ISSN 0869-6632 (Print)
ISSN 2542-1905 (Online)

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Pavlov A. N., Pavlova O. N., Sosnovtseva O. V. Interaction of rhythms in the dynamics of functional units of the kidney. Izvestiya VUZ. Applied Nonlinear Dynamics, 2007, vol. 15, iss. 2, pp. 14-28. DOI: 10.18500/0869-6632-2007-15-2-14-28

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Interaction of rhythms in the dynamics of functional units of the kidney

Pavlov Aleksej Nikolaevich, Saratov State University
Pavlova Olga Nikolaevna, Saratov State University
Sosnovtseva Olga Vladimirovna, Danmarks Tekniske Universitet

In this paper we study the phenomena of interaction between three rhythmic components of renal autoregulation. Clear distinctions of the corresponding phenomena for almost periodic dynamics of nephrons observed in normotensive rats and irregular (chaotic) dynamics that occur in the nephrons of genetically hypertensive rats are revealed.  

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  1. Tuckwell HC. Introduction to Theoretical Neurobiology. Cambridge: Cambridge University Press. Volume 2: Nonlinear and Stochastic Theories; 1998. DOI: 10.1017/CBO9780511623202.
  2. Goldbeter A. Biochemical Oscillations and Cellular Rhythms. Cambridge: Cambridge University Press, 1996. DOI: 10.1017/CBO9780511608193.
  3. Neiman A, Russell DF. Stochastic biperiodic oscillations in the electroreceptors of paddlefish. Phys. Rev. Lett. 2001;86:3443. DOI: 10.1103/physrevlett.86.3443.
  4. Tychinskii VP. Coherent phase microscopy of intracellular processes. Phys. Usp. 2001;44(6):617–629.
  5. Stefanovska A, Bracic M. Physics of the human cardiovascular system. Contemporary Physics. 1999;40(1):31–55. DOI: 10.1080/001075199181693.
  6. Sturis J, Mosekilde E, Van Cauter E. Modeling modulatory effects on pulsatility. Methods in Neurosciences. 1994;20:393.
  7. Pikovsky A, Rosenblum M, Kurths J. Synchronization: A Universal Concept in Nonlinear Sciences. Cambridge Nonlinear Science Series 12, Cambridge University Press; 2001.
  8. Mosekilde E, Maistrenko Yu, Postnov D. Chaotic Synchronization: Applications to Living Systems. Singapore: World Scientific; 2002.
  9. Schafer C, Rosenblum MG, Abel H, Kurths J. Synchronization in the human cardiorespiratory system. Phys. Rev. E. 1999;60(1):857–870. DOI: 10.1103/physreve.60.857.
  10. Rzeczinski S, Janson NB, Balanov AG, McClintock PVE. Regions of cardiorespiratory synchronization in humans under paced respiration. Phys. Rev. E. 2002;66:051909. DOI: 10.1103/PhysRevE.66.051909.
  11. Kopell N, Ermentrout GB, Whittington MA, Traub RD. Gamma rhythms and beta rhythms have different synchronization properties. Proc. Natl. Acad. Sci. U.S.A. 2000;97:1867–1872. DOI: 10.1073/pnas.97.4.1867.
  12. Glass L, Mackey M.C. From Clocks to Chaos: The Rhythms of Life. Princeton University Press. Princeton; 1988.
  13. Tass PA. Effective desynchronization with bipolar double-pulse stimulation. Phys. Rev. E. 2002;66:036226. DOI: 10.1103/PhysRevE.66.036226.
  14. Holstein-Rathlou NH, Yip KP, Sosnovtseva OV, Mosekilde E. Synchronization phenomena in nephron-nephron interaction. Chaos. 2001;11:417–426. DOI: 10.1063/1.1376398.
  15. Sosnovtseva OV, Pavlov AN, Mosekilde E, Holstein-Rathlou NH. Bimodal oscillations in nephron autoregulation. Phys. Rev. E. 2002;66:061909. DOI: 10.1103/PhysRevE.66.061909.
  16. Bracic M, Stefanovska A. Synchronization and modulation in the human cardio-respiratory system. Physica A. 2000;283:451–461. DOI: 10.1016/S0378-4371(00)00204-1.
  17. Adison PS, Watson JN. Secondary transform decoupling of shifted nonstationary signal modulation components: Application to photoplethysmography. Int. J. of Wavelets, Multiresolution and Information Processing. 2004;2:43–57.
  18. Sosnovtseva OV, Pavlov AN, Mosekilde E, Holstein-Rathlou NH, Marsh DJ. Double-wavelet approach to study frequency and amplitude modulation in renal autoregulation. Phys. Rev. E. 2004;70:031915. DOI: 10.1103/PhysRevE.70.031915.
  19. Marsh DJ, Sosnovtseva OV, Pavlov AN, Yip KP, Holstein-Rathlou NH. Frequency encoding in renal blood flow regulation. Am. J. Physiol. Regul. Integr. Comp. Physiol. 2005;288:R1160–7. DOI: 10.1152/ajpregu.00540.2004.
  20. Sosnovtseva OV, Pavlov AN, Mosekilde E, Holstein-Rathlou NH, Marsh DJ. Double-wavelet approach to studying the modulation properties of nonstationary multimode dynamics. Physiol. Measur. 2005;26:351–362. DOI: 10.1088/0967-3334/26/4/002.
  21. Sosnovtseva OV, Pavlov AN, Brazhe NA, Brazhe AR, Erokhova LA, Maksimov GV, Mosekilde E. Interference microscopy under double-wavelet analysis: A new tool to studying cell dynamics. Phys. Rev. Lett. 2005;94:218103. DOI: 10.1103/PhysRevLett.94.218103.
  22. Grossman A, Morlet J. Decomposition of Hardy functions into square integrable wavelets of constant shape. S.I.A.M. J. Math. Anal. 1984;15:723–736. DOI: 10.1137/0515056.
  23. Daubechies I. Ten lectures on Wavelets. Philadelphia: S.I.A.M.; 1992.
  24. Wavelets and Applications. Ed. Meyer Y. Berlin: Springer-Verlag; 1992.
  25. Chui C.K. An Introduction to Wavelets. New York: Academic Press; 1992.
  26. Mallat SG. A Wavelet Tour of Signal Processing. San Diego: Academic Press; 1998.
  27. Koronovskii AA, Khramov AE. Continuous Wavelet Analysis and Its Applications. Moscow: Fizmatlit; 2003. (in Russian)
  28. Holstein-Rathlou NH, Leyssac PP. TGF-mediated oscillations in the proximal intratubular pressure: Differences between spontaneously hypertensive rats and Wistar-Kyoto rats. Acta Physiol. Scand. 1986;126:333–339. DOI: 10.1111/j.1748-1716.1986.tb07824.x.
  29. Leyssac PP, Holstein-Rathlou NH. Effects of various transport inhibitors on oscillating TGF pressure response in the rat. Pflugers Arch. 1986;407:285–291. DOI: 10.1007/BF00585304.
  30. Holstein-Rathlou NH, Marsh DJ. Renal blood flow regulation and arterial pressure fluctuations: A case study in nonlinear dynamics. Physiol. Rev. 1994;74:637–681. DOI: 10.1152/physrev.1994.74.3.637.
  31. Holstein-Rathlou NH, Wagner AW, Marsh DJ. Tubuloglomerular feedback dynamics and renal blood flow autoregulation in rats. Am. J. Physiol. 1991;260:F53–68. DOI: 10.1152/ajprenal.1991.260.1.F53.
  32. Chou KH, Chen Yu-Ming, Marmarelis VZ, Marsh DJ, Holstein-Rathlou NH. Detection of interaction between myogenic and TGF mechanisms using nonlinear analysis. Am. J. Physiol. 1994;267:F160–73. DOI: 10.1152/ajprenal.1994.267.1.F160.
  33. Mosekilde E. Topics in Nonlinear Dynamics: Applications to Physics, Biology and Economic Systems. Singapore: World Scientific; 1996.
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