Incorporating energy metabolism into a growth model of multicellular tumor spheroids

Diffusion limitations in tumors create regions that are deficient in essential nutrients and contain a large number of quiescent and dying cells. Chemotherapeutic compounds are not effective against quiescent cells and therefore have reduced efficacy against tumors with extensive quiescence. We have formulated a mathematical model that predicts the extent and location of quiescence in multicellular spheroids. Multicellular spheroids are in vitro models of in vivo tumor growth that have proven to be useful experimental systems for studying radiation therapy, drug penetration, and novel chemotherapeutic strategies. Our model incorporates a realistic description of primary energy metabolism within reaction–diffusion equations to predict local glucose, oxygen, and lactate concentrations and an overall spheroid growth rate. The model development is based on the assumption that local cellular growth and death rates are determined by local ATP production generated by intracellular energy metabolism. Dynamic simulation and parametric sensitivity studies are used to evaluate model behavior, including the spatial distribution of proliferating, quiescent, and dead cells for different cellular characteristics. Using this model we have determined the critical cell survival parameters that have the greatest impact on overall spheroid physiology, and we have found that oxygen transport has a greater effect than glucose transport on the distribution of quiescent cells. By predicting the extent of quiescence based on individual cellular characteristic alone this model has the potential to predict therapeutic efficiency and can be used to design effective chemotherapeutic strategies.