Multiple Scales Approaches to Cerebral Blood Flow and Metabolism
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The cerebral vasculature comprises a highly complex network of blood vessels over a wide range of length scales, from a few micrometres to a few millimetres. The network is both highly connected and highly active in response to changes in both global stimuli (e.g., blood pressure) and local stimuli (e.g., local activation). In addition, the cerebral vasculature adapts over many different time scales, from a short-term response (seconds) to a medium-term response (hours) to a long-term response (years). Cerebrovascular and neurodegenerative diseases affect and are driven by changes over many different time scales [1]. Despite this, there has been relatively little work done to exploit the multiple length and time scales that are found in the brain. Our previous work has focused on the development of models over multiple length scales [2], exploiting perturbation methods and homogenisation techniques to enable the development of whole-brain models that can be run at low computational expense to simulate cerebral blood flow and oxygen transport over multiple length scales [3]. I will give an overview of this work and show how it can now be exploited to compute parameters such as transit time distribution and oxygen extraction fraction over multiple length scales. The current focus of our work is on the development of tools to simulate the behaviour over multiple time scales. I will first present our work on using multiple time scales to consider the movement of interstitial fluid (work in press) and then discuss how this can be further exploited, in conjunction with the constitutive mixture model, to consider the response of the cerebral vasculature to both short-term and long-term changes in parameters such as arterial blood pressure. This opens up the possibility of simulating the impact of interventions such as exercise on brain development over the course of a whole life span, and hence a greater understanding of the effects of factors such as hypertension, exercise, and sleep, on brain health. These multi-scale models thus have significant potential in both understanding brain behaviour and helping to promote better brain health in the general population through targeted interventions.