# Entropy Analysis of Neonatal Electrodermal Activity during the First Three Days after Birth

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Participants

#### 2.2. Protocol

#### 2.3. Data Analysis

^{2}) in the fitting frequency bands (very-low frequency (VLF): 0.000–0.045 Hz; low frequency (LF): 0.045–0.15 Hz; high frequency one (HF1): 0.15–0.25 Hz; high frequency two (HF2): 0.25–0.40 Hz, very-high frequency (VHF): 0.40–0.50 Hz, sympathetic frequency (Symp): 0.045–0.25 Hz, and total) were achieved according to Posada-Quintero et al. [1]. Next, the normalized EDA index of the sympathetic nervous system (EDASymp

_{n}) (n.u.) was calculated as a ratio between EDASymp and the total power. Spectral-domain indices describe information about the spectral distribution of sympathetic arousal in the skin [1]. Raw EDA, tonic EDA, SCL, NS.SCRs, and power spectra of EDA from the selected newborn during all three days of examination are illustrated in Figure 2.

#### 2.4. Approximate Entropy

^{m}, is formed into (N − m + 1) sequences of vectors composed of m consecutive points, as the following:

_{i}), u(t

_{i+1}), u(t

_{i+2}), …, u(t

_{i+m−1})].

_{i}

^{m}(r) was calculated according to the formula:

^{m}(r) was defined as:

#### 2.5. Sample Entropy

_{i}

^{m}(r), which could affect the performance of this statistical measurement [34,38]. To eliminate the self-comparison, the C

_{i}

^{m}(r) is defined as the following:

^{m}(r) is defined as:

^{m}

_{i}and C

^{m+1}

_{i}are defined [34,38,39].

#### 2.6. Fuzzy Entropy

^{m}

_{ij})

^{n}/r without a fixed boundary, as the fuzzy function to obtain a fuzzy measurement of the similarity of two vectors based on their shape, while the Heaviside function represents a conventional two-state classifier, where an input pattern is judged on its grouping into a given class according to whether it met certain exact characteristics required by the relationship, as in the ApEn and SampEn algorithms [39]. The family of exponential functions has the following properties: (A) is continuous (similarity is not abrupt) and (B) is convex (self-similarity is the maximal) [39,40]. FuzzyEn describes the general behavior of a time series and contains the vagueness and ambiguity uncertainties of the system [39,41].

_{ij}

^{m}(r)) is defined as:

^{m}(r) is defined as:

#### 2.7. Permutation Entropy

#### 2.8. Shannon Entropy

_{L}

^{ξ}= (A

^{ξ}(i), A

^{ξ}(i − 1), A

^{ξ}(i − 2), …, A

^{ξ}(i − L + 1)),

_{L}

^{ξ}= {A

_{L}

^{ξ}(i), i = 1, 2, 3, …, N-L + 1} [51].

#### 2.9. Symbolic Information Entropy

_{i}is the count number of i, and M is the number of sequences.

#### 2.10. Statistical Analysis

_{n}, and EDA entropy indices. Next, the statistical test of the main effect was followed by post hoc pairwise comparisons between the different periods, which was corrected using the Bonferroni method. The Bonferroni correction was based on a method that assisted in decision making in studies involving repetitive sampling [54]. This method is often used to adjust probability (p) values when performing multiple statistical tests in any context [55]. It is a widely used method in various experimental contexts, including: (A) comparing different groups at baseline, (B) studying the relationship between variables, (C) examining more than one endpoint in clinical studies [56], (D) correcting for ‘experimental’ and ‘family’ error rate in multiple comparisons [57], and (E) as a post hoc test after the analysis of variance [58]. In all statistical tests, a value of p < 0.05 (two-tailed) was consider statistically significant. SCL and EDA entropy parameters were expressed as mean ± SD.

## 3. Results

_{[2]}= 20.20, p < 0.001). A pairwise comparison with the Bonferroni adjusted p revealed a significantly lower SCL during the second day (p < 0.001) and third (p < 0.001) day compared to the first day. No significant change in SCL was found between the second and third days (p = 0.665, Figure 3A).

_{[2]}= 6.47, p = 0.004). The pairwise comparison revealed significantly lower lnVLF-EDA during the second day (p = 0.007) and third day (p = 0.023) compared to the first day after birth. No significant changes in lnVLF-EDA was found between the second and third days after birth (p = 0.899, Figure 3B).

_{n}) was without significant changes (p = 0.061, p = 0.111, p = 0.758, p = 0.430, p = 0.186, p = 0.495, p = 0.314, and p = 0.109, respectively).

#### 3.1. Entropy Analysis

_{[2]}= 16.00, p < 0.001; SampEn–F

_{[2]}= 7.73, p < 0.001; FuzzyEn–F

_{[2]}= 4.30, p = 0.018; PermEn–F

_{[2]}= 5.09, p = 0.008; ShanEn–F

_{[2]}= 8.98, p < 0.001; and SIEn–F

_{[2]}= 5.06, p = 0.009.

#### 3.1.1. Post Hoc Pairwise Comparison between Measurement in the First Day and Second Day

#### 3.1.2. Post Hoc Pairwise Comparison between Measurement in the First Day and Third Day

#### 3.1.3. Post Hoc Pairwise Comparison between Measurement on the Second Day and Third Day

## 4. Discussion

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 2.**Skin conductance and power spectra of electrodermal activity (EDA) during the 1st day (1st D), 2nd day (2nd D), and 3rd day (3rd D) after birth in selected newborn. (

**A**) Raw EDA signal (dashed line), tonic EDA signal (full line), and index skin conductance level (SCL) represents the mean value of tonic EDA (μS); (

**B**) non-specific skin conductance responses (NS.SCRs) (number of responses per minute) were obtained by removing the tonic EDA components from the EDA (full line); fixed threshold was used to determine number of NS.SCRs; (

**C**) power spectral density (PSD) of EDA (full line);dashed line denotes 0.045 Hz, 0.15 Hz, 0.25 Hz, and 0.40 Hz, respectively.

**Figure 3.**(

**A**) Mean ± SD values of skin conductance level during the 1st day (1st D), 2nd day (2nd D), and 3rd day (3rd D) in newborns; (

**B**) mean ± SD values of logarithmic-transformed spectral index of EDA in very low frequency band during the 1st day, 2nd day, and 3rd day after birth in newborns. Stars indicate significant differences between periods; * p < 0.05, ** p < 0.01, and *** p < 0.001.

**Figure 4.**Mean ± SD values of entropy-based indices during the 1st day (1st D), 2nd day (2nd D), and 3rd day (3rd D) after birth in newborns; all evaluated entropy-based indices were significantly affected by the main effect of periods. Post hoc pairwise comparisons between measurement periods were corrected using Bonferroni method. (

**A**) Approximate entropy, (

**B**) sample entropy, (

**C**) fuzzy entropy, (

**D**) permutation entropy, (

**E**) Shannon entropy, and (

**F**) symbolic information entropy. Stars indicate significant differences between periods; * p < 0.05, ** p < 0.01, and *** p < 0.001.

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**MDPI and ACS Style**

Visnovcova, Z.; Kozar, M.; Kuderava, Z.; Zibolen, M.; Ferencova, N.; Tonhajzerova, I.
Entropy Analysis of Neonatal Electrodermal Activity during the First Three Days after Birth. *Entropy* **2022**, *24*, 422.
https://doi.org/10.3390/e24030422

**AMA Style**

Visnovcova Z, Kozar M, Kuderava Z, Zibolen M, Ferencova N, Tonhajzerova I.
Entropy Analysis of Neonatal Electrodermal Activity during the First Three Days after Birth. *Entropy*. 2022; 24(3):422.
https://doi.org/10.3390/e24030422

**Chicago/Turabian Style**

Visnovcova, Zuzana, Marek Kozar, Zuzana Kuderava, Mirko Zibolen, Nikola Ferencova, and Ingrid Tonhajzerova.
2022. "Entropy Analysis of Neonatal Electrodermal Activity during the First Three Days after Birth" *Entropy* 24, no. 3: 422.
https://doi.org/10.3390/e24030422