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

The stochastic versus deterministic solution of the Seidel–Herzel model describing the baroreceptor control loop (which regulates the short-time heart rate) are compared with the aim of exploring the heart rate variability. The deterministic model solutions are known to bifurcate from the stable to...

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Bibliographic Details
Published in:Journal of mathematical biology 2008-07, Vol.57 (1), p.111-137
Main Authors: Dudkowska, Aleksandra, Makowiec, Danuta
Format: Article
Language:English
Subjects:
Applications of Mathematics
Baroreflex - physiology
Blood Pressure - physiology
Coronary Vessels - innervation
Heart - innervation
Heart Rate - physiology
Humans
Mathematical and Computational Biology
Mathematics
Mathematics and Statistics
Models, Cardiovascular
Oscillometry
Pressoreceptors - physiology
Stochastic Processes
Time Factors
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Summary:The stochastic versus deterministic solution of the Seidel–Herzel model describing the baroreceptor control loop (which regulates the short-time heart rate) are compared with the aim of exploring the heart rate variability. The deterministic model solutions are known to bifurcate from the stable to sustained oscillatory solutions if time delays in transfer of signals by sympathetic nervous system to the heart and vasculature are changed. Oscillations in the heart rate and blood pressure are physiologically crucial since they are recognized as Mayer waves. We test the role of delays of the sympathetic stimulation in reconstruction of the known features of the heart rate. It appears that realistic histograms and return plots are attainable if sympathetic time delays are stochastically perturbed, namely, we consider a perturbation by a white noise. Moreover, in the case of stochastic model the bifurcation points vanish and Mayer oscillations in heart period and blood pressure are observed for whole considered space of sympathetic time delays.
ISSN:0303-6812
1432-1416
DOI:10.1007/s00285-007-0148-9