Characterizing multimode interaction in renal autoregulation

The purpose of this paper is to demonstrate how modern statistical techniques of non-stationary time-series analysis can be used to characterize the mutual interaction among three coexisting rhythms in nephron pressure and flow regulation. Besides a relatively fast vasomotoric rhythm with a period of 5-8 s and a somewhat slower mode arising from an instability in the tubuloglomerular feedback mechanism, we also observe a very slow mode with a period of 100-200 s. Double-wavelet techniques are used to study how the very slow rhythm influences the two faster modes. In a broader perspective, the paper emphasizes the significance of complex dynamic phenomena in the normal and pathological function of physiological systems and discusses how simulation methods can help to understand the underlying biological mechanisms. At the present there is no causal explanation of the very slow mode. However, vascular oscillations with similar frequencies have been observed in other tissues.

[1]  Milan Palus,et al.  Interactions between cardiac, respiratory and EEG-delta oscillations in rats during anaesthesia. , 2007, The Journal of physiology.

[2]  A G Balanov,et al.  Regions of cardiorespiratory synchronization in humans under paced respiration. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[3]  K. Schäfer,et al.  Periodic firing pattern in afferent discharges from electroreceptor organs of catfish , 2004, Pflügers Archiv.

[4]  D J Marsh,et al.  Renal blood flow regulation and arterial pressure fluctuations: a case study in nonlinear dynamics. , 1994, Physiological reviews.

[5]  L. Amaral,et al.  Multifractality in human heartbeat dynamics , 1998, Nature.

[6]  Niels-Henrik Holstein-Rathlou,et al.  Frequency encoding in renal blood flow regulation. , 2005, American journal of physiology. Regulatory, integrative and comparative physiology.

[7]  Paul S. Addison,et al.  Secondary Transform Decoupling of Shifted nonstationary Signal Modulation Components: Application to Photoplethysmography , 2004, Int. J. Wavelets Multiresolution Inf. Process..

[8]  Jürgen Kurths,et al.  Synchronization: Phase locking and frequency entrainment , 2001 .

[9]  C. Aalkjær,et al.  Vasomotion: cellular background for the oscillator and for the synchronization of smooth muscle cells , 2005, British journal of pharmacology.

[10]  E. Mosekilde,et al.  Synchronization phenomena in nephron-nephron interaction. , 2001, Chaos.

[11]  N. Holstein-Rathlou,et al.  Dynamics of TGF-initiated nephron-nephron interactions in normotensive rats and SHR. , 1992, The American journal of physiology.

[12]  Vasilis Z. Marmarelis,et al.  Detection of interactions between myogenic and TGF mechanisms using nonlinear analysis , 1994 .

[13]  H. Stanley,et al.  Quantification of scaling exponents and crossover phenomena in nonstationary heartbeat time series. , 1995, Chaos.

[14]  Peter A. Tass,et al.  Development of Therapeutic Brain Stimulation Techniques with Methods from Nonlinear Dynamics and Statistical Physics , 2006, Int. J. Bifurc. Chaos.

[15]  Peter A Tass,et al.  Effective desynchronization with bipolar double-pulse stimulation. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[16]  A. Goldbeter,et al.  Optimizing Temporal Patterns of Anticancer Drug Delivery by Simulations of a Cell Cycle Automaton , 2007 .

[17]  Jürgen Kurths,et al.  Synchronization - A Universal Concept in Nonlinear Sciences , 2001, Cambridge Nonlinear Science Series.

[18]  N. Holstein-Rathlou,et al.  TGF-mediated oscillations in the proximal intratubular pressure: differences between spontaneously hypertensive rats and Wistar-Kyoto rats. , 1986, Acta physiologica Scandinavica.

[19]  S. Mallat.  A wavelet tour of signal processing , 1998 .

[20]  E Mosekilde,et al.  Interference microscopy under double-wavelet analysis: a new approach to studying cell dynamics. , 2005, Physical review letters.

[21]  Aneta Stefanovska,et al.  Synchronization and modulation in the human cardiorespiratory system , 2000 .

[22]  E. Mosekilde,et al.  Synchronization among mechanisms of renal autoregulation is reduced in hypertensive rats. , 2007, American journal of physiology. Renal physiology.

[23]  E. Mosekilde,et al.  Bimodal oscillations in nephron autoregulation. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[24]  Ingrid Daubechies,et al.  Ten Lectures on Wavelets , 1992 .

[25]  A. Just,et al.  Mechanisms of renal blood flow autoregulation: dynamics and contributions. , 2007, American journal of physiology. Regulatory, integrative and comparative physiology.

[26]  Charles K. Chui,et al.  An Introduction to Wavelets , 1992 .

[27]  Yves Meyer,et al.  Wavelets and Applications , 1992 .

[28]  M. Paluš,et al.  Interactions between cardiac, respiratory and EEG‐δ oscillations in rats during anaesthesia , 2007 .

[29]  A. N. Pavlov,et al.  Unraveling Cell Processes: Interference Imaging Interwoven with Data Analysis , 2006, Journal of biological physics.

[30]  N. Holstein-Rathlou,et al.  Analysis of interaction between TGF and the myogenic response in renal blood flow autoregulation. , 1995, The American journal of physiology.

[31]  H H Abel,et al.  Synchronization in the human cardiorespiratory system. , 1998, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[32]  Douglas Maraun,et al.  Nonlinear Processes in Geophysics , 2000 .

[33]  D J Marsh,et al.  Tubuloglomerular feedback dynamics and renal blood flow autoregulation in rats. , 1991, The American journal of physiology.

[34]  J. Rinzel,et al.  Emergence of organized bursting in clusters of pancreatic beta-cells by channel sharing. , 1988, Biophysical journal.

[35]  Zhe Sun,et al.  New technologies for dissecting the arteriolar myogenic response. , 2007, Trends in pharmacological sciences.

[36]  Erik Mosekilde.  Topics in Nonlinear Dynamics: Applications to Physics, Biology and Economic Systems , 1997 .

[37]  M. Rosenblum,et al.  Detecting direction of coupling in interacting oscillators. , 2001, Physical review. E, Statistical, nonlinear, and soft matter physics.

[38]  D. Smirnov,et al.  Estimation of interaction strength and direction from short and noisy time series. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.

[39]  E Mosekilde,et al.  Double-wavelet approach to study frequency and amplitude modulation in renal autoregulation. , 2004, Physical review. E, Statistical, nonlinear, and soft matter physics.

[40]  H E Stanley,et al.  Statistical physics and physiology: monofractal and multifractal approaches. , 1999, Physica A.

[41]  A L Goldberger,et al.  Generalized Lévy-walk model for DNA nucleotide sequences. , 1993, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[42]  N. Holstein-Rathlou,et al.  Effects of various transport inhibitors on oscillating TGF pressure responses in the rat , 1986, Pflügers Archiv.

[43]  A. Grossmann,et al.  DECOMPOSITION OF HARDY FUNCTIONS INTO SQUARE INTEGRABLE WAVELETS OF CONSTANT SHAPE , 1984 .

[44]  J. Cheung,et al.  Relaxation abnormalities in single cardiac myocytes from renovascular hypertensive rats. , 1992, The American journal of physiology.

[45]  E. Mosekilde,et al.  Chaotic Synchronization: Applications to Living Systems , 2002 .

[46]  E. Mosekilde,et al.  Bifurcation analysis of nephron pressure and flow regulation. , 1996, Chaos.

[47]  E Mosekilde,et al.  Double-wavelet approach to studying the modulation properties of nonstationary multimode dynamics. , 2005, Physiological measurement.

[48]  G. Ermentrout,et al.  Gamma rhythms and beta rhythms have different synchronization properties. , 2000, Proceedings of the National Academy of Sciences of the United States of America.