Abstract
The human brain contains billions of neurons that flexibly interconnect to support local and global computational spans. As neuronal activity propagates through the neural medium, it approaches a critical state hedged between ordered and disordered system regimes. Recent work demonstrates that this criticality coincides with the small-world topology, a network arrangement that accommodates both local (subcritical) and global (supercritical) system properties. On one hand, operating near criticality is thought to offer several neurocomputational advantages, e.g., high-dynamic range, efficient information capacity, and information transfer fidelity. On the other hand, aberrations from the critical state have been linked to diverse pathologies of the brain, such as post-traumatic epileptiform seizures and disorders of consciousness. Modulation of brain activity, through neuromodulation, presents an attractive mode of treatment to alleviate such neurological disorders, but a tractable neural framework is needed to facilitate clinical progress. Using a variation on the generative small-world model of Watts and Strogatz and Kuramoto's model of coupled oscillators, we show that the topological and dynamical properties of the small-world network are divided into two functional domains based on the range of connectivity, and that these domains play distinct roles in shaping the behavior of the critical state. We demonstrate that short-range network connections shape the dynamics of the system, e.g., its volatility and metastability, whereas long-range connections drive the system state, e.g., a seizure. Together, these findings lend support to combinatorial neuromodulation approaches that synergistically normalize the system dynamic while mobilizing the system state.
Highlights
The human brain is thought to contain billions of neurons that densely interconnect across short and long spatial distances (von Bartheld et al, 2016)
It is thought that the functional topology of the brain tends to this criticality (Takagi, 2018), flexibly maneuvering it based on an immediate operational needs; by dynamically recruiting or abandoning short- and long-range functional connections, e.g., through coherence of neuroelectric oscillations (Singer, 1999; Buzsáki, 2006; Akam and Kullmann, 2014), or neuroplasticity (Dan and Poo, 2004; Shin and Kim, 2006), the brain maneuvers clustered and disordered topological phases tuned to local and global operational spans, respectively
The small-world coefficient compares the resemblance of a network to a perfectly ordered vs. a perfectly disordered arrangement based on the extent to which the nodes of the network are clustered and the extent to which they are separated
Summary
The human brain is thought to contain billions of neurons that densely interconnect across short and long spatial distances (von Bartheld et al, 2016). It is thought that the functional topology of the brain tends to this criticality (Takagi, 2018), flexibly maneuvering it based on an immediate operational needs; by dynamically recruiting or abandoning short- and long-range functional connections, e.g., through coherence of neuroelectric oscillations (Singer, 1999; Buzsáki, 2006; Akam and Kullmann, 2014), or neuroplasticity (Dan and Poo, 2004; Shin and Kim, 2006), the brain maneuvers clustered and disordered topological phases tuned to local and global operational spans, respectively Within this theoretical framework, the dynamics of the brain essentially reflect a dialectic on one hand pulling the brain to its topological extremes (Poil et al, 2012; Shew and Plenz, 2012; Hesse and Gross, 2014), while, on the other hand, keeping it near the critical state (Shin and Kim, 2006; Hesse and Gross, 2014; Priesemann, 2015; Takagi, 2018). We discuss the implications of these differential effects on clinical neuromodulation
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