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The human brain exhibits a complex structure made of scale-free highlyconnected modules loosely interconnected by weaker links to form a small-worldnetwork. These features appear in healthy patients whereas neurologicaldiseases often modify this structure. An important open question concerns therole of brain modularity in sustaining the critical behaviour of spontaneousactivity. Here we analyse the neuronal activity of a model, successful inreproducing on non-modular networks the scaling behaviour observed inexperimental data, on a modular network implementing the main statisticalfeatures measured in human brain. We show that on a modular network, regardlessthe strength of the synaptic connections or the modular size and number,activity is never fully scale-free. Neuronal avalanches can invade differentmodules which results in an activity depression, hindering further avalanchepropagation. Critical behaviour is solely recovered if inter-module connectionsare added, modifying the modular into a more random structure.

Brain modularity controls the critical behavior of spontaneous activity