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

Hamidreza  Ramezanpour; S Setayeshi; ME Akbari

International Journal of Cancer Management

The Official Journal of Cancer Research Center (CRC), Shahid Beheshti University of Medical Sciences

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

Author(s):

Hamidreza Ramezanpour^1,*,

S Setayeshi¹,

ME Akbari²

1Amirkabir University of Technology, Tehran, Iran

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

International Journal of Cancer Management:Vol. 4, issue 4; e80750

Published online:Dec 30, 2011

Article type:Research Article

Received:May 28, 2011

Accepted:Aug 15, 2011

How to Cite:Hamidreza RamezanpourS SetayeshiME AkbariA 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.4(4):e80750.

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.

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