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

Abstract

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 3 T 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 2 mm isotropic resolution and 64 x 64 matrix size every 500 ms.

Introduction

Functional magnetic resonance imaging (fMRI) is a dynamic neuroimaging method that utilizes endogenous Blood Oxygenation Level Dependent (BOLD) contrast produced by deoxyhemoglobin to observe neuronal activity non-invasively in the brain Ogawa et al., 1990, Turner et al., 1993. Rapid whole brain imaging is of particular interest in BOLD fMRI because of increased sensitivity in detecting functional activation by acquiring a greater number of samples Posse et al. (2012), reducing aliasing of physiological noise Frank et al. (2001), and reducing sensitivity to head motion. Higher sampling rates also allow for a finer characterization of the hemodynamic response function (HRF) leading to an increased statistical power and specificity of the BOLD signal. Furthermore, high temporal resolution is useful for various cognitive fMRI studies, such as estimating brain connectivity in resting state networks Beckmann et al. (2005), that are usually detected over a broad cortex during hundreds of milliseconds.

There are numerous proposed approaches for obtaining acceleration in fMRI. One method is to use parallel imaging where the inherent spatial sensitivity information in multiple receivers is used to recover an image from its undersampled aliased version. Application of parallel imaging techniques, such as SENSE Pruessmann et al. (1999) and GRAPPA Griswold et al. (2002), to fMRI with 2D echo-planar imaging (EPI) sequences demonstrate two- to four-fold in-plane acceleration Golay et al. (2000); de Zwart et al. (2002); Afacan et al. (2012). The use of segmented 3D EPI sequences can achieve further acceleration by using coil sensitivities in both in-plane and through-plane phase-encoding directions Poser et al. (2010). Highly undersampled single-shot 3D methods show whole-brain fMRI at extremely fast sampling rates of up to 100 ms Lin et al., 2006, Zahneisen et al., 2012. Simultaneous multi-slice (SMS) imaging has also emerged as a successful single-shot acceleration strategy in fMRI Zahneisen et al., 2014, Setsompop et al., 2012 by acquiring up to 12 overlapping slices the are later separated during reconstruction. Methods have also been proposed to decrease the fMRI acquisition time by exploiting data redundancy in both the spatial and temporal domains. One of the first such methods demonstrated in fMRI, known as UNFOLD Madore et al. (1999), exploits specific distribution of the $k-t$ sampling in relation to the signal aliasing patterns. Parallel imaging approaches have also been developed to incorporate information across temporal frames such as $k-t$ GRAPPA Huang et al. (2005), for example, and have demonstrated improved spatial resolution without significant penalties on temporal resolution with accelerations up to a factor of four.

Compressed sensing (CS) Lustig et al. (2007) techniques are another method for increasing imaging speed in MRI. CS uses sparsity in image space or an appropriate transformed domain with incoherence in the acquisition to reconstruct undersampled data. CS has been successfully applied for accelerating a variety of dynamic MRI applications, such as myocardial perfusion imaging Adluru et al., 2009, Ge et al., 2009 and MR angiography Mistretta (2009), and even resulted in the development of the specific techniques, such as $k-t$ SPARSE Lustig et al. (2006) or $k-t$ FOCUSS Jung et al. (2009). $k-t$ SPARSE exploits both spatial and temporal sparsity of dynamic MRI image sequences using l₁-norm minimization of transformed dynamic data (using, for example, wavelet transform along the spatial direction and Fourier transform along the temporal direction) subject to data fidelity constraints. The method is based only on a sparse representation of the dynamic data and does not require an a-priori known spatio-temporal structure or a training set. On the other hand, the $k-t$ FOCUSS utilizes a CS framework using prediction and residual encoding where the prediction approximately estimates the dynamic images and the residual encoding takes care of the remaining signals from a small number of $k-t$ samples. Application of CS to fMRI has been shown to provide improvements in sensitivity Jung and Ye, 2009, Holland et al., 2013, temporal resolution Jeromin et al., 2012, Zong et al., 2014 and spatial resolution Nguyen and Glover, 2014, Fang et al., 2015, Nguyen and Glover, 2014. Like parallel imaging, exploiting temporal sampling redundancy results in further acceleration gains. For example Fang et al. Fang et al. (2015) used a variable density spiral acquisition and a modified $k-t$ SPARSE method, HSPARSE, to achieve high spatial resolution fMRI with acceleration factor of approximately five. Unlike $k-t$ SPARSE the HSPARSE exploits both spatial and temporal redundancy.

Techniques based on low-rank matrix completion are also gaining attention in the scientific community in application to dynamic MRI Zhao et al., 2010, Haldar and Liang, 2010. Often the dynamic information in the imaging matrix can be captured in a few singular values. Minimization of the nuclear norm of the matrix enables the recovery of missing or corrupted entries under low-rank and incoherence conditions. These methods favor large singular values of data that have a smaller number of degrees of freedom allowing for undersampling. Chiew et al. (2015) used undersampled multi-shot 3D EPI combined with low-rank matrix completion, $k-t$ FASTER, to accelerate resting-state fMRI by a factor of approximately four. In a later work, the authors used a 3D radial acquisition combined with SENSE and rank-constrained reconstruction to achieve variable acceleration factors in resting-state and task-based fMRI Chiew et al. (2016). While the application of low-rank matrix recovery techniques was shown to be beneficial for accelerating task-based fMRI, generally the assumption of a low-rank matrix might be too strong to capture the weak BOLD activation signals in addition to the relatively slow-evolving non-activation related functional brain networks.

Recent research proposes combining sparse and low-rank matrix completion techniques in application to dynamic MRI. One approach is to assume that the solution is simultaneously low-rank (L) and sparse (S) Lingala et al., 2011, Zhao et al., 2012. Another approach suggests decomposition of the data matrix as a linear combination of the L and S components, also known as robust principal component analysis (RPCA) Candès et al. (2011) or L+S decomposition Yuan and Yang (2009). Gao et al. applied this method to dynamic computed tomography Gao et al. (2011) and later to dynamic MRI applications, such as retrospectively undersampled cardiac MRI data Gao et al. (2012) and accelerated diffusion-weighted MRI data Compressive, 2013, Compressive, 2013. The method was further developed by Otazo et al. who initially demonstrated the L+S reconstruction approach for dynamic contrast enhanced imaging Otazo et al. (2013) and later for a variety of other clinical MRI applications, such as cardiac perfusion, cardiac cine, time-resolved angiography, and abdominal and breast perfusion MR imaging Otazo et al. (2015a). In parallel with Otazo's work, Tremoulheac et al. proposed an L+S model decomposition based on an alternating direction method of multipliers for cardiac MRI, called $k-t$ RPCA Trémoulhéac et al. (2014).

Most recently, Otazo et al. demonstrated the feasibility of L+S decomposition for separation of subsampled physiological noise in resting-state fMRI Otazo et al. (2015b). Unlike using low-rank matrix completion alone for modeling fMRI data, L+S assumes that activation is modeled as periodic and sparse and the low-rank component models the slowly correlated brain background. The L component can then potentially serve as a means of removing unwanted background signal from the BOLD activation. Otazo et al. showed that L+S decomposition is comparable with methods for retrospective removal of physiological noise performed by linear regression of nuisance signals due to cardiac pulsation and respiratory motion. Singh et al. (2015) also applied the L+S model to recover retrospectively undersampled block-design fMRI signal and showed that the low-rank matrix captures the temporally static T2*-weighted images while the sparse component captures the pseudo-periodic BOLD signal for an acceleration factor of three. However, the application of L+S model to prospectively accelerated fMRI data was not evaluated.

In this work we present accelerated fMRI using L+S reconstruction in both retrospectively and prospectively undersampled data acquisitions. We propose to accelerate fMRI using a partially acquired 3D stack of spirals (SoS) sequence where undersampling is performed in the $k_z-t$ domain by fully sampling the central z-phase encoding partitions and randomly excluding remaining partitions. We demonstrate that the L+S model is a good representation for fMRI data using blocked and potentially slow event-related designs. In these experiments, the time series of the activated voxels is a convolution of the BOLD HRF with a periodic stimulus. As a result the BOLD signal will be sparse in the Fourier transformed temporal domain. Additionally, non-task related signals that change slowly over time will be predominantly low-rank allowing for the possibility of removal from the BOLD time course. The results for retrospectively and prospectively undersampled fMRI experiments demonstrate that the L+S algorithm achieves good reconstruction of the aliased functional images with accurate decomposition into temporally correlated brain background in the L component and dynamic information with underlying BOLD signal in the S component with a reduction factor of four without using parallel imaging.