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State Space Correspondence and Cross-Entropy Methods in the Assessment of Bidirectional Cardiorespiratory Coupling in Heart Failure
 
 
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Article

Temporal Properties of Cardiorespiratory Coupling in Patients with Heart Failure During the Circadian Cycle

by
Natalia Buitrago-Ricaurte
1,
José Javier Reyes-Lagos
2,
Karsten Berg
3,
Rafael González Niño
4,
Thomas Penzel
5 and
Niels Wessel
3,6,*
1
Escuela de Medicina y Ciencias de la Salud, Universidad del Rosario, Bogotá 11221, Colombia
2
Sección de Bioelectrónica, Departamento de Ingeniería Eléctrica, Centro de Investigación y de Estudios Avanzados del Instituto Politécnico Nacional, Gustavo A. Madero, Ciudad de México, Mexico City 07360, Mexico
3
Department of Physics, Humboldt-Universität zu Berlin, 10099 Berlin, Germany
4
Cardiology Department, Instituto del Corazón de Bucaramanga-Sede Bogotá, Bogotá 111411, Colombia
5
Center for Sleep Medicine, Charité–Universitätsmedizin Berlin, 10117 Berlin, Germany
6
Department of Human Medicine, MSB Medical School Berlin GmbH, 14197 Berlin, Germany
*
Author to whom correspondence should be addressed.
Entropy 2026, 28(5), 524; https://doi.org/10.3390/e28050524
Submission received: 28 January 2026 / Revised: 29 April 2026 / Accepted: 29 April 2026 / Published: 6 May 2026
(This article belongs to the Special Issue Entropy Methods for Cardiorespiratory Coupling Analysis)

Abstract

Heart failure (HF) is accompanied by autonomic dysregulation and disrupted physiological rhythms, yet how cardiorespiratory coupling (CRC) reorganizes across the circadian cycle during everyday life remains incompletely characterized. We studied 24 h ambulatory ECG recordings from 88 healthy controls and 75 patients with HF. Cardiac autonomic dynamics were quantified from RR intervals using standard HRV indices and symbolic/entropy descriptors, and circadian organization was assessed with 24 h cosinor modeling. Respiratory timing was derived from ECG-derived respiration (EDR) to obtain breath-to-breath (BB) intervals and the pulse–respiration quotient (PRQ). System-level coupling was evaluated primarily as event-timing coordination using coordigram-based coordination percentages computed at two timing tolerances (ε = 0.1 s and ε = 0.2 s) over 24 h and hour-by-hour, and complemented by entropy-based timing irregularity for RR, BB, PRQ, and RR–BB cross-entropy. Patients with HF exhibited lower global HRV and reduced information content in RR dynamics, together with circadian chronodisruption characterized mainly by weaker rhythmic expression and increased inter-individual phase dispersion. CRC differences depended on both tolerance and time of day. In entropy-based profiles, RR–BB cross-entropy and RR entropy did not show hour-specific differences; instead, group separation was localized to higher early-night ApEn in BB in HF and to consistently higher daytime/early-evening FuzzEn in PRQ in controls. Together, these findings indicate a time-structured remodeling of cardiac autonomic dynamics and CRC in HF, in which autonomic function is compromised, and coupling alterations become most evident when examined at appropriate timing tolerances and with circadian (hour-resolved) resolution.
Keywords: heart failure; circadian rhythm; autonomic regulation; cardiorespiratory coupling; entropy; nonlinear dynamics heart failure; circadian rhythm; autonomic regulation; cardiorespiratory coupling; entropy; nonlinear dynamics

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MDPI and ACS Style

Buitrago-Ricaurte, N.; Reyes-Lagos, J.J.; Berg, K.; González Niño, R.; Penzel, T.; Wessel, N. Temporal Properties of Cardiorespiratory Coupling in Patients with Heart Failure During the Circadian Cycle. Entropy 2026, 28, 524. https://doi.org/10.3390/e28050524

AMA Style

Buitrago-Ricaurte N, Reyes-Lagos JJ, Berg K, González Niño R, Penzel T, Wessel N. Temporal Properties of Cardiorespiratory Coupling in Patients with Heart Failure During the Circadian Cycle. Entropy. 2026; 28(5):524. https://doi.org/10.3390/e28050524

Chicago/Turabian Style

Buitrago-Ricaurte, Natalia, José Javier Reyes-Lagos, Karsten Berg, Rafael González Niño, Thomas Penzel, and Niels Wessel. 2026. "Temporal Properties of Cardiorespiratory Coupling in Patients with Heart Failure During the Circadian Cycle" Entropy 28, no. 5: 524. https://doi.org/10.3390/e28050524

APA Style

Buitrago-Ricaurte, N., Reyes-Lagos, J. J., Berg, K., González Niño, R., Penzel, T., & Wessel, N. (2026). Temporal Properties of Cardiorespiratory Coupling in Patients with Heart Failure During the Circadian Cycle. Entropy, 28(5), 524. https://doi.org/10.3390/e28050524

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