Arterial baroreflex influence on heart rate variability: A mathematical model-based analysis

Article

Abstract

The influence of the arterial baroreflex on the heart rate variability is analysed by using a mathematical model of heart rate baroreceptor control. The basic mechanisms of the model, sufficient to elicit heart rate variability include: systemic circulation, a non-pulsatile cardiac pump and nonlinear negative feedback simulating arterial baroreflex closed-loop control of the heart rate (−3bpm/mmHg as maximum reflex sensitivity). The latter reproduces, through two distinct delayed branches (0.8 and 2.8 s), the short-term autonomic control effected respectively by sympathetic and parasympathetic divisions on the sinus node. By means of this model, two distinct self-sustained oscillatory components with incommensurate frequencies (0.1 and 0.26 Hz) are reproduced. Frequencies of these two oscillatory components closely agree with the main heart rate rhythms in humans (0.09±0.01 Hz and 0.26±0.01 Hz). When sympathetic-mediated regulation prevails over parasympathetic activity, simulated heart rate oscillation is characterised by a low frequency (∼0.1 Hz). On the other hand, a high-frequency oscillatory component (∼0.26 Hz) appears when enhanced vagal activation or partial inhibition of the sympathetic control is simulated. When both autonomic divisions are operative, both low- and high-frequency components are present and the heart rate oscillates quasi-periodically. This variability in heart rate at different frequencies is reproduced without including outside perturbations and is due to the nonlinear delayed structure of the closed-loop control. Bifurcation theory of nonlinear system is used to explain the high sensitivity of the heart rate oscillatory pattern to model parameter changes.

Keywords

Modelling of autonomic regulation Rhythm in cardiovascular signals Bifurcation in physiological modelling 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Akselrod, S., Gordon, D., Ubel, F. A., Shannon, D. C., Barger, A. C. andCohen, R. J. (1981): ‘Power spectral analysis of heart rate fluctuation: a quantitative probe of beat-to-beat cardiovascular control’,Science Wash.,213, pp. 220–224Google Scholar
  2. Bailey, J. R., Fitzgerald, D. M. andApplegate, R. J. (1996): ‘Effects of constant cardiac autonomic nerve stimulation on heart rate variability’,Am. J. Physiol.,270, pp. H2081-H2087Google Scholar
  3. Berger, R. D., Saul, J. P. andCohen, R. J. (1989): ‘Transfer function analysis of autonomic regulation in canine atrial rate response’,Am. J. Physiol.,256, pp. H142-H152Google Scholar
  4. Borst, C. andKaremaker, J. M. (1983): ‘Time delay in the human baroreceptor reflex’,J. Auton. Nerv. Syst.,9, pp. 399–409Google Scholar
  5. Cavalcanti, S. andBelardinelli, E. (1996): ‘Modelling of cardiovascular variability using differential delay equation’,IEEE Trans. Biomed. Eng.,43, pp. 982–989CrossRefGoogle Scholar
  6. Cavalcanti, S. andUrsino, M. (1996): ‘Chaotic oscillations in microvessel arterial networks’,Ann. Biom. Eng.,24, pp. 27–47Google Scholar
  7. Cavalcanti, S., Severi, S. andEnzmann, G. (1998): ‘Analysis of oscillatory components of short-term heart rate variability in hemodynamically stable and unstable patients during hemodialysis’,Artificial Organs,22, pp. 1–9CrossRefGoogle Scholar
  8. Chapleau, M. W. andAbboud, F. M. (1987): ‘Contrasting effects of static and pulsatile pressure on carotid baroreceptor activity in dogs’,Circ. Res.,61, pp. 648–658Google Scholar
  9. Chess, G. F., Tam, R. M. andCalaresu, F. R. (1975): ‘Influence of cardiac neural inputs on rhythmic variations of heart period in the cat’,Am. J. Physiol.,128, pp. 775–789Google Scholar
  10. de Boer, R. W., Karemaker, J. M. andStrackee, J. (1985): ‘Relationship between short-term blood-pressure fluctuations and heart-rate variability in resting subjects II: a simple model’,Med. Biol. Eng. Comput.,23, pp. 359–364Google Scholar
  11. de Boer, R. W., Karemaker, J. M. andStrackee, J. (1987): ‘Hemodynamic fluctuations and baroreflex sensitivity in humans: a beat-to-beat model’,Am. J. Physiol.,253, pp. H680-H689Google Scholar
  12. Franz, G. N. (1969): ‘Nonlinear rate sensitivity of the carotid sinus reflex as a consequence of static and dynamic nonlinearities in baroreceptor behavior’,Ann. NY Acad. Sci.,156, pp 811–824Google Scholar
  13. Glass, L., Hunter, P. andMacKey, M. C. (1988): ‘From Clocks to Chaos: the rhythm of life’ (Princeton University Press, Princeton)Google Scholar
  14. Goldberger, A. L., Rigney, D. R. andWest, B. J. (1990): ‘Chaos and fractals in human physiology’,Sci. Am.,262, pp. 42–49Google Scholar
  15. Guyton, A. G. andColeman, T. G. (1972): ‘Circulation: overall regulation’,Ann. Rev. Physiol.,34, pp. 13–46Google Scholar
  16. Guzzetti, S., Cogliati, C., Broggi, C., Carozzi, C., Caldiroli, D., Lombardi, F. andMalliani, A. (1994): ‘Influences of neural mechanisms on heart period and arterial pressure variabilities in quadriplegic patients’,Am. J. Physiol.,266, pp. H1112–1120Google Scholar
  17. Head, G. A. andMcCarty, R. (1987): ‘Vagal and sympathetic components of the heart rate range and gain of the baroreceptor-heart rate reflex in conscious rats’,J. Auton. Nerv. Syst.,21, pp. 203–213CrossRefGoogle Scholar
  18. Hirsch, J. A. andBishop, B., (1981): ‘Respiratory sinus arrhythmia in humans: how breathing pattern modulates heart rate’,Am. J. Physiol.,241: pp. H620-H629Google Scholar
  19. Hyndman, B. W., Kitney, R. I. andMcA Sayer, B. (1971): ‘Spontaneous rhythms in physiological control system’,Nature Lond.,233, pp. 339–341CrossRefGoogle Scholar
  20. Horner, R. L., Brooks, D., Kozar, L. F., Gan, K. andPhillipson, E. A. (1995): ‘Respiratory-related heart rate variability persists during central apnea in dogs: mechanisms and implications’,J. Appl. Physiol.,78, pp. 2003–2013Google Scholar
  21. Hosomi, H. (1978): ‘Unstable state of the arterial pressure control system after a mild hemorrhage’,Am. J. Physiol.,235, pp. R279–285Google Scholar
  22. Kamath, M. V. andFallen, E. L. (1993): ‘Power spectral analysis of heart rate variability: a non invasive signature of cardiac autonomic function’,Crit. Rev. Biomed. Eng.,21, pp. 245–311Google Scholar
  23. Kitney, R. I. andRompelman, O. (1980): ‘The study of heart rate variability’ (Clarendon Press, Oxford)Google Scholar
  24. Koepchen, H. P. (1984): ‘History of studies and concepts of blood pressure waves’ inMiyakawa, K., Koepchen, H. P. andPolosa, C. (Eds): ‘Mechanisms of Blood Pressure’ (Springer-Verlag, Berlin), pp. 3–23Google Scholar
  25. Korner, P. I., West, M. J., Shaw, J. andUther, J. B. (1974): ‘Steadystate properties of the baroreceptor-heart rate reflex in essential hypertension in man’,Clin. Exp. Pharmacol. Physiol.,1, pp. 65–76Google Scholar
  26. Kuznetsov, Y. A. (1995): ‘Elements of applied bifurcation theory’ (Springer-Verlag, Berlin)Google Scholar
  27. Levy, M. N. andZieske, H. (1969): ‘Autonomic control of cardiac pacemaker activity and atrioventricular transmission’,J. Appl. Physiol.,27, pp. 465–470Google Scholar
  28. Lipsitz, L. A., Mietus, J., Moody, G. B. andGoldberger, A. L. (1990): ‘Spectral characteristics of heart rate variability before and during paostural tilt’,Circulation,81, pp. 1803–1810Google Scholar
  29. Madwed, J. B., Albrecht, P., Mark, R. G., andCohen, R. J. (1989): ‘Low-frequency oscillations in arterial pressure and heart rate: a simple computer model’,Am. J. Physiol.,256, pp. H1573-H1579Google Scholar
  30. Maliani, A., Pagani, M., Lombardi, F. andCerutti, S. (1991): ‘Cardiovascular neural regulation explored in the frequency domain’,Circulation,84, pp. 1482–1492Google Scholar
  31. Mancia, G. andMark, A. (1983): ‘Arterial baroreflexes in humans’, inShepherd J. T. andAbboud F. M. (Eds): ‘Handbook of Physiology. Sec. 2, The Cardiovascular System Vol. III’ (Williams & Wilkins Company, Baltimore), pp 755–793Google Scholar
  32. Milnor, W. R. (1989): ‘Emodynamics’ (Williams & Wilkins, Baltimora, USA), pp. 171–172Google Scholar
  33. Mpitsos, G. J., Burton, M. R., Crecech, H. C. andSoinila, S. O. (1988): ‘Evidence for chaos in spike trains of neurons that generate rhythmic motor patterns’,Brain Res. Bull.,21, pp. 529–538Google Scholar
  34. Pomeranz, B., Macaulay, R. J., Caudill, M. A., Kutz, I., Adam, D., Gordon, D., Kilborn, K. M., Barger, A. C., Shannon, D. C. andCohen, R. J. (1985): ‘Assessment of autonomic function in humans by heart rate spectral analysis’,Am. J. Physiol.,248, pp. H151-H153Google Scholar
  35. Sayers, B. McA. (1973): ‘Analysis of heart variability’,Ergonomics,16, pp. 85–97Google Scholar
  36. Schmidt, J. A., Intaglietta, M. andBorgstrom, P. (1992): ‘Periodic hemodynamics in skeletal muscle during local arterial pressure reduction’,J. Appl. Physiol.,73, pp. 1077–1083Google Scholar
  37. Warner, M. (1994): ‘Time-course and frequency dependence of sympathetic stimulation-evoked inhibition of vagal effect at the sinus node’,J. Autonomic Nerv. Syst.,52, pp. 23–33Google Scholar
  38. Warner, H. R., andCox, A. (1991): ‘A mathematical model of heart rate control by sympathetic and vagus efferent information’,J. Appl. Physiol.,17, pp. 349–355Google Scholar
  39. Weise, F., London, G. M., Guerin, A. P., Pannier, B. M. andElghozi, J. L. (1995): ‘Effect of head-down tilt on cardiovascular control in healthy subjects: a spectral analytic approach’,Clin. Sci.,88, pp. 87–93Google Scholar
  40. Westerhof, N., Elzinga, G. andSipkema, P. (1971): ‘An artificial arterial system for pumping hearts’,J. Appl. Physiol.,31, pp. 776–781Google Scholar
  41. Zwillinger, D. (1989): ‘Handbook of differential equations’ (Academic Press, Inc., Boston, USA)Google Scholar

Copyright information

© IFMBE 2000

Authors and Affiliations

  1. 1.Laboratory of Biomedical Engineering, Department of Electronics, Computer Science and SystemsUniversity of BolognaItaly

Personalised recommendations