基于随机微分方程的肿瘤细胞灭绝性和持久性研究

发布时间：2018-03-14 10:17

本文选题：随机微分方程　切入点：随机肿瘤免疫系统　出处：《太原理工大学》2017年硕士论文　论文类型：学位论文

【摘要】：肿瘤的治疗一直以来都是医学界的难题,因此对肿瘤的研究也成为越来越多人关注的焦点。研究肿瘤生长的内在规律以及肿瘤细胞灭绝和持久的充分条件,对预防和治疗癌症具有十分重要的理论价值和临床意义。特别是随机微分方程理论在肿瘤研究中的应用,为了解肿瘤演化的潜在机制以及肿瘤治疗提供了新的思路和方法。本文基于随机微分方程和肿瘤免疫模型,系统的研究了随机涨落对肿瘤灭绝和持久的影响。本论文的主要内容和结论如下:1、研究了环境噪声诱导下肿瘤细胞灭绝和存活的阈值问题。通过给出肿瘤细胞的灭绝、弱持久、均值强持久以及随机持久的定义来表示肿瘤细胞的灭绝与持久,然后利用Ito’s公式和Lyapunov函数的方法,从纯数学的角度推导出肿瘤细胞灭绝、弱持久以及随机持久的阈值,这不同于广泛应用的Fokker-Planck方程和有效势函数的方法。研究发现,免疫系数在判断肿瘤细胞的灭绝与存活中扮演者关键性的角色,随着免疫强度的增加,肿瘤细胞将经历从随机持久到弱持久直到最终灭绝。2、研究了免疫监视下环境噪声诱导的肿瘤细胞的灭绝性。我们使用Ito’s积分的方法从纯数学的角度严格的推导出肿瘤细胞灭绝、均值强持久以及随机持久的充分条件,然后通过数值模拟发现,肿瘤细胞的灭绝与持久不仅仅依赖于免疫强度还依赖于噪声的强度。当免疫强度能够控制肿瘤细胞的增长时,免疫波动能够诱导并加速肿瘤细胞的灭绝,有益于肿瘤的治疗。当免疫强度不足以控制肿瘤细胞的扩散时,免疫波动将加强肿瘤细胞的随机波动,不利于肿瘤的治疗。3、研究了周期治疗下肿瘤细胞的灭绝性和持久性。本文给出了促使肿瘤细胞灭绝与弱持久的周期治疗强度的阈值条件,并且此结论得到严格的证明。另外研究发现肿瘤细胞的灭绝与持久既依赖于周期治疗的强度也依赖于噪声的强度,并且随着周期治疗强度的不断增加,肿瘤细胞将经历从弱持久到灭绝的转化过程。当周期治疗不足以消除癌细胞时,外部噪声将可能导致且加快肿瘤细胞的灭绝,这说明当周期治疗强度很弱时,噪声有利于肿瘤的治疗。
[Abstract]:The treatment of cancer has always been a difficult problem in the medical field, so the study of tumor has become the focus of more and more people. It has important theoretical value and clinical significance for the prevention and treatment of cancer, especially the application of stochastic differential equation theory in cancer research. It provides new ideas and methods for understanding the potential mechanism of tumor evolution and tumor therapy. Based on stochastic differential equation and tumor immune model, The effects of random fluctuations on tumor extinction and persistence are systematically studied. The main contents and conclusions of this paper are as follows: 1. The threshold of tumor cell extinction and survival induced by ambient noise is studied. The definitions of mean strong persistence and random persistence are used to denote the extinction and persistence of tumor cells. Then, by using Ito's formula and Lyapunov function, the thresholds of tumor cell extinction, weak persistence and random persistence are derived from the point of view of pure mathematics. This is different from the widely used Fokker-Planck equation and the method of effective potential function. The study found that immune coefficient plays a key role in judging the extinction and survival of tumor cells, as the immune intensity increases, Tumor cells will undergo from random persistence to weak persistence until extinction. 2. The extinction of tumor cells induced by environmental noise under immune surveillance is studied. We use the Ito's integral method to strictly deduce the extinction of tumor cells from the point of view of pure mathematics. The sufficient conditions of mean strong persistence and random persistence are found by numerical simulation. It is found that the extinction and persistence of tumor cells depend not only on the immune intensity but also on the intensity of noise. When the immune intensity can control the growth of tumor cells, Immune fluctuations can induce and accelerate the extinction of tumor cells, which is beneficial to the treatment of tumors. When the immune intensity is not enough to control the proliferation of tumor cells, immune fluctuations will enhance the random fluctuations of tumor cells. This paper studies the extinction and persistence of tumor cells under periodic therapy. In this paper, the threshold conditions for the intensity of cycle therapy to promote the extinction and weak persistence of tumor cells are given. In addition, the extinction and persistence of tumor cells depends on both the intensity of periodic therapy and the intensity of noise, and increases with the intensity of periodic therapy. When cycle therapy is not enough to eliminate cancer cells, external noise may cause and accelerate the extinction of tumor cells, indicating that when the cycle therapy intensity is very weak, Noise is beneficial to the treatment of tumors.
【学位授予单位】：太原理工大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O211.63;R73-3

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