Izvestiya of Saratov University.


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ISSN 2542-193X (Online)

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Scherbakov P. A., Astakhov O. V., Postnov D. E. Complex Waveforms and Synchronization in Functional Model of Vascular Nephron Tree. Izvestiya of Saratov University. Physics , 2009, vol. 9, iss. 1, pp. 38-53. DOI: 10.18500/1817-3020-2009-9-1-38-53

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Complex Waveforms and Synchronization in Functional Model of Vascular Nephron Tree

Scherbakov Pavel Aleksandrovich, Saratov State University
Astakhov Oleg Vladimirovich, Sirius University of Science and Technology
Postnov Dmitry Engelevich, Saratov State University

We suggest functional model that qualitatively describes oscillatory processes in renal autoregulation. Our model consists of ensemble of two-mode oscillators that are coupled by means of two different pathways. The above coupling pathways count both the geometry of ensemble (tree-like structure or local interaction) and the specific action of individual oscillator (energy distribution netrwork or diffusive coupling). We study the typical operating regimes of suggested model as well as transitions between them.

  1. Landa P.S., Rosenblum M.G. Synchronization and chaotization of oscillations in coupled self-oscillating systems // Appl. Mech. Rev. 1993. Vol.46. P.414-426.
  2. Pikovsky A., Rosenblum M., Kurths J. Synchronization: A Universal Concept in Nonlinear Sciences. Cambridge University Press, 2001. 411 p.
  3. Balanov A., Janson N., Postnov D., Sosnovtseva O. Synchronization From Simple to Complex. Springer, 2009. 406 p.
  4. Hadley P., Beasley M.R., Wiesenfeld K. Phase locking of Josephson junction series arrays // Phys. Rev. B. 1988. Vol.38. P.8712.
  5. Абарбанель Г.Д.И., Рабинович М.И., Сильверстон А., Баженов М.В., Хуэрта Р., Сущик М.М., Рубчинский Л.Л. Синхронизация в нейронных ансамблях // УФН. 1999. Т.166, №4. С.365−390.
  6. Анищенко В.С., Астахов В.В., Вадивасова Т.Е., Нейман А.Б., Стрелкова Г.И., Шиманский-Гайер Л. Нелинейные эффекты в хаотических и стохастических системах. Ижевск, 2003. 530 с.
  7. Mosekilde E., Maistrenko Y., Postnov D. Choatic synchronization. Application to living systems. World Scientific, 2002. 440 p.
  8. Meda P., Atwater I., Goncalves A., Bangham A., Orci L., Rojas E. The topography of electrical synchrony among -cells in the mouse islet of Langerhans // Q. J. Exp. Psychol. 1984. Vol.69. P.719−735.
  9. Kiss I.Z., Zhai Y., Hudson J.L. Emerging coherence in a population of chemical oscillators // Science. 2002. Vol.296. P.1676.
  10. Danø S., Hynne F., Monte S. de, Ovidio F. d’, Sorensen P.G., Westerhoff H. Synchronization of glycolytic oscillations in a yeast cell population // Faraday Discuss. 2002. Vol.120. P.261−275.
  11. Postnov D.E., Sosnovtseva O.V., Mosekilde E. Oscillator clustering in a resource consumption chain // CHAOS. 2005. Vol.15. P.1−12.
  12. Osipov G.V., Ivanchenko M. V., Kurths J., Hu B. Synchronized chaotic intermittent and spiking behavior in coupled map chains // Phys. Rev. E. 2005. Vol.71. P.056209.
  13. West J.B. Best and Taylors Physiological Basis of Medical Practice. 12th ed. Baltimore: Williams and Wilkins, 1991. 
  14. Netter F.H. The CIBA collection of medical illustration // Summit: CIBA; Kidneys, Ureters and Urinary Bladder, 1973. Vol.6.
  15. Despopoulos A., Silbernagel S. Color atlas of physiology. Stuttgard: Georg Thieme Verlag, 1991.
  16. Holstein-Rathlou N.-H., Leyssac P.P. TGF-mediated oscillations in the proximal intratubular pressure: Differences between spontaneously hypertensive rats and Wistar-Kyoto rats // Acta Physiol. Scand. 1986. Vol.126. P.333−339.
  17. Leyssac P.P., Holstein-Rathlou N.-H. Effects of various transport inhibitors on oscillating TGF pressure response in the rat // Pfflugers Arch. 1986. Vol.407. P.285.
  18. Holstein-Rathlou N.-H., Wagner A.W., Marsh D.J. Tubuloglomerular feedback dynamics and renal blood flow autoregulation in rats // Amer. J. Physiol. 1991. Vol.260. P.F53.
  19. Chou K.H., Yu-Ming Ch., Mardarelis V.Z., Marsh D.J., Holstein-Rathlou N.-H. Detection of interaction between myogenic and TGF mechanisms using nonlinear analysis // Amer. J. Physiol. 1994. Vol.267. P.F160.
  20. Feldberg R., Colding-Jorgensen M., Holstein-Rathlou N.-H. Analysis of interaction between TGF and the myogenic response in renal blood flow autoregulation // Amer. J. Physiol. 1995. Vol.269. P.F581.
  21. Holstein-Rathlou N.-H., Marsh D.J. Oscillations of tubular pressure, flow and distal chloride concentration in rats // Amer. J. Physiol. 1989. Vol.256. P.1007−1014.
  22. Yip K.-P., Holstein-Rathlou N.-H., Marsh D.J. Chaos in blood flow control in genetic and renovascular hypertensive rats // Amer. J. Physiol. 1991. Vol.261. P.400−408.
  23. Moore L.C., Rich A., Casellas D. Ascending myogenic autoregulation: interactions between tubuloglomerular feedback and myogenic mechanisms // Bull. Math. Biol. 1994. Vol.56. P.391−410.
  24. Оien A.H., Aukland K. A multinephron model of renal blood flow autoregulation by tubuloglomerular feedback and myogenic response // Acta. Physiol. Scand. 1991. Vol.143. P.71−92.
  25. Holstein-Rathlou N.-H. Synchronization of proximal intratubular pressure oscillations: evidence for interaction between nephrons // Pfflugers. Arch. 1988. Vol.408. P.438−443. 
  26. Barfred M., Mosekilde E., Holstein-Rathlou N.-H. Bifurcation analysis of nephron pressure and flow regulation // Chaos. 1996. Vol.6. P.280−287.
  27. Marsh D.J., Sosnovtseva O.V., Chon K.H., Holstein-Rathlou N.-H. Nonlinear interactions in renal blood flow regulation // Amer. J. Physiol. 2005. Vol.288. P.R1143−R1159.
  28. Jensen K.S., Mosekilde E., Holstein-Rathlou N.-H. Selfsustained oscillations and chaotic behavior in kidney pressure regulation // Mondes Develop. 1986. Vol.55. P.91−109.
  29. Holstein-Rathlou N.-H., Marsh D.J. A dynamic modelof the tubuloglomerular feedback echanism // Amer. J. Physiol. 1990. Vol.258. P.F1448−F1459.
  30. Chen Yu-Ming, Kay-Pong Yip, Marsh D.J., Holstein-Rathlou N.-H. Magnitude of TGF-initiated nephron-nephron interactions is increased in SHR // Amer. J. Physiol. 1995. Vol.269. P.F198−F204.
  31. Postnov D.E., Sosnovtseva O.V., Mosekilde E., Holstein-Rathlou N.-H. Cooperative phase dynamics in coupled nephrons // Intern. J. Mod. Phys. B. 2001. Vol.15. P.3079−3098.
  32. Постнов Д., Шишкин А., Щербаков П. Нелинейные эффекты в ансамблях осцилляторов со связью через распределение ресурса. Ч.I. Динамические режимы авторегуляции кровотока в васкулярном дереве нефронов // Изв. вузов. ПНД. 2007. Т.15, №5. С.3−22.
  33. Постнов Д., Шишкин А., Щербаков П. Нелинейные эффекты в ансамблях осцилляторов со связью через распределение ресурса. Ч.II. Колебательные режимы одномерного массива связанных через общий источник питания осцилляторов // Изв. вузов. ПНД. 2007. Т.15, №5. С.23−35.
  34. Postnov D.E., Shishkin A.V., Sosnovtseva O.V., Mosekilde E. Two-mode chaos and synchronization properties // PRE. 2005. Vol.72. P.056208. 
  35. Van-der-Pol B. Forced oscillations in a circuit with nonlinear resistance // Phil. Mag. 1927. Vol.3. P. 64−80.
  36. Postnov D.E., Sosnovtseva O.V., Scherbakov P.A., Mosekilde E. Multimode dynamics in a network with resource mediated coupling // CHAOS. 2008. Vol. 18. P. 015114.
  37. Постнов Д.Э., Жирин Р.А. Свидетельство об официальной регистрации программы для ЭВМ №2007614145. 2007. 
  38. Sosnovtseva O.V., Postnov D.E., Nekrasov A.M., Mosekilde E., Holstein-Rathlou N.-H. Phase multistability of selfmodulated oscillations // Phys. Rev. E. 2002. Vol.66. P.0362. 
  39. Постнов Д.Э., Некрасов А.М. Механизмы фазовой мультистабильности при синхронизации 3D осцилляторов // Изв. вузов. ПНД. 2005. Т.13, №1−2. С.47−62. 
  40. Некрасов А.М. Фазовая мультистабильность в диффузионно связанных нелинейных осцилляторах: Дис. … канд. физ.-мат. наук. Саратов, 2007. 160 с.