The complex spatiotemporal nature of resting-state functional connectivity has received increasing attention in recent years ^1,2. Majeed et al ³ found strong evidence for quasi-periodic spatiotemporal patterns in resting-state fMRI data acquired in both animals and humans. They presented an iterative pattern matching algorithm for finding a spatiotemporal motif, but did not consider how to construct a signal from repeated versions of the motif. Here we extend their work and present a sparse Bayesian learning approach for estimating the contributions of quasi-periodic spatiotemporal patterns in resting-state fMRI data.

Resting-state fMRI data (5 minutes, eyes closed) were acquired from a healthy subject using a 3 Tesla GE MR750 system. We used echo planar imaging with $$$166$$$ volumes, $$$30$$$ slices, $$$3.4 \times 3.4 \times 5$$$ $$$mm^{3}$$$ voxel size, $$$64\times 64$$$ matrix size, $$$TR=1.8s$$$, $$$TE=30ms$$$. We discarded the first 6 volumes and applied standard preprocessing steps to remove nuisance terms. We used the pattern matching algorithm described in Majeed et al³ with a window length of 20 pts (36 seconds) to identify the basic spatiotemporal motif, denoted as a 4D matrix $$$B$$$. This motif was then vectorized to form a space-time column vector $$$b$$$. The preprocessed data (a 4D matrix $$$Y$$$) were vectorized to form a space-time column vector $$$y$$$. Shifted and zeropadded versions of $$$b$$$ were then used to form a design matrix $$$D$$$, where the number of rows in $$$D$$$ was equal to the length of $$$y$$$ and the shift between adjacent columns was equal to the number of voxels. We hypothesized that there should be a limited number of repeats of the spatiotemporal motif within a run and therefore sought to find a representation of the data of the form $$$y \approx Dx$$$ where $$$x$$$ is an unknown vector of coefficients that is assumed to be sparse and non-negative. Optimal $$$x$$$ can be obtained by solving the traditional sparse recovery problem: $$argmin_{x \geq 0}~||y-Dx||_2 +\lambda~||x||_0.$$ However, instead of this regularization based form, we used a non-negative version of the sparse Bayesian learning algorithm ⁴, which in contrast to alternate approaches ^5,6 has the advantage of not requiring the specification of regularization parameters such as $$$\lambda$$$. As an initial assessment of the approach, we computed measures of the spatiotemporal correlation of the preprocessed data, the estimated spatiotemporal component $$$Dx$$$, and the residual $$$y-Dx$$$. This was done by computing the space-time correlation between all possible pairs of space-time blocks, where the duration of each block was 20 time points. The results are displayed as a spatiotemporal correlation matrix (STCM) where the $$$(i,j)^{th}$$$ entry corresponds to the correlation between the space-time blocks at times $$$i$$$ and $$$j$$$. We also calculated functional connectivity maps using a seed signal from the posterior cingulate cortex (PCC). These maps were computed for (1) the original preprocessed data $$$Y$$$, (2) the preprocessed data after global signal regression (GSR), and (3) the residual term $$$y-Dx$$$ after conversion back to a 4D matrix form.

Fig. 1 shows the estimated weights in the vector $$$x$$$ and the sliding window correlation between the motif $$$B$$$ and the preprocessed data. $$$Y$$$. The vector is relatively sparse, with the largest coefficients coinciding with the correlation peaks. Fig. 2 shows the STCM for the original data, the estimated spatiotemporal component, and the residual term. The STCM for the estimated spatiotemporal component largely captures the quasi-periodic structure seen in the STCM of the original data. This structure is greatly attenuated in the STCM of the residual data. Fig. 3 shows the functional connectivity maps before GSR, with GSR, and for the residual data. Note the similarity of the maps obtained with GSR and after removal of the recurring spatiotemporal component. We have presented a sparse Bayesian learning approach for estimating recurring spatiotemporal patterns in resting-state fMRI data and demonstrated the approach using a sample resting-state fMRI dataset. Our preliminary results suggest that removal of the spatiotemporal component may provide an alternative to GSR, but further work is needed to better understand the relationship between the two approaches. In this work, we used a previously described method ³ to estimate the spatiotemporal motif $$$B$$$. Alternate methods may provide better estimates and can be readily integrated into the proposed approach.