A delay recruitment model of the cardiovascular control system. (English) Zbl 1091.92024

Summary: We develop a nonlinear delay-differential equation for the human cardiovascular control system, and use it to explore blood pressure and heart rate variability under short-term baroreflex control. The model incorporates an intrinsically stable heart rate in the absence of nervous control and allows us to compare the baroreflex influence on heart rate and peripheral resistance. Analytical simplifications of the model allow a general investigarion of the roles played by gain and delay, and the effects of ageing.


92C30 Physiology (general)
34K60 Qualitative investigation and simulation of models involving functional-differential equations
93C95 Application models in control theory
Full Text: DOI Link


[1] Abbiw-Jackson, R.M., Langford, W.F.: Gain-induced oscillations in blood pressure. J. Math. Biol. 37, 203–234 (1998) · Zbl 0903.92017
[2] Berne, R.M., Levy, M.N.: Principles of Physiology. (Mosby-Year Book, Second Edn, 1996)
[3] Bertram, D., Barres, C., Cheng, Y., Julien, C.: Norepinephrine reuptake, baroreflex dynamics, and arterial pressure variability in rats. Am. J. Physiol. Regulatory Integrative Comp. Physiol. 279 (4), R1257–R1267 (2000)
[4] Bertram, D., Barres, C., Cuisinard, G., Julien, C.: The arterial baroreceptor reflex of the rat exhibits positive feedback properties at the frequency of Mayer waves. J. Physiol. - London 513 (1), 251–261 (1998)
[5] Bertram, D., Barres, C., Julien, C.: Effect of desipramine on spontaneous arterial pressure oscillations in the rat. Eur. J. Pharmacology 378 (3), 265–271 (1999)
[6] Burgess, D.E., Hundley, J.C., Li, S-G., Randall, D.C., Brown, D.R.: First-order differential-delay equation for the baroreflex predicts the 0.4-Hz blood pressure rhythm in rats. Am. J. Physiol. 273, R1878–R1884 (1997)
[7] Cavalcanti, S., Ursino, M.: Dynamical modelling of sympathetic and parasympathetic interplay on the baroreceptor heart rate control. Surv. Math. Ind. 7, 221–237 (1997) · Zbl 0927.34022
[8] Cevese, A., Gulli, G., Polati, E., Gottin, L., Grasso, R.: Baroreflex and oscillation of heart period at 0.1 Hz studied by {\(\alpha\)}-blockade and cross-spectral analysis in healthy humans. J. Physiol. 531 (1), 235–244 (2001)
[9] Chow, S.-N., Mallet-Paret, J.: Singularly perturbed delay-differential equations. In: Coupled Nonlinear Oscillators, J. Chandra, A.C. Scott (eds.), North-Holland, 1983 · Zbl 0551.34036
[10] Cooley, R.L., Montano, N., Cogliati, C., van de Borne, P., Richenbacher, W., Oren, R., Somers, V.K.: Evidence for a central origin of the low-frequency oscillation in RR-interval variability. Circulation 98, 556–561 (1998)
[11] deBoer, R.W., Karemaker, J.M., Strackee, J.: Hemodynamic fluctuations and baroreflex sensitivity in humans: a beat-to-beat model. Am. J. Physiol. 253 (Heart Circ. Physiol. 22), 680–689 (1987)
[12] Diekmann, O., van Gils, S.A., Verduyn Lunel, S.M., Walther, H.-O.: Delay Equations: Functional, Complex and Nonlinear Analysis. Appl. Math. Sci. 110, Springer, 1995 · Zbl 0826.34002
[13] Fowler, A.C.: Mathematical Models in the Applied Sciences. Cambridge Texts in Applied Mathematics, CUP 1997 · Zbl 0997.00535
[14] Gebber, G.L., Zhong, S., Zhou, S.-Y., Barman, S.M.: Nonlinear dynamics of the frequency locking of baroreceptor and sympathetic rhythms. Am. J. Physiol. 273 (Regulatory Integrative Comp. Physiol. 42), R1932–R1945 (1997)
[15] Girard, A., Meilhac, B., Mouniervehier, C., Elghozi, J.L.: Effects of beta-adrenergic-blockade on short-term variability of blood-pressure and heart rate in essential hypertension. Clinical & Exp. Hypertension 17 (Iss 1-2), 15–27 (1995)
[16] Greenwood, J.P., Stoker, J.B., Mary, D.: Single-unit sympathetic discharge — quantitative assessment in human hypertensive disease. Circulation 100, 1305–1310 (1999)
[17] Grodins, F.S.: Integrative cardiovascular physiology: a mathematical synthesis of cardiac and blood vessel hemodynamics. Q. Rev. Biol. 34, 93–116 (1959)
[18] Guyton, A.: Textbook of Medical Physiology. (W.B. Saunders Co., London, 1981)
[19] Guyton, A.C., Harris, J.W.: Pressoreceptor-autonomic oscillation: a probable cause of vasomotor waves. Am. J. Physiol. 165, 158–166 (1951)
[20] Kaplan, D.T., Furman, M.I., Pincus, S.M., Ryan, S.M., Lipsitz, L.A., Goldberger, A.L.: Aging and the complexity of cardiovascular dynamics. Biophys. J. 59, 945–949 (1991)
[21] Korner, P.: Integrative neural cardiovascular control. Physiol. Rev. 51 (2), 312–367 (1971)
[22] Libsitz, L.A., Goldberger, A.L.: Loss of complexity and aging: Potential applications of fractals and chaos theory to senescence. JAMA 267, 1806–1809 (1992)
[23] Liu, H-K., Guild, S-J., Ringwood, J.V., Barrett, C.J., Leonard, B.L., Nguang, S-K., Navakatikyan, M.A., Malpas, S.C.: Dynamic baroreflex control of blood pressure: influence of the heart vs. peripheral resistance. Am. J. Physiol. Regulatory Integrative Comp. Physiol. 283, R533–R542 (2002)
[24] Madwed, J.B., Albrecht, P., Mark, R.G., Cohen, R.J.: Low frequency oscillations in arterial pressure and heart rate: a simple computer model. Am. J. Physiol. 256, H1573–H1579 (1989)
[25] Magosso, E., Biavati, V., Ursino, M.: Role of the baroreflex in cardiovascular instability: a modeling study. Cardiov. Eng. 1 (2), 101–115 (2001)
[26] Malpas, S.C.: Neural influences on cardiovascular variability: possibilities and pitfalls. Am. J. Physiol. Heart Circ. Physiol. 282, H6–H20 (2002)
[27] Montano, N., Gnecchi-Ruscone, T., Porta, A., Lombardi, F., Malliani, A., Barman, S.M.: Presence of vasomotor and respiratory rhythms in the discharge of single medullary neurons involved in the regulation of cardiovascular system. J. Auton. Nerv. Syst. 57, 116–122 (1996)
[28] Murray, J.D.: Mathematical biology. I: an introduction. (Springer-Verlag, Berlin 2002), pp. 23–27
[29] Ottesen, J.T.: Modelling of the baroreflex-feedback mechanism with time-delay. J. Math. Biol. 36, 41–63 (1997) · Zbl 0887.92015
[30] Ottesen, J.T., Olufsen, M.S., Larsen, J.K.: Applied Mathematical Models in Human Physiology. SIAM Monographs on Mathematical Modelling and Computation, 2004 · Zbl 1097.92016
[31] Ringwood, J.V., Malpas, S.C.: Slow oscillations in blood pressure via a nonlinear feedback model. Am. J. Physiol. Regulatory Integrative Comp. Physiol. 280, R1105–R1115 (2001)
[32] Rosenblum, M., Kurths, J.: A model of neural control of the heart rate. Physica A 215, 439–450 (1995)
[33] Rowel, L.B.: Human Cardiovascular Control. Oxford University Press, 1993
[34] Seidel, H., Herzel, H.: Bifurcations in a nonlinear model of the baroreceptor-cardiac reflex. Physica D 115, 145–160 (1998) · Zbl 0932.92024
[35] Singh, N., Prasad, S., Singer, D.R., MacAllister, R.J.: Ageing is associated with impairment of nitric oxide and prostanoid dilator pathways in the human forearm. Clin. Sci. (Lond). 102 (5), 595–600 (2002)
[36] Ursino, M.: Interaction between carotid baroregulation and the pulsating heart: a mathematical model. Am. J. Physiol. 275 (Heart Circ. Physiol. 44), H1733–H1747 (1998)
[37] Ursino, M., Antonucci, M., Belardinelli, E.: Role of active changes in venous capacity by the carotid baroreflex: analysis with a mathematical model. Am. J. Physiol. 267 (Heart Circ. Physiol. 36), H2531–H2546 (1994)
[38] Ursino, M., Fiorenzi, A., Belardinelli, E.: The role of pressure pulsatility in the carotid baroreflex control: a computer simulation study. Comput. Biol. Med. 26 (4), 297–314 (1996)
[39] Wattis, J.A.D.: Bifurcations and Chaos in a Differential-Delay Equation, an MSc Dissertation in Mathematical Modelling and Numerical Analysis, University of Oxford, September 1990
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.