Hierarchical Connectome Modes and Critical State Jointly Maximize Human Brain Functional Diversity

The brain requires diverse segregated and integrated processing to perform normal functions in terms of anatomical structure and self-organized dynamics with critical features, but the fundamental relationships between the complex structural connectome, critical state, and functional diversity remain unknown. Herein, we extend the eigenmode analysis to investigate the joint contribution of hierarchical modular structural organization and critical state to brain functional diversity. We show that the structural modes inherent to the hierarchical modular structural connectome allow a nested functional segregation and integration across multiple spatiotemporal scales. The real brain hierarchical modular organization provides large structural capacity for diverse functional interactions, which are generated by sequentially activating and recruiting the hierarchical connectome modes, and the critical state can best explore the capacity to maximize the functional diversity. Our results reveal structural and dynamical mechanisms that jointly support a balanced segregated and integrated brain processing with diverse functional interactions, and they also shed light on dysfunctional segregation and integration in neurodegenerative diseases and neuropsychiatric disorders.

Figure 1

(a) The mean correlation coefficients of simulated FC matrices (blue line) and real FC matrices (green line). The shaded area indicates the standard deviation across subjects. (b) The Euclidean distance between real and simulated FC matrices at different $g$. (c) The probability distributions of group-aggregated avalanche sizes across multiple scales (54 837 voxels and 1024 regions) (left) and Gaussian model with various $g$, compared to real data of 268 regions (right). The brain shows power-law distributions of avalanche sizes with power-law exponents $\alpha =1.82$, 1.75, and 2.09 for the voxel level and 1024 and 268 regions [30, 36]. (d) The deviation between avalanche size distributions from real FMRI and simulations in each existing avalanche for all subjects. (e) Power-law distribution of avalanche durations for 268 regions with a power-law exponent $\tau =3.80$. (f) Power-law relationship between avalanche sizes and durations for 268 regions with a positive exponent ${\gamma }_r=2.53$ (black dashed line); the consistency between the theoretical prediction exponent ${\gamma }_t=[(1-\tau )/(1-\alpha )]=2.55$ and ${\gamma }_r$ is a criterion for criticality [36, 37, 38].

Figure 2

(a) The functional diversity $F_D$ of simulated FC matrices (black line) and real FC matrices (green line). (b) The contributions $S_C$ of different structural modes for different $g$. The maximum contributions of specific structural modes are highlighted by black bullets and the dashed line. (c) The total contribution $S_{\mathrm{TC}}$ of all nontrivial structural modes to simulated FC networks (black line) and real FC networks (green line). (d) The $S_C$ of nontrivial structural modes to real and simulated FC networks at different $g$.

Figure 3

(a) The group-averaged brain SC network, where the region labels are sorted according to the eigenmode analysis in (b). LH and RH refer to the left and right brain hemispheres, and the dashed white lines represent the module boundaries. (b) Examples from the intrinsic structural modes and hierarchical module partition in the group-averaged SC network. The modular partition (blue and yellow colors) according to the positivity or negativity of eigenvector components in different orders of structural modes [30]. (c) Visualization of spatial patterns corresponding to the structural modes in (b).

Figure 4

(a) The $n$-hierarchy network ($n=1$, 2) for one realization. (b) The corresponding spatial patterns of the second and third structural modes. (c) The functional diversity $F_D$ and (d) total contribution $S_{\mathrm{TC}}$ of nontrivial structural modes for brain SC networks and surrogate networks. (e) Maximal $F_D$ and $S_{\mathrm{TC}}$ for surrogate networks with different hierarchical levels, compared to those for brain SC networks (green lines).