Flow and deformation of the capillary glycocalyx in the wake of a leukocyte

An analysis is presented of the axisymmetric axial and radial flow and deformation fields throughout the endothelial-cell glycocalyx surface layer in the wake region behind a leukocyte moving steadily through a capillary. The glycocalyx, modeled as a thin poroelastic surface layer lining the capillary wall, is assumed to consist of a binary mixture of a linearly viscous fluid constituent and an isotropic, highly compressible, linearly elastic solid constituent having a vanishingly small solid-volume fraction. Invoking the asymptotic approximations of lubrication theory in a frame of reference translating with the leukocyte, closed-form solutions are obtained to the leading-order boundary-value problems governing the axial and radial flow and deformation fields throughout the glycocalyx as well as the axial and radial flow fields throughout the free capillary lumen within the wake. A simple asymptotic expression is obtained for the length l(char) of the wake region in terms of the translational speed U-0 of the leukocyte, and the equilibrium thickness h(0), permeability k(0), and aggregate elastic modulus H-A of the glycocalyx. The predicted wake length, as seen from an observer moving in a reference frame attached to the leukocyte, is consistent with the recovery time predicted from a one-dimensional analysis of glycocalyx deformation through a quiescent inviscid fluid. The two-dimensional fluid dynamical analysis presented here thus provides the appropriate relationships for extracting estimates of the mechanoelectrochemical properties of the glycocalyx from physiologically realistic constitutive models developed under simplified one-dimensional flow regimes. The directly measurable quantities l(char), U-0, and h(0), which are obtainable from in vivo observations of the wake region behind a leukocyte moving steadily through a capillary, can therefore be connected, through the results of this analysis, to estimates of the mechanoelectrochemical properties of the glycocalyx on vascular endothelial cells. (C) 2005 American Institute of Physics.