Parcellation of the cerebral cortex into functionally meaningful regions is a crucial step in studies of brain function using complex network analysis. Local functional connectivity (LFC) metrics play a key role in methods of cortical parcellation based on resting-state fMRI (rs-fMRI), by revealing patterns of correlated BOLD signal variation and hence allowing the identification of contiguous but functionally segregated regions [1]. Recently, a new method for analyzing rs-fMRI data by means of a local spatio-temporal correlation tensor was proposed [2]. Their work largely focused on the presence of anisotropic correlations in the white matter. However, they also conjectured that these tensors should be mostly isotropic in grey matter, with the exception of boundaries between regions of functional segregation. Here, we investigate the validity of this hypothesis by studying the suitability of correlational anisotropy maps (AM) calculated from rs-fMRI data collected at 7T to provide functional structure information for cortical parcellation. We employ a hierarchical parcellation method that we have previously proposed, and compare the results with the originally used metric, the stability map (SM) [3].

Data acquisition and pre-processing

Data from one healthy subject collected on a 7T whole-body scanner with a 32-channel-receive RF coil was used to test the proposed methodology. 2x5min of rs-fMRI data were collected using a GE-EPI sequence with TE=32ms, TR=2.5s, FA=75º, GRAPPA factor = 3, simultaneous-multi-slice factor = 3, nominal echo spacing = 0.82ms, whole-brain coverage by 123 sagittal slices and 1.1mm isotropic resolution. A T1-weighted structural image was also acquired using multi-echo MPRAGE, with 1mm isotropic resolution3. Data analysis was carried out using Matlab, FSL and Freesurfer tools. Pre-processing of rs-fMRI data included: motion correction; slice time correction; physiological noise correction using an extended RETROICOR based on simultaneous cardiac and respiratory data4; minimal spatial smoothing with a 1.5mm FWHM Gaussian kernel; and normalisation by removal of the temporal mean and re-scaling to unit variance. The structural image was co-registered with fMRI and MNI images, and it was subjected to tissue segmentation and cortical surface reconstruction using Freesurfer.

Anisotropy map

A local spatio-temporal correlation tensor is computed for every voxel according to [2], while using an additional constraint to ensure that the resulting symmetric 3x3 matrix representing the tensor remains positive semi-definite. The correlational anisotropy map (AM) is then obtained by computing the fractional anisotropy from each tensor according to [5]. For comparison, a stability map (SM) is also computed as in [1,3].

Cortical parcellation

The hierarchical brain parcellation method based on discrete Morse theory proposed in our previous work [3] was chosen for its ability to deal with different scales and for its high intra-subject reproducibility, as these properties could be beneficial in evaluating the role of this new metric. We model the AM projected on the cortical surface as a simplicial complex. This allows us to apply this parcellation method as it generalizes to any regular cell complex of dimension 3 or less with a function defined on its vertices [6]. Parcellations are performed using both the AM and SM, for a number of persistence thresholds.

The cortical parcellations obtained using the two metrics, AM and SM, for persistence threshold of approximately 0.4 are shown in Fig.1. Despite obvious differences, the two parcellations exhibit some matching features, which are highlighted by the contours. Some parcels are almost exactly matched (red, orange, blue, purple). In other cases, an SM-derived parcel closely matches the reunion of a number of AM-derived parcels (green, yellow). The number of parcels obtained as a function of persistence threshold is shown in Fig.2; it is systematically higher when using the AM compared to the SM, and also increases more rapidly as the persistence is decreased. Although this finding could suggest that anisotropy provides additional detail or structure, it is also possible that it reflects a higher noise level.We show that the anisotropy of local spatio-temporal correlation of rs-fMRI at 7T can be used as an LFC metric to generate functional parcellations of the cerebral cortex, which are partially consistent with the results obtained using an established LFC metric, the stability map. The differences encountered in the parcellations obtained by using the two LFC metrics suggest that the correlational anisotropy may provide additional structure relative to the stability map, or instead noisier information. Future work will be aimed at further investigating the validity and properties of the parcellations based on the proposed anisotropy metric, through the analysis of an extended dataset, the exploration of different spatial smoothing levels, and a systematic comparison with well-established techniques.