Temporal Dynamics Assessment of Spatial Overlap Pattern of Functional Brain Networks Reveals Novel Functional Architecture of Cerebral Cortex

Abstract

Objective: Various studies in the brain mapping field have demonstrated that there exist multiple concurrent functional networks that are spatially overlapped and interacting with each other during specific task performance to jointly realize the total brain function. Assessing such spatial overlap patterns of functional networks (SOPFNs) based on functional magnetic resonance imaging (fMRI) has thus received increasing interest for brain function studies. However, there are still two crucial issues to be addressed. First, the SOPFNs are assessed over the entire fMRI scan assuming the temporal stationarity, while possibly time-dependent dynamics of the SOPFNs is not sufficiently explored. Second, the SOPFNs are assessed within individual subjects, while group-wise consistency of the SOPFNs is largely unknown.

Methods: To address the two issues, we propose a novel computational framework of group-wise sparse representation of whole-brain fMRI temporal segments to assess the temporal dynamic spatial patterns of SOPFNs that are consistent across different subjects.

Results: Experimental results based on the recently publicly released Human Connectome Project grayordinate task fMRI data demonstrate that meaningful SOPFNs exhibiting dynamic spatial patterns across different time periods are effectively and robustly identified based on the reconstructed concurrent functional networks via the proposed framework. Specifically, those SOPFNs locate significantly more on gyral regions than on sulcal regions across different time periods.

Conclusion: These results reveal novel functional architecture of cortical gyri and sulci.

Significance: Moreover, these results help better understand functional dynamics mechanisms of cerebral cortex in the future.

Fig. 1

SOPFNs assessment in (a) previous studies and (b) our proposed framework. There are n tfMRI signals for each individual subject. Each signal has t total time points. In (b), there are I subjects in total. Each temporal segment (time period) has unified l time points. The four steps labeled as 1 to 4 are detailed in Section II.

Fig. 2

tfMRI temporal segments extraction. (a): The cortical surface and whole-brain tfMRI signal matrix Xⁱ of subject i. The tfMRI signal of an example grayordinate is shown and highlighted by the blue frame. (b): Examples of extracted two consecutive temporal segments within time windows w_j and w_j+1 (highlighted by yellow and blue frames, respectively). The first one starts at time point t_j and the second one starts at time point t_j+1. (c): Example of tfMRI emotion task paradigm. The blocks of the two task designs are interleaved during the entire fMRI scan time t. Window length l is smaller than the length of any of the blocks of the two task designs.

Fig. 3

(a) Conventional sparse representation of a specific temporal segment of an individual subject. (c) The proposed group-wise sparse representation of specific corresponding temporal segments across all subjects. (b): The spatial pattern of an example reconstructed functional network via mapping a specific row (highlighted by red) of α^i,w_j back onto the cortical surface based on conventional sparse representation. (d): The spatial pattern of an example group-wise consistent reconstructed functional network via mapping a specific row (highlighted by red) of P^I,w_j back onto the cortical surface based on the proposed group-wise sparse representation.

Fig. 4

Concurrent group-wise consistent functional networks across different time windows in one subject group of emotion tfMRI data. (a) Task design curves across time windows of emotion tfMRI data. The horizontal axis is the time window and the vertical axis is the task design value. Twelve example time windows are shown. There are two task design curves in emotion tfMRI data. For each time window, if the task design value is non-zero in both two curves, there are both two tasks performed in the time window. If the task design value is non-zero in only one task design curve, there is only the corresponding task performed in the time window. Note that the task design curves are not convoluted with hemodynamic response function for a better visualization. (b) The spatial patterns of task-evoked functional networks identified within the twelve example time windows. The corresponding networks identified from entire time length via sparse representation and GLM are also shown. (c) The spatial patterns of default mode networks (DMN) identified within the same twelve example time windows. The corresponding networks identified from entire time length via sparse representation and the DMN template [39] are also shown. (b) and (c) are color-coded by the z-scores values as illustrated in Section II C.

Fig. 5

Temporal dynamic spatial patterns of SOPFNs across different time windows based on emotion tfMRI data. (a) Task design curves across time windows. The horizontal axis is the time window and the vertical axis is the task design value. The same twelve example time windows as in Fig. 4 are shown. There are three time window types as shown and divided by black dashed lines. Note that the task design curves are not convoluted with hemodynamic response function for a better visualization. (b) The mean spatial patterns of SOPFNs of time windows within each of the three time window types in each of the two subject groups. The common spatial patterns of SOPFNs with relatively higher density are highlighted by red arrows; (b) are color-coded by the z-scores representing SOPFNs values as illustrated in Section II C.

Fig. 6

The mean spatial patterns of SOPFNs of time windows within each of the different time window types in one subject group of the other four tfMRI datasets in (a)-(f), respectively. The common spatial patterns of SOPFNs with relatively higher density across different time window types and different tasks are highlighted by red arrows. TW represents time window. (a)-(f) are color-coded by the z-scores as illustrated in Section II C. The detailed time window types of each task are in Supplemental Fig. 3.

Fig. 6

The mean spatial patterns of SOPFNs of time windows within each of the different time window types in one subject group of the other four tfMRI datasets in (a)-(f), respectively. The common spatial patterns of SOPFNs with relatively higher density across different time window types and different tasks are highlighted by red arrows. TW represents time window. (a)-(f) are color-coded by the z-scores as illustrated in Section II C. The detailed time window types of each task are in Supplemental Fig. 3.

Fig. 7

Temporal dynamic spatial pattern distributions of SOPFNs on gyral (G)/sulcal (S) regions in emotion tfMRI data. (a) Spatial pattern distributions of SOPFNs on gyral/sulcal regions in six example time windows (Fig. 5a). The major regions are highlighted by black arrows. (b) The mean spatial pattern distributions of SOPFNs across time windows within each of the three time window types on gyral/sulcal regions in each of the two subject groups. The common spatial patterns of SOPFNs on gyral/sulcal regions with relatively higher density are highlighted by red arrows. Note that the surfaces illustrating the SOPFNs in (a)-(b) are color-coded by the z-scores as illustrated in Section II C. The two surfaces in (a)-(b) illustrating the gyri/sulci are color-coded by the principal curvature value with gyri has higher principal curvature.

Fig. 8

The mean spatial pattern distributions of SOPFNs across time windows within one example time window type on gyral/sulcal regions in one subject group of the other six tfMRI datasets. The common spatial patterns of SOPFNs with relatively higher density across different tasks are highlighted by red arrows. Note that the surfaces illustrating the SOPFNs are color-coded by the z-scores as illustrated in Section II C. The one example surface illustrating the gyri/sulci is color-coded by the principal curvature value with gyri has higher principal curvature.

Fig. 9

The temporal dynamic distribution percentage of SOPFNs on gyri (green curve) and sulci (orange curve) across all time windows in the two groups of the seven tasks shown in (a)-(g), respectively. In each sub-figure, the horizontal axis is the time window and the vertical axis is the distribution percentage value. The details of task design curves (represented by different colors) are in Supplemental Fig. 2. Note that the task design curves are not convoluted with hemodynamic response function for a better visualization. Note that at a specific time window, the sum of percentage values of gyri and sulci equals 1.