Iterative off-resonance and signal decay estimation and correction for multi-echo MRI

Harnessing myelin water fraction as an imaging biomarker of human cerebral aging, neurodegenerative diseases, and risk factors influencing myelination: A review

Myelin water fraction (MWF) imaging has emerged as a promising magnetic resonance imaging (MRI) biomarker for investigating brain function and composition. This comprehensive review synthesizes the current state of knowledge on MWF as a biomarker of human cerebral aging, neurodegenerative diseases, and risk factors influencing myelination. The databases used include Web of Science, Scopus, Science Direct, and PubMed. We begin with a brief discussion of the theoretical foundations of MWF imaging, including its basis in MR physics and the mathematical modeling underlying its calculation, with an overview of the most adopted MRI methods of MWF imaging. Next, we delve into the clinical and research applications that have been explored to date, highlighting its advantages and limitations. Finally, we explore the potential of MWF to serve as a predictive biomarker for neurological disorders and identify future research directions for optimizing MWF imaging protocols and interpreting MWF in various contexts. By harnessing the power of MWF imaging, we may gain new insights into brain health and disease across the human lifespan, ultimately informing novel diagnostic and therapeutic strategies.

MRIReco.jl: An MRI reconstruction framework written in Julia

PURPOSE

The aim of this work is to develop a high-performance, flexible, and easy-to-use MRI reconstruction framework using the scientific programming language Julia.

METHODS

Julia is a modern, general purpose programming language with strong features in the area of signal/image processing and numerical computing. It has a high-level syntax but still generates efficient machine code that is usually as fast as comparable C/C++ applications. In addition to the language features itself, Julia has a sophisticated package management system that makes proper modularization of functionality across different packages feasible. Our developed MRI reconstruction framework MRIReco.jl can therefore reuse existing functionality from other Julia packages and concentrate on the MRI-related parts. This includes common imaging operators and support for MRI raw data formats.

RESULTS

MRIReco.jl is a simple to use framework with a high degree of accessibility. While providing a simple-to-use interface, many of its components can easily be extended and customized. The performance of MRIReco.jl is compared to the Berkeley Advanced Reconstruction Toolbox (BART) and we show that the Julia framework achieves comparable reconstruction speed as the popular C/C++ library.

CONCLUSIONS

Modern programming languages can bridge the gap between high performance and accessible implementations. MRIReco.jl leverages this fact and contributes a promising environment for future algorithmic development in MRI reconstruction.

Intravoxel B0 inhomogeneity corrected reconstruction using a low-rank encoding operator

PURPOSE

To present a general and efficient method for macroscopic intravoxel B 0 inhomogeneity corrected reconstruction from multi-TE acquisitions.

THEORY AND METHODS

A signal encoding model for multi-TE gradient echo (GRE) acquisitions that incorporates 3D intravoxel B 0 field variations is derived, and a low-rank approximation to the encoding operator is introduced under piecewise linear B 0 assumption. The low-rank approximation enables very efficient computation and memory usage, and allows the proposed signal model to be integrated into general inverse problem formulations that are compatible with multi-coil and undersampling acquisitions as well as different regularization functions.

RESULTS

Experimental multi-echo GRE data were acquired to evaluate the proposed method. Effective reduction of macroscopic intravoxel B 0 inhomogeneity induced artifacts was demonstrated. Improved R 2 ∗ estimation from the corrected reconstruction over standard Fourier reconstruction has also been obtained.

CONCLUSIONS

The proposed method can effectively correct the effects of intravoxel B 0 inhomogeneity, and can be useful for various imaging applications involving GRE-based acquisitions, including fMRI, quantitative R 2 ∗ and susceptibility mapping, and MR spectroscopic imaging.

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.

Calibration-Free B0 Correction of EPI Data Using Structured Low Rank Matrix Recovery

We introduce a structured low rank algorithm for the calibration-free compensation of field inhomogeneity artifacts in echo planar imaging (EPI) MRI data. We acquire the data using two EPI readouts that differ in echo-time. Using time segmentation, we reformulate the field inhomogeneity compensation problem as the recovery of an image time series from highly undersampled Fourier measurements. The temporal profile at each pixel is modeled as a single exponential, which is exploited to fill in the missing entries. We show that the exponential behavior at each pixel, along with the spatial smoothness of the exponential parameters, can be exploited to derive a 3-D annihilation relation in the Fourier domain. This relation translates to a low rank property on a structured multi-fold Toeplitz matrix, whose entries correspond to the measured k-space samples. We introduce a fast two-step algorithm for the completion of the Toeplitz matrix from the available samples. In the first step, we estimate the null space vectors of the Toeplitz matrix using only its fully sampled rows. The null space is then used to estimate the signal subspace, which facilitates the efficient recovery of the time series of images. We finally demonstrate the proposed approach on spherical MR phantom data and human data and show that the artifacts are significantly reduced.

Use of the NESMA Filter to Improve Myelin Water Fraction Mapping with Brain MRI

BACKGROUND AND PURPOSE

Myelin water fraction (MWF) mapping permits direct visualization of myelination patterns in the developing brain and in pathology. MWF is conventionally measured through multiexponential T₂ analysis which is very sensitive to noise, leading to inaccuracies in derived MWF estimates. Although noise reduction filters may be applied during postprocessing, conventional filtering can introduce bias and obscure small structures and edges. Advanced nonblurring filters, while effective, exhibit a high level of complexity and the requirement for supervised implementation for optimal performance. The purpose of this paper is to demonstrate the ability of the recently introduced nonlocal estimation of multispectral magnitudes (NESMA) filter to greatly improve the determination of MWF parameter estimates from gradient and spin echo (GRASE) imaging data.

METHODS

We evaluated the performance of the NESMA filter for MWF mapping from clinical GRASE imaging data of the human brain, and compared the results to those calculated from unfiltered images. Numerical and in vivo analyses of the brains of three subjects, representing different ages, were conducted.

RESULTS

Our results demonstrated the potential of the NESMA filter to permit high-quality in vivo MWF mapping. Indeed, NESMA permits substantial reduction of random variation in derived MWF estimates while preserving accuracy and detail.

CONCLUSIONS

In vivo estimation of MWF in the human brain from GRASE imaging data was markedly improved through use of the NESMA filter. The use of NESMA may contribute to the goal of high-quality MWF mapping in clinically feasible imaging times.

An Efficient Reconstruction Algorithm Based on the Alternating Direction Method of Multipliers for Joint Estimation of ${R}_{{2}}^{*}$ and Off-Resonance in fMRI

R*₂ mapping is a useful tool in blood-oxygen-level dependent fMRI due to its quantitative-nature. However, like T*₂-weighted imaging, standard R*₂ mapping based on multi-echo EPI suffers from geometric distortion, due to strong off-resonance near the air-tissue interface. Joint mapping of R*₂ and off-resonance can correct the geometric distortion and is less susceptible to motion artifacts. Single-shot joint mapping of R*₂ and off-resonance is possible with a rosette trajectory due to its frequent sampling of the k-space center. However, the corresponding reconstruction is nonlinear, ill-conditioned, large-scale, and computationally inefficient with current algorithms. In this paper, we propose a novel algorithm for joint mapping of R*₂ and off-resonance, using rosette k-space trajectories. The new algorithm, based on the alternating direction method of multipliers, improves the reconstruction efficiency by simplifying the original complicated cost function into a composition of simpler optimization steps. Compared with a recently developed trust region algorithm, the new algorithm achieves the same accuracy and an acceleration of threefold to sixfold in reconstruction time. Based on the new algorithm, we present simulation and in vivo data from single-shot, double-shot, and quadruple-shot rosettes and demonstrate the improved image quality and reduction of distortions in the reconstructed R*₂ map.

Rapid simultaneous high-resolution mapping of myelin water fraction and relaxation times in human brain using BMC-mcDESPOT

A number of central nervous system (CNS) diseases exhibit changes in myelin content and magnetic resonance longitudinal, T₁, and transverse, T₂, relaxation times, which therefore represent important biomarkers of CNS pathology. Among the methods applied for measurement of myelin water fraction (MWF) and relaxation times, the multicomponent driven equilibrium single pulse observation of T₁ and T₂ (mcDESPOT) approach is of particular interest. mcDESPOT permits whole brain mapping of multicomponent T₁ and T₂, with data acquisition accomplished within a clinically realistic acquisition time. Unfortunately, previous studies have indicated the limited performance of mcDESPOT in the setting of the modest signal-to-noise range of high-resolution mapping, required for the depiction of small structures and to reduce partial volume effects. Recently, we showed that a new Bayesian Monte Carlo (BMC) analysis substantially improved determination of MWF from mcDESPOT imaging data. However, our previous study was limited in that it did not discuss determination of relaxation times. Here, we extend the BMC analysis to the simultaneous determination of whole-brain MWF and relaxation times using the two-component mcDESPOT signal model. Simulation analyses and in-vivo human brain studies indicate the overall greater performance of this approach compared to the stochastic region contraction (SRC) algorithm, conventionally used to derive parameter estimates from mcDESPOT data. SRC estimates of the transverse relaxation time of the long T₂ fraction, T_2,l, and the longitudinal relaxation time of the short T₁ fraction, T_1,s, clustered towards the lower and upper parameter search space limits, respectively, indicating failure of the fitting procedure. We demonstrate that this effect is absent in the BMC analysis. Our results also showed improved parameter estimation for BMC as compared to SRC for high-resolution mapping. Overall we find that the combination of BMC analysis and mcDESPOT, BMC-mcDESPOT, shows excellent performance for accurate high-resolution whole-brain mapping of MWF and bi-component transverse and longitudinal relaxation times within a clinically realistic acquisition time.

Model-based reconstruction for real-time phase-contrast flow MRI: Improved spatiotemporal accuracy

PURPOSE

To develop a model-based reconstruction technique for real-time phase-contrast flow MRI with improved spatiotemporal accuracy in comparison to methods using phase differences of two separately reconstructed images with differential flow encodings.

METHODS

The proposed method jointly computes a common image, a phase-contrast map, and a set of coil sensitivities from every pair of flow-compensated and flow-encoded datasets obtained by highly undersampled radial FLASH. Real-time acquisitions with five and seven radial spokes per image resulted in 25.6 and 35.7 ms measuring time per phase-contrast map, respectively. The signal model for phase-contrast flow MRI requires the solution of a nonlinear inverse problem, which is accomplished by an iteratively regularized Gauss-Newton method. Aspects of regularization and scaling are discussed. The model-based reconstruction was validated for a numerical and experimental flow phantom and applied to real-time phase-contrast MRI of the human aorta for 10 healthy subjects and 2 patients.

RESULTS

Under all conditions, and compared with a previously developed real-time flow MRI method, the proposed method yields quantitatively accurate phase-contrast maps (i.e., flow velocities) with improved spatial acuity, reduced phase noise and reduced streaking artifacts.

CONCLUSION

This novel model-based reconstruction technique may become a new tool for clinical flow MRI in real time. Magn Reson Med 77:1082-1093, 2017. © 2016 International Society for Magnetic Resonance in Medicine.

Trust Region Methods for the Estimation of a Complex Exponential Decay Model in MRI With a Single-Shot or Multi-Shot Trajectory

Joint estimation of spin density R2* decay and OFF-resonance frequency maps is very useful in many magnetic resonance imaging applications. The standard multi-echo approach can achieve high accuracy but requires a long acquisition time for sampling multiple k-space frames. There are many approaches to accelerate the acquisition. Among them, single-shot or multi-shot trajectory-based sampling has recently drawn attention due to its fast data acquisition. However, this sampling strategy destroys the Fourier relationship between k-space and images, leading to a great challenge for the reconstruction. In this paper, we present two trust region methods based on two different linearization strategies for the nonlinear signal model. A trust region is defined as a local area in the variable space where a local linear approximation is trustable. In each iteration, the method minimizes a local approximation within a trust region so that the step size can be kept in a suitable scale. A continuation scheme is applied to reduce the regularization gradually over the parameter maps and facilitates convergence from poor initializations. The two trust region methods are compared with the two other previously proposed methods--the nonlinear conjugate gradients and the gradual refinement algorithm. Experiments based on various synthetic data and real phantom data show that the two trust region methods have a clear advantage in both speed and stability.

Analysis of mcDESPOT- and CPMG-derived parameter estimates for two-component nonexchanging systems

PURPOSE

To compare the reliability and stability of the multicomponent-driven equilibrium single pulse observation of T1 and T2 (mcDESPOT) and Carl-Purcell-Meiboom-Gill (CPMG) approaches to parameter estimation.

METHODS

The stability and reliability of mcDESPOT and CPMG-derived parameter estimates were compared through examination of energy surfaces, evaluation of model sloppiness, and Monte Carlo simulations. Comparisons were performed on an equal time basis and assuming a two-component system. Parameter estimation bias, reflecting accuracy, and dispersion, reflecting precision, were derived for a range of signal-to-noise ratios (SNRs) and relaxation parameters.

RESULTS

The energy surfaces for parameters incorporated into the mcDESPOT signal model exhibit flatness, a complex structure of local minima, and instability to noise to a much greater extent than the corresponding surfaces for CPMG. Although both mcDESPOT and CPMG performed well at high SNR, the CPMG approach yielded parameter estimates of considerably greater accuracy and precision at lower SNR.

CONCLUSION

mcDESPOT and CPMG both permit high-quality parameter estimates under SNR that are clinically achievable under many circumstances, depending upon available hardware and resolution and acquisition time constraints. At moderate to high SNR, the mcDESPOT approach incorporating two-step phase increments can yield accurate parameter estimates while providing values for longitudinal relaxation times that are not available through CPMG. However, at low SNR, the CPMG approach is more stable and provides superior parameter estimates. Magn Reson Med 75:2406-2420, 2016. © 2015 Wiley Periodicals, Inc.

R(∗)2 mapping for robust brain function detection in the presence of magnetic field inhomogeneity

T(*)2 mapping or R(*)2 mapping for brain function offers advantages such as providing quantitative measurements independent of the MRI acquisition parameters (e.g. echo time TE). However, magnetic field susceptibility in the human brain can prevent an accurate estimation of R(*)2, which in turn impacts the ability to study brain function. The present work investigates the effects of in-plane magnetic susceptibility-induced magnetic field gradients on R(*)2 decay. An iterative method is developed for R(*)2 estimation with an increased robustness to field inhomogeneity. The new method is further tested in a visual fMRI experiment with and without magnetic field gradients and its performance is compared to a standard BOLD fMRI and a BOLD fMRI based on echo summation. Reduced sensitivity in fMRI to in-plane magnetic gradients is obtained with the present methodology.

Parameter estimation approach to banding artifact reduction in balanced steady-state free precession

PURPOSE

The balanced steady-state free precession (bSSFP) pulse sequence has shown to be of great interest due to its high signal-to-noise ratio efficiency. However, bSSFP images often suffer from banding artifacts due to off-resonance effects, which we aim to minimize in this article.

METHODS

We present a general and fast two-step algorithm for 1) estimating the unknowns in the bSSFP signal model from multiple phase-cycled acquisitions, and 2) reconstructing band-free images. The first step, linearization for off-resonance estimation (LORE), solves the nonlinear problem approximately by a robust linear approach. The second step applies a Gauss-Newton algorithm, initialized by LORE, to minimize the nonlinear least squares criterion. We name the full algorithm LORE-GN.

RESULTS

We derive the Cramér-Rao bound, a theoretical lower bound of the variance for any unbiased estimator, and show that LORE-GN is statistically efficient. Furthermore, we show that simultaneous estimation of T1 and T2 from phase-cycled bSSFP is difficult, since the Cramér-Rao bound is high at common signal-to-noise ratio. Using simulated, phantom, and in vivo data, we illustrate the band-reduction capabilities of LORE-GN compared to other techniques, such as sum-of-squares.

CONCLUSION

Using LORE-GN we can successfully minimize banding artifacts in bSSFP.