Pharmacokinetic analysis of the perivascular distribution of bifunctional antibodies and haptens: comparison with experimental data

A mathematical model is developed to describe the concentration profiles around individual tumor blood vessels for two-step approaches to cancer treatment. The model incorporates plasma pharmacokinetics, interstitial diffusion, reversible binding between antibody and hapten and between antibody and tumor-associated antigens, and physiological parameters to evaluate present experimental approaches and to suggest new guidelines for the effective use of two-step approaches. Results show considerable interaction between the binding kinetics, initial drug doses, and antigen density, with optimal parameter ranges depending on the desired goal: treatment or detection. The hapten concentration in tumors was found to be nonuniform because of specific binding to antibodies. While binding of the hapten to the bifunctional antibody is necessary for improved retention, too large a binding affinity may lead to very poor penetration of the hapten into regions far away from blood vessels. The time delay between antibody and hapten injection was found to be an important parameter. Longer time delays were found to be advantageous, subject to constraints such as internalization of the antibody and tumor growth during treatment. A proper combination of initial doses for the two species was also seen to be crucial for maximum effectiveness. Comparison of the model with the experimental data of Le Doussal et al. (Cancer Res., 51: 6650-6655, 1991) and Stickney et al. (Cancer Res., 50: 3445-3452, 1990) suggests two novel, yet testable, hypotheses: (a) the early pharmacokinetics of low molecular weight agents can have an important effect on later concentrations using two-step approaches; and (b) metabolism may play an important role in reducing concentrations in the tumor and tumor:plasma concentration ratios. These results should help in the effective design of two-step strategies.