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Mathematical and Theoretical Biology Institute Modeling of Tumor Growth and its Control via Paclitaxel Using a Delay Differential Equation

Paclitaxel is shown to be antiangiogenic at low doses, but the extent of these effects is not known. Our research considers a mathematical model that describes tumor growth and response to treatment with a continuous, low dose treatment of the antimitotic drug Paclitaxel. We constructed a model with three populations: system cells, proliferating tumor cells, and tumor cells in a resting phase. A delay differential equation model accounts for the time it takes for tumor cells to complete one cycle in the proliferation phase. We analyzed the system without drug administration, and then ran numerical simulations under different levels of drug administration. We also performed sensitivity analysis on certain parameters to determine what the likely consequences of antiangiogenic effects. Studies have suggested that well-tolerated chemotherapy can exert a better antitumor effect than conventional high-dose, temporarily spacedout chemotherapy(2). Moreover, at lower doses the anti-mitotic drug Paclitaxel has been shown to have antiangiogenic effects. Since it is very hard to show the exact extent of those effects in clinical testing, we are creating a mathematical model of tumor growth with only the antimitotic effects. We can then do sensitivity analysis to determine the response of the stability of the equilibria to the antiangiogenic effects of Paclitaxel at low doses. Therefore, we consider a model that describes tumor growth with a continuous, low dose treatment of the anti-mitotic drug Paclitaxel. A delay differential equation model has been used in previous studies to analyze the role of the conventional chemotherapy treatment, and we see the delay necessary in understanding the full dynamics of tumor growth(1). For the delay case we computed the effect of different chemotherapy controls, i.e. different drug rates, on the stability of the equilibria numerically.