Signal propagation via cortical hierarchies

Abstract

The wiring of the brain is organized around a putative unimodal-transmodal hierarchy. Here we investigate how this intrinsic hierarchical organization of the brain shapes the transmission of information among regions. The hierarchical positioning of individual regions was quantified by applying diffusion map embedding to resting-state functional MRI networks. Structural networks were reconstructed from diffusion spectrum imaging and topological shortest paths among all brain regions were computed. Sequences of nodes encountered along a path were then labeled by their hierarchical position, tracing out path motifs. We find that the cortical hierarchy guides communication in the network. Specifically, nodes are more likely to forward signals to nodes closer in the hierarchy and cover a range of unimodal and transmodal regions, potentially enriching or diversifying signals en route. We also find evidence of systematic detours, particularly in attention networks, where communication is rerouted. Altogether, the present work highlights how the cortical hierarchy shapes signal exchange and imparts behaviorally relevant communication patterns in brain networks.

Keywords: Brain connectivity; Connectome; Navigation; Neural communication; Neural networks.

Figure 1.

Tracing communication paths through cortical hierarchies. Structural and functional networks are reconstructed from diffusion-weighted MRI and resting-state functional MRI, respectively. Shortest paths between all pairs of nodes are computed for structural networks using the Floyd-Warshall algorithm (Floyd, ; Roy, ; Warshall, 1962). A cortical hierarchy is recovered from functional networks using diffusion map embedding (Coifman et al., 2005). The first eigenvector is used to label nodes according to their position in the putative unimodal-transmodal hierarchy (Margulies et al., 2016). Sequences of nodes encountered along a path are labeled by their hierarchical position, tracing out path motifs. Note that some paths are longer and some are shorter, some paths ascend or descend through the hierarchy, and some paths reverse their trajectory one or more times en route to the target node.

Figure 2.

Path motifs. For each source-target pair, nodes along the corresponding path are labeled according to their position on the unimodal-transmodal cortical hierarchy. Hierarchy values are binned into 10 equally sized levels, where level 1 corresponds to unimodal cortex and level 10 corresponds to transmodal cortex. Path motifs are shown for three levels of source nodes (2, 6, and 9; rows) and three levels of target nodes (2, 6, and 9; columns). Each plot shows the mean path motifs: path position (hop) is shown on the x-axis and the hierarchical level of the node at each hop is shown on the y-axis. Paths are stratified according to their length, such that warmer colors indicate shorter paths and cooler colors indicate longer paths. Shaded regions indicate 95% confidence intervals. Supporting Information Figure S1 shows the corresponding results for a label-permuting null model.

Figure 3.

Inflection points in communication flow. As each path traverses the hierarchy, we can infer how individual brain regions direct communication flow. (A) Schematic showing a path motif, where the position along the x-axis indicates a node and the y-axis indicates the hierarchical position of the node. The slope of the curve at each point tells whether the path is ascending or descending in the hierarchy. We denote nodes where slope changes sign as turning points. Nodes where the slope changes from positive to negative are turning points down, and nodes where the slope changes from negative to positive are turning points up. (B) The mean slope of each node (y-axis) is anticorrelated with its position in the hierarchy. The mean slope of each node is shown for every brain region; warm colors indicate positive slopes, cool colors indicate negative slopes. (C) The mean slope for seven intrinsic networks (Yeo et al., 2011). (D) Mean probability of turning points up and down in seven intrinsic networks. Asterisks indicate values that are statistically significant according a label-permuting and spatial autocorrelation-preserving null distribution (P_spin < 0.01, FDR-corrected). (E) Turning point up probability for individual regions. (F) Turning point down probability for individual regions. Network assignments: DM = default mode, FP = frontoparietal, LIM = limbic, VA = ventral attention, DA = dorsal attention, SM = somatomotor, VIS = visual.

Figure 4.

Transition probabilities in communication. As paths traverse the hierarchy, we quantify the probability that the current position of a node in the unimodal-transmodal hierarchy depends on previous positions in the path. (A) With 1-hop transitions we quantify the transition probability of a path going from hierarchy level i to level j in one step or hop. With multi-hop transitions we quantify the probability of a path going from hierarchy level i to level j in k steps or hops. Thus, in a single path we consider multiple transitions. (B) Nodes are stratified by their hierarchical position in 10 equally sized bins. Transition probability matrices are shown where source nodes (hierarchy bins) are in the rows, and target nodes (hierarchy bins) are in the columns. The top row shows 1-hop transition probabilities and the bottom row shows multi-hop transition probabilities. Transitions are shown for paths of up to length 9, corresponding to the diameter of the network. Note that the values in the matrices display mean probabilities over multiple paths, hence the rows do not necessarily sum to 1 (see the Methods section for more detail).

Figure 5.

Navigation via hierarchical proximity. We evaluate the extent to which shortest paths can be recapitulated by an agent who is aware of the three-dimensional spatial positions of the nodes (spatial navigation) and/or the hierarchical positions of the nodes (hierarchical navigation), but not the topology of the network. (A) Schematic showing a putative path from source target, where an agent occupies the third node in the path. Nodes are colored according to their position in the hierarchy. If the agent navigates using spatial information, it will transition to the neighbor that is physically closest to the target (bottom). If the agent navigates using hierarchical information, it will transition to the neighbor that is hierarchically closest to the target (top). We derive the navigation preference of each node (β parameter) as the source of information that maximizes recapitulation of shortest paths (Muscoloni & Cannistraci, ; Muscoloni, Thomas, Ciucci, Bianconi, & Cannistraci, ; Seguin et al., 2018). When β is valued close to 1, paths originating from the node are better recovered using spatial proximity compared with hierarchical proximity; the opposite is true when β is valued close to 0. (B) Histogram of β values across all nodes in the network. Histograms are also shown for seven intrinsic networks. (C) Individual brain regions are colored by their preference for spatial navigation (warm colors) or hierarchical navigation (cool colors). Network assignments: DM = default mode, FP = frontoparietal, LIM = limbic, VA = ventral attention, DA = dorsal attention, SM = somatomotor, VIS = visual.