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

Abstract

We have developed a pharmacokinetic model for monoclonal antibodies (mAb) to aid in investigating protocols for targeting small primary tumors or sites of metastatic disease. The model describes the uptake of systemically-administered antibody by a prevascular spherical tumor nodule embedded in normal tissue. The model incorporates plasma kinetics, transcapillary transport, interstitial diffusion, binding reactions, and lymphatic clearance. Antigen internalization can easily be incorporated. Simulations obtained from a three-dimensional finite element analysis are used to assess errors in predictions from earlier models in which the influence of the normal tissue was collapsed into a boundary condition at the tumor surface. The model employing a Dirichlet boundary condition substantially overpredicted the mean total tumor mAb concentration at all times. Although the model with a concentration-dependent flux (composite) boundary condition underpredicted mAb concentration, the discrepancy with finite element results is only notable at early times. Sensitivity analyses were performed on mAb dose and on the coefficients for mAb diffusion in the tissue regions, since reported antibody diffusivity values have varied over 30-fold. The results of the study suggest that mAb diffusivity and mAb binding site density in tumors should have major influences on optimizing doses and scheduling of mAb administration in tumor targeting protocols.