Review of in silico models of cerebral blood flow in health and pathology

In this review, we provide a summary of the state-of-the-art in the in silico modelling of cerebral blood flow (CBF) and its application in in silico clinical trials. CBF plays a key role in the transport of nutrients, including oxygen and glucose, to brain cells, and the cerebral vasculature is a highly complex, multi-scale, dynamic system that acts to ensure that supply and demand of these nutrients are continuously balanced. It also plays a key role in the transport of other substances, such as recombinant tissue-plasminogen activator, to brain tissue. Any dysfunction in CBF can rapidly lead to cell death and permanent damage to brain regions, leading to loss of bodily functions and death. The complexity of the cerebral vasculature and the difficulty in obtaining accurate anatomical information combine to make mathematical models of CBF key in understanding brain supply, diagnosis of cerebrovascular disease, quantification of the effects of thrombi, selection of the optimum intervention, and neurosurgical planning. Similar in silico models have now been widely applied in a variety of body organs (most notably in the heart), but models of CBF are still far behind. The increased availability of experimental data in the last 15 years however has enabled these models to develop more rapidly and this progress is the focus of this review. We thus present a brief review of the cerebral vasculature and the mathematical foundations that underpin CBF in both the microvasculature and the macrovasculature. We also demonstrate how such models can be applied in the context of cerebral diseases and show how this work has recently been expanded to in silico trials for the first time. Most work to date in this context has been performed for ischaemic stroke or cerebral aneurysms, but these in-silico models have many other applications in neurodegenerative diseases where mathematical models have a vital role to play in testing hypotheses and providing test beds for clinical interventions.