A comprehensive analytical solution of macromolecular transport within an artery

Macromolecule transport within an artery is investigated and a comprehensive analytical solution is presented. The transport within the lumen and the arterial wall are coupled. Arterial wall is modeled as a four-layer porous wall. The layers are all treated as macroscopically homogeneous porous media. The volume-averaged porous media equations are employed to solve for transport through the porous arterial layers. Staverman filtration coefficient is incorporated to account for selective permeability of each porous layer to macromolecules. The problem encompasses complex interfacial transport phenomena involving various porous–porous as well as porous–fluid interfaces. The method of matched asymptotic expansions is employed to solve for the fluid flow field and species concentration distributions. For comparison purposes, the physiological and transport parameters associated with each porous layer are obtained from the literature. The analytical results are in excellent agreement with previous numerical studies. The results presented in this work provide the first comprehensive analytical solution representing arterial transport phenomena.