前列腺癌治疗的数学建模与分析

前列腺癌治疗的数学建模与分析

论文摘要

前列腺癌是一种影响老年男性的恶性肿瘤.这种恶性肿瘤集中在前列腺细胞中,但有时会扩散到周围组织和身体其他部位.这种类型的癌症通常发展缓慢,可以完全消除或诊断后成功治疗.但不幸的是,它可能是致命的.许多数学研究都集中在生物数学和医学上,以期对治疗策略有一个新的认识.因此,本论文的目的是研究前列腺癌的演变和发展,揭示不同治疗方式的疗效.在第一章中,介绍了前列腺癌的生物学背景、目前的治疗方法、与我们工作相关的前列腺癌模型的重要进展.本章也介绍了一些相关数学术语和定理.同时,简要说明了本论文的主要贡献.第二章研究了连续雄激素抑制治疗下前列腺癌的随机模型,研究了噪声和剂量对治疗策略的影响.在随机系统中,噪声对肿瘤细胞的持续和消亡起重要作用,得到了系统平均灭绝和持续的阈值条件.得到平稳分布存在的充分条件.进一步,利用数值模拟的方法对最优处理策略进行估计,最后我们考虑周期性治疗对该模型的影响并得到此种情况下周期解存在的充分条件.该模型说明由于噪音干扰的作用,一种与肿瘤细胞复制相关的药物有利于用CAS治疗策略.另外,分析结果表明如果医生找不到治疗癌症的方法,他们可以尝试去研制一种能够降低耐药细胞活性的药物.这样的作法有利于减轻癌症病人的痛苦程度从而提高其生活质量.第三章研究考虑免疫疗法的前列腺癌的ODE模型.首先,对无免疫治疗策略的模型进行理论分析,研究耐药细胞和免疫细胞之间的相互作用并讨论模型的分支现象.然后,采用数值方法研究疫苗和T-杀伤肿瘤效率对耐药细胞周期行为的影响并进行了分支分析.这一分析表明,在无法治愈的情况下,使用高疫苗量的连续树突状细胞疫苗来增强机体的免疫系统可以防止耐药细胞的复发.此外,在两个周期解存在的情况下,治疗的结果好坏取决于肿瘤细胞的初始状态.这就说明在实际中治疗的起始时间也是一个重要的问题.第四章简要总结了前列腺癌的治疗策略并提出了今后的研究方向.以期对前列腺癌的治疗策略有更深入的了解,进而提出一些有益于患者生活质量的治疗方式.

论文目录

  • 摘要
  • Abstract
  • Chapter 1 Introduction
  •   1.1 Background of prostate cancer and treatment
  •     1.1.1 Hormone therapy
  •     1.1.2 Immunotherapy
  •     1.1.3 Further treatments
  •   1.2 Literature review of mathematical models
  •   1.3 Contributions
  •   1.4 Background of stochastic noise and bifurcation theory
  •     1.4.1 Stochastic differential equations
  •     1.4.2 Bifurcation theory
  • Chapter 2 Stochastic model of CAS therapy
  •   2.1 Model formulation
  •   2.2 Mathematical analysis
  •     2.2.1 Existence and uniqueness of solution
  •     2.2.2 Persistence in mean and extinction
  •     2.2.3 Stationary distribution and ergodicity for system
  •   2.3 Approximation of optimal treatment
  •   2.4 Extension to periodic treatment
  •     2.4.1 Qualitative results
  •     2.4.2 Existence of periodic solutions
  •     2.4.3 Numerical simulations
  •   2.5 Conclusions
  • Chapter 3 Bifurcation in immunotherapy model
  •   3.1 Mathematical model
  •   3.2 Dynamics of model without immunotherapy
  •     3.2.1 Equilibrium points and their stability
  •     3.2.2 Bifurcation analysis
  •   3.3 Bifurcation of model with immunotherapy
  •     3.3.1 The effect of dendritic cells vaccines on tumor cells
  •     3.3.2 Periodic behavior of tumor cells
  •   3.4 Conclusions
  • Chapter 4 Discussions
  • References
  • Academic papers completed and published during the Ph.D.
  • Acknowledgement
  • 文章来源

    类型: 博士论文

    作者: Assia Zazoua

    导师: 王稳地

    关键词: 前列腺癌,随机噪声,持续,灭绝,平稳分布,分支

    来源: 西南大学

    年度: 2019

    分类: 基础科学,医药卫生科技

    专业: 数学,泌尿科学,肿瘤学

    单位: 西南大学

    分类号: R737.25;O175

    总页数: 121

    文件大小: 4421K

    下载量: 44

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    前列腺癌治疗的数学建模与分析
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