肺支气管内气体分布与流动的研究
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摘要
随着人们生存的外界环境的变化，如大气、水源、食品污染，人口密度剧增，以及高节奏大压力的生活方式，呼吸系统疾病已经成为危害我国人民健康的常见疾病，因而对呼吸系统疾病的研究显得十分重要及迫切。目前从生物学与临床医学角度已进行了大量工作，如从氧自由基、DNA角度研究肺病变时的分子生物学变化，通过各种显微镜进行微观形态学观察，并通过动物实验和临床观察，得到疾病的各种表观特征，指导医生进行治疗。虽然上述研究以及气体分析、医学影像技术等新技术新设备对医生诊治有很大帮助，但是仅仅通过上述手段是不够的，由于呼吸系统，特别是支气管树的特殊构造，无法定量检测出支气管树内不同部位的气体流动状况和压力分布，只能依靠其他方法间接测到肺内压和主气道压力，这对疾病的诊治不利，因此有必要从物理的力学的角度，研究呼吸时肺支气管树内的气体流动问题。
国内外学者在呼吸力学问题的研究中，通过物理实验和数学模型模拟方法，研究气管内气体流动、肺部气体交换、呼吸道的压力降以及肺的机械通气等问题，并取得了不少成果。但在肺通气阻力问题方面，这些数学模型将呼吸系统简化为几个部分，对其做整体研究，缺乏对支气管树局部的考虑，没有体现出支气管树内不同位置气体流动的差异。
本文从整体和局部两个方面研究支气管树内的气体的分布与流动情况。在整体方面利用流体网络理论，建立支气管树在前五至七级为非对称分叉，后面的分级为对称分叉结构的三参数集中参数模型，利用Gear算法求解常微分方程组，得到正常呼吸过程中气体在肺支气管树内不同分段的压力和流量分布，较好体现了气体在肺支气管树前几级的分配和压力变化。并在此基础上探讨了支
四川大学硕士学位论文
气管局部受阻时，肺支气管树内不同部位所受到的影响及压力和流量的变化，
并进行了比较;在局部方面，利用计算流体力学的基本理论和通用计算流体力
学软件，对支气管树一级分叉部位的气体流动进行了二维和三维模型的数值模
拟和分析。得到气管内的气体在一个呼吸周期非定常条件下的流动变化，模拟
结果与实验观察相吻合。并与定常条件下的计算结果进行了比较。
本文所做的工作对认识肺支气管树在生理、病理状态下的气流分布很有意
义，对进一步研究气道阻力、气道病变受阻的气体流动状况等的理论研究和临
床应用具有较大帮助。
Respiratory diseases have become very common ailments threatening people's health and lives with environmental deteriorating. Many factors, such as atmospheric pollution, water pollution, food pollution, population density leaping and high-pressured life style, etc. could be counted as the causes. Currently, variety of researches in biological and medical fields is being carried out. For instance, investigations into the changes of molecular biology in pathological changes of the lungs from the angle of oxygen-derived free radicals and DNA, the observation of micro- configuration using various microscopes, investigation of the apparent characteristics of diseases through animal test and clinic diagnosis, etc. have proved helpful approaches. Although more and more newly-developed techniques and equipment mentioned above have come into use in clinic diagnosis and therapies, many problems are kept unsolved in the research of the lungs. Pressure distribution and airflow status in the bronchial tree cannot be measured directly and exactly due to the complex and fragile structure of the bronchial tree, with only the pressure in the trachea and lungs being measured indirectly in other ways. This is an obstacle to the diagnosis and cure of the lung diseases. So physical and mechanical modeling is but a feasible method to explore the airflow and pressure distribution in bronchial tree during respiration.
Many a mathematical model about investigation into airflow in the trachea, gas exchange in the lungs, pressure drop in the bronchial passages, and lung ventilation
have been set up and some useful results have been obtained. However, in view of the resistance of pulmonary ventilation, these mathematical models simplified respiratory system into several parts in order to make a overall study, so that they are lack of considering localities of the bronchial tree and do not give the differences of airflow between various locations.
The air distribution and airflow status in the bronchial tree has been dealt with in the present thesis in two different ways - local and overall. Based on the theory of fluid network, a three-element lumped parameter model of bronchial tree was proposed in the overall treatment. It was assumed that the upper five or seven generations of the twenty-four generations of the respiratory airway are asymmetric, while the rest are symmetric. The Gear method was applied to solve the ordinary differential equations of the mathematical model. The pressure and flow rate distributions in different positions of the lungs have been computed, and fairly reasonable pressure change and air distribution along the upper generations of bronchial tree have been obtained. In addition, the effects of partial bronchial obstruction on the change of pressure and flow at different locations in the bronchial tree were compared to the results under the normal physiological conditions. Based on the basic theory and software of computational fluid mechanics, two dimensional and three dimensional flows at the bifurcation area of the first generation were modeled and solved mathematically in the local treatment. The results of the change of flow during a single respiratory period were matched with the observance of experiment by other authors. The results were also compared to those in steady conditions.
The results of this research may lead to meaningful understanding of the distribution of airflow along the bronchial tree under physiological and pathological conditions and may offer a helpful basis for the further study in the theoretical and clinical research of the resistance and the airflow along normal and blocked respiratory airways.
国内外学者在呼吸力学问题的研究中，通过物理实验和数学模型模拟方法，研究气管内气体流动、肺部气体交换、呼吸道的压力降以及肺的机械通气等问题，并取得了不少成果。但在肺通气阻力问题方面，这些数学模型将呼吸系统简化为几个部分，对其做整体研究，缺乏对支气管树局部的考虑，没有体现出支气管树内不同位置气体流动的差异。
本文从整体和局部两个方面研究支气管树内的气体的分布与流动情况。在整体方面利用流体网络理论，建立支气管树在前五至七级为非对称分叉，后面的分级为对称分叉结构的三参数集中参数模型，利用Gear算法求解常微分方程组，得到正常呼吸过程中气体在肺支气管树内不同分段的压力和流量分布，较好体现了气体在肺支气管树前几级的分配和压力变化。并在此基础上探讨了支
四川大学硕士学位论文
气管局部受阻时，肺支气管树内不同部位所受到的影响及压力和流量的变化，
并进行了比较;在局部方面，利用计算流体力学的基本理论和通用计算流体力
学软件，对支气管树一级分叉部位的气体流动进行了二维和三维模型的数值模
拟和分析。得到气管内的气体在一个呼吸周期非定常条件下的流动变化，模拟
结果与实验观察相吻合。并与定常条件下的计算结果进行了比较。
本文所做的工作对认识肺支气管树在生理、病理状态下的气流分布很有意
义，对进一步研究气道阻力、气道病变受阻的气体流动状况等的理论研究和临
床应用具有较大帮助。
Respiratory diseases have become very common ailments threatening people's health and lives with environmental deteriorating. Many factors, such as atmospheric pollution, water pollution, food pollution, population density leaping and high-pressured life style, etc. could be counted as the causes. Currently, variety of researches in biological and medical fields is being carried out. For instance, investigations into the changes of molecular biology in pathological changes of the lungs from the angle of oxygen-derived free radicals and DNA, the observation of micro- configuration using various microscopes, investigation of the apparent characteristics of diseases through animal test and clinic diagnosis, etc. have proved helpful approaches. Although more and more newly-developed techniques and equipment mentioned above have come into use in clinic diagnosis and therapies, many problems are kept unsolved in the research of the lungs. Pressure distribution and airflow status in the bronchial tree cannot be measured directly and exactly due to the complex and fragile structure of the bronchial tree, with only the pressure in the trachea and lungs being measured indirectly in other ways. This is an obstacle to the diagnosis and cure of the lung diseases. So physical and mechanical modeling is but a feasible method to explore the airflow and pressure distribution in bronchial tree during respiration.
Many a mathematical model about investigation into airflow in the trachea, gas exchange in the lungs, pressure drop in the bronchial passages, and lung ventilation
have been set up and some useful results have been obtained. However, in view of the resistance of pulmonary ventilation, these mathematical models simplified respiratory system into several parts in order to make a overall study, so that they are lack of considering localities of the bronchial tree and do not give the differences of airflow between various locations.
The air distribution and airflow status in the bronchial tree has been dealt with in the present thesis in two different ways - local and overall. Based on the theory of fluid network, a three-element lumped parameter model of bronchial tree was proposed in the overall treatment. It was assumed that the upper five or seven generations of the twenty-four generations of the respiratory airway are asymmetric, while the rest are symmetric. The Gear method was applied to solve the ordinary differential equations of the mathematical model. The pressure and flow rate distributions in different positions of the lungs have been computed, and fairly reasonable pressure change and air distribution along the upper generations of bronchial tree have been obtained. In addition, the effects of partial bronchial obstruction on the change of pressure and flow at different locations in the bronchial tree were compared to the results under the normal physiological conditions. Based on the basic theory and software of computational fluid mechanics, two dimensional and three dimensional flows at the bifurcation area of the first generation were modeled and solved mathematically in the local treatment. The results of the change of flow during a single respiratory period were matched with the observance of experiment by other authors. The results were also compared to those in steady conditions.
The results of this research may lead to meaningful understanding of the distribution of airflow along the bronchial tree under physiological and pathological conditions and may offer a helpful basis for the further study in the theoretical and clinical research of the resistance and the airflow along normal and blocked respiratory airways.
引文
1 蔡柏蔷，呼吸内科分册，中国协和医科大学出版社，2000
2 朱贵卿，呼吸内科学，人民卫生出版社，1984
3 陶仲为，呼吸系统疾病，山东科学技术出版社，1980
4 钟南山，现代呼吸病进展，中国医药科技出版社，1994
5 李真等，呼吸病诊疗全书，中国医药科技出版社，2000
6 冯元桢，生物力学，北京：科学出版社，1983
7 陶祖莱，生物流体力学，北京：科学出版社，1984
8 Haselton F.R, Scherer P. Flow visualization of steady streaming in oscillatory flow through a bifurcating tube, Journal of Fluid Mechanics 1982;123:315
9 Snyder.B, Olson,D.E. Flow development in a model airway bronchus, Journal of Fluid Mechanics 1989;207:379
10 Kulkarni,A.K, Meyers,J, McHugh,E Numerical simulation of airflow in human bronchial passages during high-frequency ventilation, Bioengineering, Proceedings of the Northeast Conference 1990:113
11 B.Vielle, G.Chauvet. Cyclic model of respiration applied to asymmetrical ventilation and periodic breathing, Journal of Biomedical. Engineering 1993;15(3):251
12 Evrensel Cahit A, Khan Md Raquid, Elli Shahram, et al. Viscous air flow through a rigid tube with a compliant lining. Journal of Biomechanical Engineering, Transactions of the ASME 1993;115(3):262
13 Popwell RE, Peattie RA. Transition to turbulence in oscillating flows through a model bronchial bifurcation, Advances in Bioengineering American Society of Mechanical Engineers, Bioengineering Division (Publication) BED 1993:26 ASME, New York.
14 Ginzburg I, Elad D. Dynamic model of the bronchial tree, Journal of Biomedical Engineering 1993; 15(4): 283
15 Ashgarian Bahman, Anjilvel Satish. Monte Carlo calculation of the deposition efficiency of inhaled particles in lower airways, Journal of Aerosol Science 1994;25(4):711
16 Ueda,Yoshiro, Okaniwa,Takashi, Oka,Kotaro, Tanishita, Kazuo. Transition to turbulence in a bifurcation airways model, American Society of Mechanical Engineers,Bioengineering Division 1996;33:17
17 Wilquem,F, Degrez,G. Numerical modeling of steady inspiratory airflow through a three-generation model of the human central airways, Journal of Biomechanical Engineering, Transactions of the ASME 1997; 119(1):59
18 Ghista Dhanjoo N. Lung ventilartory performance pressure-volume model and parametric simulation for disease detection, Annual International Conference of the IEEE Engineering in Medicine and Biology—Proceedings 1997;5:2165
19 Baruch B.Lieber, Yao Zhao. Oscillatory flow in a symmetric bifurcation airway model, Annals of Biomedical Engineering 1998;26(5):821
20 Peattie,R.A, Schwarz,W. Experimental investigation of oscillatory flow through a symmetrically bifurcating tube, Journal of Biomechanical Engineering,Transactions of the ASME 1998;120(5):584
21 Farag Ashraf, Olson Dan E, Hammersley Jeffrey, et al. Effect of a 3-dimensional inlet on the flow characteristics in a symmetric bifurcation model of human pulmonary system,Advances in Bioengineering American Society of Mechanical Engineers, Bioengineering Division (Publication) BED 1998;36:101 ASME, Fairfield, NJ, USA.
22 Renotte C, Remy M, Saucez Ph. Dynamic model of airway pressure drop, Medical &
Biological Engineering & Computing 1998;36(1): 101
23 Ramuzat,A, Richard, H, Riethmuller, M.L. Unsteady flow within lung bifurcations, Annual International Conference of the IEEE Engineering in Medicine and Biology-Proceedingsl p 348
24 G.Tanaka, T.Ogata, K.Oka, K.Tanishita. Spatial and temporal variation of secondary flow during oscillatory flow in model human central airways, Journal of Biomechanical Engineering 1999; 121:565
25 Guido Avanzolini, Paolo Barbini, Fabrizio Bernardi, et al. Role of the mechanical properties of tracheobronchial airways in determining the respiratory resistance time course, Annals of Biomedical Engineering 2001; 29(7):575
26 J.K.Comer, C.Kleinstreuer, Z.Zhang. Flow structure and particle deposition patterns in double-bifurcation airway models.Part 1.Air flow fields, Journal of Fluid Mechanics 2001;435:25
27 卢虹冰、白净、张立藩，多元非线性人体循环呼吸系统模型及其应用，第四军医大学学报 1999；20(3)：190
28 仇安琪、白净，人体呼吸系统数学模型，北京生物医学工程 2000；19(1)：6
29 高文，呼吸系统的物理模型，天津成人高等学校联合学报 2001；3(4)：90
30 周衍椒、张镜如，生理学(第二版)，人民卫生出版社，1995
31 邱树华，刘国隆，解剖生理学，上海科学技术出版社，1986
32 罗志昌，流体网络理论，机械工业出版社，1988
33 李大侃，常微分方程数值解，浙江大学出版社，1994
34 李庆扬，常微分方程数值解法(刚性问题与边值问题)，高等教育出版社，1991
35 谭浩强，C程序设计，清华大学出版社，1991
36 徐士良，C常用算法程序集，清华大学出版社，1996
37 J．F．纳恩，应用呼吸生理学，科学出版社，1983
38 许波，Matlab 工程数学应用，清华大学出版社，2000
39 刘导治，计算流体力学基础，北京航空航天大学出版社，1989
40 刘顺隆、郑群，计算流体力学，哈尔滨工程大学出版社，1998
41 熊鳌魁、詹德新，不可压流场数值模拟办法综述，武汉交通科技大学学报，1999；23(5)：523
42 顾尔祚，流体力学有限差分法基础，上海交通大学出版社，1988
43 苏铭德，计算流体力学基础，清华大学出版社，1997
44 谭浩强、田淑清，Fortran语言—Fortran77结构化程序设计，清华大学出版社，1990
45 姚征、陈康民，CFD通用软件综述，上海理工大学学报，2002：24(2)：137
46 李勇、刘志友、安亦然，介绍计算流体力学通用软件—Fluent．水动力学研究与进展，2001；16(2)：254
2 朱贵卿，呼吸内科学，人民卫生出版社，1984
3 陶仲为，呼吸系统疾病，山东科学技术出版社，1980
4 钟南山，现代呼吸病进展，中国医药科技出版社，1994
5 李真等，呼吸病诊疗全书，中国医药科技出版社，2000
6 冯元桢，生物力学，北京：科学出版社，1983
7 陶祖莱，生物流体力学，北京：科学出版社，1984
8 Haselton F.R, Scherer P. Flow visualization of steady streaming in oscillatory flow through a bifurcating tube, Journal of Fluid Mechanics 1982;123:315
9 Snyder.B, Olson,D.E. Flow development in a model airway bronchus, Journal of Fluid Mechanics 1989;207:379
10 Kulkarni,A.K, Meyers,J, McHugh,E Numerical simulation of airflow in human bronchial passages during high-frequency ventilation, Bioengineering, Proceedings of the Northeast Conference 1990:113
11 B.Vielle, G.Chauvet. Cyclic model of respiration applied to asymmetrical ventilation and periodic breathing, Journal of Biomedical. Engineering 1993;15(3):251
12 Evrensel Cahit A, Khan Md Raquid, Elli Shahram, et al. Viscous air flow through a rigid tube with a compliant lining. Journal of Biomechanical Engineering, Transactions of the ASME 1993;115(3):262
13 Popwell RE, Peattie RA. Transition to turbulence in oscillating flows through a model bronchial bifurcation, Advances in Bioengineering American Society of Mechanical Engineers, Bioengineering Division (Publication) BED 1993:26 ASME, New York.
14 Ginzburg I, Elad D. Dynamic model of the bronchial tree, Journal of Biomedical Engineering 1993; 15(4): 283
15 Ashgarian Bahman, Anjilvel Satish. Monte Carlo calculation of the deposition efficiency of inhaled particles in lower airways, Journal of Aerosol Science 1994;25(4):711
16 Ueda,Yoshiro, Okaniwa,Takashi, Oka,Kotaro, Tanishita, Kazuo. Transition to turbulence in a bifurcation airways model, American Society of Mechanical Engineers,Bioengineering Division 1996;33:17
17 Wilquem,F, Degrez,G. Numerical modeling of steady inspiratory airflow through a three-generation model of the human central airways, Journal of Biomechanical Engineering, Transactions of the ASME 1997; 119(1):59
18 Ghista Dhanjoo N. Lung ventilartory performance pressure-volume model and parametric simulation for disease detection, Annual International Conference of the IEEE Engineering in Medicine and Biology—Proceedings 1997;5:2165
19 Baruch B.Lieber, Yao Zhao. Oscillatory flow in a symmetric bifurcation airway model, Annals of Biomedical Engineering 1998;26(5):821
20 Peattie,R.A, Schwarz,W. Experimental investigation of oscillatory flow through a symmetrically bifurcating tube, Journal of Biomechanical Engineering,Transactions of the ASME 1998;120(5):584
21 Farag Ashraf, Olson Dan E, Hammersley Jeffrey, et al. Effect of a 3-dimensional inlet on the flow characteristics in a symmetric bifurcation model of human pulmonary system,Advances in Bioengineering American Society of Mechanical Engineers, Bioengineering Division (Publication) BED 1998;36:101 ASME, Fairfield, NJ, USA.
22 Renotte C, Remy M, Saucez Ph. Dynamic model of airway pressure drop, Medical &
Biological Engineering & Computing 1998;36(1): 101
23 Ramuzat,A, Richard, H, Riethmuller, M.L. Unsteady flow within lung bifurcations, Annual International Conference of the IEEE Engineering in Medicine and Biology-Proceedingsl p 348
24 G.Tanaka, T.Ogata, K.Oka, K.Tanishita. Spatial and temporal variation of secondary flow during oscillatory flow in model human central airways, Journal of Biomechanical Engineering 1999; 121:565
25 Guido Avanzolini, Paolo Barbini, Fabrizio Bernardi, et al. Role of the mechanical properties of tracheobronchial airways in determining the respiratory resistance time course, Annals of Biomedical Engineering 2001; 29(7):575
26 J.K.Comer, C.Kleinstreuer, Z.Zhang. Flow structure and particle deposition patterns in double-bifurcation airway models.Part 1.Air flow fields, Journal of Fluid Mechanics 2001;435:25
27 卢虹冰、白净、张立藩，多元非线性人体循环呼吸系统模型及其应用，第四军医大学学报 1999；20(3)：190
28 仇安琪、白净，人体呼吸系统数学模型，北京生物医学工程 2000；19(1)：6
29 高文，呼吸系统的物理模型，天津成人高等学校联合学报 2001；3(4)：90
30 周衍椒、张镜如，生理学(第二版)，人民卫生出版社，1995
31 邱树华，刘国隆，解剖生理学，上海科学技术出版社，1986
32 罗志昌，流体网络理论，机械工业出版社，1988
33 李大侃，常微分方程数值解，浙江大学出版社，1994
34 李庆扬，常微分方程数值解法(刚性问题与边值问题)，高等教育出版社，1991
35 谭浩强，C程序设计，清华大学出版社，1991
36 徐士良，C常用算法程序集，清华大学出版社，1996
37 J．F．纳恩，应用呼吸生理学，科学出版社，1983
38 许波，Matlab 工程数学应用，清华大学出版社，2000
39 刘导治，计算流体力学基础，北京航空航天大学出版社，1989
40 刘顺隆、郑群，计算流体力学，哈尔滨工程大学出版社，1998
41 熊鳌魁、詹德新，不可压流场数值模拟办法综述，武汉交通科技大学学报，1999；23(5)：523
42 顾尔祚，流体力学有限差分法基础，上海交通大学出版社，1988
43 苏铭德，计算流体力学基础，清华大学出版社，1997
44 谭浩强、田淑清，Fortran语言—Fortran77结构化程序设计，清华大学出版社，1990
45 姚征、陈康民，CFD通用软件综述，上海理工大学学报，2002：24(2)：137
46 李勇、刘志友、安亦然，介绍计算流体力学通用软件—Fluent．水动力学研究与进展，2001；16(2)：254