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Deficits in memory are seen as a canonical sign of ageing and a prodrome to dementia in older adults. However, the nature of cognitive and brain changes across a wider aperture of adulthood is not well known. We quantify the relationship between cognitive function and brain morphology from mid-life to older adulthood, and the influence of age, sex, amyloid and genetic risk for dementia. We analyzed three observational cohorts (PISA, AIBL, ADNI) with cognitive, genetic and neuroimaging measures comprising a total of 1570 healthy mid-life and older adults (mean age 72, range 49-90 years, 1330 males) and 1365 age- and sex-matched adults with mild cognitive impairment or Alzheimer’s disease. Among healthy adults, we find robust modes of co-variation between regional sulcal width and multidomain cognitive function that change from mid-life to the older age range. The most prominent cortical changes in mid-life are predominantly associated with changes in executive functions, whereas they are most strongly associated with poorer memory function in older age. These cognitive changes are accompanied by an age-dependent pattern of sulcal widening. Amyloid exerts a weak, but significant, influence on cognition, but not on sulcal width. The APOE ɛ4 allele also exerts a weak influence on cognition, but only significantly in the (larger and older) AIBL cohort. These findings provide new insights into brain and cognition in mid-life and older adults, suggesting that cognitive screening in mid-life cohorts should encompass executive functions as well as memory.