Transport of fluid and macromolecules in tumors. III. Role of binding and metabolism.

We have previously developed a general theoretical framework for transvascular exchange and extravascular transport of fluid and macromolecules in tumors. The model was first applied to a homogeneous, alymphatic tumor, with no extravascular binding (Baxter and Jain, 1989). For nonbinding molecules the interstitial pressure was found to be a major contributing factor to the heterogeneous distribution of macromolecules within solid tumors. A steep pressure gradient was predicted at the periphery of the tumor, and verified in recent experiments. The second paper in this series looked at the role of heterogeneous perfusion and lymphatics on the interstitial pressure distribution and concentration profiles of non-binding macromolecules (Baxter and Jain, 1990). The present work presents the role of specific binding and metabolism in macromolecular uptake and distribution. In this investigation the interstitial concentration profiles for IgG and its fragment, Fab, were modeled with a convective-diffusion equation which includes extravascular binding and metabolism as well as transvascular exchange. The effects of molecular weight, binding affinity, antigen density, initial dose, plasma clearance, vascular permeability, metabolism, and necrosis were considered. An expression for optimal affinity was derived. The main conclusion is that an antibody with the highest possible binding affinity should be used except when: (i) there are significant necrotic regions; (ii) the diffusive vascular permeability is very small; and (iii) a uniform concentration is required on a microscopic scale. The highest concentrations are achieved by continuous infusion, but the specificity ratio is highest for bolus injections. Antibody metabolism reduces both the total concentration and the specificity ratio, especially at later times. In addition, specific binding reduces the amount of material sequestered in a necrotic core. Our model is compared with three previous models for antibody binding found in the literature. Unlike previous models, this model combines nonuniform filtration, binding, and interstitial transport to determine macroscopic concentration profiles. In addition to supporting previous conclusions, our model offers some new strategies for therapy.