A hybrid cellular automaton model of solid tumor growth and bioreductive drug transport.

Bioreductive drugs are a class of hypoxia selective drugs that are designed to eradicate the hypoxic fraction of solid tumors. Their activity depends upon a number of biological and pharmacological factors and we used a mathematical modeling approach to explore the dynamics of tumor growth, infusion, and penetration of the bioreductive drug Tirapazamine (TPZ). An in-silico model is implemented to calculate the tumor mass considering oxygen and glucose as key microenvironmental parameters. The next stage of the model integrated extra cellular matrix (ECM), cell-cell adhesion, and cell movement parameters as growth constraints. The tumor microenvironments strongly influenced tumor morphology and growth rates. Once the growth model was established, a hybrid model was developed to study drug dynamics inside the hypoxic regions of tumors. The model used 10, 50 and 100 \mu {\rm M} as TPZ initial concentrations and determined TPZ pharmacokinetic (PK) (transport) and pharmacodynamics (cytotoxicity) properties inside hypoxic regions of solid tumor. The model results showed that diminished drug transport is a reason for TPZ failure and recommend the optimization of the drug transport properties in the emerging TPZ generations. The modeling approach used in this study is novel and can be a step to explore the behavioral dynamics of TPZ.