Selective Activation of Resting-State Networks following Focal Stimulation in a Connectome-Based Network Model of the Human Brain

The large-scale brain model works near criticality. a, Each node in the model is parameterized by γ to operate intrinsically at the same distance from the critical point if unconnected. A node shows zero activity or oscillation (∼42 Hz) in response to stimulation (red crosses). The activity at each node is described by two time-dependent variables, ψ₁(t) and ψ₂(t). The closer a node operates to the critical point, the larger and the longer lasting is the oscillation (compare γ₁ and, γ₂). When the critical point is reached, the node intrinsically performs a rhythm of constant magnitude. The model, however, is set so that the critical point is never exceeded. b, Principles of activity spreading after stimulation. The damped oscillation generated in the stimulated node (1) is sent via its efferent connections to its target node (2), triggering there, in turn, a damped oscillation with weaker amplitude and faster decay, which then propagates to the next node. Activity ψ₁ ^{( j )} (t) of node (j) is scaled by c_ij and transmitted to node (i) via homogeneous and heterogeneous connections (SCs), delayed by τ_ij in the latter case. In such a chain, activity would decay fast. c, In the large-scale brain model, multiple activity re-entry points can be found. At any time point, the dynamics of a node is influenced by all incoming activity. The response of the node to stimulation (1) is relayed to linked nodes (2–4), which may be fed back to 1 via 4 and may allow the induced activity to dissipate on a much longer time scale. The network response thus depends upon the SC and allows the network to operate near criticality. d, Activation of dynamically responsive networks. Activity after stimulating a node (1 or 2) in a series connection decays fast (as in b). However, activity may circulate and thus decays slower in a feedback network (4–5). Such remaining activity after the initial stimulation decay reveals the so-called dynamically responsive networks.

Dissipation after stimulation. a, Response of area PFCcl to the activation of three different regions PMCdl, CCp, and PCm (abbreviations are given in Table 1). Note that the amplitude, decay, and phase of the response depend upon the stimulated area. The main determinants of the response pattern are the connections, the synaptic weights, and the time delays. The envelope of the time series is computed (black, gray, and green lines for the three stimulation sites). b, Spatiotemporal activation following stimulation of three different regions. At a given time point, we extract the amplitude of the envelope for the 16,500 nodes (the 16,384 cortical nodes and the 116 subcortical ones), which we normalize to 1. The color scale thus indicates the contribution of a given region to the overall activity. The dissipation of activity after stimulating two distant brain areas, PMCdl and CCp (located far from one another: PMCdl in the lateral surface, CCp in the medial surface) leads to similar topographical patterns (for t > 640 ms). In contrast, a distinct pattern appears when stimulating PCm, which is adjacent to CCp. c, Extraction of the main activated propagation subnetworks. We use the stimulation of PMCdl as an example. We calculate the covariance among the 16,500 time series (the 16,384 cortical nodes and the 116 subcortical ones) for a time window centered at 750 ms and then perform a PCA to extract the subnetworks capturing >99% of the activity. Three different networks are thus dynamically responsive when PMCdl is stimulated.

Comparison between dynamically responsive networks to stimulation (top rows) and the experimentally observed RS networks (bottom rows) for the lateral and medial surface of the brain. a–h, Default mode, visual, auditory-phonological, somatomotor, memory, ventral-stream, dorsal attention, and working memory. We used 20% to 80% for the ratio of heterogeneous/homogeneous SC and a range of 10 mm for the homogeneous SC. The white to red scale gives the relative contribution of areas to the responsive networks (top rows) and the RS networks (bottom rows). The stimulation sites are given in Table 2 and Figure 7. Note that the bottom rows are activity masks for the 74 cortical areas constituting the RS networks, where activity is not localized within areas and uniformly color coded (see Materials and Methods). The top rows show the vector field Ψ (x, t) on the mesh of 16,384 cortical nodes and thus localized activity.

Repertoire of dynamically responsive networks. a, The number of networks responsive to cerebral stimulation depends on the spatial range of the homogeneous SC and the ratio of homogeneous SC to heterogeneous SC. b, Similar to a for the number of effective cerebral stimulation sites leading to different networks.

Influence of the structure on the RS-like networks. The pattern of each stimulation-responsive network (from Fig. 5) that best explains an experimentally observed RS network (rows) is correlated with the underlying heterogeneous SC using seven graph-theoretic measures (columns). Incoming, outgoing, or all connected ties to an area can be measured in terms of number (i.e., in-, out-, total-degree) or in terms of strength (i.e., in-, out-, total-strength). The clustering coefficient measures the degree to which areas in a graph tend to cluster together. BC indicates a matching with warmer colors, where comparisons marked with a star are statistically significant. Note that correlations may be high but not significant using a permutation test. The in-degree of the heterogeneous SC can be related to the two memory networks and the attention network. The activation of the other RS networks emerges in a way that is not predicted by the network metrics.