A Double-Permeability Poroelasticity Model for Fluid Transport in a Biological Tissue

This work presents a double-permeability poroelasticity model for fluid flows in both the microvascular and interstitial networks in a biological tissue. In the newly developed model, both networks are modeled as porous structures with distinct permeabilities and porosities. The microvascular and the interstitial fluid pressures are hydraulically as well as mechanically coupled together. The numerical results for the steady-state flow in a one-dimensional capillary bed using some preliminary material parameters show that the vascular pressure decreases almost linearly from the arteriole-side to the venule-side. The interstitial fluid pressure (IFP) is elevated by an increase in the venule-side vascular pressure as well as by a decrease in the lymphatic drainage capability. Under a transient flow condition induced by a sudden drop in the venule-side vascular pressure, the IFP may pop up during a very short period of time before decreasing to the reduced steady-state value at long times due to the mechanical coupling between the vascular pressure and IFP which acts much faster than the hydraulic coupling between the two pressures through the vascular walls. Oscillatory mechanical load may produce comparable IFP and promote fluid exchange between the microvessels and interstitium. Finally, a perturbation analysis reveals that a boundary layer for the IFP develops near the tissue boundary. For the first-order approximation, the vascular pressure is decoupled from the IFP and the IFP may be obtained with the first-order vascular pressure as a source.

Duke Scholars

Author Fan Yuan Biomedical Engineering