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Effect of fluid friction on interstitial fluid flow coupled with blood flow through solid tumor microvascular network.

Sefidgar M, Soltani M, Raahemifar K, Bazmara H - Comput Math Methods Med (2015)

Bottom Line: In this study, the effect of these assumptions is studied by considering Brinkman model.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.

View Article: PubMed Central - PubMed

Affiliation: Department of Engineering and Technology, IKI University, Qazvin 34148-96818, Iran.

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.

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Comparison of interstitial velocity along horizontal line in tumor region for Darcy and Brinkman models.
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fig11: Comparison of interstitial velocity along horizontal line in tumor region for Darcy and Brinkman models.

Mentions: The velocity profiles along horizontal and vertical lines from the tumor center are illustrated in Figures 11 and 12, respectively. Results show that the main differences between two models occurred near the tumor boundary. Prolate shapes show the effect of friction model more significant than other tumor shapes. In prolate type of tumor, the effect of pressure gradient is higher than other shapes of tumor. This effect is investigated in our previous work [11]. With increasing the pressure gradient in tumor region which has important role in the value of velocity, the effect of consideration of fluid friction on interstitial fluid flow is increased.


Effect of fluid friction on interstitial fluid flow coupled with blood flow through solid tumor microvascular network.

Sefidgar M, Soltani M, Raahemifar K, Bazmara H - Comput Math Methods Med (2015)

Comparison of interstitial velocity along horizontal line in tumor region for Darcy and Brinkman models.
© Copyright Policy - open-access
Related In: Results  -  Collection

Show All Figures
getmorefigures.php?uid=PMC4417563&req=5

fig11: Comparison of interstitial velocity along horizontal line in tumor region for Darcy and Brinkman models.
Mentions: The velocity profiles along horizontal and vertical lines from the tumor center are illustrated in Figures 11 and 12, respectively. Results show that the main differences between two models occurred near the tumor boundary. Prolate shapes show the effect of friction model more significant than other tumor shapes. In prolate type of tumor, the effect of pressure gradient is higher than other shapes of tumor. This effect is investigated in our previous work [11]. With increasing the pressure gradient in tumor region which has important role in the value of velocity, the effect of consideration of fluid friction on interstitial fluid flow is increased.

Bottom Line: In this study, the effect of these assumptions is studied by considering Brinkman model.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.

View Article: PubMed Central - PubMed

Affiliation: Department of Engineering and Technology, IKI University, Qazvin 34148-96818, Iran.

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.

Show MeSH
Related in: MedlinePlus