Comprehensive Mathematical Model of Microcirculatory Dynamics(Ⅰ)——Basic Theory

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

Volume 20 Issue 9

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Article Navigation > Applied Mathematics and Mechanics > 1999 > 20(9): 947-954

Guo Zhongsan, Xiao Fan, Guo Siwen, Wu Yueqing, Gu Leye. Comprehensive Mathematical Model of Microcirculatory Dynamics(Ⅰ)——Basic Theory[J]. Applied Mathematics and Mechanics, 1999, 20(9): 947-954.

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Comprehensive Mathematical Model of Microcirculatory Dynamics(Ⅰ)——Basic Theory

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

Received Date: 1998-07-19
Rev Recd Date: 1999-04-20
Publish Date: 1999-09-15

Abstract

Abstract

Under the basis of physiological data,a nonlinear and unsteady comprehensive mathematical model of microcirculatory dynamics with distributed parameters is developed.Hemodynamics,interstitium dynamics,lymph dynamics,dynamics of protein transport,oxygen dynamics,dynamics of heat transfer,and myogenic and metabolic regulation procedures are included.The interactions between these factors were comprehensively exhibited.The influences of arteriolar vasomotion and nonlinear viscoelasticity of blood in arteriole are considered.A simplified vessel network consisting of arteriole,open and reserved capillaries,venule,initial lymphatics and arteriole-venule anastomose is adopted as the geometrical model.This kind of comprehensive mathematical model is helpful in analyzing clinical data and developing a "numerical experiment method" in microcirculation research.
- microcirculatory system,
- comprehensive mathematical model,
- interaction,
- numerical experiment

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References(13)

References

[1]	Duran W N,Marsicano T H,Anderson R W.Capillary reserveini sometrically contractingdog hearts[J].Am J Physiol,1977,233(2):H276~ H281.
[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]	Pries A R,Secomb T W,Gaehtgens P,et al.Blood flow in microvascular networks:experiments and simulation[J].Circ Res,1990,67:826~834.
[4]	Pries A R,Ley K,Claassen M,etal.Red celldi stribution at microvascular bifurcations[J].Microvasc Res,1989,38(1):81~101.
[5]	Taylor D G,Bert J L,Bowen B D.A mathematical model of interstitialtransport I.Theory[J].Microvasc Res,1990,39(3):253~278.
[6]	Siberberg A.Transport through deformable matrices[J].Biorheology,1989,26(2):291~313.
[7]	Guyton A C,Granger H J,Taylor A E.Interstitial fluid pressure[J].Physiol Rev,1971,51(3):527~563.
[8]	Casley-Smith J R.Lymph and lymphatics[A].In:Kaley G,Altura B M Eds.Microcirculation Vol.1[C].Baltimore,London,Tokyo:Univ Park Press,1977,423~502.
[9]	Granger H J,Shepherd A P.Dynamics and control ofthe microcirculation[J].Adv in Biomed Eng,1979,7:1~63.
[10]	Hogan R D,Unthank J L.The initiallym phatics as sensors of interstitialfluid volume[J].Microvasc Res,1986,31(3):317~324.
[11]	Schmid-Schonbein G W.Microlym phatics and lymph flow[J].Physiol Rev,1990,70(4):987~1028.
[12]	郭仲三.论微循环系统中结构与介质的相互作用[A].见:曹志远主编.结构与介质的相互作用理论及其应用[C],北京:河海大学出版社,1993,125~133.
[13]	Chato J C.Therm alproperties of tissues[A].In:Skalak R,Chien S Eds.Hand book of Bioengineering[M].New York,Auckland,St Louis,San Francisco,Bogota,Hamburg,Johannes burg,London,Madrid,Mexico,Milan,Montreal,New Delhi,Panama,Paris,Sao Paulo,Singapore,Sydney,Tokyo,Toronto:Mc Graw-Hill Book Company,1987,9.1~9.13.

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