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Nonlinear Phenomena in Nephron-Nephron Interaction

  • Chapter
Synchronization: Theory and Application

Part of the book series: NATO Science Series ((NAII,volume 109))

Abstract

By controling the excretion of water and salts, the kidneys play an important role in regulating the blood pressure and maintaining a proper environment for the cells of the body. This control depends to a large extent on mechanisms that are associated with the individual functional unit, the nephron. However, a variety of cooperative phenomena arising through interactions among the nephrons may also be important. The purpose of this chapter is to present experimental evidence for a coupling between nephrons that are connected via a common piece of afferent arteriole, to develop a mathematical model that can account for the observed synchronization phenomena, and to discuss the possible physiological significance of these phenomena. We are particularly interested in synchronization effects that can occur among neighboring nephrons that individually display irregular (or chaotic) dynamics in their pressure and flow regulation.

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References

  1. L.C. Moore, Tubuloglomerular Feedback and SNGFR Autoregulation in the Rat, Am. J. Physiol. 247, F267–F276 (1984).

    Google Scholar 

  2. P.P. Leyssac and L. Baumbach, An Oscillating Intratubular Pressure Response to Alterations in Henle Loop Flow in the Rat Kidney, Acta Physiol. Scand. 117, 415–419 (1983).

    Article  Google Scholar 

  3. N.-H. Holstein-Rathlou and P.P. Leyssac, TGF-mediated Oscillations in the Proximal Intratubular Pressure: Differences between Spontaneously Hypertensive Rats and Wistar-Kyoto Rats, Acta Physiol. Scand. 126, 333–339 (1986).

    Article  Google Scholar 

  4. P.P. Leyssac and N.-H. Holstein-Rathlou, Effects of Various Transport Inhibitors on Oscillating TGF Pressure Response in the Rat, Pflügers Archiv 407, 285–291 (1986).

    Article  Google Scholar 

  5. N.-H. Holstein-Rathlou and D.J. Marsh, Renal Blood Flow Regulation and Arterial Pressure Fluctuations: A Case Study in Nonlinear Dynamics, Physiol. Rev. 74, 637–681 (1994).

    Google Scholar 

  6. K.-P. Yip, N.-H. Holstein-Rathlou, and D.J. Marsh, Chaos in Blood Flow Control in Genetic and Renovascular Hypertensive Rats, Am. J. Physiol. 261, F400–F408 (1991).

    Google Scholar 

  7. K.-P. Yip and N.-H. Holstein-Rathlou, Chaos and Non-Linear Phenomena in Renal Vascular Control, Cardiovascular Res. 31, 359–370 (1996).

    Google Scholar 

  8. K.S. Jensen, N.-H. Holstein-Rathlou, P.P. Leyssac, E. Mosekilde, and D.R. Rasmussen, Chaos in a System of Interacting Nephrons, in Chaos in Biological Systems, edited by H. Degn, A.V. Holden, and L.F. Olsen (Plenum, New York, 1987), pp. 23–32.

    Google Scholar 

  9. K.S. Jensen, E. Mosekilde, and N.-H. Holstein-Rathlou, Self-Sustained Oscillations and Chaotic Behaviour in Kidney Pressure Regulation, Mondes en Develop. 54/55, 91–109 (1986).

    Google Scholar 

  10. E. Mosekilde, Topics in Nonlinear Dynamics. Applications to Physics, Biology and Economic Systems (World Scientific, Singapore, 1996).

    MATH  Google Scholar 

  11. J. Briggs, A Simple Steady-State Model for Feedback Control of Glomerular Filtration Rate, Kidney Int. 22, Suppl. 12, S143–S150 (1982).

    Google Scholar 

  12. P.P. Leyssac and N.-H. Holstein-Rathlou, Tubulo-Glomerular Feedback Response: Enhancement in Adult Spontaneously Hypertensive Rats and Effects of Anaesthetics, Pflügers Archiv 413, 267–272 (1989).

    Article  Google Scholar 

  13. N.-H. Holstein-Rathlou and D.J. Marsh, A Dynamic Model of the Tubuloglomerular Feedback Mechanism, Am. J. Physiol. 258, F1448–F1459 (1990).

    Google Scholar 

  14. N.-H. Holstein-Rathlou and D.J. Marsh, Oscillations of Tubular Pressure, Flow, and Distal Chloride Concentration in Rats, Am. J. Physiol. 256, F1007–F1014 (1989).

    Google Scholar 

  15. H.E. Layton, E.B. Pitman and L.C. Moore,Bifurcation Analysis of TGF-Mediated Oscillations in SNGFR, Am. J. Physiol. 261, F904–F919 (1991).

    Google Scholar 

  16. N.K. Hollenberg and T. Sandor, Vasomotion of Renal Blood Flow in Essential Hypertension. Oscillations in Xenon Transit, Hypertension 6, 579–585 (1984).

    Article  Google Scholar 

  17. N.-H. Holstein-Rathlou, A.J. Wagner, and D.J. Marsh, Tubuloglomerular Feedback Dynamics and Renal Blood Flow Autoregulation in Rats, Am. J. Physiol. 260, F53–F68 (1991).

    Google Scholar 

  18. R. Feldberg, M. Colding-Jørgensen, and N.-H. Holstein-Rathlou, Analysis of Interaction between TGF and the Myogenic Response in Renal Blood Flow Autoregulation, Am. J. Physiol. 269, F581–F593 (1995).

    Google Scholar 

  19. D. Casellas, M. Dupont, N. Bouriquet, L.C. Moore, A. Artuso and A. Mimran, Anatomic Pairing of Afferent Arterioles and Renin Cell Distribution in Rat Kidneys, Am. J. Physiol. 267, F931–F936 (1994).

    Google Scholar 

  20. N.-H. Holstein-Rathlou, Synchronization of Proximal Intratubular Pressure Oscillations: Evidence for Interaction between Nephrons, Pflügers Archiv 408, 438–443 (1987).

    Article  Google Scholar 

  21. H. Bohr, K.S. Jensen, T. Petersen, B. Rathjen, E. Mosekilde, and N.-H. Holstein-Rathlou, Parallel Computer Simulation of Nearest-Neighbour Interaction in a System of Nephrons, Parallel Comp. 12, 113–120 (1989).

    Article  MATH  Google Scholar 

  22. M. Barfred, E. Mosekilde, and N.-H. Holstein-Rathlou, Bifurcation Analysis of Nephron Pressure and Flow Regulation, Chaos 6, 280–287 (1996).

    Article  ADS  Google Scholar 

  23. M.D. Andersen, N. Carlsson, E. Mosekilde, and N.-H. Holstein-Rathlou, Dynamic Model of Nephron-Nephron Interaction in Membrane Transport and Renal Physiology, edited by H. Layton and A. Weinstein (Springer-Verlag, New York, 2002).

    Google Scholar 

  24. N.-H. Holstein-Rathlou, K.-P. Yip, O.V. Sosnovtseva, and E. Mosekilde, Synchronization Phenomena in Nephron-Nephron Interaction, Chaos 11, 417–426 (2001).

    Article  ADS  Google Scholar 

  25. D.E. Postnov, O.V. Sosnovtseva, E. Mosekilde, and N.-H. Holstein-Rathlou, Cooperative Phase Dynamics in Coupled Nephrons, Int. J. Mod. Phys. B 15, 3079–3098 (2001).

    Article  ADS  Google Scholar 

  26. O.V. Sosnovtseva, D.E. Postnov, E. Mosekilde, and N.-H. Holstein-Rathlou, Synchronization of Tubular Pressure Oscillations in Interacting Nephrons, Chaos, Solitons and Fractals (2002) (in press).

    Google Scholar 

  27. E. Mosekilde, Yu. Maistrenko, and D. Postnov, Chaotic Synchronization — Applications to Living Systems (World Scientific, Singapore, 2002).

    MATH  Google Scholar 

  28. N.-H. Holstein-Rathlou and P.P. Leyssac, Oscillations in the Proximal Intratubular Pressure: A Mathematical Model, Am. J. Physiol. 252, F560–F572 (1987).

    Google Scholar 

  29. W.M. Deen, C.R. Robertson, and B.M. Brenner, A Model of Glomerular Ultrafiltration in the Rat, Am. J. Physiol. 223, 1178–1183 (1984).

    Google Scholar 

  30. M. Rosenbaum and D. Race, Frequency-Response Characteristics of Vascular Resistance Vessels, Am. J. Physiol. 215, 1397–1402 (1968).

    Google Scholar 

  31. Y.-C. B. Fung, Biomechanics. Mechanical Properties of Living Tissues (Springer, New York, 1981).

    Google Scholar 

  32. T.S. Parker and L.O. Chua, Practical Numerical Algorithms for Chaotic Systems (Springer-Verlag, Berlin, 1989).

    Book  MATH  Google Scholar 

  33. M. Marek and I. Schreiber, Chaotic Behavior in Deterministic Dissipative Systems (Cambridge University Press, England, 1991).

    Book  Google Scholar 

  34. A. Wolf, Quantifying Chaos with Lyapunov Exponents in Chaos, edited by A.V. Holden (Manchester University Press, England, 1986).

    Google Scholar 

  35. Y.-M. Chen, K.-P. Yip, D.J. Marsh and N.-H. Holstein-Rathlou, Magnitude of TGF-Initiated Nephron-Nephron Interactions is Increased in SHR, Am. J. Physiol. 269, F198–F204 (1995).

    Google Scholar 

  36. V.I. Arnol’d, Small Denominators. I. Mapping of the Circumference onto Itself, Am. Math. Soc. Transl. Ser. 2 46, 213–284 (1965).

    Google Scholar 

  37. K.-P. Yip, N.-H. Holstein-Rathlou, and D.J. Marsh, Dynamics of TGF-Initiated Nephron-Nephron Interactions in Normotensive rats and SHR, Am. J. Physiol. 262, F980–F988 (1992).

    Google Scholar 

  38. Ö. Källskog and D.J. Marsh, TGF-Initiated Vascular Interactions between Adjacent Nephrons in the Rat Kidney, Am. J. Physiol. 259, F60–F64 (1990).

    Google Scholar 

  39. M.G. Rosenblum, A.S. Pikovsky, and J. Kurths, Phase Synchronization of Chaotic Oscillators, Phys. Rev. Lett. 76, 1804–1807 (1996).

    Article  ADS  Google Scholar 

  40. A.S. Pikovsky, M.G. Rosenblum, G.V. Osipov, and J. Kurths, Phase Synchronization of Chaotic Oscillators by External Driving, Physica D 104219–238 (1997).

    Article  MathSciNet  ADS  MATH  Google Scholar 

  41. L.R. Stratonovich, Topics in the Theory of Random Noise (Gordon and Breach, New York, 1963).

    Google Scholar 

  42. D.E. Postnov, T.E. Vadivasova, O.V. Sosnovtseva, A.G. Balanov, V.S. Anishchenko, and E. Mosekilde, Role of Multistability in the Transition to Chaotic Phase Synchronization, Chaos 9, 227–232 (1999).

    Article  ADS  Google Scholar 

  43. T.E. Vadivasova, O.V. Sosnovtseva, A.G. Balanov, and V.V. Astakhov, Phase Multistability of Synchronous Chaotic Oscillations, Discrete Dynamics in Nature and Society 4, 231–243 (2000).

    Article  MATH  Google Scholar 

  44. J. Rasmusen, E. Mosekilde, and Chr. Reick, Bifurcations in Two Coupled R ö ssler Systems, Math. Comp. Sim. 40, 247–270 (1996).

    Article  Google Scholar 

  45. O.V. Sosnovtseva, D.E. Postnov, A.M. Nekrasov, and E. Mosekilde, Phase Multistability Analysis of Self-Modulated Oscillations, Phys. Rev. E (2002) (in press).

    Google Scholar 

  46. A. Grossmann, J. Morlet, S.I.A.M. J. Math. Anal. 15, 723 (1984); I. Daubechies, Ten Lectures on Wavelets (S.I.A.M., Philadelphia, 1992).

    Article  MathSciNet  MATH  Google Scholar 

  47. Y. Kuramoto, Chemical Oscillations, Waves, and Turbulence (Springer-Verlag, New York, 1984).

    Book  MATH  Google Scholar 

  48. S.H. Park, S. Kim, H.-B. Pyo, and S. Lee, Multistability analysis of phase locking patterns in an excitatory coupled neural system, Phys. Rev. E 60, 2177–2181 (1999).

    Article  ADS  Google Scholar 

  49. S.K. Han, C. Kurrer, and Y. Kuramoto, Dephasing and bursting in coupled neural oscillators, Phys. Rev. Lett. 753190–3193 (1995).

    Article  ADS  Google Scholar 

  50. D. Postnov, S.K. Han, and H. Kook, Synchronization of diffusively coupled oscillators near the homoclinic bifurcation, Phys. Rev. E 60, 2799–2807 (1999).

    Article  MathSciNet  ADS  Google Scholar 

  51. N.-H. Holstein-Rathlou, Synchronization of proximal intratubular pressure oscillation: evidence for interaction between nephrons Pflügers Archiv 408, 438–443 (1987).

    Article  Google Scholar 

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Author information

Authors and Affiliations

  1. Department of Physics, The Technical University of Denmark, 2800, Kgs. Lyngby, Denmark

    E. Mosekilde & O. V. Sosnovtseva

  2. Department of Physics, Saratov State University, Astrakhanskaya str. 83, Saratov, 410026, Russia

    O. V. Sosnovtseva

  3. Department of Medical Physiology, University of Copenhagen, 2200, Copenhagen N, Denmark

    N.-H. Holstein-Rathlou

Authors
  1. E. Mosekilde
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  2. O. V. Sosnovtseva
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  3. N.-H. Holstein-Rathlou
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Editor information

Editors and Affiliations

  1. University of Potsdam, Potsdam, Germany

    Arkady Pikovsky

  2. Institute of Mathematics, National Academy of Sciences of Ukraine, Kyiv, Ukraine

    Yuri Maistrenko

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Mosekilde, E., Sosnovtseva, O.V., Holstein-Rathlou, NH. (2003). Nonlinear Phenomena in Nephron-Nephron Interaction. In: Pikovsky, A., Maistrenko, Y. (eds) Synchronization: Theory and Application. NATO Science Series, vol 109. Springer, Dordrecht. https://doi.org/10.1007/978-94-010-0217-2_7

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  • DOI: https://doi.org/10.1007/978-94-010-0217-2_7

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-1-4020-1417-8

  • Online ISBN: 978-94-010-0217-2

  • eBook Packages: Springer Book Archive

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