Conserved Ising Model on the Human Connectome

Abstract

Dynamical models implemented on the large scale architecture of the human brain may shed light on how function arises from the underlying structure. This is the case notably for simple abstract models, such as the Ising model. We compare the spin correlations of the Ising model and the empirical functional brain correlations, both at the single link level and at the modular level, and show that their match increases at the modular level in anesthesia, in line with recent results and theories. Moreover, we show that at the peak of the specific heat (the \it{critical state}) the spin correlations are minimally shaped by the underlying structural network, explaining how the best match between structure and function is obtained at the onset of criticality, as previously observed. These findings confirm that brain dynamics under anesthesia shows a departure from criticality and could open the way to novel perspectives when the conserved magnetization is interpreted in terms of an homeostatic principle imposed to neural activity.

References in corpus (9)

• Modularity and community structure in networks
• Emergent complex neural dynamics
• Weight-conserving characterization of complex functional brain networks
• Brain organization into resting state networks emerges at criticality on a model of the human connectome
• Griffiths phases and the stretching of criticality in brain networks
• Information-based fitness and the emergence of criticality in living systems
• Ising-like dynamics in large-scale functional brain networks
• Markers of criticality in phase synchronisation
• Graph coarse-graining reveals differences in the module-level structure of functional brain networks

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