A new model of filtration and macromolecules transport across capillary walls

Abstract

Metabolic substrates, such as oxygen and glucose, are rapidly delivered to the cell through filtration across microvessels walls. Modelling this important process is complicated by the coupling between flow and transport equations, which are linked through the osmotic pressure induced by the colloidal plasma proteins. Microvessel wall is a composite media with the internal glycocalyx layer exerting a remarkable sieving effect on macromolecules, with respect to the external layer composed by endothelial cells. The physiological structure of microvessel is represented as the superimposition of two membranes with different properties; the inner membrane represents the glycocalyx, while the outer membrane represents the surrounding endothelial cells. Application of mass conservation principle and thermodynamic considerations lead to a model composed by two coupled second-order partial differential equations in the hydrostatic and osmotic pressures, one expressing volumetric mass conservation and the other, which is non-linear, expressing macromolecules mass conservation. Despite system complexity, the assumption that the properties of the layers are piece-wise constant allows us to obtain analytical solutions for the two pressures. This solution is in agreement with experimental observations, which contrary to common belief, show that flow reversal cannot occur in steady state unless luminal hydrostatic pressure drops below physiologically plausible values. The observed variations of volumetric and solute mass flux in case of a significant reduction of luminal hydrostatic pressure are in qualitative agreement with observed variations during experiments reported in the literature. On the other hand, homogenising microvessel wall into a single-layer membrane with equivalent properties leads to a different distribution of pressure across microvessel wall, not consistent with observations.