Skip to main content

Towards assessing the sympathovagal balance


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.

This is a preview of subscription content, access via your institution.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6


  1. 1.

    Abbott LF, Wise MB (1981) Dimension of a quantum-mechanical path. Am J Phys 49:37–39

    Article  MathSciNet  Google 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 20:171–177

    Article  MATH  Google 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:9032005

  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 16:64–73

    Article  Google Scholar 

  5. 5.

    Committee to Revise the Guidelines for Ambulatory Electrocardiography (1999) Acc/aha guidelines for ambulatory electrocardiography. J Am College Cardiol 3:913–948

    Google Scholar 

  6. 6.

    Dubrulle B (1994) Intermittency in fully developed turbulence: log-Poisson statistics and generalized scale covariance. Phys Rev Lett 73:959–962

    Article  Google Scholar 

  7. 7.

    Dubrulle B, Graner F (1996) Possible statistics of scale invariant systems. J Phys 6:797–816

    Article  Google Scholar 

  8. 8.

    Dubrulle B, Graner F (1996) Scale invariance and scaling exponents in fully developed turbulence. J Phys 6:817–824

    Google Scholar 

  9. 9.

    Dubrulle B, Bréon FM, Graner F, Pocheau A (1998) Towards an universal classification of scale invariant processes. Eur Phys J B 4:89–94

    Article  Google Scholar 

  10. 10.

    Eckberg DL (1997) Sympathovagal balance: a critical appraisal. Circulation 96:3224–3232

    Google Scholar 

  11. 11.

    Feigenbaum MJ (1988) Presentation functions, fixed points, and a theory of scaling function dynamics. J Stat Phys 52:527–569

    Article  MathSciNet  MATH  Google Scholar 

  12. 12.

    Feynman RP (1949) Space-time approach to quantum electrodynamics. Phys Rev 766:769

    Google Scholar 

  13. 13.

    Feynman RP, Hibbs AR (1965) Quantum mechanics and path integrals. MacGraw-Hill, New York

    MATH  Google 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 81:27–31

    Article  Google 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 80:779–783

    Article  Google Scholar 

  16. 16.

    Malliani A (2000) Principles of cardiovascular neural regulation in health and disease. Kluwer, Dordrecht

  17. 17.

    Malliani A, Pagani M, Montano N, Mela S (1998) Sympathovagal balance: a reappraisal. Circulation 98:2640–2642

    Google Scholar 

  18. 18.

    Mandelbrot B (1982) The fractal geometry of nature. Freeman, San Francisco, pp 184, 331–332

  19. 19.

    Mandelbrot BB (1997) Fractals and scaling in finance. Springer, Berlin Heidelberg New York, pp 29–31, 103–104, 50–78

  20. 20.

    Mandelbrot BB (2004) Fractals and chaos. Springer, Berlin Heidelberg New York, pp 23–36, ix–xii, 276–280, 50–51

  21. 21.

    de Melo W, Van Strien S (1993) One-dimensional dynamics. Springer, Berlin Heidelberg New York

    MATH  Google Scholar 

  22. 22.

    Nottale L (1993) Fractal space-time and microphysics: towards a theory of scale relativity. World Scientific, Singapore

    MATH  Google 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 249–261

  24. 24.

    Nottale L, Schneider J (1984) Fractals and non-standard analysis. J Math Phys 25:1296

    Article  MathSciNet  Google 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)

  26. 26.

    Perkiomaki JS, Makikallio TH, Huikuri HV (2005) Fractal and complexity measures of heart rate variability. Clin Exp Hypertens 27(2, 3):149–158

    Article  Google Scholar 

  27. 27.

    R Luzzatto MH (1805) Qlach pitchey chokhmah. Koretz, openings 49–50

  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):94–99

    Article  Google Scholar 

  29. 29.

    Sleight P, Bernardi L (1998) Sympathovagal balance. Circulation 98:2640

  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 17:354–381

    Google Scholar 

  31. 31.

    Wolfram S (2002) A new kind of science. Wolfram Media, Champaign, pp 363–369, 434, 857

  32. 32.

    Yang C, Kuo T (1999) Assessment of cardiac sympathetic regulation by respiratory-related arterial pressure variability in the rat. J Physiol 515:887–896

    Article  Google 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 51:255–262

    Article  Google Scholar 

Download references


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

Author information



Corresponding author

Correspondence to Melvyn J. Lafitte.

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Lafitte, M.J., Sauvageot, O.R., Fevre-Genoulaz, M. et al. Towards assessing the sympathovagal balance. Med Bio Eng Comput 44, 675–682 (2006).

Download citation


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