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Tumour chemotherapy strategy based on impulse control theory.

Hai-Peng Ren1, Yan Yang2, Murilo S Baptista3

  • 1Shaanxi Key Laboratory of CSCIIP, Xi'an University of Technology, Xi'an 710048, People's Republic of China renhaipeng@xaut.edu.cn.

Philosophical Transactions. Series A, Mathematical, Physical, and Engineering Sciences
|January 25, 2017
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Summary

This study applies cybernetic impulse control theory to optimize chemotherapy dosing. Analytical formulas derived can help doctors minimize drug dosage, effectively treating tumors while preserving healthy cells.

Keywords:
boundednesschemotherapyimpulse control systempermanencestability

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Area of Science:

  • Cybernetics
  • Mathematical Oncology
  • Control Theory

Background:

  • Chemotherapy is a standard cancer treatment, typically guided by empirical protocols.
  • Current dosing strategies lack analytical precision, potentially leading to under- or over-treatment.
  • Cybernetic principles offer a framework for optimizing dynamic treatment processes.

Purpose of the Study:

  • To analyze the stability of tumor chemotherapy using impulse control theory.
  • To derive conditions for stable, periodic chemotherapeutic agent prescription.
  • To provide an analytical method for optimizing drug dosage in cancer treatment.

Main Methods:

  • Application of impulse control theory to model chemotherapy.
  • Analysis of treatment stability using Lyapunov functions and comparison theorems.
  • Derivation of globally stable conditions for periodic drug administration.

Main Results:

  • A globally stable condition for periodic chemotherapy was established.
  • The permanence of the treatment process solution was verified.
  • Specific values for drug strength and application intervals were determined for tumor elimination and immune cell preservation.

Conclusions:

  • Impulse control theory provides an analytical approach to optimize chemotherapy.
  • The derived formulas can guide medical professionals in selecting minimal effective drug dosages.
  • This method aims to improve cancer treatment efficacy and reduce patient harm from over-treatment.