A simple model of filtration and macromolecule transport through microvascular walls

The walls of microvessels play an important role in maintaining the equilibrium between intravascular and extravascular fluid compartments. Under normal conditions the vessel walls are nearly impermeable to macromolecules, while lipophilic species and small hydrophilic substances are allowed to cross the walls and reach the surrounding tissue. Fluid fow and transport of dissolved molecules through the walls depends on permeability and diusivity of the membrane composing the wall. Several alterations of these processes have been observed resulting in leaking of macromolecules, which is typically attributed to the reduction of oncotic pressure, or inflammatory processes altering the endothelial structure. In this work we investigate the role of an increased blood pressure as the driving force for leaking of macromolecules. The microvessel wall is assumed to be composed of two layers with dierent permeability and porosity, as assumed in previous studies on fluid flow and macromolecules transport in heteroporous membranes. Variability in the porosity and tortuosity of the porous material leads to variations in dispersivity. In this preliminary analysis we assume permeability, porosity and tortuosity to be constant within the single layer, but variable through the layers composing the microvessel wall. With this simplied, yet realistic, model we obtain closed-form steady-state solutions for the fluid flow and solute transport through the microvessel walls, which can be used for a preliminary analysis of leaking of macromolecules due to an increased blood pressure. With this simple model we interpret experimental data available in the literature.