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Nonlinear Dynamics in Cardiovascular Signals

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A special issue of Entropy (ISSN 1099-4300). This special issue belongs to the section "Entropy and Biology".

Deadline for manuscript submissions: 15 June 2024 | Viewed by 9922

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Special Issue Editor

Dr. Claudia Lerma

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Departamento de Instrumentación Electromecánica, Instituto Nacional de Cardiología Ignacio Chávez, Juan Badiano 1, Mexico City 14080, Mexico
Interests: heart rate variability; cardiovascular control; cardiac arrhythmias

Special Issue Information

Dear Colleagues,

The cardiovascular system involves many regulatory mechanisms that preserve the stability of blood pressure by interacting strongly with other vital systems (including the respiratory, endocrine, and autonomous nervous systems). Non-invasive measurements of cardiovascular signals (such as the electrocardiogram and photopletysmographic pulse) have increased the study of the cardiovascular system, searching for deeper insights into the physiological modulation, the pathophysiology of cardiovascular and other chronic diseases, and new methods to improve diagnosis and prognosis in human health. Heart rate variability (HRV) and other time series derived from cardiovascular systems can be considered as outputs of this system that provide information about the regulatory mechanisms through the change in these time series to a given stimulus.

For this Special Issue, we welcome submissions related to analysis of HRV and other time series from the nonlinear dynamics’ perspective (entropy, complexity, self-similarity, and others) to assess pathophysiological mechanisms, clinical applications, and the development of new methods. Manuscripts reviewing the state-of-the-art of these topics are also welcome.

Dr. Claudia Lerma
Guest Editor

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Entropy is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2600 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

cardiovascular signal processing (electrocardiogram, blood pressure, and others)
assessment of nonlinear dynamics features in time series
heart rate variability, blood pressure variability, blood volume variability, and other cardiovascular time series
applications of nonlinear assessment in heart rate variability to study of pathophysiological cardiovascular mechanisms
clinical applications (diagnosis or prognosis) of nonlinear heart rate variability indices

Published Papers (7 papers)

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Research

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14 pages, 1540 KiB

Open AccessArticle

Information-Theoretic Analysis of Cardio-Respiratory Interactions in Heart Failure Patients: Effects of Arrhythmias and Cardiac Resynchronization Therapy

by Mirjana M. Platiša, Nikola N. Radovanović, Riccardo Pernice, Chiara Barà, Siniša U. Pavlović and Luca Faes

Entropy 2023, 25(7), 1072; https://doi.org/10.3390/e25071072 - 17 Jul 2023

Cited by 1 | Viewed by 1315

Abstract

The properties of cardio-respiratory coupling (CRC) are affected by various pathological conditions related to the cardiovascular and/or respiratory systems. In heart failure, one of the most common cardiac pathological conditions, the degree of CRC changes primarily depend on the type of heart-rhythm alterations. In this work, we investigated CRC in heart-failure patients, applying measures from information theory, i.e., Granger Causality (GC), Transfer Entropy (TE) and Cross Entropy (CE), to quantify the directed coupling and causality between cardiac (RR interval) and respiratory (Resp) time series. Patients were divided into three groups depending on their heart rhythm (sinus rhythm and presence of low/high number of ventricular extrasystoles) and were studied also after cardiac resynchronization therapy (CRT), distinguishing responders and non-responders to the therapy. The information-theoretic analysis of bidirectional cardio-respiratory interactions in HF patients revealed the strong effect of nonlinear components in the RR (high number of ventricular extrasystoles) and in the Resp time series (respiratory sinus arrhythmia) as well as in their causal interactions. We showed that GC as a linear model measure is not sensitive to both nonlinear components and only model free measures as TE and CE may quantify them. CRT responders mainly exhibit unchanged asymmetry in the TE values, with statistically significant dominance of the information flow from Resp to RR over the opposite flow from RR to Resp, before and after CRT. In non-responders this asymmetry was statistically significant only after CRT. Our results indicate that the success of CRT is related to corresponding information transfer between the cardiac and respiratory signal quantified at baseline measurements, which could contribute to a better selection of patients for this type of therapy. Full article

(This article belongs to the Special Issue Nonlinear Dynamics in Cardiovascular Signals)

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15 pages, 2672 KiB

Open AccessFeature PaperArticle

Pathological Heart Rate Regulation in Apparently Healthy Individuals

by Ludmila Sidorenko, Irina Sidorenko, Andrej Gapelyuk and Niels Wessel

Entropy 2023, 25(7), 1023; https://doi.org/10.3390/e25071023 - 05 Jul 2023

Cited by 1 | Viewed by 1189

Abstract

Cardiovascular diseases are the leading cause of morbidity and mortality in adults worldwide. There is one common pathophysiological aspect present in all cardiovascular diseases—dysfunctional heart rhythm regulation. Taking this aspect into consideration for cardiovascular risk predictions opens important research perspectives, allowing for the development of preventive treatment techniques. The aim of this study was to find out whether certain pathologically appearing signs in the heart rate variability (HRV) of an apparently healthy person, even with high HRV, can be defined as biomarkers for a disturbed cardiac regulation and whether this can be treated preventively by a drug-free method. This multi-phase study included 218 healthy subjects of either sex, who consecutively visited the physician at Gesundheit clinic because of arterial hypertension, depression, headache, psycho-emotional stress, extreme weakness, disturbed night sleep, heart palpitations, or chest pain. In study phase A, baseline measurement to identify individuals with cardiovascular risks was done. Therefore, standard HRV, as well as the new cardiorhythmogram (CRG) method, were applied to all subjects. The new CRG analysis used here is based on the recently introduced LF drops and HF counter-regulation. Regarding the mechanisms of why these appear in a steady-state cardiorhythmmogram, they represent non-linear event-based dynamical HRV biomarkers. The next phase of the study, phase B, tested whether the pathologically appearing signs identified via CRG in phase A could be clinically influenced by drug-free treatment. In order to validate the new CRG method, it was supported by non-linear HRV analysis in both phase A and in phase B. Out of 218 subjects, the pathologically appearing signs could be detected in 130 cases (60%), p < 0.01, by the new CRG method, and by the standard HRV analysis in 40 cases (18%), p < 0.05. Thus, the CRG method was able to detect 42% more cases with pathologically appearing cardiac regulation. In addition, the comparative CRG analysis before and after treatment showed that the pathologically appearing signs could be clinically influenced without the use of medication. After treatment, the risk group decreased eight-fold—from 130 people to 16 (p < 0.01). Therefore, progression of the detected pathological signs to structural cardiac pathology or arrhythmia could be prevented in most of the cases. However, in the remaining risk group of 16 apparently healthy subjects, 8 people died due to all-cause mortality. In contrast, no other subject in this study has died so far. The non-linear parameter which is able to quantify the changes in CRGs before versus after treatment is FWRENYI4 (symbolic dynamic feature); it decreased from 2.85 to 2.53 (p < 0.001). In summary, signs of pathological cardiac regulation can be identified by the CRG analysis of apparently healthy subjects in the early stages of development of cardiac pathology. Thus, our method offers a sensitive biomarker for cardiovascular risks. The latter can be influenced by non-drug treatments (acupuncture) to stop the progression into structural cardiac pathologies or arrhythmias in most but not all of the patients. Therefore, this could be a real and easy-to-use supplemental method, contributing to primary prevention in cardiology. Full article

(This article belongs to the Special Issue Nonlinear Dynamics in Cardiovascular Signals)

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20 pages, 4289 KiB

Open AccessArticle

Induced Relaxation Enhances the Cardiorespiratory Dynamics in COVID-19 Survivors

by Alejandra Margarita Sánchez-Solís, Viridiana Peláez-Hernández, Laura Mercedes Santiago-Fuentes, Guadalupe Lizzbett Luna-Rodríguez, José Javier Reyes-Lagos and Arturo Orea-Tejeda

Entropy 2023, 25(6), 874; https://doi.org/10.3390/e25060874 - 30 May 2023

Cited by 1 | Viewed by 1609

Abstract

Most COVID-19 survivors report experiencing at least one persistent symptom after recovery, including sympathovagal imbalance. Relaxation techniques based on slow-paced breathing have proven to be beneficial for cardiovascular and respiratory dynamics in healthy subjects and patients with various diseases. Therefore, the present study aimed to explore the cardiorespiratory dynamics by linear and nonlinear analysis of photoplethysmographic and respiratory time series on COVID-19 survivors under a psychophysiological assessment that includes slow-paced breathing. We analyzed photoplethysmographic and respiratory signals of 49 COVID-19 survivors to assess breathing rate variability (BRV), pulse rate variability (PRV), and pulse–respiration quotient (PRQ) during a psychophysiological assessment. Additionally, a comorbidity-based analysis was conducted to evaluate group changes. Our results indicate that all BRV indices significantly differed when performing slow-paced breathing. Nonlinear parameters of PRV were more appropriate for identifying changes in breathing patterns than linear indices. Furthermore, the mean and standard deviation of PRQ exhibited a significant increase while sample and fuzzy entropies decreased during diaphragmatic breathing. Thus, our findings suggest that slow-paced breathing may improve the cardiorespiratory dynamics of COVID-19 survivors in the short term by enhancing cardiorespiratory coupling via increased vagal activity. Full article

(This article belongs to the Special Issue Nonlinear Dynamics in Cardiovascular Signals)

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16 pages, 2958 KiB

Open AccessArticle

On the Different Abilities of Cross-Sample Entropy and K-Nearest-Neighbor Cross-Unpredictability in Assessing Dynamic Cardiorespiratory and Cerebrovascular Interactions

by Alberto Porta, Vlasta Bari, Francesca Gelpi, Beatrice Cairo, Beatrice De Maria, Davide Tonon, Gianluca Rossato and Luca Faes

Entropy 2023, 25(4), 599; https://doi.org/10.3390/e25040599 - 01 Apr 2023

Cited by 3 | Viewed by 1082

Abstract

Nonlinear markers of coupling strength are often utilized to typify cardiorespiratory and cerebrovascular regulations. The computation of these indices requires techniques describing nonlinear interactions between respiration (R) and heart period (HP) and between mean arterial pressure (MAP) and mean cerebral blood velocity (MCBv). We compared two model-free methods for the assessment of dynamic HP–R and MCBv–MAP interactions, namely the cross-sample entropy (CSampEn) and k-nearest-neighbor cross-unpredictability (KNNCUP). Comparison was carried out first over simulations generated by linear and nonlinear unidirectional causal, bidirectional linear causal, and lag-zero linear noncausal models, and then over experimental data acquired from 19 subjects at supine rest during spontaneous breathing and controlled respiration at 10, 15, and 20

{b r e a t h s \cdot m i n u t e}^{- 1}

as well as from 13 subjects at supine rest and during 60° head-up tilt. Linear markers were computed for comparison. We found that: (i) over simulations, CSampEn and KNNCUP exhibit different abilities in evaluating coupling strength; (ii) KNNCUP is more reliable than CSampEn when interactions occur according to a causal structure, while performances are similar in noncausal models; (iii) in healthy subjects, KNNCUP is more powerful in characterizing cardiorespiratory and cerebrovascular variability interactions than CSampEn and linear markers. We recommend KNNCUP for quantifying cardiorespiratory and cerebrovascular coupling. Full article

(This article belongs to the Special Issue Nonlinear Dynamics in Cardiovascular Signals)

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13 pages, 4103 KiB

Open AccessArticle

Nonlinear Dynamics of Heart Rate Variability after Acutely Induced Myocardial Ischemia by Percutaneous Transluminal Coronary Angioplasty

by Martín Calderón-Juárez, Itayetzin Beurini Cruz-Vega, Gertrudis Hortensia González-Gómez and Claudia Lerma

Entropy 2023, 25(3), 469; https://doi.org/10.3390/e25030469 - 08 Mar 2023

Cited by 2 | Viewed by 1178

Abstract

Several heart rate variability (HRV) characteristics of patients with myocardial ischemia are associated with a higher mortality risk. However, the immediate effect of acute ischemia on the HRV nonlinear dynamical behavior is unknown. The objective of this work is to explore the presence of nonlinearity through surrogate data testing and describe the dynamical behavior of HRV in acutely induced ischemia by percutaneous transluminal coronary angioplasty (PTCA) with linear and recurrence quantification analysis (RQA). Short-term electrocardiographic recordings from 68 patients before and after being treated with elective PTCA were selected from a publicly available database. The presence of nonlinear behavior was confirmed by determinism and laminarity in a relevant proportion of HRV time series, in up to 29.4% during baseline conditions and 30.9% after PTCA without statistical difference between these scenarios. After PTCA, the mean value and standard deviation of HRV time series decreased, while determinism and laminarity values increased. Here, the diminishment in overall variability caused by PTCA is not accompanied by a change in nonlinearity detection. Therefore, the presence of nonlinear behavior in HRV time series is not necessarily in agreement with the change of traditional and RQA measures. Full article

(This article belongs to the Special Issue Nonlinear Dynamics in Cardiovascular Signals)

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Review

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21 pages, 6690 KiB

Open AccessReview

Topological Data Analysis in Cardiovascular Signals: An Overview

by Enrique Hernández-Lemus, Pedro Miramontes and Mireya Martínez-García

Entropy 2024, 26(1), 67; https://doi.org/10.3390/e26010067 - 12 Jan 2024

Viewed by 1223

Abstract

Topological data analysis (TDA) is a recent approach for analyzing and interpreting complex data sets based on ideas a branch of mathematics called algebraic topology. TDA has proven useful to disentangle non-trivial data structures in a broad range of data analytics problems including the study of cardiovascular signals. Here, we aim to provide an overview of the application of TDA to cardiovascular signals and its potential to enhance the understanding of cardiovascular diseases and their treatment in the form of a literature or narrative review. We first introduce the concept of TDA and its key techniques, including persistent homology, Mapper, and multidimensional scaling. We then discuss the use of TDA in analyzing various cardiovascular signals, including electrocardiography, photoplethysmography, and arterial stiffness. We also discuss the potential of TDA to improve the diagnosis and prognosis of cardiovascular diseases, as well as its limitations and challenges. Finally, we outline future directions for the use of TDA in cardiovascular signal analysis and its potential impact on clinical practice. Overall, TDA shows great promise as a powerful tool for the analysis of complex cardiovascular signals and may offer significant insights into the understanding and management of cardiovascular diseases. Full article

(This article belongs to the Special Issue Nonlinear Dynamics in Cardiovascular Signals)

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Other

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12 pages, 1373 KiB

Open AccessBrief Report

Bradycardia May Decrease Cardiorespiratory Coupling in Preterm Infants

by Miguel Ángel Porta-García, Alberto Quiroz-Salazar, Eric Alonso Abarca-Castro and José Javier Reyes-Lagos

Entropy 2023, 25(12), 1616; https://doi.org/10.3390/e25121616 - 03 Dec 2023

Viewed by 982

Abstract

Bradycardia, frequently observed in preterm infants, presents significant risks due to the immaturity of their autonomic nervous system (ANS) and respiratory systems. These infants may face cardiorespiratory events, leading to severe complications like hypoxemia and neurodevelopmental disorders. Although neonatal care has advanced, the influence of bradycardia on cardiorespiratory coupling (CRC) remains elusive. This exploratory study delves into CRC in preterm infants, emphasizing disparities between events with and without bradycardia. Using the Preterm Infant Cardio-Respiratory Signals (PICS) database, we analyzed interbeat (R-R) and inter-breath intervals (IBI) from 10 preterm infants. The time series were segmented into bradycardic (B) and non-bradycardic (NB) segments. Employing information theory measures, we quantified the irregularity of cardiac and respiratory time series. Notably, B segments had significantly lower entropy values for R-R and IBI than NB segments, while mutual information was higher in NB segments. This could imply a reduction in the complexity of respiratory and cardiac dynamics during bradycardic events, potentially indicating weaker CRC. Building on these insights, this research highlights the distinctive physiological characteristics of preterm infants and underscores the potential of emerging non-invasive diagnostic tools. Full article

(This article belongs to the Special Issue Nonlinear Dynamics in Cardiovascular Signals)

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Planned Papers

The below list represents only planned manuscripts. Some of these manuscripts have not been received by the Editorial Office yet. Papers submitted to MDPI journals are subject to peer-review.

Tentative title: Recurrence plot analysis of the physiological response to a cognitive stress test in college students
Authors: César A. Morales-López, Claudia Lerma, Rebeca Guzmán-Saldaña, Abel Lerma
Affiliation: Universidad Autónoma del Estado de Hidalgo, Instituto de Ciencias de la Salud, Mexico; Instituto Nacional de Cardiología Ignacio Chávez

Tentative title: Application of Nonlinear Methodologies for Cardiorespiratory Coupling Assessment During Bradycardia Periods in Premature Infants
Authors: José Javier Reyes-Lagos, Alberto Quiroz-Salazar, Miguel Angel Porta-Garcia
Affiliation: Universidad Autónoma del Estado de México (UAEM)

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