A THEORETICAL-MODEL STUDY OF THE INFLUENCE OF FLUID STRESSES ON A CELL ADHERING TO A MICROCHANNEL WALL

We predict the amplification of mechanical stress, force, and torque o n an adherent cell due to flow within a narrow microchannel, We model this system as a semicircular bulge on a microchannel wall, with press ure-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 a nd accurately to predict the fluid stress, force, and torque based upo n the fluid viscosity, mu, channel height, H, cell size, R, and flow r ate per unit width, Q(2-d). This study shows that even for the smalles t cells (gamma = R/H much less than 1), the stress, force, and torque can be significantly greater than that predicted based on flow in a ce ll-free system. Increased flow resistance and fluid stress amplificati on occur with bigger cells (gamma > 0.25), because of constraints by t he channel wall. In these cases we find that the shear stress amplific ation is proportional to Q(2-d)(1 - gamma)(-2), and the force and torq ue are proportional to Q(2-d)(1 - gamma(2))(-5/2). Finally, we predict the fluid mechanical influence on three-dimensional immersed objects. These algebraic expressions have an accuracy of similar to 10% for fl ow in channels and thus are useful for the analysis of cells in flow c hambers. For cell adhesion in tubes, the approximations are accurate t o similar to 25% when gamma > 0.5. These calculations may thus be used to simply predict fluid mechanical interactions with cells in these c onstrained settings. Furthermore, the modeling approach may be useful in understanding more complex systems that include cell deformability and cell-cell interactions.