Differences in predictions of ODE models of tumor growth: a cautionary example (original) (raw)
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An analysis of a mathematical model describing the growth of a tumor treated with chemotherapy
Applied Mathematics and Nonlinear Sciences, 2020
We present a mathematical analysis of a mixed ODE-PDE model describing the spatial distribution and temporal evolution of tumor and normal cells within a tissue subject to the effects of a chemotherapeutic drug. The model assumes that the influx of chemotherapy is restricted to a limited region of the tissue, mimicking a blood vessel passing transversely. We provide results on the existence and uniqueness of the model solution and numerical simulations illustrating different model behaviors.
— Combination therapies are widely used in the treatment of patients with cancer. The main rationale to combine anticancer therapies in the clinic is to obtain a better response with reduced adverse effects. Here i present a pharmacokinetic/pharmacodynamic (PK/PD) model with a smooth nonlinear growth function to characterize and quantify anticancer effect of combination of chemotherapy and radiation therapies using time-dependent data. Based on such a transit two compartment model, Logistic growth Law has proposed a semi-mechanistic pharmacokinetic/ pharmacodynamic (PK/PD) model to assess the antitumor effect. This model describes mathematically the impact of anticancer treatment on the dynamics of tumor growth. From the simulation results of combination of Chemotherapy and Radiation therapy treatment it is observed that, this model will provide better performance than those treatments applied individually.