Synchronization, non-linear dynamics and low-frequency fluctuations: Analogy between spontaneous brain activity and networked single-transistor chaotic oscillators

Abstract

In this paper, the topographical relationship between functional connectivity (intended as inter-regional synchronization), spectral and non-linear dynamical properties across cortical areas of the healthy human brain is considered. Based upon functional MRI acquisitions of spontaneous activity during wakeful idleness, node degree maps are determined by thresholding the temporal correlation coefficient among all voxel pairs. In addition, for individual voxel time-series, the relative amplitude of low-frequency fluctuations and the correlation dimension (D2), determined with respect to Fourier amplitude and value distribution matched surrogate data, are measured. Across cortical areas, high node degree is associated with a shift towards lower frequency activity and, compared to surrogate data, clearer saturation to a lower correlation dimension, suggesting presence of non-linear structure. An attempt to recapitulate this relationship in a network of single-transistor oscillators is made, based on a diffusive ring (n = 90) with added long-distance links defining four extended hub regions. Similarly to the brain data, it is found that oscillators in the hub regions generate signals with larger low-frequency cycle amplitude fluctuations and clearer saturation to a lower correlation dimension compared to surrogates. The effect emerges more markedly close to criticality. The homology observed between the two systems despite profound differences in scale, coupling mechanism and dynamics appears noteworthy. These experimental results motivate further investigation into the heterogeneity of cortical non-linear dynamics in relation to connectivity and underline the ability for small networks of single-transistor oscillators to recreate collective phenomena arising in much more complex biological systems, potentially representing a future platform for modelling disease-related changes.

Injured Brains and Adaptive Networks: The Benefits and Costs of Hyperconnectivity

“…Neural systems are required to process a number of inputs on a moment-to-moment basis and, by operating at a critical point, the system maintains enough “order” to ensure coherent representations of sensory inputs, reinforcing reliable responses while simultaneously retaining a measure of “disorder” giving it flexibility to adapt. Criticality may provide neural systems with a wide dynamic range for processing various environmental inputs and maximize the opportunity for information transfer and storage [99] and hubs may play a particularly important role in maintaining these non-linear dynamics [100]. While extending these latest findings to states of injury and plasticity is speculative, the link is intriguing given the central role hubs play in guiding information transfer and the growing evidence for enhanced network involvement of centralized hubs after neurological disruption.…”

Regional Homogeneity

“…All these quantitatively validated findings highlighted the idea that the local connectivity profile within a network can essentially influence the global network dynamics. A very recent study made such efforts by fully decoding the links between local FC and remote FC from the perspective of the human brain being a complex system to generate synchronization, nonlinear dynamics, and low-frequency fluctuations ( Minati and others 2015 ).…”

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“…30 One of them, featuring particularly small size (1 BJT, 2 inductors and 1 capacitor), was later used as a building block to realize large networks, which were able to replicate some emergent phenomena originally observed in biological neural systems. 33,34 That study, however, had severe limitations. First, it did not address to what extent the evolutionary aspect of the genetic algorithm was significant, compared to the random search component introduced by random cross-over and finite mutation probability.…”