Critical dynamics on a large human Open Connectome network

Self Cite

The structural human connectome (i.e. the network of fiber connections in the brain) can be analyzed at ever finer spatial resolution thanks to advances in neuroimaging. Here we analyze several large data sets for the human brain network made available by the Open Connectome Project. We apply statistical model selection to characterize the degree distributions of graphs containing up to nodes and edges. A three-parameter generalized Weibull (also known as a stretched exponential) distribution is a good fit to most of the observed degree distributions. For almost all networks, simple power laws cannot fit the data, but in some cases there is statistical support for power laws with an exponential cutoff. We also calculate the topological (graph) dimension D and the small-world coefficient σ of these networks. While σ suggests a small-world topology, we found that D < 4 showing that long-distance connections provide only a small correction to the topology of the embedding three-dimensional space.

Section: Discussionmentioning

confidence: 99%

The topology of large Open Connectome networks for the human brain

Gastner¹,

Ódor²

2016

Self Cite

“…Our graphs are much larger than those considered before, allowing us to determine universal critical exponents that can be compared with experiments. Furthermore, we have heterogeneity in the intrinsic frequencies as well as in connection weights, which was found to be crucial in case of threshold model simulations 39 . Previously, extended discrete threshold model simulations of activity avalanches on KKI-18 did not support a critical phase transition 39 .…”

Section: Introductionmentioning

confidence: 92%

“…Furthermore, we have heterogeneity in the intrinsic frequencies as well as in connection weights, which was found to be crucial in case of threshold model simulations 39 . Previously, extended discrete threshold model simulations of activity avalanches on KKI-18 did not support a critical phase transition 39 . It turned out the weight heterogenities were too strong to allow the occurrence of criticality.…”

Section: Introductionmentioning

confidence: 92%

Critical synchronization dynamics of the Kuramoto model on connectome and small world graphs

Ódor

Kelling

2019

Self Cite

The hypothesis, that cortical dynamics operates near criticality also suggests, that it exhibits universal critical exponents which marks the Kuramoto equation, a fundamental model for synchronization, as a prime candidate for an underlying universal model. Here, we determined the synchronization behavior of this model by solving it numerically on a large, weighted human connectome network, containing 836733 nodes, in an assumed homeostatic state. Since this graph has a topological dimension d < 4, a real synchronization phase transition is not possible in the thermodynamic limit, still we could locate a transition between partially synchronized and desynchronized states. At this crossover point we observe power-law–tailed synchronization durations, with τt ≃ 1.2(1), away from experimental values for the brain. For comparison, on a large two-dimensional lattice, having additional random, long-range links, we obtain a mean-field value: τt ≃ 1.6(1). However, below the transition of the connectome we found global coupling control-parameter dependent exponents 1 < τt ≤ 2, overlapping with the range of human brain experiments. We also studied the effects of random flipping of a small portion of link weights, mimicking a network with inhibitory interactions, and found similar results. The control-parameter dependent exponent suggests extended dynamical criticality below the transition point.

“…hubs with high in-degree strength . In order to regulate network excitability, following 70 , 71 , we here propose a variant of the HTC model, by normalizing locally each entry of the structural matrix according to the following normalization rule: …”

Section: Theoretical Frameworkmentioning

confidence: 99%

Homeostatic plasticity and emergence of functional networks in a whole-brain model at criticality

Rocha

Koçillari

Suweis

et al. 2018

Understanding the relationship between large-scale structural and functional brain networks remains a crucial issue in modern neuroscience. Recently, there has been growing interest in investigating the role of homeostatic plasticity mechanisms, across different spatiotemporal scales, in regulating network activity and brain functioning against a wide range of environmental conditions and brain states (e.g., during learning, development, ageing, neurological diseases). In the present study, we investigate how the inclusion of homeostatic plasticity in a stochastic whole-brain model, implemented as a normalization of the incoming node’s excitatory input, affects the macroscopic activity during rest and the formation of functional networks. Importantly, we address the structure-function relationship both at the group and individual-based levels. In this work, we show that normalization of the node’s excitatory input improves the correspondence between simulated neural patterns of the model and various brain functional data. Indeed, we find that the best match is achieved when the model control parameter is in its critical value and that normalization minimizes both the variability of the critical points and neuronal activity patterns among subjects. Therefore, our results suggest that the inclusion of homeostatic principles lead to more realistic brain activity consistent with the hallmarks of criticality. Our theoretical framework open new perspectives in personalized brain modeling with potential applications to investigate the deviation from criticality due to structural lesions (e.g. stroke) or brain disorders.