Structure function relationship in biophysically inspired small world networks

How behavior arises from the neural activity observed in the brain is one of the main questions in neuroscience. In the resting state, synchronized and highly stable activity has been found in coordinated brain areas, forming what is known as Functional Connectivity. These brain areas are neuronal structures that are interconnected in a very particular way, generating a physical network known as Structural Connectivity. This connectivity has been studied in the light of complex networks, as it has been observed that the particular properties of the brain structure are related to small-world network topology. Interestingly, studies on Functional Connectivity have also proposed similar topology. Functional connectivity is not static, instead, it transits or “wanders” between several states of activity, which are constantly revisited. This dynamical wonder has been framed as the Functional Connectivity Dynamics. However, the relationship between this dynamic transit of Functional Connectivity and the structural basis on which it is supported remains unknown. In this work, the relationship between Structural Connectivity and Functional Connectivity Dynamics is explored by using three network topologies with a biophysically inspired model of activity. Small world metrics, integration, and segregation metrics were used for characterizing the structural connectivity, while multistability, metastability, and synchrony were used for characterizing functional connectivity dynamics. Metastability or “wandering” between activity patterns was higher in regular networks, and it diminished in small-world networks. The relationship between the segregation properties of the network explains better this observed behavior. Multistability, defined by the transit between multiples attractors, was also high in regular networks, however, the relationship between structural and dynamic was better explained by small world metrics. These analyses suggest that the dynamical richness may be originated due to the segregation properties of the network, but the transit between those states is imposed by the ratio between segregation and integration. Further analysis within the range of small-world, may help to understand the importance of this ratio in the dynamical analysis of the brain activity.