In resting-state fMRI data, dynamic quasi-periodic spatio-temporal patterns have previously been identified in both animal and humans with potential links to infra slow electrical activity ^1,2. These prior studies used an iterative pattern-finding algorithm that employed heuristic learning rules for the dynamic adjustment of correlation thresholds. Here we present a novel deterministic non-iterative approach for estimating spatiotemporal motifs in resting-state fMRI data. As the approach does not require heuristic learning rules it has the potential to be more robust across subjects and experimental conditions.

A schematic that uses a toy example to describe the overall approach is shown in Figure 1. The test motif (shown as an $$$N\times M$$$ image) represents a spatiotemporal pattern (with $$$N$$$ voxels and $$$M$$$ time-points) that we would like to estimate. To form the quasi-periodic test data, we repeat the test motif with varying amplitudes at quasi-periodic intervals and add Gaussian noise. Next, we window the test data, such that each windowed $$$N\times20$$$ spatiotemporal block contains the spatial data from 20 time points, starting at the $$$i^{th}$$$ time point. We vectorize this block to form a $$$1 \times (20N)$$$ row vector. We then stack these row vectors to form a spatiotemporal shift matrix, where the $$$i^{th}$$$ row of the matrix corresponds to the spatiotemporal block starting at the $$$i^{th}$$$ timepoint. If we take the singular value decomposition (SVD) of the spatiotemporal shift matrix, the dominant right singular vector can be used to form our estimate of the test motif. Note that the voxels in the test motif are arranged such that the pattern is visibly enhanced, but the approach works equally well if the voxels are randomly permuted such that the pattern is much harder to discern. In addition, weighted combinations of right singular vectors may also be considered to form an estimate of the motif.

As a proof of principle, we applied our approach to resting-state data (eyes closed) acquired on a 3T whole-body system (GE MR750). Functional MRI data were acquired with the following parameters: 5 minute long scan, echo planar imaging with $$$166$$$ volumes, $$$30$$$ slices, $$$3.4\times3.4\times5mm^{3}$$$ voxel size, $$$64\times64$$$ matrix size, $$$TR=1.8s$$$, $$$TE=30ms$$$. The first 6 volumes were eliminated prior to further processing. Nuisance regressors (1st+2nd order Legendre, 6 motion time courses and their first derivatives, mean BOLD signals from white matter and CSF voxels and their first derivatives, RETROICOR and RVHRCOR noise terms) were removed from the raw data through linear regression. For each voxel, a percent change time series was obtained from the pre-processed BOLD time series by subtracting the mean value and then dividing the resulting difference by the mean value. A high resolution anatomical scan was acquired and used to delineate gray matter regions, and further analysis was limited to the signal in gray matter. The approach described above was then used to identify a spatiotemporal motif, using a window length of 20 time points (36 seconds). For comparison, we also used the pattern matching approach described by Majeed et al ¹ with a 20 time point window. Figures 2 and 3 show the estimated spatiotemporal motifs obtained with the proposed approach and the pattern matching approach, respectively. Three representative slices are shown, where each row shows the pattern evolving across time for a given slice. For display purposes only the images from alternating time points in the motif are shown (i.e. the time increment is $$$2\times TR = 3.6s$$$). Both motif estimates show a spatiotemporal pattern in which the BOLD signal transitions from a relatively high amplitude to a lower amplitude as a function of a time. We have demonstrated a new approach for estimating spatiotemporal motifs in resting-state fMRI data. Our preliminary results show that the estimated motif is similar to that obtained with the prior method¹. Further work will be useful for understanding the differences between the two approaches. In particular, it will be interesting to determine which approach is more robust across a range of subjects and conditions.