Transport of fluid and macromolecules in tumors. IV. A microscopic model of the perivascular distribution

Abstract

The therapeutic efficacy of various genetically engineered macromolecules is determined by their delivery and distribution in tumors. We have recently developed mathematical models which describe the interstitial velocity, pressure, and concentration profiles of macromolecules over the length scale of a solid tumor (Baxter and Jain, Microvas. Res. 1989, 1990, 1991). Nonspecific and specific antibodies and antibody fragments were chosen as typical macromolecules. The focus of the present investigation was microscopic transport, i.e., the distribution of pressure and solutes around individual blood vessels. Analytical solutions were obtained for interstitial velocities and pressures, while the concentration profiles were calculated numerically using the finite element method. The microscopic model describes flow patterns around an individual blood vessel in an infinite medium and concentration profiles around a single blood vessel in a network of capillaries. Our analysis is novel in that it incorporates interstitial convection, asymmetric filtration, and transcapillary convection to describe interstitial transport in tumors. The purpose of this model was to determine the effect of extravascular binding and interstitial convection on the distribution of macromolecules on a microscopic scale and to test the continuum hypothesis assumed in our previously published macroscopic models. An approximate one-dimensional model was compared with a more accurate two-dimensional model. The results of our microscopic model confirm that the continuum hypothesis used in our previous macroscopic model is reasonable. On a microscopic length scale diffusion is dominant, and short range distortions in the flow field do not significantly affect the penetration of macromolecules into the tissue. In addition, our model confirms the results of Fujimori et al. (Cancer Res., 1989) concerning a "binding site barrier." The implications of our results for cancer therapy are also discussed.