Mathematical Institute, 24-29 St. Giles, Oxford, OX1 3LB, UK.
Bull Math Biol. 2010 Aug;72(6):1464-91. doi: 10.1007/s11538-010-9504-9. Epub 2010 Jan 23.
A model for fluid and drug transport through the leaky neovasculature and porous interstitium of a solid tumour is developed. The transport problems are posed on a micro-scale characterized by the inter-capillary distance, and the method of multiple scales is used to derive the continuum equations describing fluid and drug transport on the length scale of the tumour (under the assumption of a spatially periodic microstructure). The fluid equations comprise a double porous medium, with coupled Darcy flow through the interstitium and vasculature, whereas the drug equations comprise advection-reaction equations; in each case the dependence of the transport coefficients on the vascular geometry is determined by solving micro-scale cell problems.
建立了一个模型，用于描述通过实体瘤的渗漏新生血管和多孔间质的流体和药物传输。传输问题在毛细血管间距离为特征的微尺度上提出，并使用多尺度方法推导出描述肿瘤长度尺度上（在假定空间周期性微结构的情况下）流体和药物传输的连续方程。流体方程包括一个双重多孔介质，通过间质和脉管系统的耦合达西流，而药物方程包括对流-反应方程；在每种情况下，通过求解微尺度细胞问题来确定传输系数对脉管几何形状的依赖性。
