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Laboratory of Mathematical Biology, National Cancer Institute [K. F., D. G. C., J. N. W.], and Laboratory of Applied Studies, Division of Computer Research and Technology [J. E. F.], NIH, Bethesda, Maryland 20892
In order to understand the pharmacology of monoclonal antibodies and their conjugates, one must consider both global and microscopic aspects of antibody distribution. Here we present an analysis of antibody distribution in tumors based on the following factors: (a) molecular weight and valence of the antibody; (b) global pharmacokinetic profile following i.v. bolus injection; (c) penetration through the vascular wall; (d) diffusive and convective transport through interstitial space in the tumor; (e) antigen-antibody interaction; (f) antibody metabolism. Partial differential equations were developed to incorporate these factors and then solved numerically using parameter values from animal experiments, from clinical protocols at our institution, from studies of antibody binding characteristics in vitro, and from the literature.
Salient findings from this model are that (a) antigen-antibody interaction in the tumor can retard antibody percolation away from blood capillaries, thus constituting a "binding site barrier"; (b) high antibody affinity tends to decrease antibody penetration and result in a more heterogeneous distribution; (c) high molecular weight [IgG > F(ab')2 > Fab] slows percolation and results in less uniform spatial distribution; (d) the average antibody concentration in the tumor does not increase linearly with antibody dose; (e) raising the rate of antibody metabolism results in low concentration and poor percolation; (f) perhaps most interesting, there is predicted to be a range of antibody dose and affinity within which the specificity ratio and average concentration could be kept high while limiting the heterogeneity of distribution.
PERC, the computer program package developed for these analyses, provides a convenient and flexible way to assess the impact of global and microscopic parameters on the distribution of immunoglobulin in tumors. For calculations presented here, the input data were obtained from experimental sources, and qualitative features of the output proved consistent with the few interpretable observations available. However, detailed validation would require much more data than are currently at hand. The mathematical findings should therefore be considered as aids to concept development and as a set of null hypotheses with which to guide experimentation. Experiments and simulations will continue in tandem. It should be noted that the PERC package (and also the general principles delineated here) can be applied as well to biological ligands other than antibodies.
1 To whom requests for reprints should be addressed, at the Laboratory of Mathematical Biology, National Cancer Institute, Building 10, Room 4B-56, Bethesda, MD 20892.
Received 3/21/89. Revised 7/ 7/89. Accepted 7/18/89.
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