均质化(气候)
微尺度化学
毛细管作用
流体力学
多孔介质
平流
偏微分方程
机械
多尺度建模
混合理论
物理
经典力学
材料科学
数学
数学分析
多孔性
化学
热力学
统计
生物
生物多样性
数学教育
计算化学
复合材料
混合模型
生态学
作者
Raimondo Penta,Davide Carlo Ambrosi,Alfio Quarteroni
标识
DOI:10.1142/s0218202515500037
摘要
A system of differential equations for coupled fluid and drug transport in vascularized (malignant) tissues is derived by a multiscale expansion. We start from mass and momentum balance equations, stated in the physical domain, geometrically characterized by the intercapillary distance (the microscale). The Kedem–Katchalsky equations are used to account for blood and drug exchange across the capillary walls. The multiscale technique (homogenization) is used to formulate continuum equations describing the coupling of fluid and drug transport on the tumor length scale (the macroscale), under the assumption of local periodicity; macroscale variations of the microstructure account for spatial heterogeneities of the angiogenic capillary network. A double porous medium model for the fluid dynamics in the tumor is obtained, where the drug dynamics is represented by a double advection–diffusion–reaction model. The homogenized equations are straightforward to approximate, as the role of the vascular geometry is recovered at an average level by solving standard cell differential problems. Fluid and drug fluxes now read as effective mass sources in the macroscale model, which upscale the interplay between blood and drug dynamics on the tissue scale. We aim to provide a theoretical setting for a better understanding of the design of effective anti-cancer therapies.
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