Controllability of structural brain networks

Abstract

Cognitive function is driven by dynamic interactions between large-scale neural circuits or networks, enabling behaviour. However, fundamental principles constraining these dynamic network processes have remained elusive. Here we use tools from control and network theories to offer a mechanistic explanation for how the brain moves between cognitive states drawn from the network organization of white matter microstructure. Our results suggest that densely connected areas, particularly in the default mode system, facilitate the movement of the brain to many easily reachable states. Weakly connected areas, particularly in cognitive control systems, facilitate the movement of the brain to difficult-to-reach states. Areas located on the boundary between network communities, particularly in attentional control systems, facilitate the integration or segregation of diverse cognitive systems. Our results suggest that structural network differences between cognitive circuits dictate their distinct roles in controlling trajectories of brain network function.

Figure 1. Conceptual schematic.

From weighted brain networks (a), we estimate control points (b) whose large-scale regional activity can move the brain into new trajectories that traverse diverse cognitive functions (c). In c, we show the original state of the system (state 0), as well as four possible states (indicated by the blue circles) that are equidistant from state 0 in the state space (indicated by the black circular line), and which can be reached by trajectories that are more or less energetically costly (indicated by the height of the purple bars).

Figure 2. Brain network control properties.

(a) Average controllability quantifies control to many easily reached states. Here we show controllability values, averaged across three scanning sessions and eight persons, and ranked for all 234 brain regions plotted on a surface visualization. Warmer colours indicate larger values of average controllability. (b) Scatter plot of weighted degree (ranked for all 234 brain regions), averaged across three scanning sessions and eight persons, versus average controllability (Pearson correlation r=0.91, P=8 × 10⁻⁹²). (c) Modal controllability quantifies control to difficult-to-reach states. Here we show modal controllability values, averaged across three scanning sessions and eight persons, and ranked for all 234 brain regions plotted on a surface visualization. (d) Scatter plot of weighted degree (ranked for all 234 brain regions), averaged across three scanning sessions and eight persons, versus modal controllability (r=−0.99, P=2 × 10⁻²¹³). (e) Boundary controllability quantifies control to decouple or integrate network modules. Here we show boundary controllability values, averaged across three scanning sessions and eight persons, and ranked for all 234 brain regions plotted on a surface visualization. (f) Scatter plot of weighted degree (ranked for all 234 brain regions), averaged across three scanning sessions and eight persons, versus boundary controllability (r=0.13, P=0.03). In a,c,e, warmer colours indicate larger controllability values, which have been averaged over both replicates (three scanning sessions) and eight subjects. These results are reliable over a range of atlas resolutions and are consistent with findings using a network composed of only cortical circuitry (see Supplementary Methods). Note that nodes are sorted in an ascending order of the weighted degree.

Figure 3. Reliability and conservation of brain network control properties.

Brain network control properties are reliable across imaging acquisition and are conserved in non-human primates. Scatter plots of weighted degree (ranked for all 234 brain regions) versus (a,d) average controllability (Pearson correlation coefficient r=0.88, P=1.0 × 10⁻⁷⁸; r=0.90, P=4.9 × 10⁻³⁴), (b,e) modal controllability (r=−0.99, P=3.9 × 0⁻¹⁷⁹; r=−0.99, P=1.3 × 10⁻⁷²) and (c,f) boundary controllability (r=0.14, P=0.028; r=−0.19, P=0.074) for (a–c) human diffusion tensor imaging data and (d–f) macaque tract tracing data. In a–c, controllability values are averaged over 85 subjects.

Figure 4. Control roles of cognitive systems.

Cognitive control hubs are differentially located across cognitive systems. (a) Hubs of average controllability are preferentially located in the default mode system. (b) Hubs of modal controllability are predominantly located in cognitive control systems, including both the frontoparietal and cingulo-opercular systems. (c) Hubs of boundary controllability are distributed throughout all systems, with the two predominant systems being ventral and dorsal attention systems. Control hubs have been identified at the group level as the 30 regions with the highest controllability values (averaged over three replicates and eight subjects). Raw percentages of control hubs present in each system have been normalized by the number of regions in the cognitive system. By applying this normalization, systems composed of a larger number of regions have the same chance of housing one of the top 30 control hubs as systems composed of a smaller number of regions.

Figure 5. Differential recruitment of cognitive systems to network control.

Average controllability (AC), modal controllability (MC) and boundary controllability (BC) hubs are differentially located in default mode (a) frontoparietal and cingulo-opercular cognitive control (b) and attentional control (c) systems. Values are averaged over the three replicates for each of eight subjects; error bars indicate s.d. of the mean over subjects.