Towards assessing the sympathovagal balance

  • Melvyn J. LafitteEmail author
  • Orin R. Sauvageot
  • Marion Fevre-Genoulaz
  • Marc Zimmermann
Original Article


Exact assessment of the autonomic nervous system’s (ANS) activity by means of heart rate variability (HRV) is a long-standing challenge. Although many techniques have been proposed to take up the challenge, none ever proposed a rationale for the approach behind the technique or a satisfying discrimination of the two activities which underlie the autonomic control of HRV. We here propose a new method, providing both an understanding of the discrimination’s nature and a framework which we believe leads to a thorough assessment of the sympathovagal balance, as a trajectory between points in a well-chosen space. The methodology assumes tools from scale invariance/covariance physics. The sympathovagal balance is obtained on a beat-to-beat basis with the dynamics portrayed through a trajectory. Furthermore, universal trajectories are sought which would comprehensively describe the effect of atropine and isoproterenol injections on systems underlying the heart pace variations. Non-invasive assessment of the respective activities of the sympathetic and parasympathetic subsystems of the ANS would be possible through cardiac autonomic measurements.


Non-invasive monitoring Autonomic nervous system Heart rate variability Theoretical physics Experimental mathematics 



The first three authors gladly acknowledge financial support from Dyansys, Inc.


  1. 1.
    Abbott LF, Wise MB (1981) Dimension of a quantum-mechanical path. Am J Phys 49:37–39CrossRefMathSciNetGoogle Scholar
  2. 2.
    Balocchi R, Menicucci D, Santarcangelo E, Sebastiani L, Gemignani A, Ghelarducci B, Varanini M (2004) Deriving the respiratory sinus arrhythmia from the heartbeat time-series using empirical mode decomposition. Chaos Solitons Fractals 20:171–177CrossRefzbMATHGoogle Scholar
  3. 3.
    Beckers F, Verheyden B et al (2005) Ageing and non-linear heart rate control in a healthy population. Am J Physiol Heart Circ Physiol O:9032005Google Scholar
  4. 4.
    Bianchi AM, Mainardi LT, Merloni C, Chierchia S, Cerutti S (1997) Continuous monitoring of the sympatho-vagal balance through spectral analysis. IEEE Eng Med Biol 16:64–73CrossRefGoogle Scholar
  5. 5.
    Committee to Revise the Guidelines for Ambulatory Electrocardiography (1999) Acc/aha guidelines for ambulatory electrocardiography. J Am College Cardiol 3:913–948Google Scholar
  6. 6.
    Dubrulle B (1994) Intermittency in fully developed turbulence: log-Poisson statistics and generalized scale covariance. Phys Rev Lett 73:959–962CrossRefGoogle Scholar
  7. 7.
    Dubrulle B, Graner F (1996) Possible statistics of scale invariant systems. J Phys 6:797–816CrossRefGoogle Scholar
  8. 8.
    Dubrulle B, Graner F (1996) Scale invariance and scaling exponents in fully developed turbulence. J Phys 6:817–824Google Scholar
  9. 9.
    Dubrulle B, Bréon FM, Graner F, Pocheau A (1998) Towards an universal classification of scale invariant processes. Eur Phys J B 4:89–94CrossRefGoogle Scholar
  10. 10.
    Eckberg DL (1997) Sympathovagal balance: a critical appraisal. Circulation 96:3224–3232Google Scholar
  11. 11.
    Feigenbaum MJ (1988) Presentation functions, fixed points, and a theory of scaling function dynamics. J Stat Phys 52:527–569CrossRefMathSciNetzbMATHGoogle Scholar
  12. 12.
    Feynman RP (1949) Space-time approach to quantum electrodynamics. Phys Rev 766:769Google Scholar
  13. 13.
    Feynman RP, Hibbs AR (1965) Quantum mechanics and path integrals. MacGraw-Hill, New YorkzbMATHGoogle Scholar
  14. 14.
    Mäkikallio TH, Ristimae T et al (1998) Heart rate dynamics in patients with stable angina pectoris and utility of fractal and complexity measures. Am J Cardiol 81:27–31CrossRefGoogle Scholar
  15. 15.
    Mäkikallio TH, Seppänen T et al (1997) Dynamic analysis of heart rate may predict subsequent ventricular tachycardia after myocardial infarction. Am J Cardiol 80:779–783CrossRefGoogle Scholar
  16. 16.
    Malliani A (2000) Principles of cardiovascular neural regulation in health and disease. Kluwer, DordrechtGoogle Scholar
  17. 17.
    Malliani A, Pagani M, Montano N, Mela S (1998) Sympathovagal balance: a reappraisal. Circulation 98:2640–2642Google Scholar
  18. 18.
    Mandelbrot B (1982) The fractal geometry of nature. Freeman, San Francisco, pp 184, 331–332Google Scholar
  19. 19.
    Mandelbrot BB (1997) Fractals and scaling in finance. Springer, Berlin Heidelberg New York, pp 29–31, 103–104, 50–78Google Scholar
  20. 20.
    Mandelbrot BB (2004) Fractals and chaos. Springer, Berlin Heidelberg New York, pp 23–36, ix–xii, 276–280, 50–51Google Scholar
  21. 21.
    de Melo W, Van Strien S (1993) One-dimensional dynamics. Springer, Berlin Heidelberg New YorkzbMATHGoogle Scholar
  22. 22.
    Nottale L (1993) Fractal space-time and microphysics: towards a theory of scale relativity. World Scientific, SingaporezbMATHGoogle Scholar
  23. 23.
    Nottale L (1997) Scale relativity, in scale invariance and beyond. In: Dubrulle B, Graner F, Sornette D (eds) Proceedings of Les Houches school, EDP Sciences, Les Ullis/Springer, Berlin Heidelberg New York, pp 249–261Google Scholar
  24. 24.
    Nottale L, Schneider J (1984) Fractals and non-standard analysis. J Math Phys 25:1296CrossRefMathSciNetGoogle Scholar
  25. 25.
    Nottale L (2006) The theory of scale relativity: non-differentiable geometry and fractal space-time. In: Proceedings of AIP Conference 2004 (in press)Google Scholar
  26. 26.
    Perkiomaki JS, Makikallio TH, Huikuri HV (2005) Fractal and complexity measures of heart rate variability. Clin Exp Hypertens 27(2, 3):149–158CrossRefGoogle Scholar
  27. 27.
    R Luzzatto MH (1805) Qlach pitchey chokhmah. Koretz, openings 49–50Google Scholar
  28. 28.
    Shin DG, Yoo CS et al (2006) Prediction of paroxysmal atrial fibrillation using nonlinear analysis of the R-R interval dynamics before the spontaneous onset of atrial fibrillation. Circ J 70(1):94–99CrossRefGoogle Scholar
  29. 29.
    Sleight P, Bernardi L (1998) Sympathovagal balance. Circulation 98:2640Google Scholar
  30. 30.
    Task Force of The European Society of Cardiology, The North American Society of Pacing and Electrophysiology (1996) Heart rate variability. Eur Heart J 17:354–381Google Scholar
  31. 31.
    Wolfram S (2002) A new kind of science. Wolfram Media, Champaign, pp 363–369, 434, 857Google Scholar
  32. 32.
    Yang C, Kuo T (1999) Assessment of cardiac sympathetic regulation by respiratory-related arterial pressure variability in the rat. J Physiol 515:887–896CrossRefGoogle Scholar
  33. 33.
    Zhong Y, Wang H, Jan K, Ju K, Chon KH (2004) Separation of the sympathetic and parasympathetic tone using principal dynamic mode analysis. IEEE Trans BME 51:255–262CrossRefGoogle Scholar

Copyright information

© International Federation for Medical and Biological Engineering 2006

Authors and Affiliations

  • Melvyn J. Lafitte
    • 1
    • 2
    Email author
  • Orin R. Sauvageot
    • 1
  • Marion Fevre-Genoulaz
    • 1
  • Marc Zimmermann
    • 1
  1. 1.Cardiovascular DepartmentHôpital de la Tour MeyrinGenevaSwitzerland
  2. 2.DyansysAnièresSwitzerland

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