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ISSN 2542-1905 (Online)

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Pavlova O. N., Pavlov A. N., Sosnovtseva O. V. Dynamics of small groups of interacting nephrons in normal and renal hypertension states. Izvestiya VUZ. Applied Nonlinear Dynamics, 2010, vol. 18, iss. 6, pp. 3-24. DOI: 10.18500/0869-6632-2010-18-6-3-24

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Dynamics of small groups of interacting nephrons in normal and renal hypertension states

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

Based on the wavelet-analysis of experimental data, we study in this paper the phenomenon of synchronization of oscillations in the dynamics of small groups of structural units of the kidney (paired nephrons and triplets). Distinctions between synchronous dynamics of interacting nephrons in normal and hypertensive rats are discussed. We show that mean duration of synchronous oscillations is about 3 times less in hypertensive rats. We state that in-phase synchronization is the most typical case in the dynamics of interacting nephrons (more than 90% of experimental data). We compare the results of experimental data analysis and the results of mathematical modeling of the dynamics of interacting units of the kidney.

  1. Yip KP, Holstein-Rathlou NH, Marsh DJ. Chaos in blood flow control in genetic and renovascular hypertensive rats. Am. J. Physiol. Renal Fluid Electrolyte Physiol. 1991;261.F400–F408. DOI: 10.1152/ajprenal.1991.261.3.F400.
  2. Yip KP, Marsh DJ, Holstein-Rathlou NH. Evidence of low dimensional chaos in renal blood flow control in genetic and experimental hypertension. Physica D. 1995;80:95–104. DOI: 10.1016/0167-2789(95)90063-2.
  3. 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.
  4. 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.
  5. 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–R1167. DOI: 10.1152/ajpregu.00540.2004.
  6. Pavlov AN, Makarov VA, Mosekilde E, Sosnovtseva OV. Application of wavelet-based tools to study the dynamics of biological processes. Briefings in Bioinformatics. 2006;7:375–389. DOI: 10.1093/bib/bbl041.
  7. Sosnovtseva OV, Pavlov AN, Mosekilde E, Yip KP, Holstein-Rathlou NH, Marsh DJ. Synchronization among mechanisms of renal autoregulation is reduced in hypertensive rats. Am. J. Physiol. Renal Physiol. 2007;293(5):F1545–F1555. DOI: 10.1152/ajprenal.00054.2007.
  8. Marsh DJ, Sosnovtseva OV, Mosekilde E, Holstein-Rathlou NH. Vascular coupling induces synchronization, quasiperiodicity, and chaos in a nephron tree. Chaos. 2007;17(1):015114. DOI: 10.1063/1.2404774.
  9. Sakai T, Craig DA, Wexler AS, Marsh DJ. Fluid waves in renal tubules. Biophys. J. 1986;50(5):805-813. DOI: 10.1016/S0006-3495(86)83521–4.
  10. Layton HE, Pitman EB, Moore LC. Nonlinear filter properties of the thick ascending limb. Am. J. Physiol. Renal Physiol. 1997;273(4):F625–F634. DOI: 10.1152/ajprenal.1997.273.4.F625.
  11. Casellas D, Moore LC. Autoregulation and tubuloglomerular feedback in juxtame-dullary glomerular arterioles. Am. J. Physiol. Renal Fluid Electrolyte Physiol. 1990;258:F660–F669. DOI: 10.1152/ajprenal.1990.258.3.F660.
  12. Gonzalez-Fernandez JM, Ermentrout GB. On the origin and dynamics of the vasomotion of small arteries. Math. Biosci. 1994;119(2):127–167. DOI: 10.1016/0025-5564(94)90074-4.
  13. Horowitz A, Menice CB, Laporte R, Morgan KG. Mechanisms of smooth muscle contraction. Physiol. Rev. 1996;76(4):967–1003. DOI: 10.1152/physrev.1996.76.4.967.
  14. Holstein-Rathlou NH, He J, Wagner AJ, Marsh DJ. Patterns of blood pressure variability in normotensive and hypertensive rats. Am. J. Physiol. Regul. Integr. Comp. Physiol. 1995;269:R1230–R1239. DOI: 10.1152/ajpregu.1995.269.5.R1230.
  15. 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(3):333–339. DOI: 10.1111/j.1748-1716.1986.tb07824.x.
  16. Leyssac PP, Holstein-Rathlou NH. Tubulo-glomerular feedback response: enhancement in adult spontaneously hypertensive rats and effects of anaesthetics. Pflugers Arch. 1989;413(3):267–272. DOI: 10.1007/BF00583540.
  17. Wang H, Kin S, Ju K, Chon KH. A high resolution approach to estimating time-frequency spectra and their amplitudes. Ann. Biomed. Eng. 2006;34:326–338. DOI: 10.1007/s10439-005-9035-y.
  18. Quiroga R, Kraskov A, Kreuz T, Grassberger P. Performance of different synchronization measures in real data: a case study on electroencephalographic signals. Phys. Rev. E. 2002;65:041903. DOI: 10.1103/PhysRevE.65.041903.
  19. Huang NE, Shen Z, Long SR. The empirical mode decomposition and the Hilbert spectrum for nonlinear and non-stationary time series analysis. Proc. R. Soc. Lond. A. 1998;454:903–995. DOI: 10.1098/rspa.1998.0193.
  20. Mallat SG. A wavelet tour of signal processing. New York: Academic Press; 1998.
  21. Addison PS. The illustrated wavelet transform handbook: applications in science, engineering, medicine and finance. Philadelphia: IOP Publishing; 2002.
  22. Grossman A, Morlet J. Decomposition of Hardy functions into square intergable wavelets of constant shape. SIAM J. Math. Anal. 1984;15(4):723–736. DOI: 10.1137/0515056.
  23. Kaiser G. A friendly guide to wavelets. Boston: Birkhauser; 1994.
  24. Torrence C, Compo GP. A practical guide to wavelet analysis. Bull. Amer. Meteor. Soc. 1998;79:61–78. DOI: 10.1175/1520-0477(1998)079<0061:APGTWA>2.0.CO;2.
  25. Pavlov AM, Sosnovtseva OV. Application of double-wavelet analysis to study modulation phenomena in dynamics of nephrons. Izvestiya VUZ. Applied Nonlinear Dynamics.2004;12(6):105–117 (in Russian).
  26. Pavlov AN, Pavlova ON, Sosnovceva OV. Interaction of rhythms in the dynamics of functional units of the kidney. Izvestiya VUZ. Applied Nonlinear Dynamics. 2007;15(2):14–28 (in Russian). DOI: 10.18500/0869-6632-2007-15-2-14-28.
  27. Anisimov AA, Pavlova ON, Tupicyn AN, Pavlov AN. Wavelet-analysis of chirps. Izvestiya VUZ. Applied Nonlinear Dynamics. 2008;16(5):3–11. DOI: 10.18500/0869-6632-2008-16-5-3-11. (in Russian)
  28. Koronovskii AA, Hramov AE. Continuous Wavelet Analysis: Application to Nonlinear Dynamics Problems. Saratov: GosUNTs «College»; 2002. (in Russian).
  29. Koronovskii AA, Khramov AE. Continuous Wavelet Analysis and Its Applications. Moscow: Fizmatlit; 2003. (in Russian).
  30. Marsh DJ, Sosnovtseva OV, Chon KH, Holstein-Rathlou NH. Nonlinear interactions in renal blood flow regulation. Am. J. Physiol. Regul. Integr. Comp. Physiol. 2005;288:R1143–R1159. DOI: 10.1152/ajpregu.00539.2004.
  31. Holstein-Rathlou NH, Marsh DJ. A dynamic model of the tubuloglomerular feedback mechanism. Am. J. Physiol. Renal Fluid Electrolyte Physiol. 1990;258:F1448–F1459. DOI: 10.1152/ajprenal.1990.258.5.F1448.
  32. Holstein-Rathlou NH, Marsh DJ. A dynamic model of renal blood flow autoregulation. Bull. Math. Biol. 1994;56:411–429. DOI: 10.1007/BF02460465.
  33. Barfred M, Mosekilde E, Holstein-Rathlou NH. Bifurcation analysis of nephron pressure and flow regulation. Chaos. 1996;6:280–287. DOI: 10.1063/1.166175.
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