Competitive tumor growth modeling and optimal radiotherapy control via logistic equations

TL;DR

This paper develops mathematical models of tumor growth and response to radiotherapy, applying optimal control theory to identify strategies that effectively reduce tumor size while minimizing damage to healthy tissue.

Contribution

It introduces a novel combination of logistic tumor growth models with the Linear Quadratic radiotherapy model and applies optimal control to optimize treatment strategies.

Findings

Optimal control strategies outperform constant radiation doses.

Mathematical analysis provides insights into tumor dynamics under treatment.

Numerical simulations demonstrate reduced tumor burden with optimized therapy.

Abstract

The uncontrolled proliferation of cancer cells and their interaction with healthy tissue poses a major challenge in oncology. This manuscript develops and analyzes mathematical models that describe tumor response to radiotherapy by incorporating the Linear Quadratic model for cell survival. To improve therapeutic efficiency, the theory of optimal control is introduced on a system of coupled differential equations, allowing for the comparison of constant versus optimized radiation strategies. The analytical study of these models provides insights into the expected dynamics under different treatment scenarios, while numerical simulations validate the theoretical results and highlight the benefits of optimal control in reducing tumor burden with minimized collateral damage.