  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.
