Interstitial flow in cancerous tissue: Effect of fluid friction

A solid tumor is investigated as porous media for simulation fluid flow through it. Most of the research used Darcy model for porous media. In Darcy model the fluid friction is neglected and some simplified assumption is implemented. In this study the effect of these assumptions is studied by considering Brinkman model. A multi scale mathematical method which calculates fluid flow to a solid tumor is used in this study to investigate how neglecting fluid friction affects on solid tumor simulation. The mathematical method involves processes such as blood flow through vessels and solute and fluid diffusion, convective transport in extracellular matrix, and extravasation from blood vessels. The sprouting angiogenesis model is used for generating capillary network and then fluid flow governing equations are implemented to calculate blood flow through the tumor-induced capillary network Finally, two models of porous media are used for modeling fluid flow in normal and tumor tissues. Simulations of interstitial fluid transport in a solid tumor demonstrate that the simplification used in Darcy model affects on interstitial velocity and Brinkman model predicts a lower value for interstitial velocity than Darcy model.