Effect of Fluid Friction on Interstitial Fluid Flow Coupled with Blood Flow through Solid Tumor Microvascular Network

Abstract

A solid tumor is investigated as porous media for fluid flow simulation. Most of the studies use Darcy model for porous media. In Darcy model, the fluid friction is neglected and a few simplified assumptions are implemented. In this study, the effect of these assumptions is studied by considering Brinkman model. A multiscale mathematical method which calculates fluid flow to a solid tumor is used in this study to investigate how neglecting fluid friction affects the 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, the two models of porous media are used for modeling fluid flow in normal and tumor tissues in three different shapes of tumors. Simulations of interstitial fluid transport in a solid tumor demonstrate that the simplifications used in Darcy model affect the interstitial velocity and Brinkman model predicts a lower value for interstitial velocity than the values that Darcy model predicts.

Numerical simulations of the microvascular fluid balance with a non-linear model of the lymphatic system

“…They are typically used with reference to di↵erent applications. Without aiming to provide a complete literature review, we report application to: (i) oncology [25,26,27,28]; (ii) cerebral flow [29]; and (iii) tissue oxygenation [30,31]. In some of these models the contribute of the lymphatic system on the interstitial flow is considered.…”

“…Blood flow inside the capillaries, considered as cylinders with rigid vascular walls [34], is modeled using Poiseuille's law in terms of vessel radius R and a fluid viscosity µ v . Lymphatic vessel geometry is usually not included in the simulation of microcirculation [27,32,34] Using p for hydraulic pressures and u for fluid velocity, the problem to be…”

“…Linear models of the net lymphatic drainage (' lymphatics ) are typically defined using a similar approach to the one already used for the capillary vessels [14,27,32,34], based on the Starling's principle (2). Since in our simulations we consider only the vascular geometry and not the geometry of lymphatic vessels, the equation features the term S/V | LF , which is the ratio of exchange surface over the tissue volume.…”

“…Since in our simulations we consider only the vascular geometry and not the geometry of lymphatic vessels, the equation features the term S/V | LF , which is the ratio of exchange surface over the tissue volume. In addition, the high permeability of lymphatic vessels [14,27,32,34] allows us to neglect the oncotic gradient across the membrane obtaining an expression function only of hydraulic pressures (3). Therefore in this case the lymphatic drainage '…”

Activation of Apoptotic Signal in Endothelial Cells through Intracellular Signaling Molecules Blockade in Tumor-Induced Angiogenesis

“…In the next stages, the loops elongate, fuse with other sprouts or loops, and create a network of capillaries, which circulates blood in the area that is closer to or inside the tumor. The capillary network has a vital role in further tumor growth [ 9 – 11 ].…”