【作者】 黄雪玲；

【导师】 王振友；

【作者基本信息】 广东工业大学 ， 数学， 2017， 硕士

【摘要】 当今全世界每年新增癌症病例和癌症患者死亡人数都在每年地递增,肿瘤是一种复杂并且严重威胁着人类健康与生命的疾病,恶性肿瘤的治疗仍是医药学界面临的还未攻破一大难题,而肿瘤的生长是一个受很多方面影响的极其复杂的过程.肿瘤细胞区别于正常细胞是在于肿瘤细胞有持续疯狂增殖的这一特征,而要想持续的增殖就需要血管的生长来提供营养已达到其不断的增殖.因此肿瘤的生长过程可以被划分为两个阶段:肿瘤生长前期的未血管化阶段与肿瘤生长后期的血管化阶段.由于任何事物都可以简化为数学符号,并能借用数学建模的方法得以解决,最近,数学建模已成为一种人们理解和预测肿瘤生长的过程的很重要的方法,在现有模型的基础上,为了能够帮助人们正确地理解和预测未血管化的肿瘤生长趋势,本文主要研究未血管化肿瘤在体内微环境中的生长趋势,结合了混合物理论、对流扩散反应理论、生物流体力学理论和多相流模型理论,得出了肿瘤生长模型的控制方程组并对此进行了仿真模拟分析.本文在第一章的绪论中介绍了肿瘤模型的研究背景,研究意义,肿瘤生长的过程及其赖以生存的微环境的概念,然后介绍了国内外对肿瘤数学模型的研究现状和多相流的模型的概念和研究现状,最后是本文写作框架.第二章研究了肿瘤在微环境中生长的基础数学模型.这是本篇论文的前期工作,该模型是建立在对流扩散反应方程的应用基础上,构建满足肿瘤生长特性的对流扩散反应模型来模拟肿瘤的生长趋势,并通过计算机仿真,成功模拟出肿瘤的生长图及其微环境的变化图,这部分内容主要分为四个小节,分别为:细胞模型,营养物浓度扩散,模型的数值模拟的及结果分析.第三章研究的主要内容是在第二章的肿瘤生长的对流扩散反应方程模型的基础上进行了模型的改进,利用生物流体力学理论和多相流模型的理论,分别建立了满足质量守恒,动量守恒,能量守恒的微环境中未血管化肿瘤生长的多相流模型及其推导过程.更多还原

【Abstract】 The number of new cancer cases and cancer deaths in the world today is increasing every year.Tumor is a kind of complicated and severe disease which threatening human health and life,and the treatment of malignant tumor is still a big problem that the medical profession has not yet broken.And the growth of the tumor is an extremely complex process that is influenced by many aspects,Tumor cells are distinguished from normal cells by the fact that the tumor cells are continuously inflated,and the need for continuous proliferation requires the growth of blood vessels to provide Nutrition has reached its constant proliferation,so the tumor growth process can be divided into two stages: the early stage of tumor growth and avascular stage of tumor growth stage.Since anything can be simplified as a mathematical symbol and can be solved by means of mathematical modeling.Recently,mathematical modeling has become a very important method of understanding and predicting the process of tumor growth.Based on the existing model,In order to help people to correctly understand and predict the trend of avascular tumor growth,this paper mainly studies the growth trend of avascular tumors in vivo micro-environment,combined with the theory of mixture,convective diffusion theory,bio-fluid mechanics theory and Multi-phase flow model theory,the control equations of tumor growth model were obtained and simulated and analyzed.In the introduction of the first chapter,this paper introduces the research background,the significance of research,the process of tumor growth and the concept of micro-environment,and then introduces the research status and multiphase flow of tumor model at home and abroad The concept of the model and the status quo of the study,and finally the framework of this writing.The second chapter studies the basic mathematical model of tumor growth in microenvironment,which is the preliminary work of this paper.Based on the application of convective diffusion reaction equation,the convective diffusion model is constructed to meet the tumor growth characteristics.The growth trend of tumor was simulated and the changes of tumor growth pattern and microenvironment were successfully simulated bycomputer simulation.This part was divided into four sections: cell model,nutrient concentration diffusion,model value Simulation and analysis of results.The main contents of the third chapter are the improvement of the model of convective diffusion reaction equation of tumor growth in the second chapter.Based on the theory of biological fluid dynamics and the theory of multiphase flow model,The multiphase flow model of unvascularized tumor growth in the microenvironment,which satisfies the conservation of mass,momentum conservation and energy conservation,is established and its derivation process is established.更多还原