There is evidence that one of the mechanisms by which exercise benefits the brain involves exercise-induced circulating blood factors produced by the liver (1). There is evidence that one of the measurable anatomic correlates of brain benefits from regular exercise is increased brain volume (2). Links provided below with references.
REFERENCES
1. Horowitz AM, Fan X, Bieri G, et al. Blood factors transfer beneficial effects of exercise on neurogenesis and cognition to the aged brain. Science 10 Jul 2022;369:167-73.
2. Raji CA, Mesami S, Hashemi S, et al. Exercise-related physical activity relates to brain volumes in 19,125 individuals. J Alzheimers Dis 2024;97(2):829-39. doi: 10.3233/JAD-230740.