Antibody penetration into a spherical prevascular tumor nodule embedded in normal tissue

A finite-element (FE) method is used to numerically solve a pharmacokinetic model that describes the uptake of systemically administered antibody (mAb) in a prevascular spherical tumor nodule embedded in normal tissue. The model incorporates plasma kinetics, transcapillary transport, lymphatic clearance, interstitial diffusion in both the normal tissue and tumor, and binding reactions. We use results from the FE analysis to assess previous predictions that employed either a Dirichlet boundary condition (b.c.), or an approximate, composite (Dirichlet and Neumann) b.c. at the tumor surface. We find that the Dirichlet b.c. significantly overpredicted the mean total tumor mAb concentration. In contrast, the composite b.c. yielded good agreement with FE predictions, except at early times. We also used the FE model to investigate the influence of the approximately 30-fold difference in the values of mAb diffusion coefficient measured by Clauss and Jain (Cancer Res. 50:3487-3492, 1990) and Berk et al. (Proc. Natl. Acad. Sci. U.S.A. 94:1785-1790, 1997). For low diffusivity, diffusional resistance slows both mAb uptake by and efflux from the tumor. For high diffusivity at the same mAb dose, more rapid uptake produces earlier and higher peak mAb levels in the tumor, while the efflux rate is limited by the dissociation of the mAb-tumor antigen complex. The differences in spatial and temporal variation in mAb concentration between low and high diffusivities are of sufficient magnitude to be experimentally observable, particularly at short times after antibody administration.