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 therefore 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 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 resonable.
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Guo Zhongsan, Xiao Fan, Guo Siwen, et al. Comprehensive mathematical model of microcirculatory dynamics (I)—Basic theory [J].Applied Mathematics and Mechanics (English Ed), 1999,20(9): 1014–1022.
Guo Zhongsan. Fluid mechanics of microvascular vasomotion and the effects of blood viscoelasticity [J].Applied Mathematics and Mechanics (English Ed), 1992,13(2): 173–180.
Guo Zhongsan. Influence line method for transport problems across the wall of the network of permeable tubes [J].Chinese J Comp Phys, 1996,13(4): 496–500. (in Chinese)
Xiu Ruijuan, Itaglietta M. Studies on microvascular vasomotion: I. Long-term observation and computer analysis of vasomotion [A]. In: Xiu Ruijuan, Xu Hongdao eds.Microcirculatory Research in China (I) [C]. Beijing: International Cultural Publishing Co, 1987, 1–16. (in Chinese)
Taylor D G, Bert J L, Bowen B D. A mathematical model of interstitial transport II: microvascular exchange in mesentery [J].Microvasc Res, 1990,39(3): 279–306.
Kamiya A, Ando J, Shibata M, et al. The efficiency of the vascular-tissue system for oxygen transport in the skeletal muscles [J].Microvasc Res, 1990,39(2): 169–185.
Nair P K, Huang N S, Hellums J D, et al. A simple model for prediction of oxygen transport rates by flowing blood in large capillaries [J].Microvasc Res, 1990,39(2): 203–211.
Schubert R W, Whalen W J, Nair P. Myocardial PO2 distribution: relationship to coronary autoregulation [J].Amer J Physiol, 1978,223(4): H361-H370.
Chato J C.Fundamentals of Bioheat Transfer [M]. Springer-Verlag, 1989.
Caro C G, Pedley T J, Schroter R C, et al.The Mechanics of the Circulation [M]. Oxford University Press, 1978.
Fung Y C.Biomechanics [M]. Beijing: Science Press, 1983. (in Chinese)
Meyer J U, Borgstrom P, Lindbom L, et al. Vasomotion patterms in skeletal muscle arterioles during changes in arterial pressure [J].Microvasc Res, 1988,35(2): 193–203.
Chato J C. Thermal properties of tissues [A]. In: Skalak R, Chien S eds.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.
Silberberg A. Transport through deformable matrices [J].Biorheology, 1989,26(2): 291–313.
Yang Zaichun.A New Date Book of Clinic Medicine [M]. Beijing: The Golden Shield Press, 1992. (in Chinese)
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Communicated by Chien Weizang
Foundation item: the Natural Science Foundation of Sichuan Province, P R China
Biography: Guo Zhongsan (1947-)
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Zhongsan, G., Fan, X., Siwen, G. et al. Comprehensive mathematical model of microcirculatory dynamics (II)—Calculation and the results. Appl Math Mech 21, 579–584 (2000). https://doi.org/10.1007/BF02459040
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DOI: https://doi.org/10.1007/BF02459040