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  本文選題：隨機微分方程　切入點：隨機腫瘤免疫系統(tǒng)　出處：《太原理工大學》2017年碩士論文　論文類型：學位論文

【摘要】：腫瘤的治療一直以來都是醫(yī)學界的難題,因此對腫瘤的研究也成為越來越多人關(guān)注的焦點。研究腫瘤生長的內(nèi)在規(guī)律以及腫瘤細胞滅絕和持久的充分條件,對預(yù)防和治療癌癥具有十分重要的理論價值和臨床意義。特別是隨機微分方程理論在腫瘤研究中的應(yīng)用,為了解腫瘤演化的潛在機制以及腫瘤治療提供了新的思路和方法。本文基于隨機微分方程和腫瘤免疫模型,系統(tǒng)的研究了隨機漲落對腫瘤滅絕和持久的影響。本論文的主要內(nèi)容和結(jié)論如下:1、研究了環(huán)境噪聲誘導下腫瘤細胞滅絕和存活的閾值問題。通過給出腫瘤細胞的滅絕、弱持久、均值強持久以及隨機持久的定義來表示腫瘤細胞的滅絕與持久,然后利用Ito’s公式和Lyapunov函數(shù)的方法,從純數(shù)學的角度推導出腫瘤細胞滅絕、弱持久以及隨機持久的閾值,這不同于廣泛應(yīng)用的Fokker-Planck方程和有效勢函數(shù)的方法。研究發(fā)現(xiàn),免疫系數(shù)在判斷腫瘤細胞的滅絕與存活中扮演者關(guān)鍵性的角色,隨著免疫強度的增加,腫瘤細胞將經(jīng)歷從隨機持久到弱持久直到最終滅絕。2、研究了免疫監(jiān)視下環(huán)境噪聲誘導的腫瘤細胞的滅絕性。我們使用Ito’s積分的方法從純數(shù)學的角度嚴格的推導出腫瘤細胞滅絕、均值強持久以及隨機持久的充分條件,然后通過數(shù)值模擬發(fā)現(xiàn),腫瘤細胞的滅絕與持久不僅僅依賴于免疫強度還依賴于噪聲的強度。當免疫強度能夠控制腫瘤細胞的增長時,免疫波動能夠誘導并加速腫瘤細胞的滅絕,有益于腫瘤的治療。當免疫強度不足以控制腫瘤細胞的擴散時,免疫波動將加強腫瘤細胞的隨機波動,不利于腫瘤的治療。3、研究了周期治療下腫瘤細胞的滅絕性和持久性。本文給出了促使腫瘤細胞滅絕與弱持久的周期治療強度的閾值條件,并且此結(jié)論得到嚴格的證明。另外研究發(fā)現(xiàn)腫瘤細胞的滅絕與持久既依賴于周期治療的強度也依賴于噪聲的強度,并且隨著周期治療強度的不斷增加,腫瘤細胞將經(jīng)歷從弱持久到滅絕的轉(zhuǎn)化過程。當周期治療不足以消除癌細胞時,外部噪聲將可能導致且加快腫瘤細胞的滅絕,這說明當周期治療強度很弱時,噪聲有利于腫瘤的治療。
[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.
【學位授予單位】：太原理工大學
【學位級別】：碩士
【學位授予年份】：2017
【分類號】：O211.63;R73-3

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本文編號：1610768