Default Mode Network

We considered transitions from an initial state, x₀, to a target state, x_T, where T = 1 is the control horizon. Initial and target states were selected to correspond to specific cognitive systems. For example, one possible control task was to start in a state where the default mode network (DMN) was maximally active, and to transition to a state where the visual system (VIS) becomes maximally active. Intuitively, such a transition might correspond to the presentation of a visual stimulus at rest, eliciting activation of visual cortex while suppressing activation of the default mode system. In this context, the control question one asks is which nodes play a role in the minimum energy trajectory between these states. We modeled this control task by starting DMN regions in an active state at t = 0:

Similarly, when t = T, only visual regions were in an active state:

Given these boundary conditions, we calculated the optimal inputs, to effect the transition from specified initial state to specified target state. In general, state vectors at other times can take on any real value. Though we considered this limited set of states, the linear model of brain dynamics means that any transition can be written as a linear combination of the transitions we studied here.

In order to explore whole-brain gradients alteration, we merged multiple intrinsic functional connectivity-based atlases, including cortical parcellations (Schaefer et al., 2018 (link)), cerebellar parcellations (Buckner et al., 2011 (link)), striatal parcellations (Choi et al., 2012 (link)), and thalamic parcellations (Horn and Kühn, 2015 (link)). There were three subcortical regions of interest (ROIs) that were discarded during 3 mm × 3 mm × 3 mm down-sampling due to small sizes. The final remaining 1,039 ROIs have corresponding functional community annotation, including Visual (Vis), Somatomotor (SM), Dorsal Attention (DA), Ventral Attention (VA), Limbic (Lim), Frontoparietal (FP), and Default Mode Network (DMN) (Yeo et al., 2011 (link)). Pearson correlation coefficients were computed for each pair of brain regions as the functional connectome. Detailed information about this brain atlas could be found in Supplementary Table 1 or https://github.com/louxin-lab.
The functional connectome was then z-transformed and the top 10% thresholded, and the cosine similarity matrix was calculated to capture similarity in connectivity profiles (Vos de Wael et al., 2020 (link)). Principal component analysis (PCA), the most reproducible dimensionality reduction algorithm for gradient framework, was applied to identify primary gradient components for the majority of connectome variance (Hong et al., 2020 (link)). A group-level gradient component template was generated from an average connectivity matrix based on unrelated health datasets as mentioned earlier, and we performed Procrustes rotation to align components to the template (Vos de Wael et al., 2020 (link)). As with most gradient studies, we mainly focused on the primary two components (Gradient-1 and Gradient-2) as they explained the majority of the total variance. These components, initially defined in connectivity space, were then mapped back onto the ROIs to visualize macroscale transitions in overall connectivity patterns. To analyze the functional distance alteration between ROIs, we used the primary two gradients to calculate the Euclidean distance in the functional hierarchical architecture. As for statistical analysis, independent and paired t-tests were applied for VS vs. healthy controls (HCs) comparison or VS_pre vs. VS_post comparison, respectively, with False Discovery Rate (FDR) correction.