A Novel Scheme for Optimal Control of a Nonlinear Delay Differential Equations Model to Determine Effective and Optimal Administrating Chemotherapy Agents in Breast Cancer

AUTHORS

Hamidreza Ramezanpour 1 , * , S Setayeshi 1 , ME Akbari 2

1 Amirkabir University of Technology, Tehran, Iran

2 Cancer Research Centre, Shahid Beheshti University of Medical Sciences, Tehran, Iran

How to Cite: Ramezanpour H , Setayeshi S, Akbari M. A Novel Scheme for Optimal Control of a Nonlinear Delay Differential Equations Model to Determine Effective and Optimal Administrating Chemotherapy Agents in Breast Cancer, Int J Cancer Manag. 2011 ; 4(4):e80750.

ARTICLE INFORMATION

International Journal of Cancer Management: 4 (4); e80750
Published Online: December 30, 2011
Article Type: Research Article
Received: May 28, 2011
Accepted: August 15, 2011

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Abstract

Background: Determining the optimal and effective scheme for administrating the chemotherapy agents in breast cancer is the main goal of this scientific research. The most important issue here is the amount of drug or radiation administrated in chemotherapy and radiotherapy for increasing patient's survival. This is because in these cases, the therapy not only kills the tumor cells, but also kills some of the healthy tissues and causes serious damages. In this paper we investigate optimal drug scheduling effect for breast cancer model which consist of nonlinear ordinary differential time-delay equations.

Methods: In this paper, a mathematical model of breast cancer tumors is discussed and then optimal control theory is applied to find out the optimal drug adjustment as an input control of system. Finally we use Sensitivity Approach (SA) to solve the optimal control problem.

Results: The goal of this paper is to determine optimal and effective scheme for administering the chemotherapy agent, so that the tumor is eradicated, while the immune systems remains above a suitable level. Simulation results confirm the effectiveness of our proposed procedure.

Conclusion: In this paper a new scheme is proposed to design a therapy protocol for chemotherapy in Breast Cancer. In contrast to traditional pulse drug delivery, a continuous process is offered and optimized, according to the optimal control theory for time-delay systems.

Keywords

Breast Neoplasm Chemotherapy Immune system Optimal control

© 2011, Author(s). This is an open-access article distributed under the terms of the Creative Commons Attribution-NonCommercial 4.0 International License (http://creativecommons.org/licenses/by-nc/4.0/) which permits copy and redistribute the material just in noncommercial usages, provided the original work is properly cited.

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