Phys Rev E. 2016 Dec;94(6-1):062411. doi: 10.1103/PhysRevE.94.062411.

Critical dynamics on a large human Open Connectome network

Géza Ódor 

From the Department of Complex Systems MTA-EK-MFA, Research Center for Energy, Hungarian Academy of Sciences, Budapest.

Correspondence should be addressed to Géza Ódor, Department of Complex Systems MTA-EK-MFA, Research Center for Energy, Hungarian Academy of Sciences, Budapest H1121, Konkoly Thege str. 29-33.




Extended numerical simulations of threshold models have been performed on a human brain network with N = 836733 connected nodes, available from the Open Connectome Project [1]. These graphs exibit highly heterogenous, hierarchical modular topology (see Figure 1), as well as fat tailed link edge distributions [2]. While in the case of simple spreading models, like the Contact Process [3], a sharp discontinuous phase transition, without any critical dynamics arises, models with variable activation thresholds exhibit extended scaling regions with dynamical power-laws. This is attributed to fact that rare region effects [4], stemming from the topological or interaction heterogeneity of the graph, can become relevant when the input sensitivity of the nodes is equalized [5]. Nonuniversal power-law avalanche size and time distributions have been found (see Figure 2), with scaling exponents agreeing with the values obtained in electrode experiments of the human brain [6]. These occur below the critical point in an extended control parameter space region, even without the assumption of a self-organization mechanism. That means that without any fine self-tuning mechanism the system exhibits dynamical criticality, optimizing computational power and senitivity of the brain. Probably the most important result of the study [5] is that negative link weights enable local, sustained activity, observed in the brain and promote strong rare-region (Griffiths) effects without the fragmentation of the neural network. Thus, connectomes with high graph dimensions are subject to strong rare-region effects and can show measurable Griffiths effects. Another important observation is that these power-laws occur in a single network, without the need of graph sample averaging [7], due to the modular topological structure. Effects of link directedness, as well as the consequence of inhibitory connections are studied. Robustness with respect to a 20% random removal of edges suggest that connectome graph generation errors do not influence these simulated Griffiths effects qualitatively [3].





Figure 1. Modules of the KKI-18 connectome. Size of the circles show size of modules.

Figure 2. Activity size distributions of the simulated Avelanches for different control parametes. Dashed lines show fitted power-laws.




[1] See:
[2] M. T. Gastner and G. Ódor. “The topology of large Open Connectome networks for the human brain”,
Scientific Reports, vol. 5 , pp. 14451, 2015.
[3] See: G. Ódor. “Universality in nonequilibrium lattice models”, World Scientific 2008, Singapore
[4] R. B. Griffiths. Phys. Rev. Letters, vol. 23, pp. 17, 1969.
[5] G. Ódor. “Critical dynamics on a large human Open Connectome network”, Physical Review E, vol. 94, pp. 062411, 2016.
[6] J. M. Beggs and D. Plenz. “Neuronal avalanches in neocortical, circuits”, J. Neuroscience vol. 23, pp. 11167, 2003.
[7] G. Ódor, R. Dickman, and Gergely Ódor. “Griffiths phases and localization in hierarchical modular networks”, Scientific Reports vol. 5, pp. 14451, 2015.