Horizontal visibility network topology reveals pathological loss of complexity in heart rate variability

Physiological health is typically associated with complex, multiscale heart rate variability (HRV) arising from the coordinated action of regulatory mechanisms. In contrast, pathology is often marked by the progressive loss of this organization. Here we apply horizontal visibility graphs (HVGs) to RR-interval ECG time series from cohorts with Normal autonomic function, Early cardiac autonomic neuropathy (CAN) and Definite CAN.

The HVG transformation represents the signal as a network in which the nodes (amplitudes) can form links regardless of their temporal distance provided a certain inequality is satisfied. We analyze total and scale-resolved triangular motifs together with the associated Euler characteristic as indicators of network organization. These measures display a systematic monotonic reduction with increasing pathology that is robust against variation in window length and in the threshold used to define long-range structure, consistent with the interpretation that pathology is associated with a simplification in graph topology.

The strongest separation observed is between Normal and Definite CAN, while Early-stage separation remains more modest. Furthermore, the network measures are strongly correlated with conventional time-domain HRV, particularly RMSSD. Consequently while the present analysis does not establish independent or predictive information beyond standard HRV indices, it demonstrates that clinically associated differences in HRV are also expressed in the topology of the corresponding visibility graphs.

This work received institutional funding from Khalifa University. The authors acknowledge support from the Khalifa University Research and Innovation Grant KU-INT-RIG-2024-046/8474000759. Kusmartsev also acknowledges support from the Thousand Talents Program and the President’s International Fellowship Initiative of the Chinese Academy of Sciences Awards.

Department of Public Health and Epidemiology, College of Medicine and Health Sciences, PO Box 127788, Abu Dhabi, United Arab Emirates Department of Physics, College of Engineering and Physical Sciences, PO Box 127788, Abu Dhabi, United Arab Emirates Department of Medical Sciences, College of Medicine and Health Sciences and Health Engineering Innovation Group, PO Box 127788, Abu Dhabi, United Arab Emirates The authors declare no competing interests. The studies involving human participants were reviewed and approved by Charles Sturt University Human Research Ethics Committee. The patients/participants provided their written informed consent to participate in this study.

The original ethics approval and participant consent covered secondary use of the ECG/heart rate data for the analysis presented in this work. Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made.