Seidel-Herzel model of human baroreflex in cardiorespiratory system with stochastic delays

Journal of Mathematical Biology

Volumn 57, Issue 1, 2008, Pages 111-137

  Dudkowska, Aleksandra ^a   Makowiec, Danuta ^a  

^a UNIVERSITY OF GDA SK   (Poland)

Author keywords

Baroreflex control; Bifurcations; Mayer waves; Stochastic delays

Indexed keywords

ARTICLE; BIOLOGICAL MODEL; BLOOD PRESSURE; CORONARY BLOOD VESSEL; HEART; HEART RATE; HUMAN; INNERVATION; OSCILLOMETRY; PHYSIOLOGY; PRESSORECEPTOR; PRESSORECEPTOR REFLEX; STATISTICS; TIME;

BAROREFLEX; BLOOD PRESSURE; CORONARY VESSELS; HEART; HEART RATE; HUMANS; MODELS, CARDIOVASCULAR; OSCILLOMETRY; PRESSORECEPTORS; STOCHASTIC PROCESSES; TIME FACTORS;

EID: 42149154833     PISSN: 03036812     EISSN: 14321416     Source Type: Journal    
DOI: 10.1007/s00285-007-0148-9     Document Type: Article

References (44)

1. Glass L. (2001). Synchronization and rhythmic processes in physiology. Nature 410: 277
2. Peng C.K., Mietus J., Hausdorff J.M., Havlin S., Stanley H.E. and Goldberger A.L. (1993). Long-range anticorrelations and non-gaussian behavior of the heartbeat. Phys. Rev. Lett. 70: 1343
3. Yamamoto Y. and Hughson R.L. (1994). On the fractal nature of heart rate variability in humans: effects of data length and β-adrenergic blockade. Am. J. Physiol. 266: R40
4. Ivanov P.C., Amaral L.A.N., Goldberger A.L., Havlin S., Rosenblum M.G., Struzik Z.R. and Stanley H.E. (1999). Multifractality in human heart rate dynamics. Nature 399: 461
5. Makowiec D., Gałaska R., Dudkowska A., Rynkiewicz A. and Zwierz M. (2006). Long-range dependencies in heart rate signals-revisited. Physica A 369(2): 632
6. Kiyono K., Struzik Z.R., Aoyagi N., Togo F. and Yamamoto Y. (2005). Phase transition in a healthy human heart rate. Phys. Rev. Lett. 95: 058101
7. Heart rate variability. Standards of measurment, physiological interpretation, and clinical use. Eur. Heart J. 17, 354 (1996)
8. Malik M. (2004). Heart Rate Variability and Baroreflex Sensitivity in Cardiac Electrophysiology. In: Zipes, D.P. and Jalife, J. (eds) From Cell To Bedside, 4th edn, pp. Saunders, Philadelphia
9. Malpas S.C. (2002). Neural influences on cardiovascular variability: possibilities and pitfalls. Am. J. Physiol. Heart Circ. Physiol. 282: H6
10. Julien C. (2006). The enigma of Mayer waves: facts and models. Cardiovasc. Res. 70: 12
11. Eckberg D.L. and Sleight P. (1992). Human Baroreflexes in Health and Disease. Clarendon Press, Oxford
12. Bertram D., Barre's C., Cheng Y. and Julien C. (2000). Norepinephrine reuptake, baroreflex dynamics, and arterial pressure variability in rats. Am. J. Physiol. Regul. Integr. Comp. Physiol. 279: R1257
13. Pikovsky A., Rosenblum M. and Kurths J. (2000). Phase synchronization in regular and chaotic systems. Int. J. Bif. Chaos 10: 2291
14. Schäfer C.S., Rosenblum M.G., Kurths J. and Abel H. (1998). Heartbeat synchronized with ventilation. Nature 392: 239
15. Lotric M.B. and Stefanovska A. (2000). Synchronization and modulation in the human cardiorespiratory system. Physica A 283: 451
16. Prokhorov M.D., Ponomarenko V.I., Gridnev V.I., Bodrov M.B. and Bespyatov A.B. (2003). Synchronization between main rhythmic processes in the human cardiovascular system. Phys. Rev. E 68: 041913
17. Stefanovska A., Haken H., McClintock P.V.E., Hožic M., Bajrovic F. and Ribaric S. (2000). Reversible transitions between synchronization states of the cardiorespiratory system. Phys. Rev. Lett. 85: 4831
18. Censi F., Calcagnini G. and Cerutti S. (2002). Coupling patterns between spontaneous rhythms and respiration in cardiovascular variability signals. Comput. Methods Programs Biomed. 68: 37
19. Rosenblum M.G., Cimponeriu L., Bezerianos A., Patzak A. and Mrowka R. (2002). Identification of coupling direction: application to cardiorespiratory interaction. Phys. Rev. E 65: 041909
20. Smirnov D.A. and Bezruchko B.P. (2003). Estimation of interaction strength and direction from short and noisy time series. Phys. Rev. E 68: 046209
21. Ponomarenko V.I., Prokhorov M.D., Bespyatov A.B., Bodrov M.B. and Gridnev V.I. (2005). Deriving main rhythms of the human cardiovascular system from the heartbeat time series and detecting their synchronization. Chaos Solitons Fractals 23: 1429
22. Schäfer C., Rosenblum M.G., Abel H.H. and Kurths J. (1999). Synchronization in the human cardiorespiratory system. Phys. Rev. E 60: 857
23. Prokhorov M.D. and Ponomarenko V.I. (2005). Estimation of coupling between time-delay systems from time series. Phys. Rev. E 72: 016210
24. Smelyanskiy V.N., Luchinsky D.G., Stefanovska A. and McClintock P.V.E. (2005). Inference of a nonlinear stochastic model of the cardiorespiratory interaction. Phys. Rev. Lett. 94: 098101
25. DeBoer R.W., Karemaker J.M. and Strackee J. (1987). Hemodynamic fluctuations and baroreflex sensitivity in humans: a beat-to-beat model. Am. J. Physiol. 253: 680
26. Abbiw-Jackson R.M. and Langford W.F. (1998). Gain-induced oscillations in blood pressure. J. Math. Biol. 37: 203
27. Eyal S. and Akselrod S. (2000). Bifurcation in a simple model of the cardiovascular system. Method. Inform. Med. 39: 118
28. Ottesen J.T. (1997). Modelling of the baroreflex-feedback mechanism with time-delay. J. Math. Biol. 36: 41
29. Fowler A.C. and McGuinness M.J. (2005). A delay recruitment model of the cardiovascular control system. J. Math. Biol. 51: 508
30. Magosso E., Biavati V. and Ursino M. (2001). Role of the Baroreflex in Cardiovascular Instability: A Modeling Study. Cardiov. Eng. 1(2): 101
31. Seidel H. and Herzel H. (1998). Bifurcations in a nonlinear model of the baroreceptor-cardiac reflex. Physica D 115: 145
32. Seidel H. and Herzel H. (1995). Modeling heart rate variability due to respiration and baroreflex. In: Mosekilde, E. and Mouritsen, O.G. (eds) Modeling the Dynamics of Biological Systems., pp 205-229. Springer, Berlin
33. Kotani K., Takamasu K., Ashkenazy Y., Stanley H.E. and Yamamoto Y. (2002). Model for cardiorespiratory synchronization in humans. Phys. Rev. E 65: 051923
34. Kotani K., Struzik Z.R., Takamasu K., Stanley H.E. and Yamamoto Y. (2005). Model for complex heart rate dynamics in health and diseases. Phys. Rev. E 72: 041904
35. Ruelle D. (1994). Where can one hope to profitably apply the ideas of chaos?. Phys. Today 47: 29
36. Mc Clintock P.V.E. and Stefanovska A. (2002). Noise and determinism in cardiovascular dynamics. Physica A 314: 69
37. Woo M.A., Stevenson W.G., Moser D.K., Trelease R.B. and Harper R.M. (1992). Patterns of beat-to-beat heart rate variability in advanced heart failure. Am. Heart J. 123: 704
38. The NN series collected and selected in Medical Academy of Gdańsk analysed in [5], http://iftia9.univ.gda.pl/~danka/DATA/
39. Keener J.P., Hoppensteadt F.C. and Rinzel F.C. (1981). Integrate and fire models of nerve membrane response to oscillatory input. SIAM J. Appl. Math. 41: 127
40. Press W.H., Teukolsky S.A., Vetterling W.T. and Flannery B.P. (1992). Numerical Recipes in C. Cambridge University Press, Cambridge
41. Farmer J.D. (1982). Chaotic attractors of an infinite-dimensional dynamic systems. Physica D 4: 366
42. Glass L. and Malta C.P. (1990). Chaos in multi-looped negative feedback system. J. Theor. Biol. 145: 217
43. Soma R., Nozaki D., Kwak S. and Yamamoto Y. (2003). 1/f Noise outperforms white noise in sensitizing baroreflex function in the human brain. Phys. Rev. Lett. 91: 078101
44. Keyl C., Schneider A., Dambacher M. and Bernardi L. (2001). Time delay of vagally mediated cardiac baroreflex response varies with autonomic cardiovascular control. J. Appl. Physiol. 91: 283