
Computational Models of Brain Multiphysics at Multiple Time Scales
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The cerebral vasculature is a highly complex, coupled, active and dynamic system that responds to multiple stimuli to maintain cerebral perfusion within tight limits. Substantial work has been performed to model this system over a wide range of length scales, from the microvasculature to the macrocirculation. However, there has been much less work to simulate the cerebral vasculature over multiple time scales, despite the fact that processes occur over time scales from fractions of a second to many decades. In this talk, I will present recent work on modelling the cerebral vasculature across multiple time scales. This will first consider the different time scales between blood flow and interstitial flow and show how the use of multiple scales approaches can simplify this problem. Then, I will present work on the calculation of transit times and show how these results can be used to interrogate the structural properties of the cerebral circulation and their relationship to cerebral function. Finally, I will present recent work on the effects of ageing, hypertension and exercise on the cerebral circulation. Again, the use of multiple scales approaches allows for drastic simplification of the governing equations into computationally efficient forms. These results show how the behaviour of the cerebral circulation can be studied across both multiple length scales and multiple time scales. Such results provide for the first time an opportunity to explore the quantitative impact of interventions, such as exercise and antihypertensive medication, on lifetime behaviour and thus open up the possibility of integration with disease progression models and lifetime risk calculations, with multiphysics models playing a full part.