Green's function methods for analysis of oxygen delivery to tissue by microvascular networks
Green's function methods for analysis of oxygen delivery to tissue by microvascular networks
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DOI：
10.1114/b:abme.0000049036.08817.44
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发表时间：
2004-11-01
影响因子：
3.8
通讯作者：
Dewhirst, MW
中科院分区：
文献类型：
--
作者：
Secomb, TW;Hsu, R;Dewhirst, MW
向组织输送氧气是循环系统的一项基本功能。氧气扩散到耗氧组织的距离很小，因此组织的氧合作用严重依赖于组织中微血管的空间排列。已经开发出理论方法来模拟微血管网络周围组织中氧水平的空间分布。在这里，提出了基于格林函数方法的数值方法，用于从骨骼肌、脑和肿瘤组织的观察中获得真实的三维网络几何形状。相对于有限差分方法，格林函数方法减少了数值公式中的未知数，即使对于复杂的血管几何也允许快速计算。通常，计算区域外部的边界条件是未知的。施加无通量边界条件可能会导致对组织区域缺氧程度的夸大估计。描述了一种新版本的方法，该方法避免了这一问题，并且可以应用于任意形状的组织域。
Delivery of oxygen to tissue is an essential function of the circulatory system. The distance that oxygen can diffuse into oxygen-consuming tissue is small, and so tissue oxygenation is critically dependent on the spatial arrangement of microvessels in tissue. Theoretical methods have been developed to simulate the spatial distribution of oxygen levels in tissue surrounding a network of microvessels. Here, numerical methods based on a Green's function approach are presented, for realistic three-dimensional network geometries derived from observations of skeletal muscle, brain, and tumor tissues. Relative to finite-difference methods, the Green's function approach reduces the number of unknowns in the numerical formulation and allows rapid computations even for complex vascular geometries. Generally, the boundary conditions on the exterior of the computational domain are not known. Imposition of a no-flux boundary condition can lead to exaggerated estimates of the extent of hypoxia in the tissue region. A new version of the method is described that avoids this problem and can be applied to arbitrarily shaped tissue domains.