动脉血管非稳态血液流动建模及数值分析

论文总字数：31637字

摘 要

本文以主动脉血液流动问题作为研究对象，将动脉血管简化为一刚性圆柱直管，将血液看成是单相不可压缩牛顿流体，利用连续性方程及纳维-斯托克斯方程（N-S方程），建立了动脉血管非稳态血液流动模型；接着，使用两种Matlab编程方法，开发出了两个动脉血管瞬态血液流动模型的数值分析程序，得到了两种方法下的血管内血液流速分布及血流量、壁面剪切应力等一些血液流动参数。通过两者之间的对比，保证结果的正确性；最后，修改模型中的部分参数，如压强、血液运动粘度、血管半径，得到了不同参数下的血流量、壁面剪切应力等血液流动参数。通过分析它们之间的差异，得出了压强、血液运动粘度、血管半径的变化对于血液流动参数的影响，并由此得到了动脉粥样硬化等血管类疾病的大致病理过程，从而为此类疾病的预防及诊治提供了必要的理论依据。

关键词：动脉粥样硬化； 动脉血管；血液流动 ；N-S方程；数值分析

The modeling and numerical analysis of unsteady blood flow in artery

Academic No. : 02009424 Name: WangChangbao

Supervised by LinXiaohui

Abstract: With the improvement of people’s living standards, poor dietary habit gradually forms and generally induces hypertension, hyperglycemia, hyperlipidemia and obesity. Hypertension makes the blood pressure rise up, hyperglycemia and hyperlipidemia increases the blood viscosity, obesity causes the reduction of vessel diameter. All these lead to the frequent generation of vascular diseases and they have become the greatest threat to human’s health. Among the vascular diseases, atherosclerosis is the most common. Thus, to explore the pathogenesis of atherosclerosis undoubtedly has practical significance.

This paper takes aortic blood flow problems as the research object. The artery is simplified as a rigid cylindrical straight tube. The blood is considered as a single-phase incompressible Newtonian fluid. After that, using the continuity equation and Navier-Stokes equations (N-S equation) to establish the arterial unsteady blood flow model; then, this paper gives out two numerical analysis programs for arterial transient blood flow model by two Matlab programming methods, obtains the velocity distribution of blood flow in artery and some blood flow parameters, such as blood flow volume and wall shear stress under the two methods. Through the comparison of two results, the accuracy of the results can be ensured; finally, modifying some parameters in the model, such as pressure, blood kinematic viscosity, blood vessel radius, to obtain blood flow volume, wall shear stress under different parameters. By analyzing the differences between them, the paper obtains the influence on the blood flow parameters when the pressure, the kinematic viscosity of blood, blood vessel radius changes, and thus gets the general pathological process of atherosclerosis and other vascular diseases, which can provide the necessary theoretical basis for the prevention, diagnosis and treatment of such diseases.

Key words: Atherosclerosis; arteries; blood flow; N-S equation; numerical analysis

目 录

摘要 I

Abstract II

第一章 绪论 1

1.1 研究背景及意义 1

1.2 国内外研究历史及现状 1

1.3 本文主要内容 2

第二章 动脉血管血液流动理论基础 4

2.1 流体的连续介质假设和基本特性 4

2.1.1 流体的连续介质假设 4

2.1.2 流体的基本特性 4

2.2 流体运动基本控制方程 5

2.2.1 连续性方程 5

2.2.2 动量方程——纳维-斯托克斯方程 6

2.3 本章小结 9

第三章 动脉血管血液流动建模 10

3.1 血液的性质及简化模型 10

3.1.1 血液的性质 10

3.1.2 血液的简化模型 10

3.2 动脉血管血液流动建模 10

3.2.1 运动控制方程 10

3.2.2 血管入口压力拟合及压力分布 12

3.3 初始及边界条件 13

3.3.1 初始条件 13

3.3.2 边界条件 14

3.4 血液流动参数计算 14

3.4.1 血流量计算 14

3.4.2 壁面剪切应力计算 15

3.5 本章小结 15

第四章 数值分析 16

4.1 模型方程处理 16

4.1.1 无量纲化 16

4.1.2 离散化 17

4.2 龙格-库塔法 18

4.3 编程求解 19

4.3.1 Matlab直接编程 19

4.3.2 pdepe()函数编程 20

4.4 数值计算结果及分析 21

4.4.1 管内血液流速分布 21

4.4.2 血液流动参数计算结果 22

4.4.3 模型参数对结果的影响 22

4.5 本章小结 24

第五章 总结与展望 25

5.1 总结 25

5.2 展望 25

致 谢 26

参考文献 27

附录A 血压多项式拟合程序 28

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