Transmission of steady and oscillatory fluid shear stress across epithelial and endothelial surface structures

The glycocalyx on the apical surface of vascular endothelial cells and the microvilli and cilia on kidney epithelial cells have been modeled as surface layers with a hexagonal arrangement of structural elements. These elements have been proposed to serve a mechanosensory function in the initiation of intracellular signaling by fluid shear stress. In this paper we examine the response of these surface layers when steady or oscillating shear is applied at their outer edge. In the case of steady shear, our results show that the deflection of the structural elements is proportional to the product of the applied shear stress and their length L and inversely proportional to the natural damped vibration frequency of the structural element omega(c). A fluid velocity boundary layer develops at the outer edge of the surface layers when the dimensionless Brinkman parameter alpha=L/rootK(P), where K-P is the Darcy permeability, is asymptotically large. In the case of oscillating shear, we find that the motions of both the fluid and structural elements are in a quasisteady state at physiological conditions. No attenuation or phase shift of the torque is induced by the hydrodynamic drag when the applied frequency omega<omega(c) or omega(r)(=omega/omega(c))<1. However, the velocity at the tips of the structural element is pi/2 out of phase with the applied shear in this frequency range, due to the elastic recoil of the element. Furthermore, the fluid velocity at the tips can also be out of phase with the applied shear at large alpha if the closely spaced structural elements of the glycocalyx on endothelial cells or microvilli on proximal tubule cells transport substantial fluid with them. (C) 2005 American Institute of Physics.