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Laboratory of Mathematical Biology, National Cancer Institute, National Institutes of Health, Bethesda, Maryland 20892
Rational in vivo application of monoclonal antibodies for diagnosis and therapy of cancer requires an understanding of both the global and microscopic pharmacology of macromolecular ligands. Here, we introduce a new mathematical model for antibody distribution into small, prevascular, densely packed nodules (representing either primary or metastatic tumor). For the analysis, we link together several aspects of antibody pharmacology: the global (whole body) pharmacokinetics; transcapillary transport into normal tissue interstitium surrounding the nodule; diffusion into the nodule; nonspecific binding and/or partitioning; specific binding to tumor antigen; metabolism; and lymphatic outflow from the tissue space. Input parameter values are estimated from experimental studies in vitro, in animals, and in clinical trials. Our aim is to explore the sensitivity of antibody localization to variation in three of the important parameters of this model: the rate of transcapillary transport; the rate of lymphatic outflow; and the antigen density.
Predictions based on this analysis include the following: (a) High rates of transcapillary transport influx or low rates of lymphatic efflux will enhance antibody percolation into the tumor nodule at early times after injection and increase the average antibody concentration in the tumor at all times; (b) Changes in antibody influx rate will affect the antibody distribution in the tumor at earlier times than do changes in the efflux rate; (c) Reducing the antigen concentration will increase the uniformity of antibody penetration but lower the average concentration in the tumor at all times after injection; and (d) Counter to intuition, lowering the antigen concentration can increase the peak concentrations achieved toward the center of the nodule. If, in addition, there is any metabolism of bound antibody, the concentration-time integral (i.e., the "area under the curve") for the center of the nodule will also be increased by decreasing the antigen concentration. These predictions directly reflect the "binding site barrier" hypothesis of Weinstein et al. (Ann. NY Acad. Sci., 507: 199–210, 1987) and Fujimori et al. (Cancer Res., 49: 5656–5663, 1989; J. Nucl. Med., 31: 1191–1198, 1990). In general, and perhaps surprisingly until one considers the problem carefully, the parameters governing antibody percolation can have opposite effects on the uniformity of antibody distribution at early and late times.
These calculations, using the PERC program set, were done for antibodies, but we believe that the "binding site barrier" will also prove important for other injected macromolecules, for at least some highly bindable injected small molecules, for lymphokines and cytokines released from transfected cells injected in vivo, and, indeed, for endogenous species such as the autocrine-paracrine factors.
1 To whom requests for reprints should be addressed, at NIH, Building 10, Room 4B-56, 9000 Rockville Pike, Bethesda, MD 20892.
2 Permanent address: Department of Nuclear Medicine, School of Medicine, Hokkaido University. N15 W7 Kita-ku, Sapporo, Japan 060.
Received 5/28/91. Accepted 7/ 1/91.
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