The Static Standing Postural Stability Measured by Average Entropy

Wei, Sung Yang; Chang, Helen; Lee, Yun Ju; Hsu, Lih‐Hsing; Chi, Sien

doi:10.3390/e21121210

Cited by 3 publications

(4 citation statements)

References 22 publications

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“…Figure 4 depicts the plot of the EoE versus the AE values of the 79 SI time series of databases D2 and D3. The comparison of the EoE and AE plot exhibited an inverted U curve [ 21 ], which is another example of a complexity versus disorder inverted U curve for physiologic signals [ 17 , 18 , 24 , 35 ], as expected. We find that a threshold of AE th = 1.06, the dashed line in the figure, is optimal to differentiate the healthy from the diseased.…”

Section: Resultssupporting

confidence: 53%

“…In 2019, we first demonstrated that the plot of complexity measured by EoE versus the disorder measured by AE of the beat-to-beat intervals time series of electrocardiography exhibited a distinct inverted U relation [ 17 ]. In 2020, we illustrated that the EoE and the AE values of the center-of-pressure trajectories of the subjects under different kinds of balance conditions exhibited an inverted U relation [ 24 ]. In this study, we further showed that the EoE versus AE plot of the 79 SI time series in gait also exhibited an inverted U curve.…”

Section: Discussionmentioning

confidence: 99%

“…It has been long considered that the complexity is relatively high for a complex system intermediate between extreme order and disorder [ 16 , 19 , 20 , 21 , 22 , 23 ]. Accordingly, the expected inverted U curves of complexity (EoE) versus disorder (AE) have been realized for simulated colored noise and real physiological signals such as heart rate signals and static standing postural stability [ 17 , 18 , 21 , 24 ]. In addition, both EoE and AE remain effective for short time series.…”

Section: Introductionmentioning

confidence: 99%

“…In the application of the AE to static standing postural stability, the AE values of the center-of-pressure trajectory time series of each of the individuals in testing was found to increase from stable to unstable balance conditions [ 24 ]. The study suggested that disorder measurement is useful in a nonautonomically controlled nervous system “such as the static standing, which is under one’s own consciousness”, and complexity measurement is useful in an autonomic system “such as heart beating” [ 24 ]. Since walking is controlled by the nonautonomic nervous systems (the somatic nervous system), disorder measurement is also expected useful in gait analysis.…”

Section: Introductionmentioning

confidence: 99%

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Gait Stability Measurement by Using Average Entropy

Huang

Chang

Mao

et al. 2021

Entropy

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Gait stability has been measured by using many entropy-based methods. However, the relation between the entropy values and gait stability is worth further investigation. A research reported that average entropy (AE), a measure of disorder, could measure the static standing postural stability better than multiscale entropy and entropy of entropy (EoE), two measures of complexity. This study tested the validity of AE in gait stability measurement from the viewpoint of the disorder. For comparison, another five disorders, the EoE, and two traditional metrics methods were, respectively, used to measure the degrees of disorder and complexity of 10 step interval (SPI) and 79 stride interval (SI) time series, individually. As a result, every one of the 10 participants exhibited a relatively high AE value of the SPI when walking with eyes closed and a relatively low AE value when walking with eyes open. Most of the AE values of the SI of the 53 diseased subjects were greater than those of the 26 healthy subjects. A maximal overall accuracy of AE in differentiating the healthy from the diseased was 91.1%. Similar features also exists on those 5 disorder measurements but do not exist on the EoE values. Nevertheless, the EoE versus AE plot of the SI also exhibits an inverted U relation, consistent with the hypothesis for physiologic signals.

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Section: Resultssupporting

confidence: 53%

Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Gait Stability Measurement by Using Average Entropy

Huang

Chang

Mao

et al. 2021

Entropy

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The autonomic balance of heart rhythm complexity after renal artery denervation: insight from entropy of entropy and average entropy analysis

Lin

Huang

et al. 2022

BioMed Eng OnLine

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Background The current method to evaluate the autonomic balance after renal denervation (RDN) relies on heart rate variability (HRV). However, parameters of HRV were not always predictive of response to RDN. Therefore, the complexity and disorder of heart rhythm, measured by entropy of entropy (EoE) and average entropy (AE), have been used to analyze autonomic dysfunction. This study evaluated the dynamic changes in autonomic status after RDN via EoE and AE analysis. Methods Five patients were prospectively enrolled in the Global SYMPLICITY Registry from 2020 to 2021. 24-h Holter and ambulatory blood pressure monitoring (ABPM) was performed at baseline and 3 months after RDN procedures. The autonomic status was analyzed using the entropy-based AE and EoE analysis and the conventional HRV-based low frequency (LF), high frequency (HF), and LF/HF. Results After RDN, the ABPM of all patients showed a significant reduction in blood pressure (BP) and heart rate. Only AE and HF values of all patients had consistent changes after RDN (p < 0.05). The spearman rank-order correlation coefficient of AE vs. HF was 0.86, but AE had a lower coefficient of variation than HF. Conclusions Monitoring the AE and EoE analysis could be an alternative to interpreting autonomic status. In addition, a relative change of autonomic tone, especially an increasing parasympathetic activity, could restore autonomic balance after RDN.

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Complexity and Disorder of 1/fα Noises

Chang

Hsu

Chi

2020

Entropy

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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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The Static Standing Postural Stability Measured by Average Entropy

Cited by 3 publications

References 22 publications

Gait Stability Measurement by Using Average Entropy

Gait Stability Measurement by Using Average Entropy

The autonomic balance of heart rhythm complexity after renal artery denervation: insight from entropy of entropy and average entropy analysis

Complexity and Disorder of 1/fα Noises

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