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Model of active peristaltic transport in biosystems

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Abstract

A nonlinear distributed mathematical model of a soft vessel with a nonmonotonic static characteristic is proposed and considered. The model describes space-time dynamics of the vascular lumen. Wave phenomena in vessels of different nature and the possibility of peristaltic fluid pumping are discussed and analyzed. The model is quite general in character and represents a broad class of transport phenomena. Lymphatic vessels are considered as an example.

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References

  1. R. S. Orlov, A. V. Borisov, and R. P. Borisova, Lymphatic Vessels (Nauka, Leningrad, 1983) [in Russian].

    Google Scholar 

  2. T. Ohhashi, T. Azuma, and M. Sakaguchi, Amer. J. Physiol. 239(8), H88 (1980).

    Google Scholar 

  3. B. Folkow and E. Neil, Circulation (Oxford University Press, 1971; [Russ. transl.] Meditsina, Moscow, 1976).

    Google Scholar 

  4. C. G. Caro, T. J. Pedley, R. C. Schroter, and W. A. Seed, The Mechanics of the Circulation (Oxford University Press, 1978; [Russ. transl.] Mir, Moscow, 1981).

    MATH  Google Scholar 

  5. Physiology of the Circulation. Physiology of the Vascular System (Nauka, Leningrad, 1984) [in Russian].

  6. Y.C. Fung, Biodynamics. Circulation (Springer-Verlag, N.Y., 1984).

    Google Scholar 

  7. V. B. Parashin and G. P. Itkin, Biomechanics of the Circulation (MGTU, Moscow, 2005) [in Russian].

    Google Scholar 

  8. Yu. M. Romanovskii, N. V. Stepanova, and D. S. Chernavsky, Mathematical Modeling in Biophysics. Introduction to Theoretical Biophysics, 2nd edn. (IKI, Moscow-Izhevsk, 2004) [in Russian].

    Google Scholar 

  9. B. N. Klochkov, in Collective Dynamics of Excitations and Structure Formation in Biological Tissues, Ed. by V. G. Yakhno (IPF AN SSSR, Gorky, 1988), pp. 156–164 [in Russian].

  10. B. N. Klochkov and E. A. Kuznetsova, Izv. VUZov, Radiofiz. 43, 793 (2000).

    MathSciNet  Google Scholar 

  11. B. N. Klochkov and A. M. Reiman, in Nonlinear Waves. Synchronization and Structures, Ed. by M. I. Rabinovich and V. D. Shalfeev (NNGU, N. Novgorod, 1995), Vol. 2, pp. 111–118 [in Russian].

  12. B. N. Klochkov, Yu. Yu. Eliseeva, and P. A. Shilyagin, Akust. Zh. 55, 506 (2009).

    Google Scholar 

  13. S. A. Regirer and I. M. Rutkevich, Izv. AN SSSR, Mekh. Zhidk. Gaza, no. 1, 45 (1975).

    Google Scholar 

  14. B. N. Klochkov, A. M. Reiman and Yu. A. Stepanyants, Izv. AN SSSR, Mekh. Zhidk. Gaza, no. 3, 94 (1985).

    Google Scholar 

  15. E. E. Kireeva and B. N. Klochkov, Izv. AN SSSR, Mekh. Zhidk. Gaza, no. 3, 17 (1986).

    Google Scholar 

  16. B. N. Klochkov and E. A. Kuznetsova, Izv. RAN, Mekh. Zhidk. Gaza, no. 4, 46 (2000).

    Google Scholar 

  17. S. A. Regirer and N. Kh. Shadrina, Biophysics (Moscow) 47, 845 (2002).

    Google Scholar 

  18. S. A. Regirer and N. Kh. Shadrina, Biophysics (Moscow) 50, 454 (2005).

    Google Scholar 

  19. N. Kh. Shadrina and V. A. Buchin, Biophysics (Moscow) 54, 188 (2009).

    Article  Google Scholar 

  20. V. A. Buchin and N. Kh. Shadrina, Izv. RAN, Mekh. Zhidk. Gaza, no. 2, 51 (2010).

    Google Scholar 

  21. A. N. Kolmogorov, I. G. Petrovskii, and N. S. Piskunov, Byull. MGU, Sect. A, 1(6), 1 (1937).

    Google Scholar 

  22. A. D. Polyanin and V. F. Zaitsev, Reference Book on Nonlinear Equations of Mathematical Physics (Fizmatlit, Moscow, 2002) [in Russian].

    Google Scholar 

  23. Human Physiology, Ed. by R. Schmidt and G. Thews (Springer-Verlag, Berlin, 1983; [Russ. transl.] Mir, Moscow, 1986, Vol. 3).

    Google Scholar 

  24. O. A. Dudchenko and G. Th. Guria, Phys. Rev. E 85, 020902(R) (2012).

    Article  ADS  Google Scholar 

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Correspondence to B. N. Klochkov.

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Original Russian Text © B.N. Klochkov, A.S. Romanov, 2013, published in Biofizika, 2013, Vol. 58, No. 5, pp. 882–886.

The paper has been additionally edited for the English version.

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Klochkov, B.N., Romanov, A.S. Model of active peristaltic transport in biosystems. BIOPHYSICS 58, 699–702 (2013). https://doi.org/10.1134/S0006350913050060

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  • DOI: https://doi.org/10.1134/S0006350913050060

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