Gaver D P, Kute S M
Department of Biomedical Engineering, Tulane University, New Orleans, Louisiana 70118 USA.
Biophys J. 1998 Aug;75(2):721-33. doi: 10.1016/S0006-3495(98)77562-9.
We predict the amplification of mechanical stress, force, and torque on an adherent cell due to flow within a narrow microchannel. We model this system as a semicircular bulge on a microchannel wall, with pressure-driven flow. This two-dimensional model is solved computationally by the boundary element method. Algebraic expressions are developed by using forms suggested by lubrication theory that can be used simply and accurately to predict the fluid stress, force, and torque based upon the fluid viscosity, muoffhannel height, H, cell size, R, and flow rate per unit width, Q2-d. This study shows that even for the smallest cells (gamma = R/H << 1), the stress, force, and torque can be significantly greater than that predicted based on flow in a cell-free system. Increased flow resistance and fluid stress amplification occur with bigger cells (gamma > 0.25), because of constraints by the channel wall. In these cases we find that the shear stress amplification is proportional to Q2-d(1-gamma)-2, and the force and torque are proportional to Q2-d(1-gamma2)-5/2. Finally, we predict the fluid mechanical influence on three-dimensional immersed objects. These algebraic expressions have an accuracy of approximately 10% for flow in channels and thus are useful for the analysis of cells in flow chambers. For cell adhesion in tubes, the approximations are accurate to approximately 25% when gamma > 0.5. These calculations may thus be used to simply predict fluid mechanical interactions with cells in these constrained settings. Furthermore, the modeling approach may be useful in understanding more complex systems that include cell deformability and cell-cell interactions.
我们预测由于狭窄微通道内的流动，附着细胞上的机械应力、力和扭矩会增大。我们将此系统建模为微通道壁上的半圆形凸起，并存在压力驱动的流动。通过边界元法对这个二维模型进行计算求解。利用润滑理论提出的形式推导出代数表达式，这些表达式可基于流体粘度、微通道高度(H)、细胞大小(R)以及单位宽度的流速(Q_{2 - d})，简单而准确地预测流体应力、力和扭矩。本研究表明，即使对于最小的细胞（(\gamma = R/H << 1)），应力、力和扭矩也可能显著大于基于无细胞系统中流动所预测的值。对于较大的细胞（(\gamma > 0.25)），由于通道壁的限制，会出现流动阻力增加和流体应力放大的情况。在这些情况下，我们发现剪切应力放大与(Q_{2 - d}(1 - \gamma)^{-2})成正比，力和扭矩与(Q_{2 - d}(1 - \gamma^2)^{-5/2})成正比。最后，我们预测流体力学对三维浸没物体的影响。这些代数表达式对于通道内的流动，精度约为(10%)，因此可用于分析流动腔中的细胞。对于管内的细胞黏附，当(\gamma > 0.5)时，近似精度约为(25%)。因此，这些计算可用于简单预测在这些受限环境中细胞与流体的力学相互作用。此外，该建模方法可能有助于理解包括细胞可变形性和细胞间相互作用在内的更复杂系统。
