未血管化腫瘤生長的多相流模型
發(fā)布時間：2019-05-18 22:22
【摘要】：當今全世界每年新增癌癥病例和癌癥患者死亡人數都在每年地遞增,腫瘤是一種復雜并且嚴重威脅著人類健康與生命的疾病,惡性腫瘤的治療仍是醫(yī)藥學界面臨的還未攻破一大難題,而腫瘤的生長是一個受很多方面影響的極其復雜的過程.腫瘤細胞區(qū)別于正常細胞是在于腫瘤細胞有持續(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來提供營養(yǎng)已達到其不斷的增殖.因此腫瘤的生長過程可以被劃分為兩個階段:腫瘤生長前期的未血管化階段與腫瘤生長后期的血管化階段.由于任何事物都可以簡化為數學符號,并能借用數學建模的方法得以解決,最近,數學建模已成為一種人們理解和預測腫瘤生長的過程的很重要的方法,在現有模型的基礎上,為了能夠幫助人們正確地理解和預測未血管化的腫瘤生長趨勢,本文主要研究未血管化腫瘤在體內微環(huán)境中的生長趨勢,結合了混合物理論、對流擴散反應理論、生物流體力學理論和多相流模型理論,得出了腫瘤生長模型的控制方程組并對此進行了仿真模擬分析.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,腫瘤生長的過程及其賴以生存的微環(huán)境的概念,然后介紹了國內外對腫瘤數學模型的研究現狀和多相流的模型的概念和研究現狀,最后是本文寫作框架.第二章研究了腫瘤在微環(huán)境中生長的基礎數學模型.這是本篇論文的前期工作,該模型是建立在對流擴散反應方程的應用基礎上,構建滿足腫瘤生長特性的對流擴散反應模型來模擬腫瘤的生長趨勢,并通過計算機仿真,成功模擬出腫瘤的生長圖及其微環(huán)境的變化圖,這部分內容主要分為四個小節(jié),分別為:細胞模型,營養(yǎng)物濃度擴散,模型的數值模擬的及結果分析.第三章研究的主要內容是在第二章的腫瘤生長的對流擴散反應方程模型的基礎上進行了模型的改進,利用生物流體力學理論和多相流模型的理論,分別建立了滿足質量守恒,動量守恒,能量守恒的微環(huán)境中未血管化腫瘤生長的多相流模型及其推導過程.
[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.
【學位授予單位】：廣東工業(yè)大學
【學位級別】：碩士
【學位授予年份】：2017
【分類號】：R73-3;O359
本文編號：2480383
[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.
【學位授予單位】：廣東工業(yè)大學
【學位級別】：碩士
【學位授予年份】：2017
【分類號】：R73-3;O359
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