Abstract
Background: Various mathematical models have been proposed for studying the growth of tumor cells under chemotherapeutic drug administration. In most of the deterministic models, the drug is administered as per the rate equation of time.
Objective: In this paper we have studied the behavior of a predator-prey model when the drug infusion rate is governed by a sinusoidal function.
Method: A logistic growth model, to study the response of tumor growth to chemotherapeutic drug dosage is considered. The model has been suitably modified to introduce periodic drug infusion rate which is a sinusoidal function. In this paper, an extensive sensitivity analysis on the parameters, tumor cells division rate, cell kill rate, rate at which the drug becomes ineffective and the drug decay rate has been carried out to determine how these parameters affect the growth of the tumor and how the drug accumulates in the body.
Results: 1000 sets of these four parameters were randomly chosen from appropriate Gamma distributions and corresponding curves for the number of tumor cells and average drug accumulation have been obtained. A comparative study of drug administration at a constant rate and at a periodic rate has been done. Effect of changes in the parameters governing the drug infusion rate have been analyzed and how the parameters used in the model relate to pharmacokinetics and pharmacodynamics of a drug has been pointed out.
Conclusion: We have been able to show that controlled periodic drug infusion is a better strategy than administering the drug of a constant rate.
Keywords: Tumor cells, periodic drug infusion rate, tumor cells division rate, cell kill rate, average drug accumulation, pharmacokinetics.
Graphical Abstract
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