Abstract:
:The cerebral microvasculature plays a key role in the transport of blood and the delivery of nutrients to the cells that perform brain function. Although recent advances in experimental imaging techniques mean that its structure and function can be interrogated to very small length scales, allowing individual vessels to be mapped to a fraction of 1 μm, these techniques currently remain confined to animal models. In-vivo human data can only be obtained at a much coarser length scale, of order 1 mm, meaning that mathematical models of the microvasculature play a key role in interpreting flow and metabolism data. However, there are close to 10,000 vessels even within a single voxel of size 1 mm3. Given the number of vessels present within a typical voxel and the complexity of the governing equations for flow and volume changes, it is computationally challenging to solve these in full, particularly when considering dynamic changes, such as those found in response to neural activation. We thus consider here the governing equations and some of the simplifications that have been proposed in order more rigorously to justify in what generations of blood vessels these approximations are valid. We show that two approximations (neglecting the advection term and assuming a quasi-steady state solution for blood volume) can be applied throughout the cerebral vasculature and that two further approximations (a simple first order differential relationship between inlet and outlet flows and inlet and outlet pressures, and matching of static pressure at nodes) can be applied in vessels smaller than approximately 1 mm in diameter. We then show how these results can be applied in solving flow fields within cerebral vascular networks providing a simplified yet rigorous approach to solving dynamic flow fields and compare the results to those obtained with alternative approaches. We thus provide a framework to model cerebral blood flow and volume within the cerebral vasculature that can be used, particularly at sub human imaging length scales, to provide greater insight into the behaviour of blood flow and volume in the cerebral vasculature.
journal_name
Neuroimagejournal_title
NeuroImageauthors
Payne SJ,El-Bouri WKdoi
10.1016/j.neuroimage.2018.04.037subject
Has Abstractpub_date
2018-08-01 00:00:00pages
124-137eissn
1053-8119issn
1095-9572pii
S1053-8119(18)30347-1journal_volume
176pub_type
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