Finite element model of antibody penetration in a prevascular tumor noduleembedded in normal tissue

We have developed a pharmacokinetic model for monoclonal antibodies (mAb) t o aid in investigating protocols for targeting small primary tumors or site s of metastatic disease. The model describes the uptake of systemically-adm inistered antibody by a prevascular spherical tumor nodule embedded in norm al tissue. The model incorporates plasma kinetics, transcapillary transport , interstitial diffusion, binding reactions, and lymphatic clearance. Antig en internalization can easily be incorporated. Simulations obtained from a three-dimensional finite element analysis are used to assess errors in pred ictions from earlier models in which the influence of the normal tissue was collapsed into a boundary condition at the tumor surface. The model employ ing a Dirichlet boundary condition substantially overpredicted the mean tot al tumor mAb concentration at all times. Although the model with a concentr ation-dependent flux (composite) boundary condition underpredicted mAb conc entration, the discrepancy with finite element results is only notable at e arly times. Sensitivity analyses were performed on mAb dose and on the coef ficients for mAb diffusion in the tissue regions, since reported antibody d iffusivity values have varied over 30-fold. The results of the study sugges t that rnAb diffusivity and mAb binding site density in tumors should have major influences on optimizing doses and scheduling of mAb administration i n tumor targeting protocols. (C) 2001 Elsevier Science B.V. All rights rese rved.