Structural and Functional Brain Networks: From Connections to Cognition

Background The human brain presents a puzzling and challenging paradox: Despite a fixed anatomy, characterized by its connectivity, its functional repertoire is vast, enabling action, perception, and cognition. This contrasts with organs like the heart that have a dynamic anatomy but just one function. The resolution of this paradox may reside in the brain's network architecture, which organizes local interactions to cope with diverse environmental demands—ensuring adaptability, robustness, resilience to damage, efficient message passing, and diverse functionality from a fixed structure. This review asks how recent advances in understanding brain networks elucidate the brain’s many-to-one (degenerate) function-structure relationships. In other words, how does diverse function arise from an apparently static neuronal architecture? We conclude that the emergence of dynamic functional connectivity, from static structural connections, calls for formal (computational) approaches to neuronal information processing that may resolve the dialectic between structure and function. Schematic of the multiscale hierarchical organization of brain networks. Brain function or cognition can be described as the global integration of local (segregated) neuronal operations that underlies hierarchical message passing among cortical areas, and which is facilitated by hierarchical modular network architectures. Advances Much of our understanding of brain connectivity rests on the way that it is measured and modeled. We consider two complementary approaches: the first has its basis in graph theory that aims to describe the network topology of (undirected) connections of the sort measured by noninvasive brain imaging of anatomical connections and functional connectivity (correlations) between remote sites. This is compared with model-based definitions of context-sensitive (directed) effective connectivity that are grounded in the biophysics of neuronal interactions. Recent topological network analyses of brain circuits suggest that modular and hierarchical structural networks are particularly suited for the functional integration of local (functionally specialized) neuronal operations that underlie cognition. Measurements of spontaneous activity reveal functional connectivity patterns that are similar to structural connectivity, suggesting that structural networks constrain functional networks. However, task-related responses that require context-sensitive integration disclose a divergence between function and structure that appears to rest mainly on long-range connections. In contrast to methods that describe network topology phenomenologically, model-based theoretical and computational approaches focus on the mechanisms of neuronal interactions that accommodate the dynamic reconfiguration of effective connectivity. We highlight the consilience between hierarchical topologies (based on structural and functional connectivity) and the effective connectivity that would be required for hierarchical message passing of the sort suggested by computational neuroscience. Outlook In summary, neuronal interactions represent dynamics on a fixed structural connectivity that underlie cognition and behavior. Such divergence of function from structure is, perhaps, the most intriguing property of the brain and invites intensive future research. By studying the dynamics and self-organization of functional networks, we may gain insight into the true nature of the brain as the embodiment of the mind. The repertoire of functional networks rests upon the (hidden) structural architecture of connections that enables hierarchical functional integration. Understanding these networks will require theoretical models of neuronal processing that underlies cognition. How rich functionality emerges from the invariant structural architecture of the brain remains a major mystery in neuroscience. Recent applications of network theory and theoretical neuroscience to large-scale brain networks have started to dissolve this mystery. Network analyses suggest that hierarchical modular brain networks are particularly suited to facilitate local (segregated) neuronal operations and the global integration of segregated functions. Although functional networks are constrained by structural connections, context-sensitive integration during cognition tasks necessarily entails a divergence between structural and functional networks. This degenerate (many-to-one) function-structure mapping is crucial for understanding the nature of brain networks. The emergence of dynamic functional networks from static structural connections calls for a formal (computational) approach to neuronal information processing that may resolve this dialectic between structure and function.