Time irreversibility and complexity of heart rate variability

Abstract

Intrioution. The heart rate variability is based on measuring (time) intervals between R-peaks (of RR-intervals) of an electrocardiogram and plotting a rhythmogram on their basis with its subsequent analysis by various mathematical methods. Using nonlinear methods in HRV and ECG analysis has proven to be very advantageous. Time irreversibility is a fundamental parameter of a system, it defines justification and necessity of applying nonlinear methods for analysis of a system’s dynamics. Objective. We propose an algorithm for testing the probability of a time series' irreversibility, showing its effectiveness in the process of HRV analysis. In this article, complexity of HRV will be described by two parameters: entropy EnRE [18] and correlation dimension D2 [19]. Naturally, the chosen parameters EnRE and D2 in no way can be used for comprehensive description of complexity of HRV, but we will be able to tress the necessary sufficiency of such an approach. Materials and methods. We used long-term HRV records by Massachusetts Institute of Technology – Boston’s Beth Israel Hospital (MIT-BIH) from [15], a free-access, on-line archive of physiological signals for Normal Sinus Rhythm (NSR) RR Interval, Congestive Heart Failure (CHF) RR Interval and Atrial Fibrillation (AF) Databases [16]. In [17], we have developed a special modification to the classic Mann-Whitney (MW) U-test in order to use the test for comparison of Time Series with an equal number of elements N – Time Series MW M-test. Here the new statistical -test was proposed for finding the probability of time series' irreversibility. Conclusion. In this article, we propose a statistical -test for assessment of probability of irreversibility of time series. It has been shown that the new statistical -test accurately identifies times series reversibility and irreversibility in known cases of synthetic data. For long-term HRV records of MIT-BIH database for NSR, CHF and AF groups, we have compared values of z-score, which statistically defines the limit of irreversibility of time series, and values of HRV complexity indicators: entropy EnRE [18] and correlation dimension D2 [19]. We have noted the following: HRV is time irreversible nonlinear dynamic process, with the exception of AF episodes; nonlinear indicators of HRV complexity – entropy EnRE and correlation dimension D2 – have been analyzed, and there is a conclusive difference between NSR and analyzed pathological states; analyzed time series have been presented in D2-z-EnRE phase space, and their reliable separability has been shown. It can be stated that the analyzed D2-z-EnRE phase space is sufficient for research of nonlinear HRV events in this case.

The value of some indices of heart rate variability in the diagnosis of fetal growth retardation

“…Даних про значення часової незворотності у вигляді показника Z плода на сьогодні ще немає. Складність ВСР описано у даній статті двома параметрами: ентропією -EnRE і хаотичною розмірністю -D2 [15,16]. Існує багато визначень складності, але «одне з найбільш консенсусних полягає у тому, що складність є властивістю кожної системи, яка визначає кількість структурованої інформації» [17].…”

Fuzzy logic approach for heart rate variability

“…Визначено функції приналежності до будь-якого індексу ВСР і правила дефуззіфікації для оцінок FL. Для реалізації запропонованого алгоритму в наукових публікаціях по ВСР знайдені задані параметри середніх значень показників ВСР (М) і їх стандартного відхилення (σ) [1,3,7,8,9,10]. Демонстрація Journal of V. N. Karazin` KhNU.…”

“…Определены функции принадлежности к любому индексу ВСР и правила дефуззификации для оценок FL. Для реализации предложенного алгоритма в научных публикациях по ВСР найдены заданные параметры средних значений показателей ВСР (М) и их стандартного отклонения (σ) [1,3,7,8,9,10]. Демонстрация работы предложенного алгоритма выполнялась на основании 24-часовых записей ВСР из базы данных MIT-BIH [11] для пациентов с нормальным синусовым ритмом (NSR), сердечной недостаточностью (CHF) и фибрилляцией предсердей (AF) [12].…”

“…Membership functions of any HRV index and defuzzification rules for FL scores was defined. In order to implement the proposed algorithm, specified parameters of mean values of HRV (М) indicators and their standard deviation (σ) have been found in scientific publications on HRV [1,3,7,8,9,10]. We use for FL algorithm demonstration a long-term HRV records by Massachusetts Institute of Technology -Boston's Beth Israel Hospital (MIT-BIH) from [11], a free-access, on-line archive of physiological signals for Normal Sinus Rhythm (NSR) RR Interval, Congestive Heart Failure (CHF) RR Interval and Atrial Fibrillation (AF) Databases [12].…”