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Efficient complex systems have a modular structure, but modularity does notguarantee robustness, because efficiency also requires an ingenious interplayof the interacting modular components. The human brain is the elementalparadigm of an efficient robust modular system interconnected as a network ofnetworks (NoN). Understanding the emergence of robustness in such modulararchitectures from the interconnections of its parts is a long-standingchallenge that has concerned many scientists. Current models of dependencies inNoN inspired by the power grid express interactions among modules with fragilecouplings that amplify even small shocks, thus preventing functionality.Therefore, we introduce a model of NoN to shape the pattern of brainactivations to form a modular environment that is robust. The model predictsthe map of neural collective influencers (NCIs) in the brain, through theoptimization of the influence of the minimal set of essential nodes responsiblefor broadcasting information to the whole-brain NoN. Our results suggest newintervention protocols to control brain activity by targeting influentialneural nodes predicted by network theory.

Model of Brain Activation Predicts the Neural Collective Influence Map of the Brain