Comprehensive Mathematical Model of Microcirculatory Dynamics(Ⅱ)——Calculation and the Results

Guo Zhongsan; Xiao Fan; Guo Siwen; Wu Yueqing; Gu Leye

Article Contents

Article Navigation > Applied Mathematics and Mechanics > 2000 > 21(5): 523-528

Guo Zhongsan, Xiao Fan, Guo Siwen, Wu Yueqing, Gu Leye. Comprehensive Mathematical Model of Microcirculatory Dynamics(Ⅱ)——Calculation and the Results[J]. Applied Mathematics and Mechanics, 2000, 21(5): 523-528.

Citation:

PDF( 262 KB)

Comprehensive Mathematical Model of Microcirculatory Dynamics(Ⅱ)——Calculation and the Results

Chengdu Institute of Computer Application, Academia Sinica, Chengdu 610041, P. R. China

Received Date: 1999-08-01
Rev Recd Date: 1999-12-23
Publish Date: 2000-05-15

Abstract

Abstract

The mathematical model described in Part I was solved using "influence line method" combining analytical method and finite element method. Many important aspects of microcirculatory dynamics were analyzed and discussed. It show that interstitial fluid pressure changes its sign twice within one arteriolar vasomotion period and it is therefor not important that interstitial fluid pressure is a little higher or lower than atmospheric pressure; arteriolar vasomotion can periodically result in lymph formation and interstitial total pressure plays an important role in this procedure; local regulation of microcirculation can meet metabolic need to some extent in the form of dynamic equilibrium. The property of arteriole as a "resistant vessel" and the efficiency of microvascular network as heat exchanger are also shown. These results show that the comprehensive mathematical model developed in Part I is physiologically reasonable.
- “influence line method”,
- analytical method,
- finite element method,
- microcirculatory dynamics

FullText(HTML)

References(15)

References

[1]	郭仲三,肖帆,郭四稳,等.微循环系统动力学综合数学模型研究(Ⅰ)——理论基础[J].应用数学和力学,1999,20(9):947～954.
[2]	郭仲三.微血管自律运动的流体力学及血液粘弹性质的影响[J].应用数学和力学,1992,13(2):157～163.
[3]	郭仲三.可渗透管网络跨壁传输问题的影响线算法[J].计算物理,1996,13(4):496～500.
[4]	修瑞娟,Intaglietta M.微血管自律运动的研究Ⅰ:微血管自律运动的连续动态观察及电子计算机分析[A].见:修瑞娟,徐弘道编.当代中国的微循环研究[C].卷1.北京:国际文化出版公司,1987:1～16.
[5]	Taylor D G,Dert J L,Bowen B D.A mathematical model of interstitial transport Ⅱ:microvascular exchange in mesentery[J].Microvasc Res,1990,39(3):279～306.
[6]	Kamiya A,Ando J,Shibata M,et al.The efficiency of the vascular-tissue system for oxygen transport in the skeletal muscles[J].Microvasc Re s,1990,39(2):169～185.
[7]	Nair P K,Huang N S,Hellums J D,et al.A simple model fo r prediction of oxygen transportrates by flowing blood in large capillaries[J].Microvasc Res,1990,39(2):203～211.
[8]	Schubert R W,Whalen W J,Nair P.Myocardial PO₂ distrib ution:r elationship to coronary autoregulation[J].Amer J Physiol,1978,223 (4):H361～H370.
[9]	Chato J C.生物传热学基础[M].徐云生,钱壬章译.北京:科学出版社,1991.
[10]	Caro C G,Pedley T J,Schroter R C,et al.血液循环力学[M].丁启明、倪一伟译.北京:科学出版社,1986.
[11]	冯元侦.生物力学[M].北京:科学出版社,1983.
[12]	Meyer J U,Borgstrom P,Lindbom L,et al.Vasomotion patterns in skeletal muscle arterioles during changes in arterial pressure[J].Microvasc Res,1988,35(2):193～203.
[13]	Chato J C.Thermal properties of tissues[A].In:Skalak R,Chien Seds.Handbook of Bioengineering[C].New York,St,Louis,San Francisco,Auckland,Bogota,Hamburg,Johannesburg,London,Madrid,Mexico,Milan,Montreal,New Delhi,Panama,Paris,Sao Paulo,Singapore,Sydney,Tokyo,Toronto:McGraw-Hill Book Company,1987,9.1～9.13.
[14]	Silberberg A.Transport through deformable matrices[J].Biorheology,1989,26(2):291～313.
[15]	杨再春.新编临床医学数据手册[M].北京:金盾出版社,1992.