Permutation entropy analysis of heart rate variability for the assessment of cardiovascular autonomic neuropathy in type 1 diabetes mellitus

Permutation Entropy (PE) is a time series complexity measure commonly used in a variety of contexts, with medicine being the prime example. In its general form, it requires three input parameters for its calculation: time series length N, embedded dimension m, and embedded delay τ . Inappropriate choices of these parameters may potentially lead to incorrect interpretations. However, there are no specific guidelines for an optimal selection of N, m, or τ , only general recommendations such as N > > m ! , τ = 1 , or m = 3 , … , 7 . This paper deals specifically with the study of the practical implications of N > > m ! , since long time series are often not available, or non-stationary, and other preliminary results suggest that low N values do not necessarily invalidate PE usefulness. Our study analyses the PE variation as a function of the series length N and embedded dimension m in the context of a diverse experimental set, both synthetic (random, spikes, or logistic model time series) and real–world (climatology, seismic, financial, or biomedical time series), and the classification performance achieved with varying N and m. The results seem to indicate that shorter lengths than those suggested by N > > m ! are sufficient for a stable PE calculation, and even very short time series can be robustly classified based on PE measurements before the stability point is reached. This may be due to the fact that there are forbidden patterns in chaotic time series, not all the patterns are equally informative, and differences among classes are already apparent at very short lengths.

Section: Materials and Methodsmentioning

confidence: 99%

Embedded Dimension and Time Series Length. Practical Influence on Permutation Entropy and Its Applications

Cuesta–Frau

Murillo-Escobar

Orrego

et al. 2019

“…One of the very first applications of sample entropy (SampEn) was the analysis of neonatal HRV [ 11 ]. Other approaches based on ordinal patterns instead of amplitude differences have also been successful in classifying HRV records, in this case for the diagnosis of cardiovascular autonomic neuropathy [ 12 ]. In summary, EEG and HRV records have been extensively processed using approximate entropy (ApEn), SampEn, distribution entropy (DistEn), fuzzy entropy (FuzzyEn), permutation entropy (PE), and many more, in isolation or in comparative studies.…”

Section: Introductionmentioning

confidence: 99%

Model Selection for Body Temperature Signal Classification Using Both Amplitude and Ordinality-Based Entropy Measures

Cuesta–Frau

Miró-Martínez

Oltra-Crespo

et al. 2018

Many entropy-related methods for signal classification have been proposed and exploited successfully in the last several decades. However, it is sometimes difficult to find the optimal measure and the optimal parameter configuration for a specific purpose or context. Suboptimal settings may therefore produce subpar results and not even reach the desired level of significance. In order to increase the signal classification accuracy in these suboptimal situations, this paper proposes statistical models created with uncorrelated measures that exploit the possible synergies between them. The methods employed are permutation entropy (PE), approximate entropy (ApEn), and sample entropy (SampEn). Since PE is based on subpattern ordinal differences, whereas ApEn and SampEn are based on subpattern amplitude differences, we hypothesized that a combination of PE with another method would enhance the individual performance of any of them. The dataset was composed of body temperature records, for which we did not obtain a classification accuracy above 80% with a single measure, in this study or even in previous studies. The results confirmed that the classification accuracy rose up to 90% when combining PE and ApEn with a logistic model.

“…The decrease in HRV complexity provided additional information to that obtained with traditional HRV methods. Using Dimensions 3 and 4 provided similar results, but the correlation coefficients with the classical time and frequency domain parameters of HRV were low and mostly non-significant [ 32 ]. Graff et al [ 44 ] tried to differentiate vasovagal syncope patients by examining time-domain and entropy-based HRV parameters recorded in advance to the head-up tilt testing.…”

Section: Discussionmentioning

confidence: 99%

“…The correlation coefficient of the PE values for

and

was

. Changing the time delay from 1 up to 10 had been attempted in the literature, and thereby the results have inevitably changed [ 32 , 33 ]. The point is that the rhythms inherent in HRV will also be present in the PE time-series, and will non-linearly distort the PE values according to this rhythmic change (see Figure 2 ).…”

Section: Methodsmentioning

confidence: 99%

Monitoring Autonomic and Central Nervous System Activity by Permutation Entropy during Short Sojourn in Antarctica

Cotuk

Duru

Aktaş

2019

The aim of this study was to monitor acute response patterns of autonomic and central nervous system activity during an encounter with Antarctica by synchronously recording heart rate variability (HRV) and electroencephalography (EEG). On three different time-points during the two-week sea journey, the EEG and HRV were recorded from nine male scientists who participated in “The First Turkish Antarctic Research Expedition”. The recordings were performed in a relaxed state with the eyes open, eyes closed, and during a space quantity perception test. For the EEG recordings, the wireless 14 channel EPOC-Emotiv device was used, and for the HRV recordings, a Polar heart rate monitor S810i was used. The HRV data were analyzed by time/frequency domain parameters and ordinal pattern statistics. For the EEG data, spectral band power in the conventional frequency bands, as well as permutation entropy values were calculated. Regarding HRV, neither conventional nor permutation entropy calculations produced significant differences for the different journey time-points, but only permutation entropy was able to differentiate between the testing conditions. During the cognitive test, permutation entropy values increased significantly, whereas the conventional HRV parameters did not show any significant differences. In the EEG analysis, the ordinal pattern statistics revealed significant transitions in the course of the sea voyage as permutation entropy values decreased, whereas spectral band power analysis could not detect any significant difference. Permutation entropy analysis was further able to differentiate between the three testing conditions as well between the brain regions. In the conventional spectral band power analysis, alpha band power could separate the three testing conditions and brain regions, and beta band power could only do so for the brain regions. This superiority of permutation entropy in discerning subtle differences in the autonomic and central nervous system’s responses to an overwhelming subjective experience renders it suitable as an analysis tool for biomonitoring in extreme environments.