Multi-projection magnetic resonance inverse imaging of the human visuomotor system
Highlights
► Inverse imaging (InI) achieves fast sampling rate using an RF coil array. ► The lower spatial resolution of InI is due to solving ill-posed inverse problem. ► Multi-projection InI (mInI) combines projections to improve spatial resolution. ► mInI has more homogeneous and higher spatial resolution than InI with TR = 10 Hz.
Introduction
Functional magnetic resonance imaging (fMRI) (Belliveau et al., 1991) using blood-oxygen-level-dependent (BOLD) contrast (Kwong et al., 1992, Ogawa et al., 1990) has become a prevailing method of studying human brain function non-invasively. With a typical in-plane spatial resolution of 3–5 mm, acquisition of BOLD-contrast fMRI is usually accomplished by echo-planar imaging (EPI) (Mansfield, 1977) using fast gradient switching in order to complete 2D k-space traversal in approximately 80 ms per slice or 2 s with the whole brain coverage. The quest for a higher temporal resolution in fMRI has been motivated by, for example, its potential to monitor and to suppress physiological fluctuations not related to the hemodynamics in order to improve the sensitivity of detecting brain activity (Kruger and Glover, 2001, Lin et al., 2011). This is due to the fact that the conventional 0.5 Hz/volume sampling rate is too low to resolve the aliased cardiac (1.0–1.3 Hz) and respiratory (0.2–0.3 Hz) cycles. The other motivation for high temporal resolution fMRI is to provide hemodynamic timing information at neuronally relevant scale (Lin et al., 2010a). Additionally, it has been suggested that an fMRI with a faster sampling rate can significantly improve the power of detecting causal modulations among brain areas during tasks and cognition (Deshpande et al., 2010, Kayser et al., 2009, Roebroeck et al., 2005).
With advances in radio-frequency (RF) receiver coil technology, the feasibility of accelerating MRI data acquisition rate via simultaneous data acquisition from multiple channels of an RF coil array and the associated image reconstruction algorithms in either image-space or k-space (Pruessmann et al., 1999, Sodickson and Manning, 1997) has been successfully demonstrated. MR inverse imaging (InI) is an extreme variant of such a parallel MRI strategy: using highly parallel detection, dynamic images with the associated statistical maps can be obtained at the 20 ms temporal resolution using minimal gradient encoding for 2D single slice imaging (Lin et al., 2006). InI is closely related to the MR-encephalography (MREG) method (Hennig et al., 2007) and it has been applied to volumetric imaging with different reconstruction alternatives (Lin et al., 2008a, Lin et al., 2008b, Lin et al., 2010b, Liou et al., 2011). Currently, BOLD-contrast fMRI using InI can achieve 100 ms temporal resolution with whole-brain coverage and approximately 5 mm spatial resolution at cortex (Lin et al., 2008a, Lin et al., 2008b, Lin et al., 2010b).
InI and more generally pMRI reconstruct images by solving a system of linear equations. In contrast to solving over-determined inverse problems in typical pMRI applications, the InI image reconstruction has been intrinsically under-determined since the time-consuming partition encoding steps have been left out in order to achieve the temporal acceleration. The absence of gradient encoded spatial information along the partition encoding direction is complemented by RF coil sensitivity information and prior constraints. Consequently, InI has anisotropic spatial resolution. This challenge can be partially mitigated by optimizing k-space trajectory (Grotz et al., 2009). However, InI generally has a lower spatial resolution at the center of head and a higher spatial resolution at locations close to the RF coils.
In InI acquisitions, leaving out all partition encoding steps is equivalent to acquiring a projection image. In most BOLD-contrast fMRI experiments, repetitive measurements are usually required to compensate the relatively low contrast-to-noise ratio (CNR) in order to detect activated brain areas with a sufficient statistical significance. Such a data acquisition protocol opens up the possibility of combining InI acquisitions across different runs to improve the spatial resolution. Here we propose the multi-projection InI reconstruction method (mInI) to achieve fast 3D MR inverse imaging with an improved spatial resolution. Specifically, rather than repetitively measuring the same projection images, more spatial information can be obtained by changing the axes of frequency, phase, and partition encoding such that different projection images are acquired. The collection of projection images can be combined to improve the spatial resolution in dynamic InI reconstructions. Compared to InI using only one projection image, as demonstrated in our numerical analysis, the mInI's encoding matrix is likely to be better conditioned because more measurements with distinct spatial information are included. This is due to the fact that different projection images from a coil array with evenly distributed coil elements in 3D can include non-redundant spatial information to thus improve the conditioning of the mInI encoding matrix. As the COBRA method demonstrated the utility of a multi-projection acquisition strategy in 2D fMRI using an eight-channel coil array (Grotz et al., 2009), here we use numerical simulations and in vivo visuomotor fMRI data with a 32-channel head coil array to demonstrate that mInI's spatial resolution can be improved significantly compared to InI with only one single projection in 3D volumetric acquisition with whole brain coverage.
Section snippets
Participants and tasks
Written informed consents were obtained from participants (n = 12), in accord with the National Taiwan University Hospital and National Yang Ming University ethical committees. The participants were presented with left or right visual hemifield reversing (8 Hz) checkerboard stimuli in a rapid event-related fMRI design. The hemifield checkerboard subtended 4.3° visual angle and was generated from 24 evenly distributed radial wedges and eight concentric rings of equal radii. The stimuli were
Conditioning of forward operator
We first studied how the condition number changes when different projection images were included in the forward operator. The condition numbers of the forward operator with using one (coronal) or two (coronal + sagittal) projections in 64 × 64 × 64 image matrix were 8.16 × 1023 and 7.19 × 1015 respectively. The condition numbers of the forward with using one (coronal), two (coronal + sagittal), and three (coronal + sagittal + transverse) projections in 32 × 32 × 32 image matrix were 9.18 × 1012, 2.76 × 107, and 1.23 × 10
Discussion
In this study we demonstrated both theoretically and empirically that spatial resolution of fast (10 Hz) whole-head fMRI can be substantially improved by integrating spatial information from multiple projections. Compared to InI using only one projection, three-projection mInI can improve the spatial resolution quantified by the FWHM of PSF in the cortex by 17% (1.2 pixels to 1.0 pixels). At the deep brain area, the FWHM of PSF was found improved by 50% (2.6 pixels to 1.3 pixels). Since fMRI
Acknowledgments
The authors thank Drs. Jonathan R. Polimeni and Joseph B. Mandeville for technical support and inspiring discussion. This work was supported by the National Institutes of Health Grants by R01DA14178, R01HD040712, R01NS037462, P41RR14075, R01EB006847, R01EB000790, R01MH083744, the National Center for Research Resources, NSC 98-2320-B-002-004-MY3, NSC 100-2325-B-002-046 (National Science Council, Taiwan), NHRI-EX100-9715EC (National Health Research Institute, Taiwan), 100-EC-17-A-19-S1-175 (
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