(656a) Incorporating Cell Cycle Progression and Drug Penetration into Metabolic Models of Multicellular Tumor Spheriod Growth

Chemotherapeutic compounds that show promise in monolayer culture studies often prove substantially less effective in tumors due to pronounced diffusion limitations in key nutrients such as glucose and oxygen that produce nutrient deficient regions that eventually become necrotic in tumors in-vivo. Cancer cells are known to consume considerably more glucose than normal cells under identical conditions. While tumor cells oxidize a portion of the glucose they uptake, a large fraction is converted to lactate. Analysis of tumor interstitial fluid suggests that the tricarboxylic acid (TCA) cycle is saturable, which could explain the high rate of lactate production. Clinical trials have shown that high lactate and low oxygen concentrations in in-vivo tumors are each correlated with increased likelihood of metastases, tumor recurrence, and reduced patient survival. The presence of hypoxia is known to reduce the effectiveness of radiation therapy, as this treatment strategy is dependant on presence of oxygen radicals.

In vitro multicellular spheroids mimic the heterogeneous microenvironments present in in-vivo three dimensional tissues which are not present in monolayer cultures. Therefore, multicellular spheroids represent a useful model system to study the effects of nutrient diffusion on tumor metabolism and growth. Mathematical models of spheroid growth have the potential to guide the design of improved chemotherapeutic strategies. Most existing spheroid models are based on simple descriptions of cellular metabolism and the assumption of a single growth limiting nutrient. We recently developed a multi-nutrient model in which diffusion limitations create spatial oxygen, glucose, and lactate gradients that alter local energy metabolism, which in turn affects overall spheroid physiology (Venkatasubramanian et al., 2006). The cellular growth and death rates were assumed to be determined by the ATP generation rate, which was stochiometrically calculated from the nutrient uptake rates. This model successfully predicted the presence of proliferating, quiescent, and necrotic regions observed in fully developed spheroids.

In this presentation, we present a significantly extended version of our original model that accounts for the effects of cell cycle progression and chemotherapeutic drugs. Most other tumor growth models are based on the simplifying assumption of a single type of cycling cell. The incorporation of distinct cell cycle phases is important because some chemotherapeutics are known to be cytotoxic only to cycling cells in a particular phase (e.g., Paclitaxel primarily targets G2/M phase cells). Progression through the five cell cycle phases (G0, G1, S, G2, M) is modeled with simple ATP-dependent rate expressions such that the radial distribution of cells in each phase is consistent with existing data. The rate of cell death from each phase is also described with an ATP-dependent expression. A three-compartment pharmacokinetic model is used to determine the extracellular drug concentration at the spheroid boundary. Drug penetration is modeled with an effective diffusivity coefficient that accounts for drug uptake by the cells. The cellular death rate due to the chemotherapeutic is parameterized in terms of the local extracellular drug concentration. The resulting model consisting of a coupled set of nonlinear partial differential, ordinary differential, and algebraic equations with a moving outer boundary is solved using orthogonal collocation on a moving grid of finite elements. We investigate the effect of drug diffusivity, the targeted cell cycle phase, and phenotypic cell behavior on the efficacy of different drug treatment protocols. Our model produces some counterintuitive results, such as drugs with intermediate diffusion coefficients are most effective at reducing spheroid volume.

References

R. Venkatasubramanian, M. A. Henson, and N. S. Forbes, ?Incorporating Cellular Metabolism into Growth Models of Multicellular Tumor Spheriods,? Journal of Theoretical Biology, in press.