A QSP PDE model of ADC transport and kinetics in a growing or shrinking tumor

When a tumor is treated with an antibody-drug conjugate (ADC) complex biochemistry occurs in a domain-the tumor-whose size and structure are changing. Some parts of the tumor may be growing because tumor cells proliferate. Other parts may be stagnant, or nearly so, because the cells there have been damaged by the cytotoxin. Still others may be shrinking because the cells there have been killed by the cytotoxin and are being cleared. Chemical concentrations within the tumor, which influence kinetics and transport, change as the tumor grows or shrinks. Cell surface antigen, to which ADCs are designed to bind, is lost when cells are cleared and is freshly introduced when cells proliferate. For these reasons, and because shrinking the tumor by killing its cells is the purpose of ADC treatment, it is important in a quantitative systems pharmacology (QSP) approach to the problem to model the evolution of tumor size and structure over the course of ADC treatment. In this paper we present a partial differential equation (PDE) model of ADC transport and kinetics in a growing and shrinking Krogh cylinder tumor. We present results of several studies we performed with the model, including an antigen concentration study that shows tumor growth inhibition to be non-monotone as a function of antigen concentration, and a study of the effects of co-administration of mAb and ADC that shows that the greater the delay between mAb and ADC administration the less the effect of co-administration, and which suggests the mechanism for this effect.