Estimating coupling strengths between the branches of sympathetic control in a mathematical model of circulation using deep learning approach

Year - Volume - Issue
2026, volume 7,
Issue 1
Authors
Anna M. Vakhlaeva, Yury M. Ishbulatov, Elizaveta S. Dubinkina, Boris P. Bezruchko, Anatoly S. Karavaev
Heading
Digital Health
Article type
Original article
PDF File
Saratov_Med_J-2026-0103.pdf
Abstract
Directional coupling diagnostics is a promising method for the early noninvasive diagnosis of cardiovascular diseases. However, the complexity of living systems imposes unique requirements, necessitating the development of specialized approaches. This study explored the feasibility of solving the problem of directional coupling diagnostics using deep machine learning methods. Three fundamentally different artificial neural network architectures were considered: fully connected, recurrent, and convolutional. These architectures were compared for the accuracy of estimating the strength of directional coupling and their robustness to noise typically present in actual cardiac signals. The artificial neural networks were trained and tested on synthetic data: time series generated by functional mathematical models simulating the low-frequency oscillatory components of actual heart rate variability and mean blood pressure (Mayer waves). The fully connected artificial neural networks achieved an error of less than 3% when analyzing signals lasting only 70 seconds. The obtained results are promising in terms of the development of noninvasive methods for monitoring the state of autonomic circulatory control and for the advance of personalized medicine.
Keywords
directional coupling,
mathematical modeling,
deep learning; cardiovascular system
Cite as
Vakhlaeva AM, Ishbulatov YuM, Dubinkina ES, Bezruchko BP, Karavaev AS. Estimating coupling strengths between the branches of sympathetic control in a mathematical model of circulation using deep learning approach. Saratov Medical Journal 2026; 7 (1): e0103. https://doi.org/10.15275/sarmj.2026.0103
CID
e0103
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About the Authors

Anna M. Vakhlaeva – MSc Student, Department of Dynamical Modeling and Biomedical Engineering, https://orcid.org/0009-0009-3079-188Х;

Yury M. Ishbulatov – PhD, Associate Professor, Department of Dynamical Modeling and Biomedical Engineering, https://orcid.org/0000-0003-2871-5465;

Elizaveta S. Dubinkina – Undergraduate Student, Department of Dynamical Modeling and Biomedical Engineering, https://orcid.org/0000-0002-4636-3937;

Boris P. Bezruchko - DSc, Professor, Department of Dynamical Modeling and Biomedical Engineering, https://orcid.org/0000-0002-6691-8653;

Anatoly S. Karavaev – DSc, Chair of the Department of Dynamical Modeling and Biomedical Engineering, https://orcid.org/0000-0003-4678-3648.

 

Received 12 January 2026, Accepted 6 March 2026

 

Correspondence to - Yury M. Ishbulatov, ishbulatov95@mail.ru 

DOI
10.15275/sarmj.2026.0103
Author(s)
Anna M. Vakhlaeva ,
Yury M. Ishbulatov,
Elizaveta S. Dubinkina,
Boris P. Bezruchko ,
Anatoly S. Karavaev