Hierarchical Organization Unveiled by Functional Connectivity in Complex Brain Networks

How do diverse dynamical patterns arise from the topology of complex networks? We study synchronization dynamics in the cortical brain network of the cat, which displays a hierarchically clustered organization, by modeling each node (cortical area) with a subnetwork of interacting excitable neurons. We find that in the biologically plausible regime the dynamics exhibits a hierarchical modular organization, in particular, revealing functional clusters coinciding with the anatomical communities at different scales. Our results provide insights into the relationship between network topology and functional organization of complex brain networks.

Figure 1

(a) Anatomical connection matrix $M^A$ of the cortical network of the cat brain. The symbols represent different densities (weights) of the fiber connections: 1 (•, sparse), 2 (∘, intermediate), and 3 (*, dense). The organization of the system into four topological communities (functional subsystems V, A, SM, and FL) is indicated by the solid lines. (b) The number of connections between the four communities.

Figure 2

Mean activity $X$ of one area at various couplings: (a) $g=0.06$, (b) $g=0.082$, and (c) $g=0.09$. (d) The average correlation coefficient $⟨R⟩=\frac{1}{N(N-1)}\sum _{I\ne J}^{N}R(I,J)$ ($N=53$) vs $g$.

Figure 3

Correlation matrices $R(I,J)$ at (a) weak coupling $g=0.06$ and (b) strong coupling $g=0.09$.

Figure 4

(a) Distribution of the correlation $R$ ($g=0.07$) for all nodes (solid line), P2 (dotted line), P1 (dashed line), and P0 (light solid line) and for surrogate data (dashed-dotted line). (b) Modularity $Q^F$ (solid line) and Hamming distance $H$ (dashed line) vs $R_{\mathrm{th}}$. The horizontal solid line is $Q^{\mathrm{all}}$. The vertical solid lines in (a) and (d) denote the natural threshold $R_{\mathrm{th}}=0.019$. The functional networks $M^F$ (∘) at various thresholds (c) $R_{\mathrm{th}}=0.070$, (d) $R_{\mathrm{th}}=0.065$, (e) $R_{\mathrm{th}}=0.055$, and (f) $R_{\mathrm{th}}=0.019$. The small dots indicate the anatomical connections.

Figure 5

(a) The hierarchical tree of the dynamical clusters at $g=0.07$. (b) Modularities $Q^C$ (∘) and $Q^A$ (•) vs the number of clusters $N_c$. The dashed line denotes $Q^{\mathrm{all}}$.