echo Acquisition and Deep Neural Network

Quantitative magnetic resonance imaging (MRI) is of great value to both clinical diagnosis and scientific research. However, most MRI experiments remain qualitative, especially dynamic MRI, because repeated sampling with variable weighting parameter makes quantitative imaging time-consuming and sensitive to motion artifacts. A single-shot quantitative T₂ mapping method based on multiple overlapping-echo acquisition (dubbed MOLED-4) was proposed to obtain reliable T₂ mapping in milliseconds. Different from traditional MRI acceleration methods, such as compressed sensing and parallel imaging, MOLED-4 accelerates quantitative T₂ mapping via synchronized multisampling and then deep learning to map the complex nonlinear relationship that is difficult to solve by traditional optimization-based methods. The results of simulation, phantom, and in vivo human brain experiments show the great performance of the proposed method. The principle of MOLED-4 may be extended to other ultrafast quantitative parameter mappings and potentially lead to new dynamic MRI with high efficiency to catch quantitative variation of tissue properties.

OEDIPUS: An Experiment Design Framework for Sparsity-Constrained MRI

This paper introduces a new estimation-theoretic framework for experiment design in the context of MR image reconstruction under sparsity constraints. The new framework is called OEDIPUS (Oracle-based Experiment Design for Imaging Parsimoniously Under Sparsity constraints) and is based on combining the constrained Cramér-Rao bound with classical experiment design techniques. Compared to popular random sampling approaches, OEDIPUS is fully deterministic and automatically tailors the sampling pattern to the specific imaging context of interest (i.e., accounting for coil geometry, anatomy, image contrast, etc.). OEDIPUS-based experiment designs are evaluated using retrospectively subsampled in vivo MRI data in several different contexts. The results demonstrate that OEDIPUS-based experiment designs have some desirable characteristics relative to conventional MRI sampling approaches.

SUPER: A blockwise curve-fitting method for accelerating MR parametric mapping with fast reconstruction

PURPOSE

To investigate Shift Undersampling improves Parametric mapping Efficiency and Resolution (SUPER), a novel blockwise curve-fitting method for accelerating parametric mapping with very fast reconstruction.

METHODS

SUPER uses interleaved k-space undersampling, which enables a blockwise decomposition of the otherwise large-scale cost function to improve the reconstruction efficiency. SUPER can be readily combined with SENSE to achieve at least 4-fold acceleration. D-factor, a parametric-mapping counterpart of g-factor, was proposed and formulated to compare spatially heterogeneous noise amplification because of different acceleration methods. As a proof-of-concept, SUPER/SUPER-SENSE was validated using T1 mapping, by comparing them to alternative model-based methods, including MARTINI and GRAPPATINI, via simulations, phantom imaging, and in vivo brain imaging (N = 5), over criteria of normalized root-mean-squares error (NRMSE), average d-factor, and computational time per voxel (TPV). A novel SUPER-SENSE MOLLI cardiac T1 -mapping sequence with improved resolution (1.4 mm × 1.4 mm) was compared to standard MOLLI (1.9 mm × 2.5 mm) in 8 healthy subjects.

RESULTS

In brain imaging, 2-fold SUPER achieved lower NRMSE (0.04 ± 0.02 vs. 0.11 ± 0.02, P < 0.01), lower average d-factor (1.01 ± 0.002 vs. 1.12 ± 0.004, P < 0.001), and lower TPV (4.6 ms ± 0.2 ms vs. 79 ms ± 3 ms, P < 0.001) than 2-fold MARTINI. Similarly, 4-fold SUPER-SENSE achieved lower NRMSE (0.07 ± 0.01 vs. 0.13 ± 0.03, P = 0.02), lower average d-factor (1.15 ± 0.01 vs. 1.20 ± 0.01, P < 0.001), and lower TPV (4.0 ms ± 0.1 ms vs. 72 ms ± 3 ms, P < 0.001) than 4-fold GRAPPATINI. In cardiac T1 mapping, SUPER-SENSE MOLLI yielded similar myocardial T1 (1151 ms ± 63 ms vs. 1159 ms ± 32 ms, P = 0.6), slightly lower blood T1 (1643 ms ± 86 ms vs. 1680 ms ± 79 ms, P = 0.004), but improved spatial resolution compared with standard MOLLI in the same imaging time.

CONCLUSION

SUPER and SUPER-SENSE provide fast model-based reconstruction methods for accelerating parametric mapping and improving its clinical appeal.

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

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

Rapid compositional mapping of knee cartilage with compressed sensing MRI

More than a decade after the introduction of compressed sensing (CS) in MRI, researchers are still working on ways to translate it into different research and clinical applications. The greatest advantage of CS in MRI is the reduced amount of k-space data needed to reconstruct images, which can be exploited to reduce scan time or to improve spatial resolution and volumetric coverage. Efficient data acquisition using CS is extremely important for compositional mapping of the musculoskeletal system in general and knee cartilage mapping techniques in particular. High-resolution quantitative information about tissue biochemical composition could be obtained in just a few minutes using CS MRI. However, in order to make this goal a reality, some issues still need to be addressed. In this article we review the current state of the art of CS methods for rapid compositional mapping of knee cartilage. Specifically, data acquisition strategies, image reconstruction algorithms, and data fitting models are discussed. Different CS studies for T2 and T1ρ mapping of knee cartilage are reviewed, with illustrative results. Future directions, opportunities, and challenges of rapid compositional mapping techniques are also discussed. Level of Evidence: 4 Technical Efficacy: Stage 6 J. Magn. Reson. Imaging 2018;47:1185-1198.

Rapid T1 quantification from high resolution 3D data with model-based reconstruction

Purpose

Magnetic resonance imaging protocols for the assessment of quantitative information suffer from long acquisition times since multiple measurements in a parametric dimension are required. To facilitate the clinical applicability, accelerating the acquisition is of high importance. To this end, we propose a model‐based optimization framework in conjunction with undersampling 3D radial stack‐of‐stars data.

Theory and Methods

High resolution 3D T₁ maps are generated from subsampled data by employing model‐based reconstruction combined with a regularization functional, coupling information from the spatial and parametric dimension, to exploit redundancies in the acquired parameter encodings and across parameter maps. To cope with the resulting non‐linear, non‐differentiable optimization problem, we propose a solution strategy based on the iteratively regularized Gauss‐Newton method. The importance of 3D‐spectral regularization is demonstrated by a comparison to 2D‐spectral regularized results. The algorithm is validated for the variable flip angle (VFA) and inversion recovery Look‐Locker (IRLL) method on numerical simulated data, MRI phantoms, and in vivo data.

Results

Evaluation of the proposed method using numerical simulations and phantom scans shows excellent quantitative agreement and image quality. T₁ maps from accelerated 3D in vivo measurements, e.g. 1.8 s/slice with the VFA method, are in high accordance with fully sampled reference reconstructions.

Conclusions

The proposed algorithm is able to recover T₁ maps with an isotropic resolution of 1 mm³ from highly undersampled radial data by exploiting structural similarities in the imaging volume and across parameter maps.

Compressed sensing acceleration of biexponential 3D-T1ρ relaxation mapping of knee cartilage

PURPOSE

Use compressed sensing (CS) for 3D biexponential spin-lattice relaxation time in the rotating frame (T_1ρ ) mapping of knee cartilage, reducing the total scan time and maintaining the quality of estimated biexponential T_1ρ parameters (short and long relaxation times and corresponding fractions) comparable to fully sampled scans.

METHODS

Fully sampled 3D-T_1ρ -weighted data sets were retrospectively undersampled by factors 2-10. CS reconstruction using 12 different sparsifying transforms were compared for biexponential T_1ρ -mapping of knee cartilage, including temporal and spatial wavelets and finite differences, dictionary from principal component analysis (PCA), k-means singular value decomposition (K-SVD), exponential decay models, and also low rank and low rank plus sparse models. Synthetic phantom (N = 6) and in vivo human knee cartilage data sets (N = 7) were included in the experiments. Spatial filtering before biexponential T_1ρ parameter estimation was also tested.

RESULTS

Most CS methods performed satisfactorily for an acceleration factor (AF) of 2, with relative median normalized absolute deviation (MNAD) around 10%. Some sparsifying transforms, such as low rank with spatial finite difference (L + S SFD), spatiotemporal finite difference (STFD), and exponential dictionaries (EXP) significantly improved this performance, reaching MNAD below 15% with AF up to 10, when spatial filtering was used.

CONCLUSION

Accelerating biexponential 3D-T_1ρ mapping of knee cartilage with CS is feasible. The best results were obtained by STFD, EXP, and L + S SFD regularizers combined with spatial prefiltering. These 3 CS methods performed satisfactorily on synthetic phantom as well as in vivo knee cartilage for AFs up to 10, with median error below 15%.

SCOPE: signal compensation for low-rank plus sparse matrix decomposition for fast parameter mapping

Magnetic resonance (MR) parameter mapping is useful for many clinical applications. However, its practical utility is limited by the long scan time. To address this problem, this paper developed a novel image reconstruction method for fast MR parameter mapping. The proposed method (SCOPE) used a low-rank plus sparse model to reconstruct the parameter-weighted images from highly undersampled acquisitions. A signal compensation strategy was introduced to promote low rankness along the parametric direction and thus improve the reconstruction accuracy. Specifically, compensation was performed by multiplying the original signal by the inversion of the mono-exponential decay at each voxel. The performance of SCOPE was evaluated via quantitative T _1ρ mapping. The results of the simulation and in vivo experiments with acceleration factors from 3 to 5 are shown. The performance of SCOPE was verified via comparisons with several low-rank and sparsity-based methods. The experimental results showed that the T _1ρ maps obtained using SCOPE were more accurate than those obtained using competing methods and were comparable to the reference, even when the acceleration factor reached 5. SCOPE can greatly reduce the scan time of parameter mapping while still achieving high accuracy. This technique might therefore help facilitate fast MR parameter mapping in clinical use.

Dictionary-Free MRI PERK: Parameter Estimation via Regression with Kernels

This paper introduces a fast, general method for dictionary-free parameter estimation in quantitative magnetic resonance imaging (QMRI) parameter estimation via regression with kernels (PERK). PERK first uses prior distributions and the nonlinear MR signal model to simulate many parameter-measurement pairs. Inspired by machine learning, PERK then takes these parameter-measurement pairs as labeled training points and learns from them a nonlinear regression function using kernel functions and convex optimization. PERK admits a simple implementation as per-voxel nonlinear lifting of MRI measurements followed by linear minimum mean-squared error regression. We demonstrate PERK for $ {\textit {T}_{1}}, {\textit {T}_{2}}$ estimation, a well-studied application where it is simple to compare PERK estimates against dictionary-based grid search estimates and iterative optimization estimates. Numerical simulations as well as single-slice phantom and in vivo experiments demonstrate that PERK and other tested methods produce comparable $ {\textit {T}_{1}}, {\textit {T}_{2}}$ estimates in white and gray matter, but PERK is consistently at least $140\times $ faster. This acceleration factor may increase by several orders of magnitude for full-volume QMRI estimation problems involving more latent parameters per voxel.

Fast Interleaved Multislice T1 Mapping: Model-Based Reconstruction of Single-Shot Inversion-Recovery Radial FLASH

Purpose

To develop a high-speed multislice T1 mapping method based on a single-shot inversion-recovery (IR) radial FLASH acquisition and a regularized model-based reconstruction.

Methods

Multislice radial k-space data are continuously acquired after a single nonselective inversion pulse using a golden-angle sampling scheme in a spoke-interleaved manner with optimized flip angles. Parameter maps and coil sensitivities of each slice are estimated directly from highly undersampled radial k-space data using a model-based nonlinear inverse reconstruction in conjunction with joint sparsity constraints. The performance of the method has been validated using a numerical and experimental T1 phantom as well as demonstrated for studies of the human brain and liver at 3T.

Results

The proposed method allows for 7 simultaneous T1 maps of the brain at 0.5 × 0.5 × 4 mm³ resolution within a single IR experiment of 4 s duration. Phantom studies confirm similar accuracy and precision as obtained for a single-slice acquisition. For abdominal applications, the proposed method yields three simultaneous T1 maps at 1.25 × 1.25 × 6 mm³ resolution within a 4 s breath hold.

Conclusion

Rapid, robust, accurate, and precise multislice T1 mapping may be achieved by combining the advantages of a model-based nonlinear inverse reconstruction, radial sampling, parallel imaging, and compressed sensing.

Accelerated MR parameter mapping with a union of local subspaces constraint

PURPOSE

A new reconstruction method for multi-contrast imaging and parameter mapping based on a union of local subspaces constraint is presented.

THEORY

Subspace constrained reconstructions use a predetermined subspace to explicitly constrain the relaxation signals. The choice of subspace size ( K ) impacts the approximation error vs noise-amplification tradeoff associated with these methods. A different approach is used in the model consistency constraint (MOCCO) framework to leverage the subspace model to enforce a softer penalty. Our proposed method, MOCCO-LS, augments the MOCCO model with a union of local subspaces (LS) approach. The union of local subspaces model is coupled with spatial support constraints and incorporated into the MOCCO framework to regularize the contrast signals in the scene.

METHODS

The performance of the MOCCO-LS method was evaluated in vivo on T₁ and T₂ mapping of the human brain and with Monte-Carlo simulations and compared against MOCCO and the explicit subspace constrained models.

RESULTS

The results demonstrate a clear improvement in the multi-contrast images and parameter maps. We sweep across the model order space ( K ) to compare the different reconstructions and demonstrate that the reconstructions have different preferential operating points. Experiments on T₂ mapping show that the proposed method yields substantial improvements in performance even when operating at very high acceleration rates.

CONCLUSIONS

The use of a union of local subspace constraints coupled with a sparsity promoting penalty leads to improved reconstruction quality of multi-contrast images and parameter maps.

Accelerating 3D-T1ρ mapping of cartilage using compressed sensing with different sparse and low rank models

PURPOSE

To evaluate the feasibility of using compressed sensing (CS) to accelerate 3D-T_1ρ mapping of cartilage and to reduce total scan times without degrading the estimation of T_1ρ relaxation times.

METHODS

Fully sampled 3D-T_1ρ datasets were retrospectively undersampled by factors 2-10. CS reconstruction using 12 different sparsifying transforms were compared, including finite differences, temporal and spatial wavelets, learned transforms using principal component analysis (PCA) and K-means singular value decomposition (K-SVD), explicit exponential models, low rank and low rank plus sparse models. Spatial filtering prior to T_1ρ parameter estimation was also tested. Synthetic phantom (n = 6) and in vivo human knee cartilage datasets (n = 7) were included.

RESULTS

Most CS methods performed satisfactorily for an acceleration factor (AF) of 2, with relative T_1ρ error lower than 4.5%. Some sparsifying transforms, such as spatiotemporal finite difference (STFD), exponential dictionaries (EXP) and low rank combined with spatial finite difference (L+S SFD) significantly improved this performance, reaching average relative T_1ρ error below 6.5% on T_1ρ relaxation times with AF up to 10, when spatial filtering was used before T_1ρ fitting, at the expense of smoothing the T_1ρ maps. The STFD achieved 5.1% error at AF = 10 with spatial filtering prior to T_1ρ fitting.

CONCLUSION

Accelerating 3D-T_1ρ mapping of cartilage with CS is feasible up to AF of 10 when using STFD, EXP or L+S SFD regularizers. These three best CS methods performed satisfactorily on synthetic phantom and in vivo knee cartilage for AFs up to 10, with T_1ρ error of 6.5%.

Accelerated T2 mapping combining parallel MRI and model-based reconstruction: GRAPPATINI

BACKGROUND

Quantitative T₂ measurements are sensitive to intra- and extracellular water accumulation and myelin loss. Therefore, quantitative T₂ promises to be a good biomarker of disease. However, T₂ measurements require long acquisition times.

PURPOSE

To accelerate T₂ quantification and subsequent generation of synthetic T₂ -weighted (T₂ -w) image contrast for clinical research and routine. To that end, a recently developed model-based approach for rapid T₂ and M₀ quantification (MARTINI) based on undersampling k-space, was extended by parallel imaging (GRAPPA) to enable high-resolution T₂ mapping with access to T₂ -w images in less than 2 minutes acquisition time for the entire brain.

STUDY TYPE

Prospective cross-sectional study.

SUBJECTS/PHANTOM

Fourteen healthy subjects and a multipurpose phantom.

FIELD STRENGTH/SEQUENCE

Carr-Purcell-Meiboom-Gill sequence at a 3T scanner.

ASSESSMENT

The accuracy and reproducibility of the accelerated T₂ quantification was assessed. Validations comprised MRI studies on a phantom as well as the brain, knee, prostate, and liver from healthy volunteers. Synthetic T₂ -w images were generated from computed T₂ and M₀ maps and compared to conventional fast spin-echo (SE) images.

STATISTICAL TESTS

Root mean square distance (RMSD) to the reference method and region of interest analysis.

RESULTS

The combination of MARTINI and GRAPPA (GRAPPATINI) lead to a 10-fold accelerated T₂ mapping protocol with 1:44 minutes acquisition time and full brain coverage. The RMSD of GRAPPATINI increases less (4.3%) than a 10-fold MARTINI reconstruction (37.6%) in comparison to the reference. Reproducibility tests showed low standard deviation (SD) of T₂ values in regions of interest between scan and rescan (<0.4 msec) and across subjects (<4 msec).

DATA CONCLUSION

GRAPPATINI provides highly reproducible and fast whole-brain T₂ maps and arbitrary synthetic T₂ -w images in clinically compatible acquisition times of less than 2 minutes. These abilities are expected to support more widespread clinical applications of quantitative T₂ mapping.

LEVEL OF EVIDENCE

2 Technical Efficacy: Stage 1 J. MAGN. RESON. IMAGING 2018;48:359-368.

Recovery of Damped Exponentials Using Structured Low Rank Matrix Completion

We introduce a structured low rank matrix completion algorithm to recover a series of images from their under-sampled measurements, where the signal along the parameter dimension at every pixel is described by a linear combination of exponentials. We exploit the exponential behavior of the signal at every pixel, along with the spatial smoothness of the exponential parameters to derive an annihilation relation in the Fourier domain. This relation translates to a low-rank property on a structured matrix constructed from the Fourier samples. We enforce the low-rank property of the structured matrix as a regularization prior to recover the images. Since the direct use of current low rank matrix recovery schemes to this problem is associated with high computational complexity and memory demand, we adopt an iterative re-weighted least squares algorithm, which facilitates the exploitation of the convolutional structure of the matrix. Novel approximations involving 2-D fast Fourier transforms are introduced to drastically reduce the memory demand and computational complexity, which facilitates the extension of structured low-rank methods to large scale 3-D problems. We demonstrate our algorithm in the MR parameter mapping setting and show improvement over the state-of-the-art methods.