Functional magnetic resonance imaging (fMRI) (Belliveau et al., 1991) using blood-oxygen-level-dependency (BOLD) contrast (Kwong et al., 1992; Ogawa et al., 1990) has been extensively used in human neuroscience research because of its noninvasiveness and higher spatial resolution compared to Positron Emission Tomography (PET). Traditionally, MRI encodes the spatial information by collecting the projection of the unknown object over spatial harmonics generated by magnetic gradient coils. This sequential acquisition can be expressed as k-space traversal.
Therefore, the sampling rate of MRI is closely related to the k-space traversing time.
Echo-planar imaging (EPI) (Mansfield, 1977) utilizes fast switching gradients to achieve the whole k-space traversal after a single RF excitation. Nowadays, a single-slice EPI can be completed within 100 ms. The sampling rate for a volume imaging with the whole brain coverage and approximately 3-5 mm spatial resolution is about 1 to 3 seconds. Instead of traversing the whole k-space defined by the Nyquist sampling theorem using fast switching gradients, previous studies suggested that the sampling rate of MRI data can be accelerated by neglecting part of the k-space, which can be reconstructed by exploiting the complex conjugate data symmetry in the k-space (McGibney et al., 1993; Noll et al., 1991).
Multiple channel radio-frequency (RF) coil arrays have been demonstrated to improve the signal-to-noise ratio (SNR) of MRI (Roemer et al., 1990), and previous studies suggested that this SNR benefit can be traded-off for a higher spatial and/or temporal resolution. Parallel MRI (pMRI) is the technique using the spatially distinct sensitivity information across multiple channels of a coil array to reconstruct images.
Specifically, pMRI can be categorized into either the k-space methods, such as simultaneous acquisition of spatial harmonics (SMASH) (Sodickson and Manning, 1997), or images space methods, such as sensitivity encoding (SENSE) (Pruessmann et al., 1999). EPI combined with pMRI can achieve several advantages, including a higher spatial or temporal resolution (Golay et al., 2004), artifact reduction (Farzaneh et al., 1990; Griswold et al., 1999), and acoustic noise reduction (de Zwart et al., 2002).
SENSE MRI needs explicit RF coil sensitivity information to reconstruct under-sampled data. Practically, accurate sensitivity maps are difficult to obtain.
Inaccurate estimation of sensitivity map can amplify the noise in the reconstructed image (Blaimer et al., 2004). To avoid this difficulty, the k-space pMRI methods using the auto-calibration scan (ACS) have proposed in AUTO-SMASH (Jakob et al., 1998), and GRAPPA (Griswold et al., 2002). Specifically, the ACS is first acquired to estimate the reconstruction coefficients. Then in the accelerated scan (ACC), the estimated reconstruction coefficients together with the ACC data are used to interpolate the skipped data. ACS can be integrated in ACC in anatomical imaging. Alternatively, ACS and ACC can be separated in dynamic MRI experiments. The ACS can prevent reconstruction artifacts due to inaccurate sensitivity maps estimation.
Previously, we proposed the magnetic resonance inverse imaging (InI) (Lin et al., 2006; Lin et al., 2008a; Lin et al., 2008b) using a multiple channels RF coil array to achieve very accelerated fMRI acquisitions. This can be done because the spatial encoding steps along the partition encoding direction are omitted. The three dimensional spatial information is only encoded by a two dimensional EPI encoding.
Similar to the one-voxel-one-coil (OVOC) MR-encephalography technique (Hennig et al., 2007), InI reconstructs the aliased spatial information along the partition encoding direction by using the RF sensitivity maps. Mathematically, the volumetric images are
reconstructed by solving a set of ill-posed inverse problems. Using a 32-channel head coil array at 3T, InI can achieve 10 Hz sampling rate (100 ms per volume) with the whole brain coverage with anisotropic 5 - 10 mm spatial resolution after reconstructing the image using the minimum-norm estimates (MNE) (Lin et al., 2006; Lin et al., 2008a), the linear-constraint minimum variance (LCMV) beamformer spatial filtering (Lin et al., 2008b), or in the k-space domain (K-InI) (Lin et al., 2010).
K-InI shares the similar mathematical principle with k-space GRAPPA reconstruction method. Specifically, in K-InI we collect fully-sampled ACS data before fMRI repetitive measurements in order to estimate the reconstruction kernel, which is then used to reconstruct the accelerated ACC data. This K-InI technique has been shown to have higher source localization accuracy in the visual cortex. Based on in vivo visual fMRI experimental data and analysis, we found that K-InI provides 3 to 5 fold improvement in detection sensitivity compared to that using the MNE (Lin et al., 2010).
Recently, it has been suggested that the self-consistent property among k-space data across multiple channels of an RF coil array can be used to reconstruct the under-sampled k-space data with better image quality than conventional GRAPPA (Lustig and Pauly, 2010). Inspired by this study, we attempt to use the self-consistent property to improve the K-InI reconstruction. The self-consistent K-InI uses an iteratively GRAPPA-like algorithm called iterative self-consistent parallel imaging reconstruction from arbitrary k-space (SPIRiT) (Lustig and Pauly, 2010) to interpolate the k-space data left out in the accelerated fMRI measurements. In the following sections, we present the self-consistent K-InI formulation and use numerical simulations to quantify the spatial resolution and localization accuracy. In vivo fMRI data were also reconstructed by the self-consistent K-InI in order to compare the image quality and the sensitivity of detecting activated brain areas in response to the visual stimulation with
K-InI. Our results show that self-consistent K-InI can improve the spatial resolution and has higher detection sensitivity to brain activity in BOLD fMRI experiments.