Older people that had better upper or lower body muscle strength also had better cognitive function.
Interestingly, handgrip strength was not associated with better cognitive function. The study measured lower body strength (ie. leg extension, leg flexion, and leg press), upper body strength (ie. chest press and seated row), and handgrip strength which is often used as a proxy for upper body strength since it is easy to measure. The fact that both upper and lower body muscle strength but not handgrip strength was linked to better cognitive function suggests that handgrip strength may not be a good proxy to measure upper body strength.
Other studies have also found that lower body muscle strength is associated with improved brain aging. Some of the mechanisms that are thought to play a role in this association have to do with increased blood flow to the brain and also lower inflammatory processes which cause brain atrophy.