Mathematical model of antibody targeting: important parameters defined using clinical data

Antibody-targeted therapy of cancer has shown benefits in the treatment of some cancers but selective delivery has not been optimized. Many parameters influence antibody targeting; some will have a greater effect than others and their effects will generally be interrelated. They include effects of blood flow and pressure, vascular permeability, venous and lymphatic drainage, permeation through extravascular spaces, antibody clearance, specificity, affinity and resistance to degradation. Quantitative data about the behaviour of targeting systems can be collected, and it is possible to describe the system in terms of compartments interconnected by equations defining the passage of targeting agents between them. A mathematical model of antibody targeting can thus be built. We have collected data on the time course of the distribution of four different antibody molecules of molecular weight 27, 100 and 150 kDa directed against carcinoembryonic antigen in patients with colorectal cancer. Laboratory data were used for parameters which could not be measured in patients. These data have been used to test the validity of the model for man and to develop it so that it is consistent with the diverse clinical data. The model is then used to understand the effects of changes to a parameter on tumour targeting efficiency and to select those parameters which have the greatest effect in therapy. Affinity of antibody, flow of antibody through the tumour and rate of elimination of antibody from the tumour were shown to be the most powerful parameters determining antibody localization. These concepts can be used to determine design parameters for antibody-targeted cancer therapy.