Leakage through a permeable capillary tube into a poroelastic tumor interstitium

Fluid flow through a permeable circular tube embedded in an infinite poroelastic ambient medium is studied as a model of blood flow through the vasculature of a solid tumor. The flow through the interstitium is described by Darcy's law for an isotropic porous medium with a pressure-dependent permeability, the flow along the tube is described by Poiseuille's law, and the extravasation flux across the tube surface is described by Starling's law involving the transmural pressure. Kirchhoff's transformation is applied to derive Laplace's equation for a modified interstitial pressure. Given the arterial, venous, and ambient pressures, the problem is formulated in terms of a coupled system of integral, differential, and algebraic equations for the vascular and interstitial pressures. The overall hydrodynamics is described in terms of hydraulic conductivity coefficients for the arterial, venous, and extravasation flow rates. Solutions obtained by a boundary-element method confirm that interstitium dilatation promotes the rate of extravasation.