实体肿瘤内毛细血管—跨毛细血管壁—组织间质流体耦合流动的解析解

Intracapillary-Transcapillary-Interstitium Coupling Fluid flow in Solid Tumor

在微观尺度上建立实体肿瘤组织内单根毛细血管—跨毛细血管壁—组织间质内流体的不定常耦合流动模型,求解析解。模型中假设毛细血管为一可渗透刚性圆柱管,周围组织为各向同性多孔弹性介质。毛细血管内流动遵循Navier-Stokes方程,跨血管壁和间质内组织液流动采用Starling定律和Darcy定律。所得解析解结果显示①微观尺度上可忽略毛细血管内液体渗出量,管内流动可视为Poiseuille流动;②肿瘤组织间质压分布平坦,组织液流动缓慢,物质对流扩散困难。同时不定常解析解的取得也为今后肿瘤药物施药方案的进一步研究提供了数学上的准备。

At microscopic scales, we develop a coupled intracapillary transcapillary-interstitial fluid unsteady flow model, and obtain a set of analytical solutions. In this model, capillary is assumed as a permeable rigid cylinder embeded in an isotropic poroelastic medium （tumor tissues）. Intracapillary flow is governed by Navier-Stokes equations, transcapillary and interstitial fluid flow are described by Starling＇s law and Darcy＇s law respectively. The results theoretically confirm that： ①in microscale, fluid extravasation from capillary can be negligible, and Poiseuille＇s flow is a quite precise approximation for intracapillary flow; ②In tumor tissues, both pressure gradient and flow velocity is small, which make it difficult for convective transport. Unsteady analytical solutions will be prepared for future research about drug delivery in tumor.