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 b lood flow and pressure, vascular permeability, venous and lymphatic drainag e, 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 interc onnected 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 diffe rent antibody molecules of molecular weight 27, 100 and 150 kDa directed ag ainst carcinoembryonic antigen in patients with colorectal cancer. Laborato ry data were used for parameters which could not be measured in patients. T hese data have been used to test the validity of the model for man and to d evelop it so that it is consistent with the diverse clinical data. The mode l is then used to understand the effects of changes to a parameter on tumou r targeting efficiency and to select those parameters which have the greate st effect in therapy. Affinity of antibody, flow of antibody through the tu mour and rate of elimination of antibody from the tumour were shown to be t he most powerful parameters determining antibody localization. These concep ts can be used to determine design parameters for antibody-targeted cancer therapy.