Multi-scale homogenization of blood flow in 3-dimensional human cerebral microvascular networks
Journal
Journal of Theoretical Biology
Journal Volume
380
Pages
40-47
Date Issued
2015
Author(s)
Abstract
The microvasculature plays a crucial role in the perfusion of blood through cerebral tissue. Current models of the cerebral microvasculature are discrete, and hence only able to model the perfusion over small voxel sizes before becoming computationally prohibitive. Larger models are required to provide comparisons and validation against imaging data. In this work, multi-scale homogenization methods were employed to develop continuum models of blood flow in a capillary network model of the human cortex. Homogenization of the local scale blood flow equations produced an averaged form of Darcy[U+05F3]s law, with the permeability tensor encapsulating the capillary bed topology. A statistically accurate network model of the human cortex microvasculature was adapted to impose periodicity, and the elements of the permeability tensor calculated over a range of voxel sizes. The permeability tensor was found to converge to an effective permeability as voxel size increased. This converged permeability tensor was isotropic, reflecting the mesh-like structure of the cerebral microvasculature, with off-diagonal terms normally distributed about zero. A representative elementary volume of 375μm, with a standard deviation of 4.5% from the effective permeability, was determined. Using the converged permeability values, the cerebral blood flow was calculated to be around 55mLmin-1100g-1, which is in very close agreement with experimental values. These results open up the possibility of future multi-scale modeling of the cerebral vascular network. ? 2015 Elsevier Ltd.
Subjects
biomechanics
blood
continuum mechanics
imaging method
model validation
network analysis
Article
blood flow velocity
blood pressure
blood viscosity
blood volume
brain blood flow
brain perfusion
capillary density
capillary permeability
hematological procedure
homogenization
human
microvascularization
periodicity
pressure gradient
priority journal
biological model
blood flow
brain circulation
Cerebrovascular Circulation
Humans
Models, Biological
Regional Blood Flow
SDGs
Type
journal article