Information content of brain states is explained by structural constraints on state energetics

Signal propagation along the structural connectome of the brain induces changes in the patterns of activity. These activity patterns define global brain states and contain information in accordance with their expected probability of occurrence. Being the physical substrate upon which information propagates, the structural connectome, in conjunction with the dynamics, determines the set of possible brain states and constrains the transition between accessible states. Yet, precisely how these structural constraints on state transitions relate to their information content remains unexplored. To address this gap in knowledge, we defined the information content as a function of the activation distribution, where statistically rare values of activation correspond to high information content. With this numerical definition in hand, we studied the spatiotemporal distribution of information content in functional magnetic resonance imaging (fMRI) data from the Human Connectome Project during different tasks, and report four key findings. First, information content strongly depends on cognitive context; its absolute level and spatial distribution depend on the cognitive task. Second, while information content shows similarities to other measures of brain activity, it is distinct from both Neurosynth maps and task contrast maps generated by a general linear model applied to the fMRI data. Third, the brain's structural wiring constrains the cost to control its state, where the cost to transition into high information content states is larger than that to transition into low information content states. Finally, all state transitions—especially those to high information content states—are less costly than expected from random network null models, thereby indicating the brains marked efficiency. Taken together, our findings establish an explanatory link between the information contained in a brain state and the energetic cost of attaining that state, thereby laying important groundwork for our understanding of large-scale cognitive computations.

Figure 1

Calculation of information content and transition cost of brain states. (a) fMRI activation intensities of different brain parcels define instantaneous brain state, and are represented by dots in an $N$-dimensional state space, where $N$ is the number of brain parcels. (b) An example histogram of the resting-state data of the parcel showing the median information content of a single subject. Resting-state time series were used to estimate the probability density of activation values for each brain parcel and each subject. (c) Top panel: The activation time series of the same parcel during the working memory task. Middle panel: Corresponding parcel information content $I_{\mathrm{parcel}}$. Bottom panel: Whole brain information content $I_{\mathrm{state}}$, as obtained by summation over all parcels. (d)–(f) By injecting control signals that diffuse on the underlying substrate of the structural connectivity matrix [schematically shown in (d)], the instantaneous state of the brain is moved from an initial state to a target state (e). (f) The cost of such a transition is determined by an underlying energy landscape and was estimated as the cost of control in the framework of network control theory.

Figure 2

Information content across different tasks. (a) Mean information content. Among all seven tasks considered in this work, the brain exhibited the highest overall information content during the social task ($p<0.001$ after Bonferroni correction for multiple comparisons), and the lowest information content in the emotion and gambling tasks. (b) Regional skew of information content. For the different tasks, the mean parcel information content $I_{\text{parcel}}$ across all subjects was calculated. The parcels were then sorted by $I_{\text{parcel}}$ for every task, and the resulting declining lines were plotted for every task.

Figure 3

Regional distribution of three different measures derived from fMRI activation. Brain parcels with involvement for the different tasks according to community consensus (Neurosynth [39], top), a classical generalized linear model approach (GLM, middle), as well as the proposed information content metric (bottom). For information content, the difference between information content of the task fMRI distribution and the rs-fMRI base distribution, averaged over all subjects and time points, is visualized. Red: Positive values; blue: Negative values. All nonsignificant parcels ($p>0.01$ after Bonferroni correction) were set to zero and colored in gray. As the results are approximately symmetric across the hemispheres, only the left hemisphere is visualized here. The right hemisphere can be found in Supplemental Material Sec. 3 [30].

Figure 4

Energetics of information content. (a) The scheme of calculating the improvement in the cost of transition using the actual structural connectivity ( on the left) of the brain over that calculated using a null model ( on the right). Heat maps show an example structural connectivity matrix (on the left) and a randomized null model (on the right). The minimum control energy to reach all the observed brain states calculated using each model was then compared with the other to calculate the improvement. (b) Mean state information against mean minimum control energy for all subjects and all tasks in the HCP data set. For an uncluttered representation, only every 50th data point is plotted. (c) Efficiency of actual brain wiring. Comparison of real-world control energy vs control energy of connectivity null models for high, middling, and low information content states.