Investigating Spatial Signatures of Spin-Glass Criticality in the Human Brain

Abstract

The human brain is a highly complex network of interconnected neurons exhibiting emergent phenomena. The theory of the brain functioning at a critical state - near a second-order phase transition where its capabilities for memory, learning, and information processing - has gained widespread popularity in recent years. This criticality has often been likened to the critical state observed in the Ising model, which is influenced by a temperature parameter. Neural dysfunction due to neurodegenerative conditions such as Alzheimer’s Disease influences the proximity to this critical state. We study the disrupted proximity to criticality of the dysfunctional Alzheimer’s brain using a spin-lattice pairwise maximum entropy model where connectivity is inferred from resting-state fMRI data. The closeness to criticality is quantified through the critical temperature, which is derived by analysing the susceptibility of the system. We find an insignificant difference between the two classes, which we attribute to the dependence of susceptibility on spatial dynamics, with the hypothesis that the existence of a spin-glass-like criticality could hinder the sensitivity of this metric. To characterise the nature of brain criticality, we explore the spatial characteristics and temporal correlations of criticality for both normal and Alzheimer’s brains. We find a weak distinction in the spatial dynamics between the two classes - the sizes and number of spatial domains formed, as well as the self-averaging behaviour of the system, were not found to vary significantly. However, we notice a stretched exponential form in the temporal relaxation times, which is characteristic of spin-glasses. We find a significant difference between the relaxation behaviour of Alzheimer’s and Cognitively Normal subjects. In spin-glass systems, a third phase exists near the phase transition boundary - the spin-glass phase. This phase is characterised by frustration and competing interactions. It allows for the emergence of complex properties such as long-term memory, which are features not found in simple Ising-like criticality. Despite the difference in closeness to criticality, the lack of a significant distinction in the spatial correlation lengths can be attributed to local frustrations, which might not allow the system to reach equilibrium domain distributions. Based on the differences observed between the spatial and temporal correlations, we conclude that the criticality found in the brain is more akin to a spin-glass criticality, which is more sensitive to temporal rather than spatial measures.