scholarly journals On the Standardization of Approximate Entropy: Multidimensional Approximate Entropy Index Evaluated on Short-Term HRV Time Series

Complexity ◽  
2018 ◽  
Vol 2018 ◽  
pp. 1-15
Author(s):  
Juan Bolea ◽  
Raquel Bailón ◽  
Esther Pueyo
Keyword(s):  
Heart Rate ◽  
Time Series ◽  
Healthy Subjects ◽  
Approximate Entropy ◽  
Pink Noise ◽  
Entropy Index ◽  
Rr Interval ◽  
Similarity Threshold ◽  
Interval Time Series ◽  
Night Period

Background. Nonlinear heart rate variability (HRV) indices have extended the description of autonomic nervous system (ANS) regulation of the heart. One of those indices is approximate entropy, ApEn, which has become a commonly used measure of the irregularity of a time series. To calculate ApEn, a priori definition of parameters like the threshold on similarity and the embedding dimension is required, which has been shown to be critical for interpretation of the results. Thus, searching for a parameter-free ApEn-based index could be advantageous for standardizing the use and interpretation of this widely applied entropy measurement. Methods. A novel entropy index called multidimensional approximate entropy, MApEnmax, is proposed based on summing the contribution of maximum approximate entropies over a wide range of embedding dimensions while selecting the similarity threshold leading to maximum ApEn value in each dimension. Synthetic RR interval time series with varying levels of stochasticity, generated by both MIX(P) processes and white/pink noise, were used to validate the properties of the proposed index. Aging and congestive heart failure (CHF) were characterized from RR interval time series of available databases. Results. In synthetic time series, MApEnmax values were proportional to the level of randomness; i.e., MApEnmax increased for higher values of P in generated MIX(P) processes and was larger for white than for pink noise. This result was a consequence of all maximum approximate entropy values being increased for higher levels of randomness in all considered embedding dimensions. This is in contrast to the results obtained for approximate entropies computed with a fixed similarity threshold, which presented inconsistent results for different embedding dimensions. Evaluation of the proposed index on available databases revealed that aging was associated with a notable reduction in MApEnmax values. On the other hand, MApEnmax evaluated during the night period was considerably larger in CHF patients than in healthy subjects. Conclusion. A novel parameter-free multidimensional approximate entropy index, MApEnmax, is proposed and tested over synthetic data to confirm its capacity to represent a range of randomness levels in HRV time series. MApEnmax values are reduced in elderly patients, which may correspond to the reported loss of ANS adaptability in this population segment. Increased MApEnmax values measured in CHF patients versus healthy subjects during the night period point to greater irregularity of heart rate dynamics caused by the disease.

scholarly journals Does the Temporal Asymmetry of Short-Term Heart Rate Variability Change during Regular Walking? A Pilot Study of Healthy Young Subjects

2018 ◽  
Vol 2018 ◽  
pp. 1-9 ◽  
Author(s):  
Xinpei Wang ◽  
Chang Yan ◽  
Bo Shi ◽  
Changchun Liu ◽  
Chandan Karmakar ◽  
...  
Keyword(s):  
Heart Rate ◽  
Time Series ◽  
Short Term ◽  
Area Index ◽  
Temporal Asymmetry ◽  
Interval Time ◽  
Rr Interval ◽  
Rate Asymmetry ◽  
Interval Time Series

The acceleration and deceleration patterns in heartbeat fluctuations distribute asymmetrically, which is known as heart rate asymmetry (HRA). It is hypothesized that HRA reflects the balancing regulation of the sympathetic and parasympathetic nervous systems. This study was designed to examine whether altered autonomic balance during exercise can lead to HRA changes. Sixteen healthy college students were enrolled, and each student undertook two 5-min ECG measurements: one in a resting seated position and another while walking on a treadmill at a regular speed of 5 km/h. The two measurements were conducted in a randomized order, and a 30-min rest was required between them. RR interval time series were extracted from the 5-min ECG data, and HRA (short-term) was estimated using four established metrics, that is, Porta’s index (PI), Guzik’s index (GI), slope index (SI), and area index (AI), from both raw RR interval time series and the time series after wavelet detrending that removes the low-frequency component of <~0.03 Hz. Our pilot data showed a reduced PI but unchanged GI, SI, and AI during walking compared to resting seated position based on the raw data. Based on the wavelet-detrended data, reduced PI, SI, and AI were observed while GI still showed no significant changes. The reduced PI during walking based on both raw and detrended data which suggests less short-term HRA may underline the belief that vagal tone is withdrawn during low-intensity exercise. GI may not be sensitive to short-term HRA. The reduced SI and AI based on detrended data suggest that they may capture both short- and long-term HRA features and that the expected change in short-term HRA is amplified after removing the trend that is supposed to link to long-term component. Further studies with more subjects and longer measurements are warranted to validate our observations and to examine these additional hypotheses.

scholarly journals Discrimination of the Healthy and Sick Cardiac Autonomic Nervous System by a New Wavelet Analysis of Heartbeat Intervals

Fractals ◽  
1998 ◽  
Vol 06 (03) ◽  
pp. 197-203 ◽  
Author(s):  
Y. Ashkenazy ◽  
M. Lewkowicz ◽  
J. Levitan ◽  
H. Moelgaard ◽  
P. E. Bloch Thomsen ◽  
...  
Keyword(s):  
Time Series ◽  
Nervous System ◽  
Autonomic Nervous System ◽  
Healthy Subjects ◽  
Wavelet Coefficient ◽  
Diagnostic Value ◽  
Rr Intervals ◽  
Cardiac Autonomic Nervous System ◽  
Rr Interval ◽  
Interval Time Series

We demonstrate that it is possible to distinguish with a complete certainty between healthy subjects and patients with various dysfunctions of the cardiac nervous system by way of multiresolutional wavelet transform of RR intervals. We repeated the study of Thurner et al. on different ensemble of subjects. We show that reconstructed series using a filter which discards wavelet coefficient related with higher scales enables one to classify individuals for which the method otherwise is inconclusive. We suggest a delimiting diagnostic value of the standard deviation of the filtered, reconstructed RR interval time series in the range of ~ 0.035 (for the above mentioned filter), below which individuals are at risk.

Testing heart rate asymmetry in long, nonstationary 24 hour RR-interval time series

2019 ◽  
Vol 40 (10) ◽  
pp. 105001 ◽  
Author(s):  
J Piskorski ◽  
J Ellert ◽  
T Krauze ◽  
W Grabowski ◽  
A Wykretowicz ◽  
...  
Keyword(s):  
Heart Rate ◽  
Time Series ◽  
Interval Time ◽  
Rr Interval ◽  
Rate Asymmetry ◽  
Heart Rate Asymmetry ◽  
Interval Time Series

scholarly journals Complexity and Disorder of 1/fα Noises

Entropy ◽  
2020 ◽  
Vol 22 (10) ◽  
pp. 1127
Author(s):  
Chang Francis Hsu ◽  
Long Hsu ◽  
Sien Chi
Keyword(s):  
Atrial Fibrillation ◽  
Time Series ◽  
Spectral Analysis ◽  
White Noise ◽  
Healthy Subjects ◽  
Pink Noise ◽  
Rr Interval

The complexity and the disorder of a 1/fα noise time series are quantified by entropy of entropy (EoE) and average entropy (AE), respectively. The resulting EoE vs. AE plot of a series of 1/fα noises of various values of α exhibits a distinct inverted U curve. For the 1/fα noises, we have shown that α decreases monotonically as AE increases, which indicates that α is also a measure of disorder. Furthermore, a 1/fα noise and a cardiac interbeat (RR) interval series are considered equivalent as they have the same AE. Accordingly, we have found that the 1/fα noises for α around 1.5 are equivalent to the RR interval series of healthy subjects. The pink noise at α = 1 is equivalent to atrial fibrillation (AF) RR interval series while the white noise at α = 0 is more disordered than AF RR interval series. These results, based on AE, are different from the previous ones based on spectral analysis. The testing macro-average F-score is 0.93 when classifying the RR interval series of three groups using AE-based α, while it is 0.73 when using spectral-analysis-based α.

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