Mass transport in solid tumors (I)—Fluid dynamics

A three-porous-medium model for transvascular exchange and extravascular transport of fluid and macromolecules in a spherical solid tumor is developed. The microvasculature, lymphatics, and tissue space are each treated as a porous medium with the flow of blood, lymph, and interstitial fluid obeying Darcy's law and Starling's assumption. In this part, the role of interstitial pressure and fluid convection are studied. The analytical solutions are obtained for the isolated tumor and the normal-tissue-surrounded tumor respectively. The calculated interstitial pressure projue are consistent with the experimental observation that the elevated interstitial pressure is a major barrier in the penetration of macromolecular drug into tumors. The factors which may reduce the interstitial pressure are analyzed in details.