Fractal Dimension Analysis: Unlocking Ageing-Related Changes in Brain Criticality

Fractal Dimension (FD) is a powerful computational neuroscience method that captures local oscillations and network topology through univariate measures. A central concept in neuroscience is criticality, which describes the brain's optimal operating state at the edge of chaos, balancing stability and flexibility. Quantifying this delicate balance is a frontier in neuroscience.

The Hurst Exponent (HE) is one of the most popular FD measures and a key way to quantify the balance of criticality. The HE measures scale-free, long-term memory in temporal dynamics and has been confirmed as an essential performance indicator of brain dynamics.

In this research, we investigated the effect of healthy ageing on known resting-state functional networks (RSNs) using the HE. Using Group-Independent Component Analysis (GICA) on fMRI data from young adults (YAs) and older adults (OAs), we characterised baseline fractality in the YA group. We found that increasing HE values differentiates between subcortical, primary, and cognitive networks. This suggests that greater temporal complexity may reflect increased integrative processing in the brain.

Comparing the groups revealed widespread significant differences between young and old adults, with a general loss of scale-free long-term persistence (a decline in HE) across networks. This change may be specific to a loss of integration capability in higher cognitive functions.

Specifically, the visuospatial and dorsal default mode networks (dDMNs) were the most affected by ageing. Machine learning classifiers highlighted them as the best predictors of ageing based on the HE. Interestingly, these high-order networks exhibited a signal complexity level in OAs that resembled that of subcortical structures. We also observed increased segregation (functional decoupling) within the dDMN, as the ventral part (vDMN) showed no significant difference in HE between YA and OA.

The HE can detect early deviations from optimal function and may mark the transition from healthy ageing to pathology.