Establishing Communication between Neuronal Populations through Competitive Entrainment

The role of gamma frequency oscillation in neuronal interaction, and the relationship between oscillation and information transfer between neurons, has been the focus of much recent research. While the biological mechanisms responsible for gamma oscillation and the properties of resulting networks are well studied, the dynamics of changing phase coherence between oscillating neuronal populations are not well understood. To this end we develop a computational model of competitive selection between multiple stimuli, where the selection and transfer of population-encoded information arises from competition between converging stimuli to entrain a target population of neurons. Oscillation is generated by Pyramidal-Interneuronal Network Gamma through the action of recurrent synaptic connections between a locally connected network of excitatory and inhibitory neurons. Competition between stimuli is driven by differences in coherence of oscillation, while transmission of a single selected stimulus is enabled between generating and receiving neurons via Communication-through-Coherence. We explore the effect of varying synaptic parameters on the competitive transmission of stimuli over different neuron models, and identify a continuous region within the parameter space of the recurrent synaptic loop where inhibition-induced oscillation results in entrainment of target neurons. Within this optimal region we find that competition between stimuli of equal coherence results in model output that alternates between representation of the stimuli, in a manner strongly resembling well-known biological phenomena resulting from competitive stimulus selection such as binocular rivalry

Oscillatory dynamics as a mechanism of integration in complex networks of neurons

The large-scale integrative mechanisms of the brain, the means by which the activity of functionally segregated neuronal regions are combined, are not well understood. There is growing agreement that a flexible mechanism of integration must be present in order to support the myriad changing cognitive demands under which we are placed. Neuronal communication through phase-coherent oscillation stands as the prominent theory of cognitive integration. The work presented in this thesis explores the role of oscillation and synchronisation in the transfer and integration of information in the brain. It is first shown that complex metastable dynamics suitable for modelling phase-coherent neuronal synchronisation emerge from modularity in networks of delay and pulse-coupled oscillators. Within a restricted parameter regime these networks display a constantly changing set of partially synchronised states where some modules remain highly synchronised while others desynchronise. An examination of network phase dynamics shows increasing coherence with increasing connectivity between modules. The metastable chimera states that emerge from the activity of modular oscillator networks are demonstrated to be synchronous with a constant phase relationship as would be required of a mechanism of large-scale neural integration. A specific example of functional phase-coherent synchronisation within a spiking neural system is then developed. Competitive stimulus selection between converging population encoded stimuli is demonstrated through entrainment of oscillation in receiving neurons. The behaviour of the model is shown to be analogous to well-known competitive processes of stimulus selection such as binocular rivalry, matching key experimentally observed properties for the distribution and correlation of periods of entrainment under differing stimuli strength. Finally two new measures of network centrality, knotty-centrality and set betweenness centrality, are developed and applied to empirically derived human structural brain connectivity data. It is shown that human brain organisation exhibits a topologically central core network within a modular structure consistent with the generation of synchronous oscillation with functional phase dynamics

Complexity of multi-dimensional spontaneous EEG decreases during propofol induced general anaesthesia

Emerging neural theories of consciousness suggest a correlation between a specific type of neural dynamical complexity and the level of consciousness: When awake and aware, causal interactions between brain regions are both integrated (all regions are to a certain extent connected) and differentiated (there is inhomogeneity and variety in the interactions). In support of this, recent work by Casali et al (2013) has shown that Lempel-Ziv complexity correlates strongly with conscious level, when computed on the EEG response to transcranial magnetic stimulation. Here we investigated complexity of spontaneous high-density EEG data during propofol-induced general anaesthesia. We consider three distinct measures: (i) Lempel-Ziv complexity, which is derived from how compressible the data are; (ii) amplitude coalition entropy, which measures the variability in the constitution of the set of active channels; and (iii) the novel synchrony coalition entropy (SCE), which measures the variability in the constitution of the set of synchronous channels. After some simulations on Kuramoto oscillator models which demonstrate that these measures capture distinct ‘flavours’ of complexity, we show that there is a robustly measurable decrease in the complexity of spontaneous EEG during general anaesthesia

Knotty-Centrality: Finding the Connective Core of a Complex Network

A network measure called knotty-centrality is defined that quantifies the extent to which a given subset of a graph’s nodes constitutes a densely intra-connected topologically central connective core. Using this measure, the knotty centre of a network is defined as a sub-graph with maximal knotty-centrality. A heuristic algorithm for finding subsets of a network with high knotty-centrality is presented, and this is applied to previously published brain structural connectivity data for the cat and the human, as well as to a number of other networks. The cognitive implications of possessing a connective core with high knotty-centrality are briefly discussed

Frustrated hierarchical synchronization and emergent complexity in the human connectome network

The spontaneous emergence of coherent behavior through synchronization plays a key role in neural function, and its anomalies often lie at the basis of pathologies. Here we employ a parsimonious (mesoscopic) approach to study analytically and computationally the synchronization (Kuramoto) dynamics on the actual human-brain connectome network. We elucidate the existence of a so-far-uncovered intermediate phase, placed between the standard synchronous and asynchronous phases, i.e. between order and disorder. This novel phase stems from the hierarchical modular organization of the connectome. Where one would expect a hierarchical synchronization process, we show that the interplay between structural bottlenecks and quenched intrinsic frequency heterogeneities at many different scales, gives rise to frustrated synchronization, metastability, and chimera-like states, resulting in a very rich and complex phenomenology. We uncover the origin of the dynamic freezing behind these features by using spectral graph theory and discuss how the emerging complex synchronization patterns relate to the need for the brain to access –in a robust though flexible way– a large variety of functional attractors and dynamical repertoires without ad hoc fine-tuning to a critical pointWe acknowledge financial support from J. de Andalucía, grant P09-FQM-4682 and we thank O. Sporns for providing us access to the human connectome data

Chimera-like states in modular neural networks

Chimera states, namely the coexistence of coherent and incoherent behavior, were previously analyzed in complex networks. However, they have not been extensively studied in modular networks. Here, we consider a neural network inspired by the connectome of the C. elegans soil worm, organized into six interconnected communities, where neurons obey chaotic bursting dynamics. Neurons are assumed to be connected with electrical synapses within their communities and with chemical synapses across them. As our numerical simulations reveal, the coaction of these two types of coupling can shape the dynamics in such a way that chimera-like states can happen. They consist of a fraction of synchronized neurons which belong to the larger communities, and a fraction of desynchronized neurons which are part of smaller communities. In addition to the Kuramoto order parameter ?, we also employ other measures of coherence, such as the chimera-like ? and metastability ? indices, which quantify the degree of synchronization among communities and along time, respectively. We perform the same analysis for networks that share common features with the C. elegans neural network. Similar results suggest that under certain assumptions, chimera-like states are prominent phenomena in modular networks, and might provide insight for the behavior of more complex modular networks

A biophysical model of dynamic balancing of excitation and inhibition in fast oscillatory large-scale networks

Over long timescales, neuronal dynamics can be robust to quite large perturbations, such as changes in white matter connectivity and grey matter structure through processes including learning, aging, development and certain disease processes. One possible explanation is that robust dynamics are facilitated by homeostatic mechanisms that can dynamically rebalance brain networks. In this study, we simulate a cortical brain network using the Wilson-Cowan neural mass model with conduction delays and noise, and use inhibitory synaptic plasticity (ISP) to dynamically achieve a spatially local balance between excitation and inhibition. Using MEG data from 55 subjects we find that ISP enables us to simultaneously achieve high correlation with multiple measures of functional connectivity, including amplitude envelope correlation and phase locking. Further, we find that ISP successfully achieves local E/I balance, and can consistently predict the functional connectivity computed from real MEG data, for a much wider range of model parameters than is possible with a model without ISP