一个在肿瘤细胞中可复制的病毒模型的数学分析

数学物理学报

一个在肿瘤细胞中可复制的病毒模型的数学分析

陶有山

东华大学应用数学系上海 200051

收稿日期:2003-01-29 修回日期:2005-01-26 出版日期:2006-04-25 发布日期:2006-04-25
通讯作者: 陶有山
基金资助:
国家自然科学基金(NSFC10571023)和上海市“曙光计划”资助

Mathematical Analysis of a Model of a Replication-competent Virus in Tumor Cells

Tao Youshan

Department of Applied Mathematics, Dong Hua University, Shanghai 200051

Received:2003-01-29 Revised:2005-01-26 Online:2006-04-25 Published:2006-04-25
Contact: Tao Youshan

摘要/Abstract

摘要： 作者考虑一种向肿瘤注射可复制病毒的癌症治疗方法.病毒感染肿瘤细胞,在其中复制,最终引起肿瘤细胞死亡(溶解).一旦肿瘤细胞死亡,其中的病毒释放并感染邻近的肿瘤细胞.上述过程可用一个(一阶)双曲偏微分方程系统的自由边界问题来刻画,其中自由边界是肿瘤的表面.未知变量包含未被感染的细胞、感染的细胞、坏死的细胞密度、自由病毒密度、肿瘤中细胞的速度以及自由边界r=R(t).该文的目的是对上述数学模型进行分析并找一个使得肿瘤体积收缩到零的条件.

关键词: 肿瘤, 可复制病毒, 双曲系统, 自由边界问题

Abstract: The author considers a procedure for cancer therapy which consists of injecting replication-competent viruses into the tumor. The viruses infect tumor cells, replicate insider them, and eventually cause their death. As
infected cells die, the viruses inside them are released and then proceed to infect adjacent tumor cells. This process is modelled as a free boundary problem for a nonlinear system of hyperbolic differential equations, where the free boundary is the surface of the tumor. The unknowns are the densities of uninfected cells, infected cells, necrotic cells and the free virus particles, and the velocity of cells within the tumor as well as the free boundary r=R(t). The aim of this paper is to explore the conditions under which the tumor can be made to shrink to zero.

Key words: Tumor, Replication-competent virus, Hyperbolic system, Free boundary problem.

中图分类号:

35R35

陶有山. 一个在肿瘤细胞中可复制的病毒模型的数学分析[J]. 数学物理学报, 2006, 26(2): 183-199.

Tao Youshan. Mathematical Analysis of a Model of a Replication-competent Virus in Tumor Cells[J]. Acta mathematica scientia,Series A, 2006, 26(2): 183-199.

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