Fast joint reconstruction of dynamic R2* and field maps in functional MRI

Manifold Regularizer for High-Resolution fMRI Joint Reconstruction and Dynamic Quantification

Oscillating Steady-State Imaging (OSSI) is a recently developed fMRI acquisition method that can provide 2 to 3 times higher SNR than standard fMRI approaches. However, because the OSSI signal exhibits a nonlinear oscillation pattern, one must acquire and combine nc (e.g., 10) OSSI images to get an image that is free of oscillation for fMRI, and fully sampled acquisitions would compromise temporal resolution. To improve temporal resolution and accurately model the nonlinearity of OSSI signals, instead of using subspace models that are not well suited for the data, we build the MR physics for OSSI signal generation as a regularizer for the undersampled reconstruction. Our proposed physics-based manifold model turns the disadvantages of OSSI acquisition into advantages and enables joint reconstruction and quantification. OSSI manifold model (OSSIMM) outperforms subspace models and reconstructs high-resolution fMRI images with a factor of 12 acceleration and without spatial or temporal smoothing. Furthermore, OSSIMM can dynamically quantify important physics parameters, including R2∗ maps, with a temporal resolution of 150 ms.

Off-resonance artifact correction for MRI: A review

In magnetic resonance imaging (MRI), inhomogeneity in the main magnetic field used for imaging, referred to as off-resonance, can lead to image artifacts ranging from mild to severe depending on the application. Off-resonance artifacts, such as signal loss, geometric distortions, and blurring, can compromise the clinical and scientific utility of MR images. In this review, we describe sources of off-resonance in MRI, how off-resonance affects images, and strategies to prevent and correct for off-resonance. Given recent advances and the great potential of low-field and/or portable MRI, we also highlight the advantages and challenges of imaging at low field with respect to off-resonance.

Free-Breathing Liver Fat, R₂* and B₀ Field Mapping Using Multi-Echo Radial FLASH and Regularized Model-Based Reconstruction

This work introduced a stack-of-radial multi-echo asymmetric-echo MRI sequence for free-breathing liver volumetric acquisition. Regularized model-based reconstruction was implemented in Berkeley Advanced Reconstruction Toolbox (BART) to jointly estimate all physical parameter maps (water, fat, R2∗ , and B0 field inhomogeneity maps) and coil sensitivity maps from self-gated k -space data. Specifically, locally low rank and temporal total variation regularization were employed directly on physical parameter maps. The proposed free-breathing radial technique was tested on a water/fat & iron phantom, a young volunteer, and obesity/diabetes/hepatic steatosis patients. Quantitative fat fraction and R2∗ accuracy were confirmed by comparing our technique with the reference breath-hold Cartesian scan. The multi-echo radial sampling sequence achieves fast k -space coverage and is robust to motion. Moreover, the proposed motion-resolved model-based reconstruction allows for free-breathing liver fat and R2∗ quantification in multiple motion states. Overall, our proposed technique offers a convenient tool for non-invasive liver assessment with no breath holding requirement.

Quantitative MRI by nonlinear inversion of the Bloch equations

PURPOSE

Development of a generic model-based reconstruction framework for multiparametric quantitative MRI that can be used with data from different pulse sequences.

METHODS

Generic nonlinear model-based reconstruction for quantitative MRI estimates parametric maps directly from the acquired k-space by numerical optimization. This requires numerically accurate and efficient methods to solve the Bloch equations and their partial derivatives. In this work, we combine direct sensitivity analysis and pre-computed state-transition matrices into a generic framework for calibrationless model-based reconstruction that can be applied to different pulse sequences. As a proof-of-concept, the method is implemented and validated for quantitative T 1 $$ {\mathrm{T}}_1 $$ and T 2 $$ {\mathrm{T}}_2 $$ mapping with single-shot inversion-recovery (IR) FLASH and IR bSSFP sequences in simulations, phantoms, and the human brain.

RESULTS

The direct sensitivity analysis enables a highly accurate and numerically stable calculation of the derivatives. The state-transition matrices efficiently exploit repeating patterns in pulse sequences, speeding up the calculation by a factor of 10 for the examples considered in this work, while preserving the accuracy of native ordinary differential equations solvers. The generic model-based method reproduces quantitative results of previous model-based reconstructions based on the known analytical solutions for radial IR FLASH. For IR bSFFP it produces accurate T 1 $$ {\mathrm{T}}_1 $$ and T 2 $$ {\mathrm{T}}_2 $$ maps for the National Insitute of Standards and Technology (NIST) phantom in numerical simulations and experiments. Feasibility is also shown for human brain, although results are affected by magnetization transfer effects.

CONCLUSION

By developing efficient tools for numerical optimizations using the Bloch equations as forward model, this work enables generic model-based reconstruction for quantitative MRI.

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'.

Local perturbation responses and checkerboard tests: Characterization tools for nonlinear MRI methods

PURPOSE

Modern methods for MR image reconstruction, denoising, and parameter mapping are becoming increasingly nonlinear, black-box, and at risk of "hallucination." These trends mean that traditional tools for judging confidence in an image (visual quality assessment, point-spread functions (PSFs), g-factor maps, etc.) are less helpful than before. This paper describes and evaluates an approach that can help with assessing confidence in images produced by arbitrary nonlinear methods.

THEORY AND METHODS

We propose to characterize nonlinear methods by examining the images they produce before and after applying controlled perturbations to the measured data. This results in functions known as local perturbation responses (LPRs) that can provide useful insight into sensitivity, spatial resolution, and aliasing characteristics. LPRs can be viewed as generalizations of classical PSFs, and are are very flexible-they can be applied to arbitary nonlinear methods and arbitrary datasets across a range of different reconstruction, denoising, and parameter mapping applications. Importantly, LPRs do not require a ground truth image.

RESULTS

Impulse-based and checkerboard-pattern LPRs are demonstrated in image reconstruction and denoising scenarios. We observe that these LPRs provide insights into spatial resolution, signal leakage, and aliasing that are not available with other methods. We also observe that popular reference-based image quality metrics (eg, mean-squared error and structural similarity) do not always correlate with good LPR characteristics.

CONCLUSIONS

LPRs are a useful tool that can be used to characterize and assess confidence in nonlinear MR methods, and provide insights that are distinct from and complementary to existing quality assessments.

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.

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.

Joint B0 and image estimation integrated with model based reconstruction for field map update and distortion correction in prostate diffusion MRI

In prostate Diffusion Weighted MRI, differences in susceptibility values exist at the interface between the prostate and rectal-air. This can result in off-resonance magnetic field leading to geometric distortions including signal stretching and signal pile-up in the reconstructed images. Using a set of EPI data acquired with blip-up and blip-down phase encoding gradient directions, model based reconstruction has recently been proposed that can correct these distortions by using a B0 field estimated from a separate B0 scan. However, change in the size of the rectal air region across time can occur that can result in a mismatch of the B0 field to the EPI scan. Also, the measured B0 field itself can be erroneous in regions of low Signal to Noise ratio around the prostate rectal air interface. In this work, using a set of single shot EPI data acquired with blip-up and blip-down phase encoding gradient directions, a novel joint model based reconstruction is proposed that can account for changes in the off resonance effects between the B0 and EPI scans. For ten prostate patients, using a measured B0 field as an initial B0 estimate, on a 5-point scale (1-5) image quality scores evaluated by an experienced radiologist, the proposed framework achieved scores of 3.50 ± 0.85 and 3.40 ± 0.51 for b-values of 0 and 500 s/mm2, respectively compared to 3.40 ± 0.70 and 3.30 ± 0.67 for model based reconstruction. The proposed framework is also capable of estimating a distortion corrected EPI image even without an initial B0 field estimate in situations where a separate B0 scan cannot be obtained due to time constraint.

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.

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.

SNR-weighted regularization of ADC estimates from double-echo in steady-state (DESS)

PURPOSE

To improve the homogeneity and consistency of apparent diffusion coefficient (ADC) estimates in cartilage from the double-echo in steady-state (DESS) sequence by applying SNR-weighted regularization during post-processing.

METHODS

An estimation method that linearizes ADC estimates from DESS is used in conjunction with a smoothness constraint to suppress noise-induced variation in ADC estimates. Simulations, phantom scans, and in vivo scans are used to demonstrate how the method reduces ADC variability. Conventional diffusion-weighted echo-planar imaging (DW EPI) maps are acquired for comparison of mean and standard deviation (SD) of the ADC estimate.

RESULTS

Simulations and phantom scans demonstrated that the SNR-weighted regularization can produce homogenous ADC maps at varying levels of SNR, whereas non-regularized maps only estimate ADC accurately at high SNR levels. The in vivo maps showed that the SNR-weighted regularization produced ADC maps with similar heterogeneity to maps produced with standard DW EPI, but without the distortion of such reference scans.

CONCLUSION

A linear approximation of a simplified model of the relationship between DESS signals allows for fast SNR-weighted regularization of ADC maps that reduces estimation error in relatively short T₂ tissue such as cartilage.

Design of spectral-spatial phase prewinding pulses and their use in small-tip fast recovery steady-state imaging

PURPOSE

Spectrally selective "prewinding" radiofrequency pulses can counteract B0 inhomogeneity in steady-state sequences, but can only prephase a limited range of off-resonance. We propose spectral-spatial small-tip angle prewinding pulses that increase the off-resonance bandwidth that can be successfully prephased by incorporating spatially tailored excitation patterns.

THEORY AND METHODS

We present a feasibility study to compare spectral and spectral-spatial prewinding pulses. These pulses add a prephasing term to the target magnetization pattern that aims to recover an assigned off-resonance bandwidth at the echo time. For spectral-spatial pulses, the design bandwidth is centered at the off-resonance frequency for each spatial location in a field map. We use these pulses in the small-tip fast recovery steady-state sequence, which is similar to balanced steady-state free precession. We investigate improvement of spectral-spatial pulses over spectral pulses using simulations and small-tip fast recovery scans of a gel phantom and human brain.

RESULTS

In simulation, spectral-spatial pulses yielded lower normalized root mean squared excitation error than spectral pulses. For both experiments, the spectral-spatial pulse images are also qualitatively better (more uniform, less signal loss) than the spectral pulse images.

CONCLUSION

Spectral-spatial prewinding pulses can prephase over a larger range of off-resonance than their purely spectral counterparts. Magn Reson Med 79:1377-1386, 2018. © 2017 International Society for Magnetic Resonance in Medicine.

Fast Spatial Resolution Analysis of Quadratic Penalized Least-Squares Image Reconstruction With Separate Real and Imaginary Roughness Penalty: Application to fMRI

Penalized least-squares iterative image reconstruction algorithms used for spatial resolution-limited imaging, such as functional magnetic resonance imaging (fMRI), commonly use a quadratic roughness penalty to regularize the reconstructed images. When used for complex-valued images, the conventional roughness penalty regularizes the real and imaginary parts equally. However, these imaging methods sometimes benefit from separate penalties for each part. The spatial smoothness from the roughness penalty on the reconstructed image is dictated by the regularization parameter(s). One method to set the parameter to a desired smoothness level is to evaluate the full width at half maximum of the reconstruction method's local impulse response. Previous work has shown that when using the conventional quadratic roughness penalty, one can approximate the local impulse response using an FFT-based calculation. However, that acceleration method cannot be applied directly for separate real and imaginary regularization. This paper proposes a fast and stable calculation for this case that also uses FFT-based calculations to approximate the local impulse responses of the real and imaginary parts. This approach is demonstrated with a quadratic image reconstruction of fMRI data that uses separate roughness penalties for the real and imaginary parts.

Model-based T1 mapping with sparsity constraints using single-shot inversion-recovery radial FLASH

PURPOSE

To develop a model-based reconstruction technique for single-shot T₁ mapping with high spatial resolution, accuracy, and precision using an inversion-recovery (IR) fast low-angle shot (FLASH) acquisition with radial encoding.

METHODS

The proposed model-based reconstruction jointly estimates all model parameters, that is, the equilibrium magnetization, steady-state magnetization, 1/ T1*, and all coil sensitivities from the data of a single-shot IR FLASH acquisition with a small golden-angle radial trajectory. Joint sparsity constraints on the parameter maps are exploited to improve the performance of the iteratively regularized Gauss-Newton method chosen for solving the nonlinear inverse problem. Validations include both a numerical and experimental T₁ phantom, as well as in vivo studies of the human brain and liver at 3 T.

RESULTS

In comparison to previous reconstruction methods for single-shot T₁ mapping, which are based on real-time MRI with pixel-wise fitting and a model-based approach with a predetermination of coil sensitivities, the proposed method presents with improved robustness against phase errors and numerical precision in both phantom and in vivo studies.

CONCLUSION

The comprehensive model-based reconstruction with L1 regularization offers rapid and robust T₁ mapping with high accuracy and precision. The method warrants accelerated computing and online implementation for extended clinical trials. Magn Reson Med 79:730-740, 2018. © 2017 International Society for Magnetic Resonance in Medicine.

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.

The effects of concomitant gradients on chemical shift encoded MRI

PURPOSE

The purpose of this work was to characterize the effects of concomitant gradients (CGs) on chemical shift encoded (CSE)-based estimation of B₀ field map, proton density fat fraction (PDFF), and R2*.

THEORY

A theoretical framework was used to determine the effects of CG-induced phase errors on CSE-MRI data.

METHODS

Simulations, phantom experiments, and in vivo experiments were conducted at 3 Tesla to assess the effects of CGs on quantitative CSE-MRI techniques. Correction of phase errors attributable to CGs was also investigated to determine whether these effects could be removed.

RESULTS

Phase errors attributed to CGs introduce errors in the estimation of B₀ field map, PDFF, and R2*. Phantom and in vivo experiments demonstrated that CGs can introduce estimation errors greater than 30 Hz in the B₀ field map, 10% in PDFF, and 16 s^-1 in R2*, 16 cm off isocenter. However, CG phase correction before parameter estimation was able to reduce estimation errors to less than 10 Hz in the B₀ field map, 1% in PDFF, and 2 s^-1 in R2*.

CONCLUSION

CG effects can impact CSE-MRI, leading to inaccurate estimation of B₀ field map, PDFF, and R2*. However, correction for phase errors caused by CGs improve the accuracy of quantitative parameters estimated from CSE-MRI acquisitions. Magn Reson Med 78:730-738, 2017. © 2016 International Society for Magnetic Resonance in Medicine.

Direct and accelerated parameter mapping using the unscented Kalman filter

PURPOSE

To accelerate parameter mapping using a new paradigm that combines image reconstruction and model regression as a parameter state-tracking problem.

METHODS

In T2 mapping, the T2 map is first encoded in parameter space by multi-TE measurements and then encoded by Fourier transformation with readout/phase encoding gradients. Using a state transition function and a measurement function, the unscented Kalman filter can describe T2 mapping as a dynamic system and directly estimate the T2 map from the k-space data. The proposed method was validated with a numerical brain phantom and volunteer experiments with a multiple-contrast spin echo sequence. Its performance was compared with a conjugate-gradient nonlinear inversion method at undersampling factors of 2 to 8. An accelerated pulse sequence was developed based on this method to achieve prospective undersampling.

RESULTS

Compared with the nonlinear inversion reconstruction, the proposed method had higher precision, improved structural similarity and reduced normalized root mean squared error, with acceleration factors up to 8 in numerical phantom and volunteer studies.

CONCLUSION

This work describes a new perspective on parameter mapping by state tracking. The unscented Kalman filter provides a highly accelerated and efficient paradigm for T2 mapping.

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.

Accelerated regularized estimation of MR coil sensitivities using augmented Lagrangian methods

Several magnetic resonance parallel imaging techniques require explicit estimates of the receive coil sensitivity profiles. These estimates must be accurate over both the object and its surrounding regions to avoid generating artifacts in the reconstructed images. Regularized estimation methods that involve minimizing a cost function containing both a data-fit term and a regularization term provide robust sensitivity estimates. However, these methods can be computationally expensive when dealing with large problems. In this paper, we propose an iterative algorithm based on variable splitting and the augmented Lagrangian method that estimates the coil sensitivity profile by minimizing a quadratic cost function. Our method, ADMM-Circ, reformulates the finite differencing matrix in the regularization term to enable exact alternating minimization steps. We also present a faster variant of this algorithm using intermediate updating of the associated Lagrange multipliers. Numerical experiments with simulated and real data sets indicate that our proposed method converges approximately twice as fast as the preconditioned conjugate gradient method over the entire field-of-view. These concepts may accelerate other quadratic optimization problems.

Accelerating MR parameter mapping using sparsity-promoting regularization in parametric dimension

MR parameter mapping requires sampling along additional (parametric) dimension, which often limits its clinical appeal due to a several-fold increase in scan times compared to conventional anatomic imaging. Data undersampling combined with parallel imaging is an attractive way to reduce scan time in such applications. However, inherent SNR penalties of parallel MRI due to noise amplification often limit its utility even at moderate acceleration factors, requiring regularization by prior knowledge. In this work, we propose a novel regularization strategy, which uses smoothness of signal evolution in the parametric dimension within compressed sensing framework (p-CS) to provide accurate and precise estimation of parametric maps from undersampled data. The performance of the method was demonstrated with variable flip angle T1 mapping and compared favorably to two representative reconstruction approaches, image space-based total variation regularization and an analytical model-based reconstruction. The proposed p-CS regularization was found to provide efficient suppression of noise amplification and preservation of parameter mapping accuracy without explicit utilization of analytical signal models. The developed method may facilitate acceleration of quantitative MRI techniques that are not suitable to model-based reconstruction because of complex signal models or when signal deviations from the expected analytical model exist.

Advances in longitudinal MRI diagnostic tests

INTRODUCTION

The past decade has seen an explosion of functional magnetic resonance imaging (MRI) studies in neuroscience. As the technology progresses, it is now possible to carry out longitudinal studies using functional MRI. Such studies can be used to understand the progression of mental and neurological disorders and the effectiveness of different treatments by obtaining direct measures of brain activity as well as markers of tissue health and connectivity.

AREAS COVERED

We review six popular neuroimaging tools that can be used for longitudinal studies: blood oxygen level-dependent (BOLD)-weighted imaging, BOLD-based functional connectivity, arterial spin labeling, dynamic R2* imaging, voxel-based morphometry, and diffusion tensor imaging.

EXPERT OPINION

Each of these techniques is targeted to probe a specific feature of brain function or brain structure and can reveal important information about the progression of a pathological condition. We anticipate that in the near future, the MRI techniques discussed here may become standard tools in clinical use and will not be used for research purposes only.

Compressed sensing reconstruction for magnetic resonance parameter mapping

Compressed sensing (CS) holds considerable promise to accelerate the data acquisition in magnetic resonance imaging by exploiting signal sparsity. Prior knowledge about the signal can be exploited in some applications to choose an appropriate sparsifying transform. This work presents a CS reconstruction for magnetic resonance (MR) parameter mapping, which applies an overcomplete dictionary, learned from the data model to sparsify the signal. The approach is presented and evaluated in simulations and in in vivo T(1) and T(2) mapping experiments in the brain. Accurate T(1) and T(2) maps are obtained from highly reduced data. This model-based reconstruction could also be applied to other MR parameter mapping applications like diffusion and perfusion imaging.

MODEL-BASED IMAGE RECONSTRUCTION FOR MRI

Magnetic resonance imaging (MRI) is a sophisticated and versatile medical imaging modality. Traditionally, MR images are reconstructed from the raw measurements by a simple inverse 2D or 3D fast Fourier transform (FFT). However, there are a growing number of MRI applications where a simple inverse FFT is inadequate, e.g., due to non-Cartesian sampling patterns, non-Fourier physical effects, nonlinear magnetic fields, or deliberate under-sampling to reduce scan times. Such considerations have led to increasing interest in methods for model-based image reconstruction in MRI.

Rapid 3D radial multi-echo functional magnetic resonance imaging

Functional magnetic resonance imaging with readouts at multiple echo times is useful for optimizing sensitivity across a range of tissue T2* values as well as for quantifying T2*. With single-shot acquisitions, both the minimum TE value and the number of TEs which it is possible to collect within a single TR are limited by the long echo-planar imaging readout duration (20-40 ms). In the present work, a multi-shot 3D radial acquisition which allows rapid whole-brain imaging at a range of echo times is proposed. The proposed 3D k-space coverage is implemented via a series of rotations of a single 2D interleaf. Data can be reconstructed at a variety of temporal resolutions from a single dataset, allowing for a flexible tradeoff between temporal resolution and BOLD contrast to noise ratio. It is demonstrated that whole-brain images at 5 echo times (TEs from 10 to 46 ms) can be acquired at a temporal rate as rapid as 400 ms/volume (3.75 mm isotropic resolution). Activation maps for a simultaneous motor/visual task consistent across multiple acceleration factors are obtained. Weighted combination of the echoes results in Z-scores that are significantly (p=0.016) higher than those resulting from any of the individual echo time images.

Basic properties of SS-PARSE parameter estimates

Single shot parameter assessment by retrieval from signal encoding (SS-PARSE) is a recently introduced method to obtain quantitative parameter maps from a single-shot (typically 65 ms) magnetic resonance imaging (MRI) signal. Because it explicitly models local magnetization decay and phase evolution occurring during the signal 1) it can provide quantitative estimates of local transverse magnetization magnitude and phase, frequency, and relaxation rate and 2) it is free of geometric distortion or blurring due to field nonuniformities within the tissues. These properties promise to be advantageous in functional brain MRI (fMRI) and other dynamic imaging applications. In this paper, the basic phenomena underlying the performance of SS-PARSE in practice are discussed. Basic sources of bias errors in the parameter estimates are discussed, and performance of the method is characterized in terms of parameter estimates from simulation, experimental phantoms, and in vivo studies. Characteristics of the sum-of-square-error cost function and the iterative search algorithm are discussed, and their relative roles in determining estimation accuracy are described. Practical guidelines for use of the method are presented and discussed. In vivo parameter maps are also presented.

Model-based iterative reconstruction for radial fast spin-echo MRI

In radial fast spin-echo magnetic resonance imaging (MRI), a set of overlapping spokes with an inconsistent T2 weighting is acquired, which results in an averaged image contrast when employing conventional image reconstruction techniques. This work demonstrates that the problem may be overcome with the use of a dedicated reconstruction method that further allows for T2 quantification by extracting the embedded relaxation information. Thus, the proposed reconstruction method directly yields a spin-density and relaxivity map from only a single radial data set. The method is based on an inverse formulation of the problem and involves a modeling of the received MRI signal. Because the solution is found by numerical optimization, the approach exploits all data acquired. Further, it handles multicoil data and optionally allows for the incorporation of additional prior knowledge. Simulations and experimental results for a phantom and human brain in vivo demonstrate that the method yields spin-density and relaxivity maps that are neither affected by the typical artifacts from TE mixing, nor by streaking artifacts from the incomplete k-space coverage at individual echo times.