發(fā)布時(shí)間：2019-05-18 22:22

【摘要】：當(dāng)今全世界每年新增癌癥病例和癌癥患者死亡人數(shù)都在每年地遞增,腫瘤是一種復(fù)雜并且嚴(yán)重威脅著人類(lèi)健康與生命的疾病,惡性腫瘤的治療仍是醫(yī)藥學(xué)界面臨的還未攻破一大難題,而腫瘤的生長(zhǎng)是一個(gè)受很多方面影響的極其復(fù)雜的過(guò)程.腫瘤細(xì)胞區(qū)別于正常細(xì)胞是在于腫瘤細(xì)胞有持續(xù)瘋狂增殖的這一特征,而要想持續(xù)的增殖就需要血管的生長(zhǎng)來(lái)提供營(yíng)養(yǎng)已達(dá)到其不斷的增殖.因此腫瘤的生長(zhǎng)過(guò)程可以被劃分為兩個(gè)階段:腫瘤生長(zhǎng)前期的未血管化階段與腫瘤生長(zhǎng)后期的血管化階段.由于任何事物都可以簡(jiǎn)化為數(shù)學(xué)符號(hào),并能借用數(shù)學(xué)建模的方法得以解決,最近,數(shù)學(xué)建模已成為一種人們理解和預(yù)測(cè)腫瘤生長(zhǎng)的過(guò)程的很重要的方法,在現(xiàn)有模型的基礎(chǔ)上,為了能夠幫助人們正確地理解和預(yù)測(cè)未血管化的腫瘤生長(zhǎng)趨勢(shì),本文主要研究未血管化腫瘤在體內(nèi)微環(huán)境中的生長(zhǎng)趨勢(shì),結(jié)合了混合物理論、對(duì)流擴(kuò)散反應(yīng)理論、生物流體力學(xué)理論和多相流模型理論,得出了腫瘤生長(zhǎng)模型的控制方程組并對(duì)此進(jìn)行了仿真模擬分析.本文在第一章的緒論中介紹了腫瘤模型的研究背景,研究意義,腫瘤生長(zhǎng)的過(guò)程及其賴(lài)以生存的微環(huán)境的概念,然后介紹了國(guó)內(nèi)外對(duì)腫瘤數(shù)學(xué)模型的研究現(xiàn)狀和多相流的模型的概念和研究現(xiàn)狀,最后是本文寫(xiě)作框架.第二章研究了腫瘤在微環(huán)境中生長(zhǎng)的基礎(chǔ)數(shù)學(xué)模型.這是本篇論文的前期工作,該模型是建立在對(duì)流擴(kuò)散反應(yīng)方程的應(yīng)用基礎(chǔ)上,構(gòu)建滿(mǎn)足腫瘤生長(zhǎng)特性的對(duì)流擴(kuò)散反應(yīng)模型來(lái)模擬腫瘤的生長(zhǎng)趨勢(shì),并通過(guò)計(jì)算機(jī)仿真,成功模擬出腫瘤的生長(zhǎng)圖及其微環(huán)境的變化圖,這部分內(nèi)容主要分為四個(gè)小節(jié),分別為:細(xì)胞模型,營(yíng)養(yǎng)物濃度擴(kuò)散,模型的數(shù)值模擬的及結(jié)果分析.第三章研究的主要內(nèi)容是在第二章的腫瘤生長(zhǎng)的對(duì)流擴(kuò)散反應(yīng)方程模型的基礎(chǔ)上進(jìn)行了模型的改進(jìn),利用生物流體力學(xué)理論和多相流模型的理論,分別建立了滿(mǎn)足質(zhì)量守恒,動(dòng)量守恒,能量守恒的微環(huán)境中未血管化腫瘤生長(zhǎng)的多相流模型及其推導(dǎo)過(guò)程.
[Abstract]:Nowadays, the number of new cancer cases and deaths from cancer patients is increasing every year in the world. Tumors are a complex and serious threat to human health and life. The treatment of malignant tumors is still a difficult problem that has not yet been solved in the field of medicine, and the growth of tumors is an extremely complex process affected by many aspects. The difference between tumor cells and normal cells is that tumor cells have the characteristic of continuous crazy proliferation, and in order to continue to proliferate, the growth of blood vessels is needed to provide nutrition to achieve the continuous proliferation of tumor cells. Therefore, the growth process of tumor can be divided into two stages: the unvascularization stage in the early stage of tumor growth and the vascularization stage in the later stage of tumor growth. Because anything can be simplified as a mathematical symbol and can be solved by means of mathematical modeling, mathematical modeling has recently become a very important method for people to understand and predict the process of tumor growth, on the basis of the existing models. In order to help people correctly understand and predict the growth trend of unvascularized tumors, this paper mainly studies the growth trend of unvascularized tumors in vivo microenvironment, combined with mixture theory and convective diffusion reaction theory. Based on the theory of biological fluid mechanics and multiphase flow model, the governing equations of tumor growth model are obtained and simulated and analyzed. In the introduction of the first chapter, this paper introduces the research background and significance of tumor model, the process of tumor growth and the concept of microenvironment on which it depends. Then the research status of tumor mathematical model and the concept and research status of multiphase flow model at home and abroad are introduced. finally, the writing framework of this paper is presented. In the second chapter, the basic mathematical model of tumor growth in microenvironment is studied. This is the preliminary work of this paper. The model is based on the application of convective diffusion reaction equation, and a convective diffusion reaction model satisfying the growth characteristics of tumor is constructed to simulate the growth trend of tumor, and the model is simulated by computer. The growth map of the tumor and the change map of its microenvironment were successfully simulated. This part of the content is mainly divided into four sections: cell model, nutrient concentration diffusion, numerical simulation of the model and analysis of the results. The main content of the third chapter is to improve the model on the basis of the convective diffusion reaction equation model of tumor growth in the second chapter. By using the theory of biological fluid mechanics and the theory of multiphase flow model, the mass conservation is established respectively. Multiphase flow model of unvascularized tumor growth in microenvironment with conservation of momentum and energy and its derivation process.
【學(xué)位授予單位】：廣東工業(yè)大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2017
【分類(lèi)號(hào)】：R73-3;O359

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本文編號(hào)：2480383