Abstract
In this review, we discuss critical dynamics of simple nonequilibrium models on large connectomes, obtained by diffusion MRI, representing the white matter of the human brain. In the first chapter, we overview graph theoretical and topological analysis of these networks, pointing out that universality allows selecting a representative network, the KKI-18, which has been used for dynamical simulation. The critical and sub-critical behaviour of simple, two- or three-state threshold models is discussed with special emphasis on rare-region effects leading to robust Griffiths phases (GP). Numerical results of synchronization phenomena, studied by the Kuramoto model, are also shown, leading to a continuous analog of the GP, termed frustrated synchronization. The models presented here exhibit dynamical scaling behaviour with exponents in agreement with brain experimental data if local homeostasis is provided.
Highlights
The critical and sub-critical behaviour of simple, two- or three-state threshold models is discussed with special emphasis on rare-region effects leading to robust Griffiths phases (GP)
The organization of resting-state activity presumably plays a critical role, because it requires a large part of the total energy budget [1, 2]
Neural variability makes the brain more efficient [128], and one must, consider its effect in modelling. To study this effect, extended dynamical simulations have been performed on large human connectome models
Summary
The organization of resting-state activity (i.e. the dynamics of the brain that causes switching between different ‘functional modes’) presumably plays a critical role, because it requires a large part of the total energy budget [1, 2]. Neuronal avalanches are cascading sequences of increasing activations that reveal critical behaviour, in which brain functions are optimized by enhancing, for example, input sensitivity and dynamic range [20]. The simplest one is the Hopf model [67], which has been used frequently in neuroscience because it can describe a critical point with scale-free avalanches that have a sharpened frequency response and enhanced input sensitivity Another complex model, describing more non-linearity, is the Kuramoto model [68, 69] that was studied analytically and computationally in the absence of frequency heterogeneity on a human connectome graph with 998 nodes and on hierarchical modular networks, in which moduli exist within moduli in a nested way at various scales [70]. We compare the emerging dynamical behaviour with those of a discrete threshold models on the same large human connectomes
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