The Open Hypertension Journal


ISSN: 1876-5262 ― Volume 12, 2020

Estimation of Delay Times in Coupling Between Autonomic Regulatory Loops of Human Heart Rate and Blood Flow Using Phase Dynamics Analysis

Vladimir S Khorev1, Anatoly S Karavaev1, 2, Elena E Lapsheva1, Tatyana A Galushko1, Mikhail D Prokhorov2, Anton R Kiselev1, 3, 4, *
1 Department of Dynamic Modeling and Biomedical Engineering, Saratov State University; 83, Astrakhanskaya str., Saratov, 410012, Russia
2 Saratov Branch of the Institute of Radio Engineering and Electronics of Russian Academy of Sciences, 38, Zelyonaya str, Saratov; 410019, Russia
3 Department of New Cardiological Informational Technologies, Research Institute of Cardiology, Saratov State Medical University n.a. V.I. Razumovsky; 112, Bolshaya Kazachya str, Saratov, 410012, Russia
4 Department of Surgical Treatment for Interactive Pathology, Bakulev Scientific Center for Cardiovascular Surgery; 135, Rublevskoe Shosse, Moscow, 121552, Russia



We assessed the delay times in the interaction between the autonomic regulatory loop of Heart Rate Variability (HRV) and autonomic regulatory loop of photoplethysmographic waveform variability (PPGV), showing low-frequency oscillations.

Material and Methods:

In eight healthy subjects aged 25–30 years (3 male, 5 female), we studied at rest (in a supine position) the simultaneously recorded two-hour signals of RR intervals (RRIs) chain and finger photoplethysmogram (PPG). To extract the low-frequency components of RRIs and PPG signal, associated with the low-frequency oscillations in HRV and PPGV with a frequency of about 0.1 Hz, we filtered RRIs and PPG with a bandpass 0.05-0.15 Hz filter. We used a method for the detection of coupling between oscillatory systems, based on the construction of predictive models of instantaneous phase dynamics, for the estimation of delay times in the interaction between the studied regulatory loops.


Averaged value of delay time in coupling from the regulatory loop of HRV to the loop of PPGV was 0.9±0.4 seconds (mean ± standard error of the means) and averaged value of delay time in coupling from PPGV to HRV was 4.1±1.1 seconds.


Analysis of two-hour experimental time series of healthy subjects revealed the presence of delay times in the interaction between regulatory loops of HRV and PPGV. Estimated delay time in coupling regulatory loops from HRV to PPGV was about one second or even less, while the delay time in coupling from PPGV to HRV was about several seconds. The difference in delay times is explained by the fact that PPGV to HRV response is mediated through the autonomic nervous system (baroreflex), while the HRV to PPGV response is mediated mechanically via cardiac output.

Keywords: Cardiovascular system, Autonomic regulation, Coupling analysis, Phase dynamics, Delay time.

Article Information

Identifiers and Pagination:

Year: 2017
Volume: 9
First Page: 16
Last Page: 22
Publisher Id: TOHYPERJ-9-16
DOI: 10.2174/1876526201709010016

Article History:

Received Date: 30/6/2017
Revision Received Date: 24/11/2017
Acceptance Date: 17/12/2017
Electronic publication date: 29/12/2017
Collection year: 2017

© 2017 Khorev et al.

open-access license: This is an open access article distributed under the terms of the Creative Commons Attribution 4.0 International Public License (CC-BY 4.0), a copy of which is available at: This license permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

* Address correspondence to this author at the Department of Dynamic Modeling and Biomedical Engineering, Saratov State University; 83, Astrakhanskaya str., Saratov, 410012, Russia; Tel: 845-2393978; E-mail:

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