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一种用于非线性延迟微分方程模型最优控制的新方案,以确定乳腺癌中有效和最优的化疗药物给药方式。

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

作者信息

Ramezanpour H R, Setayeshi S, Akbari M E

机构信息

Amirkabir University of Technology, Tehran, Iran.

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

出版信息

Iran J Cancer Prev. 2011 Fall;4(4):154-62.

PMID:26322192
原文链接:https://pmc.ncbi.nlm.nih.gov/articles/PMC4551285/
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.

摘要

背景

确定乳腺癌化疗药物的最佳有效给药方案是本科研的主要目标。这里最重要的问题是化疗和放疗中使用的药物剂量或辐射量,以提高患者的生存率。这是因为在这些情况下,治疗不仅会杀死肿瘤细胞,还会杀死一些健康组织并造成严重损害。在本文中,我们研究了由非线性常微分时滞方程组成的乳腺癌模型的最佳药物调度效果。

方法

本文讨论了乳腺癌肿瘤的数学模型,然后应用最优控制理论找出最优药物调整作为系统的输入控制。最后我们使用灵敏度方法(SA)来解决最优控制问题。

结果

本文的目标是确定化疗药物的最佳有效给药方案,以便在免疫系统保持在适当水平以上的同时根除肿瘤。仿真结果证实了我们提出的程序的有效性。

结论

本文提出了一种新的方案来设计乳腺癌化疗的治疗方案。与传统的脉冲给药不同,根据时滞系统的最优控制理论,提供并优化了一个连续过程。

https://cdn.ncbi.nlm.nih.gov/pmc/blobs/721a/4551285/1911ef7530de/IJCP-05-154f2.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/721a/4551285/9cc1cf069e40/IJCP-05-154f1.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/721a/4551285/1911ef7530de/IJCP-05-154f2.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/721a/4551285/9cc1cf069e40/IJCP-05-154f1.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/721a/4551285/1911ef7530de/IJCP-05-154f2.jpg

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Immunotherapy: an optimal control theory approach.免疫疗法:最优控制理论方法。
Math Biosci Eng. 2005 Jul;2(3):499-510. doi: 10.3934/mbe.2005.2.499.
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An evolutionary hybrid cellular automaton model of solid tumour growth.一种实体肿瘤生长的进化混合细胞自动机模型。
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Chemotherapy for tumors: an analysis of the dynamics and a study of quadratic and linear optimal controls.肿瘤化疗:动力学分析及二次和线性最优控制研究
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