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Int J Biol Sci 2013; 9(10):1050-1056. doi:10.7150/ijbs.7242

Research Paper

Simulation of Interstitial Fluid Flow in Ligaments: Comparison among Stokes, Brinkman and Darcy Models

Wei Yao, Zhoufeng Shen, Guanghong Ding

Department of Mechanics and Engineering Science, Fudan University, Shanghai Research Center of Acupuncture, Shanghai, 200433.

Abstract

In this paper, we use Stokes, Brinkman and Darcy equations to approximate the porous continuum media of ligament tissues respectively, simulate the flow field with FLUENT software, and study the shear stress on the cell surface due to the interstitial fluid flow. Since the Brinkman equation approaches Stokes equation well in high hydraulic permeability (kp) condition (kp ≥1.0×10-8 m2 in our numerical simulation), and it is an approximation to Darcy model in low kp condition (kp ≤5.0×10-12 m2 in our numerical simulation), we used the Brinkman model to simulate the interstitial fluid flow in the ligament where kp is approximately 1.0×10-16 m2. It shows kp and anisotropic property have a little effect on the flow field, but have a great effect on the shear stress on the membrane of interstitial cells (τcell). There is a linear relationship between τcell and Int J Biol Sci inline graphic, when kp =1.0×10-16 m2 and the maximum τcell (τcell,max) is approximately 10 Pa. The anisotropic property will affect τcell's distribution on the cell surface. When kx/ky>1, low τcell dominates the cell, while when kx/ky<1, high τcell dominants the cell.

Keywords: Interstitial fluid flow, porous media, numerical simulation, sheer stress, anisotropy.

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How to cite this article:
Yao W, Shen Z, Ding G. Simulation of Interstitial Fluid Flow in Ligaments: Comparison among Stokes, Brinkman and Darcy Models. Int J Biol Sci 2013; 9(10):1050-1056. doi:10.7150/ijbs.7242. Available from http://www.ijbs.com/v09p1050.htm