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.
Similar content being viewed by others
References
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. 220–224
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-H2087
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-H152
Borst, C. andKaremaker, J. M. (1983): ‘Time delay in the human baroreceptor reflex’,J. Auton. Nerv. Syst.,9, pp. 399–409
Cavalcanti, S. andBelardinelli, E. (1996): ‘Modelling of cardiovascular variability using differential delay equation’,IEEE Trans. Biomed. Eng.,43, pp. 982–989
Cavalcanti, S. andUrsino, M. (1996): ‘Chaotic oscillations in microvessel arterial networks’,Ann. Biom. Eng.,24, pp. 27–47
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. 1–9
Chapleau, M. W. andAbboud, F. M. (1987): ‘Contrasting effects of static and pulsatile pressure on carotid baroreceptor activity in dogs’,Circ. Res.,61, pp. 648–658
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. 775–789
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. 359–364
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-H689
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 811–824
Glass, L., Hunter, P. andMacKey, M. C. (1988): ‘From Clocks to Chaos: the rhythm of life’ (Princeton University Press, Princeton)
Goldberger, A. L., Rigney, D. R. andWest, B. J. (1990): ‘Chaos and fractals in human physiology’,Sci. Am.,262, pp. 42–49
Guyton, A. G. andColeman, T. G. (1972): ‘Circulation: overall regulation’,Ann. Rev. Physiol.,34, pp. 13–46
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. H1112–1120
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. 203–213
Hirsch, J. A. andBishop, B., (1981): ‘Respiratory sinus arrhythmia in humans: how breathing pattern modulates heart rate’,Am. J. Physiol.,241: pp. H620-H629
Hyndman, B. W., Kitney, R. I. andMcA Sayer, B. (1971): ‘Spontaneous rhythms in physiological control system’,Nature Lond.,233, pp. 339–341
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. 2003–2013
Hosomi, H. (1978): ‘Unstable state of the arterial pressure control system after a mild hemorrhage’,Am. J. Physiol.,235, pp. R279–285
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. 245–311
Kitney, R. I. andRompelman, O. (1980): ‘The study of heart rate variability’ (Clarendon Press, Oxford)
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. 3–23
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. 65–76
Kuznetsov, Y. A. (1995): ‘Elements of applied bifurcation theory’ (Springer-Verlag, Berlin)
Levy, M. N. andZieske, H. (1969): ‘Autonomic control of cardiac pacemaker activity and atrioventricular transmission’,J. Appl. Physiol.,27, pp. 465–470
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. 1803–1810
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-H1579
Maliani, A., Pagani, M., Lombardi, F. andCerutti, S. (1991): ‘Cardiovascular neural regulation explored in the frequency domain’,Circulation,84, pp. 1482–1492
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 755–793
Milnor, W. R. (1989): ‘Emodynamics’ (Williams & Wilkins, Baltimora, USA), pp. 171–172
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. 529–538
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-H153
Sayers, B. McA. (1973): ‘Analysis of heart variability’,Ergonomics,16, pp. 85–97
Schmidt, J. A., Intaglietta, M. andBorgstrom, P. (1992): ‘Periodic hemodynamics in skeletal muscle during local arterial pressure reduction’,J. Appl. Physiol.,73, pp. 1077–1083
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. 23–33
Warner, H. R., andCox, A. (1991): ‘A mathematical model of heart rate control by sympathetic and vagus efferent information’,J. Appl. Physiol.,17, pp. 349–355
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. 87–93
Westerhof, N., Elzinga, G. andSipkema, P. (1971): ‘An artificial arterial system for pumping hearts’,J. Appl. Physiol.,31, pp. 776–781
Zwillinger, D. (1989): ‘Handbook of differential equations’ (Academic Press, Inc., Boston, USA)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Cavalcanti, S. Arterial baroreflex influence on heart rate variability: A mathematical model-based analysis. Med. Biol. Eng. Comput. 38, 189–197 (2000). https://doi.org/10.1007/BF02344775
Received:
Accepted:
Issue Date:
DOI: https://doi.org/10.1007/BF02344775