A hybrid discrete-continuous model of in vitro spheroid tumor growth and drug response

Anti-cancer therapy efficacy in solid tumors mainly depends on drug transportation through the vasculature system and the extracellular matrix, on diffusion gradients and clonal heterogeneity within the tumor mass, as well as on the responses of the individual tumor cells to drugs and their interactions with each other and their local microenvironment. In this work, we develop a mathematical predictive model for tumor growth and drug response based on 3D spheroids experiments that possess several in vivo features of tumors and are considered better for drug screening. The model takes into account the diffusion gradients of both oxygen and drug through the tumor volume, describes the tumor population at cell level and assumes a simple underlying cellular dose-response curve that is translated to a cell death probability. The model shows that although the endpoint tumor regression can be well approximated, the effects of the drug on cell fate necessitate a more sophisticated model to explain the temporal evolution of tumor regression and more quantitative information regarding the number and topology of dead and living cells, which is highly important for in vivo clinical relevant predictions. The model is built in a way that can be constrained by experimentally derived set of parameters and is capable of accommodating cell heterogeneity, sub-cellular regulatory mechanisms and drug-induced signaling cascades, as well as additional mechanisms of adapted resistance.