Multi‐scale modelling of the effects of ageing, hypertension and exercise on the cerebral vasculature

Ageing and hypertension both have substantial, well-documented effects on the cerebral vasculature. The effects of aerobic exercise on cerebrovascular function and development, although less well understood, have also recently received significantly increased attention. There is now clear evidence that aerobic exercise yields both short- and long-term changes to cerebrovascular health, with significant potential to improve population brain health. However, there has as yet been no mathematical model of this, making it challenging to quantify the effects of aerobic exercise. One reason for this is the very different time scales between exercise (minutes/hours) and cerebrovascular development (years/decades). Here, a new mathematical model is proposed, one that incorporates short-term changes within a longer time scale. The model is calibrated against various experimental data sources and used to quantify the effects of ageing, hypertension, and exercise interventions on lifetime cerebrovascular health. The model predicts that high-intensity exercise has a significant positive effect on cerebral health; that antihypertensive treatment has a significant positive effect even after prolonged periods of hypertension; and that different interventions can strongly interact with each other. This model provides the foundation for future quantitative investigations into the critical role of aerobic exercise and other interventions in cerebrovascular health. KEY POINTS: Exercise has a significant and lifetime positive effect on the cerebral vasculature, which can counterbalance the negative effects of ageing and hypertension. A new model is presented that incorporates the effects of all three effects on the cerebral vasculature, using multiple time scales to include both short- and long-term effects. The model is calibrated against a range of experimental data and used to quantify the effects of different exercise regimes on cerebrovascular health for the first time. This model can be used in future to explore the lifetime effects of different lifestyles and interventions on population brain health.