El-Bouri Wahbi K, Payne Stephen J
Department of Engineering Science, Institute of Biomedical Engineering, University of Oxford, Parks Road, Oxford OX1 3PJ, UK.
J Theor Biol. 2015 Sep 7;380:40-7. doi: 10.1016/j.jtbi.2015.05.011. Epub 2015 May 15.
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׳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(-1)100g(-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.
微血管系统在脑组织的血液灌注中起着至关重要的作用。目前的脑微血管系统模型是离散的，因此在计算变得难以承受之前，只能对小体素尺寸的灌注进行建模。需要更大的模型来与成像数据进行比较和验证。在这项工作中，采用多尺度均匀化方法来建立人类皮质毛细血管网络模型中血流的连续体模型。局部尺度血流方程的均匀化产生了达西定律的平均形式，渗透率张量封装了毛细血管床的拓扑结构。对人类皮质微血管系统的一个统计精确的网络模型进行了调整，以施加周期性，并在一系列体素尺寸上计算渗透率张量的元素。发现随着体素尺寸的增加，渗透率张量收敛到有效渗透率。这种收敛的渗透率张量是各向同性的，反映了脑微血管系统的网状结构，非对角项围绕零呈正态分布。确定了一个代表性单元体积为375μm，与有效渗透率的标准偏差为4.5%。使用收敛的渗透率值，计算出脑血流量约为55mLmin(-1)100g(-1)，这与实验值非常接近。这些结果为未来脑血管网络的多尺度建模开辟了可能性。
