We investigated age-related structural covariance properties and their associations with age and cognition using a large sample of 42,075 participants drawn from the UK Biobank. Firstly, with advancing age, there was a significant increase in the variance of whole brain structural covariance, indicating a greater variability in the relationships between brain regions. Additionally, we observed a decrease in entropy, suggesting a reduction in the complexity and diversity of these structural covariance patterns in older individuals. Secondly, there was significant and stable enrichment of pairwise correlations within the regions of the occipital lobe in the ageing process. Thirdly, both cortical thickness and subcortical volume covariances in the older groups were significantly different from those in the youngest group. This discrepancy was particularly pronounced among females. Fourthly, brain structural covariances were not stable though the ageing process, with the pairwise correlations between some brain regions strengthening and some weakening. Lastly, the significant pairwise correlations between brain regions were also associated with cognitive abilities.

Cortical integration means that different brain regions co-vary in pace or were shaped with similar biological processes (Nadig et al. 2021). Our findings suggest that brain structural covariance matrices have greater variability in older age, which may be speculated as cortical integration loosening in the older brain. Given the changes of structural covariance observed in the developmental stages during childhood and adolescence (Vijayakumar et al. 2021; Váša et al. 2018), we hypothesised that the structural covariance in the ageing brain would also be ‘dynamic’ rather than ‘static’; and our results confirmed this premise. One finding was that the variance of correlations within the matrix increased across 84 age groups, but the entropy decreased in the ageing brain. Similar phenomenon was found for Shannon entropy which is known to be negatively correlated with the variance (Wang et al. 2015). In the ageing brain, brain entropy quantifies brain’s capacity for adaptation, and smaller entropy corresponds to less complexity of the brain (Cieri et al. 2021). The decreased entropy in the ageing brain means the loss of complexity in brain connectivity networks, which may contribute to cognitive declines (Keshmiri 2020). Additionally, with ageing, females showed higher variance and lower entropy than males, suggesting potential differences in brain networks between genders. The observed sex differences on the whole brain variability properties may be attributed to known differences in brain structure and function between males and females (Canli et al. 2002; Cosgrove et al. 2007). However, our analysis did not specifically investigate their causal relationships, emphasizing the need for future studies designed to address this issue. Overall, our findings suggest that cortical integration appears to weaken in the ageing process.

By comparing covariance matrices of the youngest versus the older groups, we found that the older the age group was, the more significant the difference it had in comparison with the youngest group. There was a noticeable acceleration of the differences at ~ 64 years of age (age group #40), which suggests that age-related differences of human brain covariance begin at this age. This finding is in line with the findings of degenerative dementias, such as Alzheimer’s disease, whose rate of onset increases exponentially after the age of 65 (Fox and Schott 2004). It is worth noting that the structural covariances for females in older age diverged more from the youngest group than for males. This sex-related divergence was also evident in the differential rate of age-related increase of variance of whole brain covariances between males and females: females started lower than the males; they then surpassed the males at the age of 70 (Fig. 2).

The cortical thickness correlations between frontal lobe with other brain regions such as temporal, parietal, and occipital lobes were significantly different with ageing. For example, the correlations in superior and middle frontal-parietal, superior and middle frontal-occipital lobe were significantly decreased with advancing age. Notably, a positive correlation with age could signify either a strengthening of a pairwise correlation or a weakening of an anti-correlation. Similarly, a negative age correlation can imply either weakening or strengthening, depending on the direction and strength of the correlation. Associations between the anterior cingulate and transverse temporal regions are good examples to demonstrate this (Fig. S2, pair index 305 and 325). The existence of both positive and negative correlations in relation to older age between certain brain regions suggests that the interaction between these brain regions was variable: some correlations were strengthening, some weakening, and some were reversed in direction over time. Given that brain structures generally decline in the ageing brain, such as cortical thinning and subcortical atrophy, our finding demonstrates that there are diverse ageing-related differences occurring in different brain structures. We found that the regions in the occipital lobe were highly correlated with each other, and it has been reported that they share similar genetic underpinnings (Grasby et al. 2020; Hofer et al. 2020). This could also perhaps explain our observed enrichment of correlation coefficients within the occipital lobe. Our findings indicate that the enrichment in occipital correlations was significant though the ageing process, and these correlations were significantly associated with age as well. Additionally, our findings indicated that when mean cortical thickness was not controlled for, most pairwise correlations were positive and showed an increase across age groups, unlike the results when controlling for mean cortical thickness. This suggests that mean cortical thickness influences pairwise correlations, particularly in older age groups, where regions tend to be more closely associated.

Like cortical thickness, subcortical volumetric covariances were also associated with the ageing process. As one of the important subcortical regions, the hippocampus plays a critical role in memory and learning, as well as spatial navigation (Burgess et al. 2002). It is vulnerable to neurodegenerative diseases, especially Alzheimer’s disease (Mu and Gage 2011). In our analysis, the correlations between hippocampal volume with thalamus, putamen, and accumbens, were all significantly increased with increasing age, suggesting synchronised patterns in their volumes during the ageing process. The significantly decreased correlations between accumbens and caudate, putamen and pallidum, caudate and pallidum may indicate that these pairs of subcortical structures have independent trajectories during the ageing process. The amygdala and hippocampus are key components of the medial temporal lobe and are involved in emotional perception and regulation (Groen et al. 2010). Our study showed that the covariance between these two regions remained relatively stable during ageing.

We found significant associations between structural covariance and global cognition, processing speed, executive function, as well as memory. Previous work has shown that structural covariance of the default network was associated with cognitive ability (Spreng and Turner 2013), and that the synergy in the human brain may have evolved to support higher cognitive function (Luppi et al. 2022). Additionally, our finding of a high correlation between cognition and age (Fig. S8) was not on the individual level. Instead, the correlations were calculated by using the median age and median cognition of each group across all 84 age groups, thus the individual variance of each group for these measures was effectively smoothed out. Given the highly negative correlation between the age and cognition, as well as the associations between the structural covariance and age found in our study, it is not surprising that there were also associations between structural covariance and cognition, and their association direction was opposite to that of between structural covariance and age. In contrast to the positive associations between subcortical covariances and age, many subcortical covariances were found to be negatively associated with global cognition across all 84 age groups, especially the correlations between hippocampus and thalamus and those between caudate and thalamus.

Our study has some limitations. First, our data were cross-sectional in nature, which would not allow causal interpretation for the relationships of structural covariances and their relationships with cognition. Our study design which divided participants into 84 age groups allowed us to explore age related differences in structural covariance, but these differences should not be interpreted as real changes. Second, in order to explore the associations between structural covariance and age, we computed brain structural covariance in the group with 500 participants. This grouping was empirically explored and decided, and there may be biases associated with such grouping. We, therefore, also tested grouping of 300 and 800 participants. Robustness for each group increased with the increase of group size, but increasing group size would result in smaller number of groups. While there is no fixed rule for this, we did consider several factors, such as statistical power, stability and reliability of the correlations, the study design, and our research question. Third, we acknowledge the potential impact of noise on our findings, which may stem from FreeSurfer estimation error. Additionally, due to ageing, older populations may have greater variances in cortical thickness/volumetric data compared to younger (middle-aged) individuals. Finally, the generalisability of our results may not extend to other racial/ethnic groups, as we restricted our analyses to individuals of British ancestry.

In conclusion, we utilized a large cross-sectional dataset to provide an overview of associations between structural covariance and age, revealing varying regional interactions related to brain morphology in ageing. These findings could help better understand how brain regions interplay with each other during the ageing process.