Sub-second whole brain imaging using Simultaneous Multi-Slice (SMS) imaging is of particular interest in Blood Oxygen Level Dependent (BOLD) functional Magnetic Resonance Imaging (fMRI) ^1-3. Faster acquisitions with higher temporal sampling of the BOLD time course provides several advantages including increased sensitivity in detecting functional activation by acquiring a greater number of samples, the possibility of filtering out physiological noise for improving temporal SNR, and freezing out head motion. The most commonly used strategy to accelerate image acquisition time using SMS involves using parallel imaging methods ^4-5, where non-acquired k-space data are estimated using receiver array coil sensitivity information. We propose to accelerate SMS imaging by under sampling the number of excited slices in the k_z-t domain and L+S matrix decomposition method for reconstruction of slice aliased functional images. We present human fMRI results at 3T using 3D spiral sampling with SMS excitation and L+S reconstruction of the aliased slice data.

The fMRI data can be structured as the space-time matrix M, where each column is a temporal frame, and decomposed into low-rank (L) and sparse (S) components by solving the following optimization problem:

$$ min \parallel L \parallel_*+\lambda \parallel S \parallel_1, s.t. M=W(L+S) $$

where $$$\parallel L \parallel _*$$$ and $$$\parallel S \parallel_1$$$ are the nuclear-norm and $$$l_1$$$ norms of $$$L$$$ and $$$S$$$, $$$\lambda=1/\sqrt{n_1 n_2}$$$ is the nuclear norm vs $$$l_1$$$ norm weight. The decomposition results in matrix $$$L$$$ and matrix $$$S$$$, where $$$L$$$ represents a highly-stuctured information, such as tissue, or slowly-changing periodic information, such as cardic pulsation or respiratory movement. $$$S$$$ captures less-structured information, such as new localized dynamic information. $$$L+S$$$ results in matrix $$$M$$$ that represents background information with overlaid localized dynamic components.

We applied the L+S method to fMRI on a healthy adult volunteer on a 3T scanner (Siemens, Tim Trio) with a 12-channel head coil. An SMS 3D spiral sequence was used to acquire fully sampled fMRI data. The imaging parameters were: FOV=22 cm, 64x64 matrix resolution, 16 simultaneous 3 mm thick slices, TR/TE=100/30ms, flip angle 30 degrees and 150 temporal frames. Sixteen z phase encodes were applied such that each slice could be separated during a 3D image reconstruction. The paradigm was a flashing checkerboard consisting of four 30 sec “on” and 30 sec “off” blocks for a total duration of 4 minutes. The data were then retrospectively undersampled by a x4 factor in the k_z-t domain by keeping the two centre lines of k_z-space and randomly excluding the remaining two planes at every time point (Fig. 1). L+S reconstructions were then performed using a temporal FFT as a sparsifying transform. Statistical analysis of the BOLD based activation was accomplished using a generalized linear model (GLM) after spatial smoothing.Fig. 2 shows L+S decomposition results for one slice in the vicinity of occipital lobe for the fully sampled data. Activation maps, scaled from t=6 to 10, were overlaid on the reconstructed images. From the time profile among the green line it can be seen that the L component absorbs the static brain background, while S captures localized dynamic components with activation. Fig. 3 shows L+S reconstructions from x4 retrospectively undersampled data of the same slice with overlaid activation maps. Good recovery of activation maps is seen in the S and M components compared with B x4 images computed from undersampled data. Activation patterns in the S and M components are qualitatively consistent to those from the fully sampled data shown in Fig. 2. Finally, Fig. 4 shows L+S reconstruction results from x4 retrospectively undersampled data for multiple slices in the vicinity of motor and visual cortex. It can be seen that L+S was able to produce aliasing artifact corrected images and successfully decompose images into the static component L and the dynamic component S which captures activation. Again, activations patterns in the S and M images are qualitatively consistent with those computed from the fully sampled data seen in Fig. 2.

In this work we demonstrated that a spiral SMS acquisition combined with L+S reconstruction can accelerate fMRI acquisition by a factor of x4. We have also shown that L+S algorithm is able to produce slice aliasing corrected images and successfully decompose them into L and S components comparable with the those obtained from the fully sampled data. Future work will be to add coil sensitivity encoding for higher acceleration than SMS with parallel imaging alone. We will also add blipped-spiral acquisitors for improved k_z-t sampling⁶.