Bifurcation in a Simple Model of the Cardiovascular System
07 February 2018 (online)
A simple nonlinear beat-to-beat model of the human cardiovascular system has been studied. The model, introduced by DeBoer et al. was a simplified linearized version. We present a modified model which allows to investigate the nonlinear dynamics of the cardiovascular system. We found that an increase in the -sympathetic gain, via a Hopf bifurcation, leads to sustained oscillations both in heart rate and blood pressure variables at about 0.1 Hz (Mayer waves). Similar oscillations were observed when increasing the -sympathetic gain or decreasing the vagal gain. Further changes of the gains, even beyond reasonable physiological values, did not reveal another bifurcation. The dynamics observed were thus either fixed point or limit cycle. Introducing respiration into the model showed entrainment between the respiration frequency and the Mayer waves.
- 1 Guyton AC. Textbook of Medical Physiology (8th ed). London: WB Saunders Company; 1991: 194-204.
- 2 DeBoer RW, Karemaker JM, Strackee J. Hemodynamic fiuctuations and baroreflex sensitivity in humans: a beat-to-beat model. Am J Physiol 1987; 253: 680-9.
- 3 Whittam AM, Clayton RH, Lord SW, McComb JM, Murray A. Computers in Cardiol. 1998 25. 149-52.
- 4 Seidel H, Herzel H. Bifurcations in a nonlinear model of the baroreceptor-cardiac reflex. Physica 1998; 115D: 145-60.
- 5 Karemaker JM. Cardiac cycle time effects: information processing and the latencies involved. On: Orlebeke JF, Mulder G, VanDoornen LJP. eds. Psychophysiology of Cardiovascular Control. New York: Plenum; 1985: 535-48.
- 6 Glass L, Mackey MC. From clocks to chaos (1st ed). Princeton: Princeton University Press; 1988: 136