A distributed pharmacokinetic model of two-step imaging and treatment protocols: application to streptavidin-conjugated monoclonal antibodies and radiolabeled biotin.

Two-step imaging and treatment protocols involve injecting a suitably prepared monoclonal antibody that can bind both to a specific tumor antigen and to a second reagent which carries a drug or radionuclide. The second component is injected later, after the antibody has distributed throughout the target tumors and been largely cleared from the plasma and normal tissues. We introduce a mathematical model for the analysis of such protocols and apply it to the case of a streptavidinylated monoclonal antibody and radiolabeled biotin diffusing into small, prevascular, densely cellular nodules that represent either primary or metastatic tumors. We examine the distribution of streptavidinylated antibody and radiolabeled biotin within a tumor nodule and compare the two-step protocol to a one-step protocol using radiolabeled antibody. Our analysis predicts that (1) streptavidinylation reduces both the amount of antibody that distributes into the tumor nodule and the homogeneity of that distribution; (2) streptavidinylated antibody in the nodule can be saturated by initial plasma concentrations of free radiolabeled biotin substantially lower than the initial plasma concentration of free streptavidinylated antibody; (3) radiolabeled biotin diffuses rapidly, but binds so quickly that it will not penetrate deeply into the nodule if too low a dose is given. Hence, nonuniform localization of radiolabel may result from a "binding site barrier" to diffusion of either or both components; and (4) the two-step protocol permits imaging sooner after injection of radiolabeled material than the one-step protocol and produces a higher exposure in tumor relative to plasma, even in the presence of antigen turnover.