Improving temporal resolution in fMRI using a 3D spiral acquisition and low rank plus sparse (L+S) reconstruction

Hi-Fi fMRI: High-resolution, fast-sampled and sub-second whole-brain functional MRI at 3T in humans

Functional magnetic resonance imaging (fMRI) is a methodological cornerstone of neuroscience. Most studies measure blood-oxygen-level-dependent (BOLD) signal using echo-planar imaging (EPI), Cartesian sampling, and image reconstruction with a one-to-one correspondence between the number of acquired volumes and reconstructed images. However, EPI schemes are subject to trade-offs between spatial and temporal resolutions. We overcome these limitations by measuring BOLD with a gradient recalled echo (GRE) with 3D radial-spiral phyllotaxis trajectory at a high sampling rate (28.24ms) on standard 3T field-strength. The framework enables the reconstruction of 3D signal time courses with whole-brain coverage at simultaneously higher spatial (1mm ³ ) and temporal (up to 250ms) resolutions, as compared to optimized EPI schemes. Additionally, artifacts are corrected before image reconstruction; the desired temporal resolution is chosen after scanning and without assumptions on the shape of the hemodynamic response. By showing activation in the calcarine sulcus of 20 participants performing an ON-OFF visual paradigm, we demonstrate the reliability of our method for cognitive neuroscience research.

Compressed sensing based dynamic MR image reconstruction by using 3D-total generalized variation and tensor decomposition: k-t TGV-TD

PURPOSE

Compressed Sensing Magnetic Resonance Imaging (CS-MRI) is a promising technique to accelerate dynamic cardiac MR imaging (DCMRI). For DCMRI, the CS-MRI usually exploits image signal sparsity and low-rank property to reconstruct dynamic images from the undersampled k-space data. In this paper, a novel CS algorithm is investigated to improve dynamic cardiac MR image reconstruction quality under the condition of minimizing the k-space recording.

METHODS

The sparse representation of 3D cardiac magnetic resonance data is implemented by synergistically integrating 3D total generalized variation (3D-TGV) algorithm and high order singular value decomposition (HOSVD) based Tensor Decomposition, termed k-t TGV-TD method. In the proposed method, the low rank structure of the 3D dynamic cardiac MR data is performed with the HOSVD method, and the localized image sparsity is achieved by the 3D-TGV method. Moreover, the Fast Composite Splitting Algorithm (FCSA) method, combining the variable splitting with operator splitting techniques, is employed to solve the low-rank and sparse problem. Two different cardiac MR datasets (cardiac perfusion and cine MR datasets) are used to evaluate the performance of the proposed method.

RESULTS

Compared with the state-of-art methods, such as k-t SLR, 3D-TGV, HOSVD based tensor decomposition and low-rank plus sparse method, the proposed k-t TGV-TD method can offer improved reconstruction accuracy in terms of higher peak SNR (PSNR) and structural similarity index (SSIM). The proposed k-t TGV-TD method can achieve significantly better and stable reconstruction results than state-of-the-art methods in terms of both PSNR and SSIM, especially for cardiac perfusion MR dataset.

CONCLUSIONS

This work proved that the k-t TGV-TD method was an effective sparse representation way for DCMRI, which was capable of significantly improving the reconstruction accuracy with different acceleration factors.

Subspace-constrained approaches to low-rank fMRI acceleration

Acceleration methods in fMRI aim to reconstruct high fidelity images from under-sampled k-space, allowing fMRI datasets to achieve higher temporal resolution, reduced physiological noise aliasing, and increased statistical degrees of freedom. While low levels of acceleration are typically part of standard fMRI protocols through parallel imaging, there exists the potential for approaches that allow much greater acceleration. One such existing approach is k-t FASTER, which exploits the inherent low-rank nature of fMRI. In this paper, we present a reformulated version of k-t FASTER which includes additional L2 constraints within a low-rank framework.

We evaluated the effect of three different constraints against existing low-rank approaches to fMRI reconstruction: Tikhonov constraints, low-resolution priors, and temporal subspace smoothness. The different approaches are separately tested for robustness to under-sampling and thermal noise levels, in both retrospectively and prospectively-undersampled finger-tapping task fMRI data. Reconstruction quality is evaluated by accurate reconstruction of low-rank subspaces and activation maps.

The use of L2 constraints was found to achieve consistently improved results, producing high fidelity reconstructions of statistical parameter maps at higher acceleration factors and lower SNR values than existing methods, but at a cost of longer computation time. In particular, the Tikhonov constraint proved very robust across all tested datasets, and the temporal subspace smoothness constraint provided the best reconstruction scores in the prospectively-undersampled dataset. These results demonstrate that regularized low-rank reconstruction of fMRI data can recover functional information at high acceleration factors without the use of any model-based spatial constraints.

High-Resolution Oscillating Steady-State fMRI Using Patch-Tensor Low-Rank Reconstruction

The goals of fMRI acquisition include high spatial and temporal resolutions with a high signal to noise ratio (SNR). Oscillating Steady-State Imaging (OSSI) is a new fMRI acquisition method that provides large oscillating signals with the potential for high SNR, but does so at the expense of spatial and temporal resolutions. The unique oscillation pattern of OSSI images makes it well suited for high-dimensional modeling. We propose a patch-tensor low-rank model to exploit the local spatial-temporal low-rankness of OSSI images. We also develop a practical sparse sampling scheme with improved sampling incoherence for OSSI. With an alternating direction method of multipliers (ADMM) based algorithm, we improve OSSI spatial and temporal resolutions with a factor of 12 acquisition acceleration and 1.3 mm isotropic spatial resolution in prospectively undersampled experiments. The proposed model yields high temporal SNR with more activation than other low-rank methods. Compared to the standard grad- ient echo (GRE) imaging with the same spatial-temporal resolution, 3D OSSI tensor model reconstruction demonstrates 2 times higher temporal SNR with 2 times more functional activation.

Highly accelerated submillimeter resolution 3D GRASE with controlled T 2 blurring in T 2 -weighted functional MRI at 7 Tesla: A feasibility study

PURPOSE

To achieve highly accelerated submillimeter resolution T 2 -weighted functional MRI at 7T by developing a three-dimensional gradient and spin echo imaging (GRASE) with inner-volume selection and variable flip angles (VFA).

METHODS

GRASE imaging has disadvantages in that (a) k-space modulation causes T 2 blurring by limiting the number of slices and (b) a VFA scheme results in partial success with substantial SNR loss. In this work, accelerated GRASE with controlled T 2 blurring is developed to improve a point spread function (PSF) and temporal signal-to-noise ratio (tSNR) with a large number of slices. To this end, the VFA scheme is designed by minimizing a trade-off between SNR and blurring for functional sensitivity, and a new GRASE-optimized random encoding, which takes into account the complex signal decays of T 2 and T 2 ∗ weightings, is proposed by achieving incoherent aliasing for constrained reconstruction. Numerical and experimental studies were performed to validate the effectiveness of the proposed method over regular and VFA GRASE (R- and V-GRASE).

RESULTS

The proposed method, while achieving 0.8 mm isotropic resolution, functional MRI compared to R- and V-GRASE improves the spatial extent of the excited volume up to 36 slices with 52%-68% full width at half maximum (FWHM) reduction in PSF but approximately 2- to 3-fold mean tSNR improvement, thus resulting in higher BOLD activations.

CONCLUSIONS

We successfully demonstrated the feasibility of the proposed method in T 2 -weighted functional MRI. The proposed method is especially promising for cortical layer-specific functional MRI.

R-fMRI reconstruction from k-t undersampled data using a subject-invariant dictionary model and VB-EM with nested minorization

Higher spatial resolution in resting-state functional magnetic resonance imaging (R-fMRI) can give reliable information about the functional networks in the cerebral cortex. Typical methods can achieve higher spatial or temporal resolution by speeding up scans using either (i) complex pulse-sequence designs or (ii) k-space undersampling coupled with priors on the signal. We propose to undersample the R-fMRI acquisition in k-space and time to speedup scans in order to improve spatial resolution. We propose a novel model-based R-fMRI reconstruction framework using a robust, subject-invariant, spatially regularized dictionary prior on the signal. Furthermore, we propose a novel inference framework based on variational Bayesian expectation maximization with nested minorization (VB-EM-NM). Our inference framework allows us to provide an estimate of uncertainty of the reconstruction, unlike typical reconstruction methods. Empirical evaluation of (i) simulated R-fMRI reconstruction and (ii) functional-network estimates from brain R-fMRI reconstructions demonstrate that our framework improves over the state of the art, and, additionally, enables significantly higher spatial resolution.

Improved statistical efficiency of simultaneous multi-slice fMRI by reconstruction with spatially adaptive temporal smoothing

We introduce an approach to reconstruction of simultaneous multi-slice (SMS)-fMRI data that improves statistical efficiency. The method incorporates regularization to adjust temporal smoothness in a spatially varying, encoding-dependent manner, reducing the g-factor noise amplification per temporal degree of freedom. This results in a net improvement in tSNR and GLM efficiency, where the efficiency gain can be derived analytically as a function of the encoding and reconstruction parameters. Residual slice leakage and aliasing is limited when fMRI signal energy is dominated by low frequencies. Analytical predictions, simulated and experimental results demonstrate a marked improvement in statistical efficiency in the temporally regularized reconstructions compared to conventional slice-GRAPPA reconstructions, particularly in central brain regions. Furthermore, experimental results confirm that residual slice leakage and aliasing errors are not noticeably increased compared to slice-GRAPPA reconstruction. This approach to temporally regularized image reconstruction in SMS-fMRI improves statistical power, and allows for explicit choice of reconstruction parameters by directly assessing their impact on noise variance per degree of freedom.

Recovering task fMRI signals from highly under-sampled data with low-rank and temporal subspace constraints

Recent developments in highly accelerated fMRI data acquisition have employed low-rank and/or sparsity constraints for image reconstruction, as an alternative to conventional, time-independent parallel imaging. When under-sampling factors are high or the signals of interest are low-variance, however, functional data recovery can be poor or incomplete. We introduce a method for improving reconstruction fidelity using external constraints, like an experimental design matrix, to partially orient the estimated fMRI temporal subspace. Combining these external constraints with low-rank constraints introduces a new image reconstruction model that is analogous to using a mixture of subspace-decomposition (PCA/ICA) and regression (GLM) models in fMRI analysis. We show that this approach improves fMRI reconstruction quality in simulations and experimental data, focusing on the model problem of detecting subtle 1-s latency shifts between brain regions in a block-design task-fMRI experiment. Successful latency discrimination is shown at acceleration factors up to R = 16 in a radial-Cartesian acquisition. We show that this approach works with approximate, or not perfectly informative constraints, where the derived benefit is commensurate with the information content contained in the constraints. The proposed method extends low-rank approximation methods for under-sampled fMRI data acquisition by leveraging knowledge of expected task-based variance in the data, enabling improvements in the speed and efficiency of fMRI data acquisition without the loss of subtle features.

PEAR: PEriodic And fixed Rank separation for fast fMRI

PURPOSE

In functional MRI (fMRI), faster acquisition via undersampling of data can improve the spatial-temporal resolution trade-off and increase statistical robustness through increased degrees-of-freedom. High-quality reconstruction of fMRI data from undersampled measurements requires proper modeling of the data. We present an fMRI reconstruction approach based on modeling the fMRI signal as a sum of periodic and fixed rank components, for improved reconstruction from undersampled measurements.

METHODS

The proposed approach decomposes the fMRI signal into a component which has a fixed rank and a component consisting of a sum of periodic signals which is sparse in the temporal Fourier domain. Data reconstruction is performed by solving a constrained problem that enforces a fixed, moderate rank on one of the components, and a limited number of temporal frequencies on the other. Our approach is coined PEAR - PEriodic And fixed Rank separation for fast fMRI.

RESULTS

Experimental results include purely synthetic simulation, a simulation with real timecourses and retrospective undersampling of a real fMRI dataset. Evaluation was performed both quantitatively and visually versus ground truth, comparing PEAR to two additional recent methods for fMRI reconstruction from undersampled measurements. Results demonstrate PEAR's improvement in estimating the timecourses and activation maps versus the methods compared against at acceleration ratios of R = 8,10.66 (for simulated data) and R = 6.66,10 (for real data).

CONCLUSIONS

This paper presents PEAR, an undersampled fMRI reconstruction approach based on decomposing the fMRI signal to periodic and fixed rank components. PEAR results in reconstruction with higher fidelity than when using a fixed-rank based model or a conventional Low-rank + Sparse algorithm. We have shown that splitting the functional information between the components leads to better modeling of fMRI, over state-of-the-art methods.

Improving temporal resolution in fMRI using a 3D spiral acquisition and low rank plus sparse (L+S) reconstruction

Rapid whole-brain dynamic Magnetic Resonance Imaging (MRI) is of particular interest in Blood Oxygen Level Dependent (BOLD) functional MRI (fMRI). Faster acquisitions with higher temporal sampling of the BOLD time-course provide several advantages including increased sensitivity in detecting functional activation, the possibility of filtering out physiological noise for improving temporal SNR, and freezing out head motion. Generally, faster acquisitions require undersampling of the data which results in aliasing artifacts in the object domain. A recently developed low-rank (L) plus sparse (S) matrix decomposition model (L+S) is one of the methods that has been introduced to reconstruct images from undersampled dynamic MRI data. The L+S approach assumes that the dynamic MRI data, represented as a space-time matrix M, is a linear superposition of L and S components, where L represents highly spatially and temporally correlated elements, such as the image background, while S captures dynamic information that is sparse in an appropriate transform domain. This suggests that L+S might be suited for undersampled task or slow event-related fMRI acquisitions because the periodic nature of the BOLD signal is sparse in the temporal Fourier transform domain and slowly varying low-rank brain background signals, such as physiological noise and drift, will be predominantly low-rank. In this work, as a proof of concept, we exploit the L+S method for accelerating block-design fMRI using a 3D stack of spirals (SoS) acquisition where undersampling is performed in the k_z-t domain. We examined the feasibility of the L+S method to accurately separate temporally correlated brain background information in the L component while capturing periodic BOLD signals in the S component. We present results acquired in control human volunteers at 3T for both retrospective and prospectively acquired fMRI data for a visual activation block-design task. We show that a SoS fMRI acquisition with an acceleration of four and L+S reconstruction can achieve a brain coverage of 40 slices at 2mm isotropic resolution and 64 x 64 matrix size every 500ms.