Computational models of antibody-based tumor imaging and treatment protocols

We present improved computational models for investigating monoclonal antibody-based protocols for diagnostic imaging and therapy of solid tumors. Our earlier models used a boundary condition (Dirichlet) that specified concentrations of diffusing molecular species at the interface between a prevascular tumor nodule and surrounding normal tissue. Here we introduce a concentration-dependent flux boundary condition with finite rates of diffusion in the normal tissue. We then study the effects of this new condition on the tumor's temporal uptake and spatial distribution of radiolabeled targeting agents. We compare these results to ones obtained with the Dirichlet boundary condition and also conduct parameter sensitivity analyses. Introducing finite diffusivity for any molecular species in normal tissue retards its delivery to and removal from the tumor nodule. Effects are protocol- and dose regimen-dependent: generally, however, mean radionuclide concentration and tumor-to-blood ratio declined, whereas relative exposure and mean residence time increased. Finite diffusivity exacerbates the negative effects of antigen internalization. Also, the sensitivity analyses show that mean concentration and tumor-to-blood ratio are quite sensitive to transcapillary permeability and lymphatic efflux values, yet relatively insensitive to precise values of diffusion coefficients. Our analysis underscores that knowledge of antigen internalization rates and doses required to saturate antigen in the tumor will be important for exploiting antibody-based imaging and treatment approaches.