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.
Highlights
For examining the results for generated network induced by angiogenesis, results obtained by mathematical method are in qualitative agreement with the experimental results carried out in animal corneal models [23, 24] and mathematical model presented by Anderson et al [17, 19]
Since the mathematical model which is used for network generation is not a physical model, all vessels do not make a loop in the network. These vessels are removed by a mathematical pruning method before the simulation of blood flow in the capillary network is calculated
The results showed that neglecting fluid friction can
Summary
Based on findings from clinical applications, most drug treatments fail to eliminate malignant tumors completely even though drug delivery through systemic administration may inhibit their growth [1]. Better understanding of tumor formation is crucial in developing more effective therapeutics [2]. For this purpose, nowadays, solid tumor modeling and simulation results are used to predict how therapeutic drugs are transported to tumor cells by blood flow through capillaries and tissues. There are two approaches in the simulation of fluid flow to solid tumors: macroscopic and microscopic. Only the distribution of variables, such as interstitial pressure and concentration, over the length scale of the tumor radius is important. Characteristics such as structure of microvascular network, blood flow through microvascular network, and interaction between microvascular wall and flow in peripheral flow are involved directly in the model
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