No Arabic abstract
We implement the dynamical Ising model on the large scale architecture of white matter connections of healthy subjects in the age range 4-85 years, and analyze the dynamics in terms of the synergy, a quantity measuring the extent to which the joint state of pairs of variables is projected onto the dynamics of a target one. We find that the amount of synergy in explaining the dynamics of the hubs of the structural connectivity (in terms of degree strength) peaks before the critical temperature, and can thus be considered as a precursor of a critical transition. Conversely the greatest amount of synergy goes into explaining the dynamics of more central nodes. We also find that the aging of the structural connectivity is associated to significant changes in the simulated dynamics: there are brain regions whose synergy decreases with age, in particular the frontal pole, the Subcallosal area and the Supplementary Motor area; these areas could then be more likely to show a decline in terms of the capability to perform higher order computation (if structural connectivity was the sole variable). On the other hand, several regions in the temporal cortex show a positive correlation with age in the first 30 years of life, i.e. during brain maturation.
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 $simeq 10^6$ nodes and $simeq 10^8$ 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 $sigma$ of these networks. While $sigma$ 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.
Anatomical connectivity imposes strong constraints on brain function, but there is no general agreement about principles that govern its organization. Based on extensive quantitative data we tested the power of three models to predict connections of the primate cerebral cortex: architectonic similarity (structural model), spatial proximity (distance model) and thickness similarity (thickness model). Architectonic similarity showed the strongest and most consistent influence on connection features. This parameter was strongly associated with the presence or absence of inter-areal connections and when integrated with spatial distance, the model allowed predicting the existence of projections with very high accuracy. Moreover, architectonic similarity was strongly related to the laminar pattern of projections origins, and the absolute number of cortical connections of an area. By contrast, cortical thickness similarity and distance were not systematically related to connection features. These findings suggest that cortical architecture provides a general organizing principle for connections in the primate brain.
We show that in model neuronal cultures, where the probability of interneuronal connection formation decreases exponentially with increasing distance between the neurons, there exists a small number of spatial nucleation centers of a network spike, from where the synchronous spiking activity starts propagating in the network typically in the form of circular traveling waves. The number of nucleation centers and their spatial locations are unique and unchanged for a given realization of neuronal network but are different for different networks. In contrast, if the probability of interneuronal connection formation is independent of the distance between neurons, then the nucleation centers do not arise and the synchronization of spiking activity during a network spike occurs spatially uniform throughout the network. Therefore one can conclude that spatial proximity of connections between neurons is important for the formation of nucleation centers. It is also shown that fluctuations of the spatial density of neurons at their random homogeneous distribution typical for the experiments $textit{in vitro}$ do not determine the locations of the nucleation centers. The simulation results are qualitatively consistent with the experimental observations.
We introduce an exactly integrable version of the well-known leaky integrate-and-fire (LIF) model, with continuous membrane potential at the spiking event, the c-LIF. We investigate the dynamical regimes of a fully connected network of excitatory c-LIF neurons in the presence of short-term synaptic plasticity. By varying the coupling strength among neurons, we show that a complex chaotic dynamics arises, characterized by scale free avalanches. The origin of this phenomenon in the c-LIF can be related to the order symmetry breaking in neurons spike-times, which corresponds to the onset of a broad activity distribution. Our analysis uncovers a general mechanism through which networks of simple neurons can be attracted to a complex basin in the phase space.
In this work, we study the extent to which structural connectomes and topological derivative measures are unique to individual changes within human brains. To do so, we classify structural connectome pairs from two large longitudinal datasets as either belonging to the same individual or not. Our data is comprised of 227 individuals from the Alzheimers Disease Neuroimaging Initiative (ADNI) and 226 from the Parkinsons Progression Markers Initiative (PPMI). We achieve 0.99 area under the ROC curve score for features which represent either weights or network structure of the connectomes (node degrees, PageRank and local efficiency). Our approach may be useful for eliminating noisy features as a preprocessing step in brain aging studies and early diagnosis classification problems.