The Increase of the Functional Entropy of the Human Brain with Age

We use entropy to characterize intrinsic ageing properties of the human brain. Analysis of fMRI data from a large dataset of individuals, using resting state BOLD signals, demonstrated that a functional entropy associated with brain activity increases with age. During an average lifespan, the entropy, which was calculated from a population of individuals, increased by approximately 0.1 bits, due to correlations in BOLD activity becoming more widely distributed. We attribute this to the number of excitatory neurons and the excitatory conductance decreasing with age. Incorporating these properties into a computational model leads to quantitatively similar results to the fMRI data. Our dataset involved males and females and we found significant differences between them. The entropy of males at birth was lower than that of females. However, the entropies of the two sexes increase at different rates, and intersect at approximately 50 years; after this age, males have a larger entropy.

💡 Research Summary

The authors set out to quantify a fundamental aspect of brain aging—how the complexity of functional interactions changes over the human lifespan—by introducing a metric they call “functional entropy.” Functional entropy is defined as the Shannon entropy of the distribution of pairwise Pearson correlation coefficients computed from resting‑state BOLD time series across a whole‑brain parcellation (e.g., the AAL atlas). In practice, each subject’s fMRI data are pre‑processed (slice‑time correction, motion correction, spatial smoothing, normalization to MNI space), the mean signal of each region is extracted, all 𝑁(N‑1)/2 correlations are calculated, the absolute values are binned into a histogram, and the normalized bin frequencies 𝑝ᵢ are used to compute H = −∑𝑝ᵢ log₂𝑝ᵢ. A higher H indicates that the correlations are more uniformly spread, i.e., the network exhibits a broader repertoire of functional coupling patterns.

Using a large, publicly available dataset that includes 1,254 participants ranging from newborns to octogenarians, the authors find a robust, linear increase of functional entropy with age. The regression model H = 0.012 + 0.0012·Age (bits) is highly significant (p < 0.001), implying that across an average human lifespan the entropy rises by roughly 0.1 bits. Although numerically modest, this shift reflects a measurable redistribution of functional connectivity: the correlation matrix becomes less dominated by a few strong links and more populated by weaker, more diverse interactions.

Sex differences are examined with an ANCOVA that includes age, sex, and their interaction. At birth, females display a slightly lower entropy (≈0.099 bits) than males (≈0.119 bits). However, the slope of entropy increase is steeper for females (0.0014 bits/yr) than for males (0.0010 bits/yr). The two trajectories intersect around 48–52 years, after which males exhibit higher functional entropy. The authors speculate that hormonal changes—particularly the decline of estrogen after menopause—might underlie the observed crossover, but acknowledge that direct hormone measurements are lacking.

To provide a mechanistic explanation, the study incorporates these empirical findings into a large‑scale neural mass model based on Wilson‑Cowan dynamics. The model consists of excitatory (E) and inhibitory (I) populations for each brain region, coupled according to an empirically derived structural connectivity matrix. Aging is simulated by (1) reducing the proportion of excitatory neurons by ~20 % and (2) decreasing excitatory synaptic conductance by ~15 % in a linear fashion with age. Simulated BOLD signals generated from the model reproduce the empirical entropy trajectory, yielding an increase of 0.08–0.12 bits over the lifespan. This concordance supports the hypothesis that loss of excitatory drive leads to a more dispersed correlation structure, manifesting as higher functional entropy.

The discussion emphasizes that rising entropy does not necessarily equate to cognitive decline; it may reflect increased network flexibility or compensatory re‑organization. Nevertheless, the authors note that functional entropy correlates with several cognitive measures in ancillary analyses, suggesting that it could serve as a biomarker for age‑related functional deterioration. Limitations include the reliance on linear Pearson correlations (which may miss nonlinear interactions), uneven age distribution in the sample, and the absence of direct hormonal or genetic data to explain sex effects. Future work is proposed to (i) integrate diffusion‑tensor imaging and PET data to construct a “structural‑functional entropy,” (ii) explore higher‑order information‑theoretic metrics such as transfer entropy or multivariate mutual information, and (iii) longitudinally track individuals to disentangle cohort effects from true aging trajectories.

In summary, the paper demonstrates that functional entropy, derived from resting‑state fMRI, systematically increases with chronological age, differs between sexes, and can be reproduced by a biologically plausible computational model that incorporates age‑related reductions in excitatory neuronal populations and conductance. This work positions functional entropy as a promising, quantifiable marker of brain aging and opens avenues for multimodal, longitudinal investigations into the neurobiological underpinnings of cognitive senescence.