Mathematical Modeling of Cancer and Designing an Optimal Chemotherapy Protocol Based on Lyapunov Stability Criteria

Document Type : Original Article (s)

Authors

1 Professor, Department of Solid Mechanics and Design, School of Mechanical Engineering, K. N. Toosi University of Technology, Tehran, Iran

2 MSc Student, Department of Solid Mechanics and Design, School of Mechanical Engineering, K. N. Toosi University of Technology, Tehran, Iran

Abstract

Background: Mathematical models can provide insights into the growth of cancerous cells and their interaction with healthy cells, immune cells, and chemotherapeutic drugs that are used in cancer therapy. Moreover, mathematical models have been developed to aid in describing the mechanisms of availability of cytotoxic drugs and their effects on healthy cell populations. Finding a desirable treatment protocol for patients is one of the most important objectives of mathematical modeling. The conventional method in designing the optimal chemotherapy strategies is making use of the classical optimal control theory.Methods: In this study, a new mathematical model was developed to analyze dynamics of cancerous cells in different phases of cell cycle, immune cells, chemotherapeutic drug concentration, and toxicity. Finally, Lyapunov stability theory was applied to design an optimal treatment protocol.Findings: The results of simulation showed that after 7 times of chemotherapy during 50 days, all cancerous cells would be killed. In addition, the disease would remain in this desirable state up to 6 months.Conclusion: In this research, a new mathematical model for describing the dynamics of a cancerous system has been proposed. An optimal treatment protocol has also been designed applying Lyapunov stability theory. Using such a protocol, the population of cancerous cells would be decreased to zero. This state can be maintained for 6 months. In addition, by applying vaccine therapy the growth of cancerous cells could be prevented. Vaccine therapy changes the parameters of the system and stabilizes tumor free equilibrium point.

Keywords

References

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Journal of Isfahan Medical School
Volume 29, Issue 174 - Serial Number 174
November and December 2011
Pages 3117-3126

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History

  • Receive Date: 10 August 2011
  • Revise Date: 01 November 2024
  • Accept Date: 06 April 2022

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