Investigation of effect of neglecting friction within the fluid in simulation of fluid flow insolid tumors

Investigation of effect of neglecting friction within the fluid in simulation of fluid flow insolid tumors

A solid tumor is investigated as porous media for simulation fluid flow through it. Most of the research used Darcy model for porous media. This model neglects the friction within the fluid and exchange of momentum between the fluid and solid phases. In this study the effect of these assumptions is studied by considering Brinkman model. A mathematical model of interstitial fluid flow is developed, based on the application of the governing equations for fluid flow, i.e., the conservation laws for mass and momentum, to physiological systems containing solid tumors. The discretized form of the governing equations, with appropriate boundary conditions, is developed for predefined tumor geometry. The interstitial fluid pressure and velocity are calculated using a numerical method, element based finite volume. Simulations of interstitial fluid transport in a homogeneous solid tumor demonstrate that, in a uniformly perfused tumor, the simplification used in Darcy model affects on interstitial velocity and Brinkman model predicts a lower value for interstitial velocity than Darcy model.