Model-based reconstruction of undersampled diffusion tensor k-space data

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.

A Joint Framework for Denoising and Estimating Diffusion Kurtosis Tensors Using Multiple Prior Information

Diffusion kurtosis imaging (DKI) has been shown to be valuable in a wide range of neuroscientific and clinical applications. However, reliable estimation of DKI tensors is often compromised by noise, especially for the kurtosis tensor (KT). Here, we propose a joint denoising and estimating framework that integrates multiple sources of prior information, including nonlocal structural self-similarity (NSS), local spatial smoothness (LSS), physical relevance (PR) of the DKI model, and noise characteristics of magnitude diffusion MRI (dMRI) images for improved estimation of DKI tensors. The local and nonlocal spatial smoothing constraints are complementary to each other, making the proposed framework highly effective in reducing the noise fluctuations on DKI tensors, especially KT. As an additional refinement, we propose to impose a physically relevant constraint within our joint denoising and estimation framework. We further adopt the first-moment noise-corrected fitting model (M¹NCM) to remove the noncentral χ -distribution noise bias. The effectiveness of integrating multiple sources of priors into the joint framework is verified by comparing the proposed M¹NCM-NSS-LSS-PR method with various versions of M¹NCM-based estimators and two state-of-the-art methods. Results show that the proposed method outperformed the compared methods in simulations and in-vivo dMRI datasets of both spatially stationary and nonstationary noise distributions. The in-vivo experiments also show that the proposed M¹NCM-NSS-LSS-PR method was robust to the number of diffusion directions.

Multi-contrast multi-shot EPI for accelerated diffusion MRI

The clinical application of diffusion MRI is practically hindered by its long scan time. In this work, we introduce a novel imaging and parameter estimation framework for time-efficient diffusion MRI. To improve the scan efficiency, we propose ADEPT (Accelerated Diffusion EPI with multi-contrast shoTs), in which diffusion contrast settings are allowed to change between shots in a multi-shot EPI acquisition (i.e. intra-scan modulation). The framework simultaneously corrects for artifacts related to shot-to-shot phase inconsistencies in multi-shot imaging by iteratively estimating the phase map parameters along with the diffusion model parameters directly from the acquired intra-scan modulated k-space data. Monte Carlo simulation experiments show the effective estimation of diffusion tensor parameters in multi-shot EPI diffusion imaging.

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'.

Accelerated model-based quantitative diffusion MRI: A feasibility study for musculoskeletal application

PURPOSE

To develop a model-based reconstruction technique for diffusion quantification based on accelerated two-dimensional echo planar data, obtained with multiple b-weightings. In combination with a dedicated undersampling pattern, acceleration factors above three were proven feasible in a clinical setting.

METHODS

The proposed model-based method minimizes a cost function considering the l₂-norm of the difference between the Fourier transformation of a synthetic diffusion-model-generated k-space and the measured k-space data. Further regularization is performed by introduction of a total variation (TV) constraint to the cost function. Acceleration is achieved by a non-random undersampling pattern using acceleration factors that correspond to the total number of b-values. A rectangular region of variable size, centered in k-space, remains fully sampled for correction of phase variations, introduced by the different diffusion-encoding strengths.

RESULTS

Qualitative analysis of the resulting images (S₀ and ADC) demonstrates the potential of the suggested undersampling pattern in combination with a model-based iterative reconstruction. An edge analysis highlights the preservation of high-frequency information for all investigated undersampling factors. In comparison to a conventional SENSE-accelerated reconstruction, the quantitative analysis of the ADC maps revealed a significantly (P<0.05) superior performance of the suggested technique, enabling acceleration factors of R=3.65 without compromising diffusion data fidelity.

CONCLUSION

The presented work shows the potential of model-based ADC quantification, which, in combination with a suited undersampling pattern for multiple b-values, enables more than three-fold acceleration using two-dimensional EPI without sacrificing ADC fidelity.

Magnetic resonance diffusion tensor tractography of a midbrain auditory circuit in Alligator

Knowledge of brain circuitry is critical for understanding the organization, function, and evolution of central nervous systems. Most commonly, brain connections have been elucidated using histological and experimental methods that require animal sacrifice. On the other hand, magnetic resonance diffusion tensor imaging and associated tractography have emerged as a preferred method to noninvasively visualize brain white matter tracts. However, existing studies have primarily examined large, heavily myelinated fiber tracts. Whether tractography can visualize fiber bundles that contain thin and poorly myelinated axons is uncertain. To address this question, the midbrain auditory pathway to the thalamus was investigated in Alligator. This species was chosen because of its evolutionary importance as it is the reptilian group most closely related to birds and because its brain contains many thin and poorly myelinated tracts. Furthermore, this auditory pathway is well documented in other reptiles, including a related crocodilian. Histological observations and experimental determination of anterograde connections confirmed this path in Alligator. Tractography identified these tracts in Alligator and provided a 3-dimensional picture that accurately identified the neural elements of this circuit. In addition, tractography identified one possible unrecognized pathway. These results demonstrate that tractography can visualize circuits containing thin, poorly myelinated fibers. These findings open the door for future studies to examine these types of pathways in other vertebrates.

Challenges for biophysical modeling of microstructure

The biophysical modeling efforts in diffusion MRI have grown considerably over the past 25 years. In this review, we dwell on the various challenges along the journey of bringing a biophysical model from initial design to clinical implementation, identifying both hurdles that have been already overcome and outstanding issues. First, we describe the critical initial task of selecting which features of tissue microstructure can be estimated using a model and which acquisition protocol needs to be implemented to make the estimation possible. The model performance should necessarily be tested in realistic numerical simulations and in experimental data - adapting the fitting strategy accordingly, and parameter estimates should be validated against complementary techniques, when/if available. Secondly, the model performance and validity should be explored in pathological conditions, and, if appropriate, dedicated models for pathology should be developed. We build on examples from tumors, ischemia and demyelinating diseases. We then discuss the challenges associated with clinical translation and added value. Finally, we single out four major unresolved challenges that are related to: the availability of a microstructural ground truth, the validation of model parameters which cannot be accessed with complementary techniques, the development of a generalized standard model for any brain region and pathology, and the seamless communication between different parties involved in the development and application of biophysical models of diffusion.

Model-Based Deep Learning for Reconstruction of Joint k-q Under-sampled High Resolution Diffusion MRI

We propose a model-based deep learning architecture for the reconstruction of highly accelerated diffusion magnetic resonance imaging (MRI) that enables high resolution imaging. The proposed reconstruction jointly recovers all the diffusion weighted images in a single step from a joint k-q under-sampled acquisition in a parallel MRI setting. We propose the novel use of a pre-trained denoiser as a regularizer in a model-based reconstruction for the recovery of highly under-sampled data. Specifically, we designed the denoiser based on a general diffusion MRI tissue microstructure model for multi-compartmental modeling. By using a wide range of biologically plausible parameter values for the multi-compartmental microstructure model, we simulated diffusion signal that spans the entire microstructure parameter space. A neural network was trained in an unsupervised manner using an autoencoder to learn the diffusion MRI signal subspace. We employed the autoencoder in a model-based reconstruction and show that the autoencoder provides a strong denoising prior to recover the q-space signal. We show reconstruction results on a simulated brain dataset that shows high acceleration capabilities of the proposed method.

Acceleration of three-dimensional diffusion magnetic resonance imaging using a kernel low-rank compressed sensing method

Diffusion Magnetic Resonance Imaging (dMRI) has shown great potential in probing tissue microstructure and structural connectivity in the brain but is often limited by the lengthy scan time needed to sample the diffusion profile by acquiring multiple diffusion weighted images (DWIs). Although parallel imaging technique has improved the speed of dMRI acquisition, attaining high resolution three dimensional (3D) dMRI on preclinical MRI systems remained still time consuming. In this paper, kernel principal component analysis, a machine learning approach, was employed to estimate the correlation among DWIs. We demonstrated the feasibility of such correlation estimation from low-resolution training DWIs and used the correlation as a constraint to reconstruct high-resolution DWIs from highly under-sampled k-space data, which significantly reduced the scan time. Using full k-space 3D dMRI data of post-mortem mouse brains, we retrospectively compared the performance of the so-called kernel low rank (KLR) method with a conventional compressed sensing (CS) method in terms of image quality and ability to resolve complex fiber orientations and connectivity. The results demonstrated that the KLR-CS method outperformed the conventional CS method for acceleration factors up to 8 and was likely to enhance our ability to investigate brain microstructure and connectivity using high-resolution 3D dMRI.

Tracer kinetic models as temporal constraints during brain tumor DCE-MRI reconstruction

Purpose

To apply tracer kinetic models as temporal constraints during reconstruction of under‐sampled brain tumor dynamic contrast enhanced (DCE) magnetic resonance imaging (MRI).

Methods

A library of concentration vs time profiles is simulated for a range of physiological kinetic parameters. The library is reduced to a dictionary of temporal bases, where each profile is approximated by a sparse linear combination of the bases. Image reconstruction is formulated as estimation of concentration profiles and sparse model coefficients with a fixed sparsity level. Simulations are performed to evaluate modeling error, and error statistics in kinetic parameter estimation in presence of noise. Retrospective under‐sampling experiments are performed on a brain tumor DCE digital reference object (DRO), and 12 brain tumor in‐vivo 3T datasets. The performances of the proposed under‐sampled reconstruction scheme and an existing compressed sensing‐based temporal finite‐difference (tFD) under‐sampled reconstruction were compared against the fully sampled inverse Fourier Transform‐based reconstruction.

Results

Simulations demonstrate that sparsity levels of 2 and 3 model the library profiles from the Patlak and extended Tofts‐Kety (ETK) models, respectively. Noise sensitivity analysis showed equivalent kinetic parameter estimation error statistics from noisy concentration profiles, and model approximated profiles. DRO‐based experiments showed good fidelity in recovery of kinetic maps from 20‐fold under‐sampled data. In‐vivo experiments demonstrated reduced bias and uncertainty in kinetic mapping with the proposed approach compared to tFD at under‐sampled reduction factors >= 20.

Conclusions

Tracer kinetic models can be applied as temporal constraints during brain tumor DCE‐MRI reconstruction. The proposed under‐sampled scheme resulted in model parameter estimates less biased with respect to conventional fully sampled DCE MRI reconstructions and parameter estimation. The approach is flexible, can use nonlinear kinetic models, and does not require tuning of regularization parameters.

Accelerating cardiac diffusion tensor imaging combining local low-rank and 3D TV constraint

OBJECTIVE

Diffusion tensor magnetic resonance imaging (DT-MRI, or DTI) is a promising technique for invasively probing biological tissue structures. However, DTI is known to suffer from much longer acquisition time with respect to conventional MRI and the problem is worsened when dealing with in vivo acquisitions. Therefore, faster DTI for both ex vivo and in vivo scans is highly desired.

MATERIALS AND METHODS

This paper proposes a new compressed sensing (CS) reconstruction method that employs local low-rank (LLR) model and three-dimensional (3D) total variation (TV) constraint to reconstruct cardiac diffusion-weighted (DW) images from highly undersampled k-space data. The LLR model takes the set of DW images corresponding to different diffusion gradient directions as a 3D image volume and decomposes the latter into overlapping 3D blocks. Then, the 3D blocks are stacked as two-dimensional (2D) matrix. Finally, low-rank property is applied to each block matrix and the 3D TV constraint to the 3D image volume. The underlying constrained optimization problem is finally solved using the first-order fast method. The proposed method is evaluated on real ex vivo cardiac DTI data as a prerequisite to in vivo cardiac DTI applications.

RESULTS

The results on real human ex vivo cardiac DTI images demonstrate that the proposed method exhibits lower reconstruction errors for DTI indices, including fractional anisotropy (FA), mean diffusivities (MD), transverse angle (TA), and helix angle (HA), compared to existing CS-based DTI image reconstruction techniques.

CONCLUSION

The proposed method provides better reconstruction quality and more accurate DTI indices in comparison with the state-of-the-art CS-based DW image reconstruction methods.

Highly accelerated, model-free diffusion tensor MRI reconstruction using neural networks

PURPOSE

The purpose of this study was to develop a neural network that accurately performs diffusion tensor imaging (DTI) reconstruction from highly accelerated scans.

MATERIALS AND METHODS

This retrospective study was conducted using data acquired between 2013 and 2018 and was approved by the local institutional review board. DTI acquired in healthy volunteers (N = 10) was used to train a neural network, DiffNet, to reconstruct fractional anisotropy (FA) and mean diffusivity (MD) maps from small subsets of acquired DTI data with between 3 and 20 diffusion-encoding directions. FA and MD maps were then reconstructed in volunteers and in patients with glioblastoma multiforme (GBM, N = 12) using both DiffNet and conventional reconstructions. Accuracy and precision were quantified in volunteer scans and compared between reconstructions. The accuracy of tumor delineation was compared between reconstructed patient data by evaluating agreement between DTI-derived tumor volumes and volumes defined by contrast-enhanced T1-weighted MRI. Comparisons were performed using areas under the receiver operating characteristic curves (AUC).

RESULTS

DiffNet FA reconstructions were more accurate and precise compared with conventional reconstructions for all acceleration factors. DiffNet permitted reconstruction with only three diffusion-encoding directions with significantly lower bias than the conventional method using six directions (0.01 ± 0.01 vs 0.06 ± 0.01, P < 0.001). While MD-based tumor delineation was not substantially different with DiffNet (AUC range: 0.888-0.902), DiffNet FA had higher AUC than conventional reconstructions for fixed scan time and achieved similar performance with shorter scans (conventional, six directions: AUC = 0.926, DiffNet, three directions: AUC = 0.920).

CONCLUSION

DiffNet improved DTI reconstruction accuracy, precision, and tumor delineation performance in GBM while permitting reconstruction from only three diffusion-encoding directions.&!#6.

Enhancing intravoxel incoherent motion parameter mapping in the brain using k-b PCA

Intravoxel incoherent motion (IVIM) imaging of diffusion and perfusion parameters in the brain using parallel imaging suffers from local noise amplification. To address the issue, signal correlations in space and along the diffusion encoding dimension are exploited jointly using a constrained image reconstruction approach. IVIM imaging was performed on a clinical 3 T MR system with diffusion weighting along six gradient directions and 16 b-values encoded per direction across a range of 0-900 s/mm² . Data were collected in 11 subjects, retrospectively undersampled in k-space with net factors ranging from 2 to 6 and reconstructed using CG-SENSE and the proposed k-b PCA approach. Results of k-b PCA and CG-SENSE from retrospectively undersampled data were compared with those from the fully sampled reference. In addition, prospective single-shot k-b undersampling was implemented and data were acquired in five additional volunteers. IVIM parameter maps were derived using a segmented least-squares method. The proposed k-b PCA method outperformed CG-SENSE in terms of reconstruction errors for effective undersampling factors of 3 and beyond. Undersampling artifacts were effectively removed with k-b PCA up to sixfold undersampling. At net sixfold undersampling, relative errors (compared with the fully sampled reference) of image magnitude and IVIM parameters (D, f and D^* ) were (median ± interquartile range): 3.5 ± 3.7 versus 25.3 ± 25.8%, 2.7 ± 3.6 versus 14.2 ± 20.4%, 15.1 ± 26.1 versus 96.6 ± 67.4% and 14.8 ± 26.6 versus 100 ± 195.1% for k-b PCA versus CG-SENSE, respectively. Acquisition with sixfold prospective undersampling yielded average IVIM parameters in the brain of 0.79 ± 0.18 × 10^-3  mm² /s for D, 7.35 ± 7.27% for f and 7.11 ± 2.39 × 10^-3  mm² /s for D^* . Constrained reconstruction using k-b PCA improves IVIM parameter mapping from undersampled data when compared with CG-SENSE reconstruction. Prospectively undersampled single-shot echo planar imaging acquisition was successfully employed using k-b PCA, demonstrating a reduction of image artifacts and noise relative to parallel imaging.

Whole mouse brain structural connectomics using magnetic resonance histology

Diffusion tensor histology holds great promise for quantitative characterization of structural connectivity in mouse models of neurological and psychiatric conditions. There has been extensive study in both the clinical and preclinical domains on the complex tradeoffs between the spatial resolution, the number of samples in diffusion q-space, scan time, and the reliability of the resultant data. We describe here a method for accelerating the acquisition of diffusion MRI data to support quantitative connectivity measurements in the whole mouse brain using compressed sensing (CS). The use of CS allows substantial increase in spatial resolution and/or reduction in scan time. Compared to the fully sampled results at the same scan time, the subtle anatomical details of the brain, such as cortical layers, dentate gyrus, and cerebellum, were better visualized using CS due to the higher spatial resolution. Compared to the fully sampled results at the same spatial resolution, the scalar diffusion metrics, including fractional anisotropy (FA) and mean diffusivity (MD), showed consistently low error across the whole brain (< 6.0%) even with 8.0 times acceleration. The node properties of connectivity (strength, cluster coefficient, eigenvector centrality, and local efficiency) demonstrated correlation of better than 95.0% between accelerated and fully sampled connectomes. The acceleration will enable routine application of this technology to a wide range of mouse models of neurologic diseases.

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.

Direct estimation of tracer-kinetic parameter maps from highly undersampled brain dynamic contrast enhanced MRI

PURPOSE

The purpose of this work was to develop and evaluate a T₁ -weighted dynamic contrast enhanced (DCE) MRI methodology where tracer-kinetic (TK) parameter maps are directly estimated from undersampled (k,t)-space data.

THEORY AND METHODS

The proposed reconstruction involves solving a nonlinear least squares optimization problem that includes explicit use of a full forward model to convert parameter maps to (k,t)-space, utilizing the Patlak TK model. The proposed scheme is compared against an indirect method that creates intermediate images by parallel imaging and compressed sensing before to TK modeling. Thirteen fully sampled brain tumor DCE-MRI scans with 5-second temporal resolution are retrospectively undersampled at rates R = 20, 40, 60, 80, and 100 for each dynamic frame. TK maps are quantitatively compared based on root mean-squared-error (rMSE) and Bland-Altman analysis. The approach is also applied to four prospectively R = 30 undersampled whole-brain DCE-MRI data sets.

RESULTS

In the retrospective study, the proposed method performed statistically better than indirect method at R ≥ 80 for all 13 cases. This approach provided restoration of TK parameter values with less errors in tumor regions of interest, an improvement compared to a state-of-the-art indirect method. Applied prospectively, the proposed method provided whole-brain, high-resolution TK maps with good image quality.

CONCLUSION

Model-based direct estimation of TK maps from k,t-space DCE-MRI data is feasible and is compatible up to 100-fold undersampling. Magn Reson Med 78:1566-1578, 2017. © 2016 International Society for Magnetic Resonance in Medicine.

Maximum Likelihood Reconstruction for Magnetic Resonance Fingerprinting

This paper introduces a statistical estimation framework for magnetic resonance (MR) fingerprinting, a recently proposed quantitative imaging paradigm. Within this framework, we present a maximum likelihood (ML) formalism to estimate multiple MR tissue parameter maps directly from highly undersampled, noisy k-space data. A novel algorithm, based on variable splitting, the alternating direction method of multipliers, and the variable projection method, is developed to solve the resulting optimization problem. Representative results from both simulations and in vivo experiments demonstrate that the proposed approach yields significantly improved accuracy in parameter estimation, compared to the conventional MR fingerprinting reconstruction. Moreover, the proposed framework provides new theoretical insights into the conventional approach. We show analytically that the conventional approach is an approximation to the ML reconstruction; more precisely, it is exactly equivalent to the first iteration of the proposed algorithm for the ML reconstruction, provided that a gridding reconstruction is used as an initialization.

Cardiac diffusion tensor imaging based on compressed sensing using joint sparsity and low-rank approximation

Diffusion tensor magnetic resonance (DTMR) imaging and diffusion tensor imaging (DTI) have been widely used to probe noninvasively biological tissue structures. However, DTI suffers from long acquisition times, which limit its practical and clinical applications. This paper proposes a new Compressed Sensing (CS) reconstruction method that employs joint sparsity and rank deficiency to reconstruct cardiac DTMR images from undersampled k-space data. Diffusion-weighted images acquired in different diffusion directions were firstly stacked as columns to form the matrix. The matrix was row sparse in the transform domain and had a low rank. These two properties were then incorporated into the CS reconstruction framework. The underlying constrained optimization problem was finally solved by the first-order fast method. Experiments were carried out on both simulation and real human cardiac DTMR images. The results demonstrated that the proposed approach had lower reconstruction errors for DTI indices, including fractional anisotropy (FA) and mean diffusivities (MD), compared to the existing CS-DTMR image reconstruction techniques.

Parametric Modeling of the Mouse Left Ventricular Myocardial Fiber Structure

Magnetic resonance diffusion tensor imaging (DTI) has greatly facilitated detailed quantifications of myocardial structures. However, structural patterns, such as the distinctive transmural rotation of the fibers, remain incompletely described. To investigate the validity and practicality of pattern-based analysis, 3D DTI was performed on 13 fixed mouse hearts and fiber angles in the left ventricle were transformed and fitted to parametric expressions constructed from elementary functions of the prolate spheroidal spatial variables. It was found that, on average, the myocardial fiber helix angle could be represented to 6.5° accuracy by the equivalence of a product of 10th-order polynomials of the radial and longitudinal variables, and 17th-order Fourier series of the circumferential variable. Similarly, the fiber imbrication angle could be described by 10th-order polynomials and 24th-order Fourier series, to 5.6° accuracy. The representations, while relatively concise, did not adversely affect the information commonly derived from DTI datasets including the whole-ventricle mean fiber helix angle transmural span and atlases constructed for the group. The unique ability of parametric models for predicting the 3D myocardial fiber structure from finite number of 2D slices was also demonstrated. These findings strongly support the principle of parametric modeling for characterizing myocardial structures in the mouse and beyond.

Assessment of the Characteristics of Orientation Distribution Functions in HARDI Using Morphological Metrics

Orientation distribution functions (ODFs) are widely used to resolve fiber crossing problems in high angular resolution diffusion imaging (HARDI). The characteristics of the ODFs are often assessed using a visual criterion, although the use of objective criteria is also reported, which are directly borrowed from classic signal and image processing theory because they are intuitive and simple to compute. However, they are not always pertinent for the characterization of ODFs. We propose a more general paradigm for assessing the characteristics of ODFs. The idea consists in regarding an ODF as a three-dimensional (3D) point cloud, projecting the 3D point cloud onto an angle-distance map, constructing an angle-distance matrix, and calculating metrics such as length ratio, separability, and uncertainty. The results from both simulated and real data show that the proposed metrics allow for the assessment of the characteristics of ODFs in a quantitative and relatively complete manner.

Accelerated exponential parameterization of T2 relaxation with model-driven low rank and sparsity priors (MORASA)

PURPOSE

This work is to develop a novel image reconstruction method from highly undersampled multichannel acquisition to reduce the scan time of exponential parameterization of T2 relaxation.

THEORY AND METHODS

On top of the low-rank and joint-sparsity constraints, we propose to exploit the linear predictability of the T2 exponential decay to further improve the reconstruction of the T2-weighted images from undersampled acquisitions. Specifically, the exact rank prior (i.e., number of non-zero singular values) is adopted to enforce the spatiotemporal low rankness, while the mixed L2-L1 norm of the wavelet coefficients is used to promote joint sparsity, and the Hankel low-rank approximation is used to impose linear predictability, which integrates the exponential behavior of the temporal signal into the reconstruction process. An efficient algorithm is adopted to solve the reconstruction problem, where corresponding nonlinear filtering operations are performed to enforce corresponding priors in an iterative manner.

RESULTS

Both simulated and in vivo datasets with multichannel acquisition were used to demonstrate the feasibility of the proposed method. Experimental results have shown that the newly introduced linear predictability prior improves the reconstruction quality of the T2-weighted images and benefits the subsequent T2 mapping by achieving high-speed, high-quality T2 mapping compared with the existing fast T2 mapping methods.

CONCLUSION

This work proposes a novel fast T2 mapping method integrating the linear predictable property of the exponential decay into the reconstruction process. The proposed technique can effectively improve the reconstruction quality of the state-of-the-art fast imaging method exploiting image sparsity and spatiotemporal low rankness. Magn Reson Med 76:1865-1878, 2016. © 2016 International Society for Magnetic Resonance in Medicine.

Quantitative representation and description of intravoxel fiber complexity in HARDI

Diffusion tensor imaging and high angular resolution diffusion imaging are often used to analyze the fiber complexity of tissues. In these imaging techniques, the most commonly calculated metric is anisotropy, such as fractional anisotropy (FA), generalized anisotropy (GA), and generalized fractional anisotropy (GFA). The basic idea underlying these metrics is to compute the deviation from free or spherical diffusion. However, in many cases, the question is not really to know whether it concerns spherical diffusion. Instead, the main concern is to describe and quantify fiber complexity such as fiber crossing in a voxel. In this context, it would be more direct and effective to compute the deviation from a single fiber bundle instead of a sphere. We propose a new metric, called PEAM (PEAnut Metric), which is based on computing the deviation of orientation diffusion functions (ODFs) from a single fiber bundle ODF represented by a peanut. As an example, the proposed PEAM metric is used to classify intravoxel fiber configurations. The results on simulated data, physical phantom data and real brain data consistently showed that the proposed PEAM provides greater accuracy than FA, GA and GFA and enables parallel and complex fibers to be better distinguished.

Higher-Order Motion-Compensation for In Vivo Cardiac Diffusion Tensor Imaging in Rats

Motion of the heart has complicated in vivo applications of cardiac diffusion MRI and diffusion tensor imaging (DTI), especially in small animals such as rats where ultra-high-performance gradient sets are currently not available. Even with velocity compensation via, for example, bipolar encoding pulses, the variable shot-to-shot residual motion-induced spin phase can still give rise to pronounced artifacts. This study presents diffusion-encoding schemes that are designed to compensate for higher-order motion components, including acceleration and jerk, which also have the desirable practical features of minimal TEs and high achievable b-values. The effectiveness of these schemes was verified numerically on a realistic beating heart phantom, and demonstrated empirically with in vivo cardiac diffusion MRI in rats. Compensation for acceleration, and lower motion components, was found to be both necessary and sufficient for obtaining diffusion-weighted images of acceptable quality and SNR, which yielded the first in vivo cardiac DTI demonstrated in the rat. These findings suggest that compensation for higher order motion, particularly acceleration, can be an effective alternative solution to high-performance gradient hardware for improving in vivo cardiac DTI.

Prospective acceleration of diffusion tensor imaging with compressed sensing using adaptive dictionaries

PURPOSE

Diffusion MRI requires acquisition of multiple diffusion-weighted images, resulting in long scan times. Here, we investigate combining compressed sensing and a fast imaging sequence to dramatically reduce acquisition times in cardiac diffusion MRI.

METHODS

Fully sampled and prospectively undersampled diffusion tensor imaging data were acquired in five rat hearts at acceleration factors of between two and six using a fast spin echo (FSE) sequence. Images were reconstructed using a compressed sensing framework, enforcing sparsity by means of decomposition by adaptive dictionaries. A tensor was fit to the reconstructed images and fiber tractography was performed.

RESULTS

Acceleration factors of up to six were achieved, with a modest increase in root mean square error of mean apparent diffusion coefficient (ADC), fractional anisotropy (FA), and helix angle. At an acceleration factor of six, mean values of ADC and FA were within 2.5% and 5% of the ground truth, respectively. Marginal differences were observed in the fiber tracts.

CONCLUSION

We developed a new k-space sampling strategy for acquiring prospectively undersampled diffusion-weighted data, and validated a novel compressed sensing reconstruction algorithm based on adaptive dictionaries. The k-space undersampling and FSE acquisition each reduced acquisition times by up to 6× and 8×, respectively, as compared to fully sampled spin echo imaging. Magn Reson Med 76:248-258, 2016. © 2015 Wiley Periodicals, Inc.

A model-based reconstruction for undersampled radial spin-echo DTI with variational penalties on the diffusion tensor

Radial spin-echo diffusion imaging allows motion-robust imaging of tissues with very low T2 values like articular cartilage with high spatial resolution and signal-to-noise ratio (SNR). However, in vivo measurements are challenging, due to the significantly slower data acquisition speed of spin-echo sequences and the less efficient k-space coverage of radial sampling, which raises the demand for accelerated protocols by means of undersampling. This work introduces a new reconstruction approach for undersampled diffusion-tensor imaging (DTI). A model-based reconstruction implicitly exploits redundancies in the diffusion-weighted images by reducing the number of unknowns in the optimization problem and compressed sensing is performed directly in the target quantitative domain by imposing a total variation (TV) constraint on the elements of the diffusion tensor. Experiments were performed for an anisotropic phantom and the knee and brain of healthy volunteers (three and two volunteers, respectively). Evaluation of the new approach was conducted by comparing the results with reconstructions performed with gridding, combined parallel imaging and compressed sensing and a recently proposed model-based approach. The experiments demonstrated improvements in terms of reduction of noise and streaking artifacts in the quantitative parameter maps, as well as a reduction of angular dispersion of the primary eigenvector when using the proposed method, without introducing systematic errors into the maps. This may enable an essential reduction of the acquisition time in radial spin-echo diffusion-tensor imaging without degrading parameter quantification and/or SNR.

Probing dynamic myocardial microstructure with cardiac magnetic resonance diffusion tensor imaging

This article is an invited editorial comment on the paper entitled "In vivo cardiovascular magnetic resonance diffusion tensor imaging shows evidence of abnormal myocardial laminar orientations and mobility in hypertrophic cardiomyopathy" by Ferreira et al., and published as Journal of Cardiovascular Magnetic Resonance 2014; 16:87.

Parallel imaging and compressed sensing combined framework for accelerating high-resolution diffusion tensor imaging using inter-image correlation

PURPOSE

Increasing acquisition efficiency is always a challenge in high-resolution diffusion tensor imaging (DTI), which has low signal-to-noise ratio and is sensitive to reconstruction artifacts. In this study, a parallel imaging (PI) and compressed sensing (CS) combined framework is proposed, which features motion error correction, PI calibration, and sparsity model using inter-image correlation tailored for high-resolution DTI.

THEORY AND METHODS

The proposed method, named anisotropic sparsity SPIRiT, consists of three steps: (i) motion-induced phase error estimation, (ii) initial CS reconstruction and PI kernel calibration, and (iii) final reconstruction combining PI and CS. Inter-image correlation of diffusion-weighted images are used through anisotropic signals for improved sparsity. A specific implementation based on multishot variable density spiral DTI is used to demonstrate the method.

RESULTS

The proposed reconstruction method was compared with CG-SENSE, CS-based joint reconstruction, and PI and CS combined methods with L1 and joint sparsity regularization, in brain DTI experiments at acceleration factors of 3 to 5. Both qualitative and quantitative results demonstrated that the proposed method resulted in better preserved image quality and more accurate DTI parameters than other methods.

CONCLUSION

The proposed method can accelerate high-resolution DTI acquisition effectively by using the sharable information among different diffusion encoding directions.

PCLR: phase-constrained low-rank model for compressive diffusion-weighted MRI

PURPOSE

This work develops a compressive sensing approach for diffusion-weighted (DW) MRI.

THEORY AND METHODS

A phase-constrained low-rank (PCLR) approach was developed using the image coherence across the DW directions for efficient compressive DW MRI, while accounting for drastic phase changes across the DW directions, possibly as a result of eddy current, and rigid and nonrigid motions. In PCLR, a low-resolution phase estimation was used for removing phase inconsistency between DW directions. In our implementation, GRAPPA (generalized autocalibrating partial parallel acquisition) was incorporated for better phase estimation while allowing higher undersampling factor. An efficient and easy-to-implement image reconstruction algorithm, consisting mainly of partial Fourier update and singular value decomposition, was developed for solving PCLR.

RESULTS

The error measures based on diffusion-tensor-derived metrics and tractography indicated that PCLR, with its joint reconstruction of all DW images using the image coherence, outperformed the frame-independent reconstruction through zero-padding FFT. Furthermore, using GRAPPA for phase estimation, PCLR readily achieved a four-fold undersampling.

CONCLUSION

The PCLR is developed and demonstrated for compressive DW MRI. A four-fold reduction in k-space sampling could be readily achieved without substantial degradation of reconstructed images and diffusion tensor measures, making it possible to significantly reduce the data acquisition in DW MRI and/or improve spatial and angular resolutions.