# Application of Multiscale Sample Entropy in Assessing Effects of Exercise Training on Skin Blood Flow Oscillations in People with Spinal Cord Injury

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## Abstract

**:**

## 1. Introduction

## 2. Methods

#### 2.1. Subjects

#### 2.2. Experimental Protocol

#### 2.3. Time Domain Assessment of SBF

#### 2.4. Multiscale Sample Entropy Analysis

#### 2.5. Surrogate Tests

#### 2.6. Statistical Analysis

## 3. Results

## 4. Discussion

^{−3}in the SSCI group, p < 10

^{−4}in the ASCI group, and p < 10

^{−6}in the AB group). For the between-group comparisons (ANOVA and t-test), during the second peak period, ${E}_{ms}(m,r,\tau ,N)$ in the SSCI group was significantly lower than in both the ASCI and AB groups for most $\tau $ values between 1 and 15. *, p < 0.05; **, p < 10

^{−2}; ***, p < 10

^{−3}.

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 1.**Illustration of the relationship between delay $\tau $ and entropy ${E}_{ms}(m,r,\tau ,N)$ for SBF signals. (

**A**) Examples of mutual information function $MI(\tau )$ of a SBF signal during the baseline and second peak periods. The values of $\tau $ determined as the first minima of $MI(\tau )$ for the two signal epochs are 10 and 5, respectively. (

**B**) ${E}_{ms}(m,r,\tau ,N)$ increases initially with increasing values of $\tau $ and when $\tau $ takes a value around that determined as the first minimum of $MI(\tau )$.

**Figure 2.**The optimal values of $\tau $, determined as the first minimum of $MI(\tau )$, in three groups for SBF signals during the baseline and second peak periods.

**Figure 3.**(

**A**) A typical SBF response to local heating. (

**B**) Biphasic thermal index (ratios of the first peak, nadir, and second peak to baseline) in three groups. The results are presented as the mean ± standard deviation. The differences in three ratios between three groups were examined using one-way ANOVA and the t test but no significant difference was observed.

**Figure 4.**Comparisons of ${E}_{ms}(m,r,\tau ,N)$ between the baseline and second peak periods and between three groups. The results are presented as the mean ± standard deviation. For the within-group comparisons, ${E}_{ms}(m,r,\tau ,N)$ in all groups significantly reduced during the second peak period for $\tau $ from 1 to 15 (p < 0.0001) in the SSCI and AB groups and p < 0.01 in the ASCI group (paired t-test). For the between-group comparisons, only during the second peak period, ${E}_{ms}(m,r,\tau ,N)$ was significantly larger in the AB and ASCI groups than in the SSCI group for most values of $\tau $ (ANOVA and t-test). *, p < 0.05; **, p < 0.01; ***, p < 0.001.

**Figure 5.**Statistical results of $\sigma $ (Equation (4)). The results are presented as the mean ± standard deviation. * and **, respectively, indicate p < 0.05 and p < 0.01 for comparisons between the SSCI and ASCI groups and between the SSCI and AB groups.

**Figure 6.**(

**A**) Comparisons of ${E}_{ms}(m,r,\tau ,N)$ of SBF signals after removing the cardiac component between the baseline and second peak periods and between three groups. Only the results for $\tau $ = 1, 5, …, 49 are shown and presented as the mean ± standard deviation. Compared to the baseline period, ${E}_{ms}(m,r,\tau ,N)$ was significantly lower during the second peak period for $\tau $ from 34 to 45 in the SSCI group and for $\tau $ from 6 to 16 in the ASCI group. +, p < 0.05 (paired t-test). (

**B**) Comparisons of ${E}_{ms}(m,r,\tau ,N)$ of the cardiac component between the baseline and second peak periods and between three groups.

**Figure 7.**Scatterplot showing relative amplitude (${A}_{r}$) and regularity degree (${E}_{ms}$, $\tau $ = 7) of the cardiac component for each subject during the baseline and second peak periods.

**Figure 8.**(

**A**) Comparisons of ${E}_{ms}(m,r,\tau ,N)$ of the myogenic component (downsampled to 4 Hz) between the baseline and second peak periods and between three groups. +, p < 0.05; ++, p < 0.01 (paired t-test). (

**B**) Scatterplot showing relative amplitude (${A}_{r}$) and regularity degree (${E}_{ms}$, $\tau $ = 9) of the myogenic component for each subject during the baseline and second peak periods.

Demographics | SSCI | ASCI | AB |
---|---|---|---|

Number of subjects | 9 | 12 | 16 |

Gender (M/F) | 5/4 | 9/3 | 11/5 |

Age (year) | 35.8 ± 11.0 | 35.1 ± 11.9 | 29.4 ± 6.2 |

Body mass index (kg/m^{2}) | 23.3 ± 2.5 | 25.8 ± 4.9 | 23.4 ± 2.9 |

Duration of injury (year) | 9.7 ± 3.8 | 6.7 ± 5.9 | / |

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**MDPI and ACS Style**

Liao, F.; Zhao, H.; Lin, C.-F.; Chen, P.; Chen, P.; Onyemere, K.; Jan, Y.-K.
Application of Multiscale Sample Entropy in Assessing Effects of Exercise Training on Skin Blood Flow Oscillations in People with Spinal Cord Injury. *Entropy* **2023**, *25*, 690.
https://doi.org/10.3390/e25040690

**AMA Style**

Liao F, Zhao H, Lin C-F, Chen P, Chen P, Onyemere K, Jan Y-K.
Application of Multiscale Sample Entropy in Assessing Effects of Exercise Training on Skin Blood Flow Oscillations in People with Spinal Cord Injury. *Entropy*. 2023; 25(4):690.
https://doi.org/10.3390/e25040690

**Chicago/Turabian Style**

Liao, Fuyuan, Hengyang Zhao, Cheng-Feng Lin, Panpan Chen, Philbert Chen, Kingsley Onyemere, and Yih-Kuen Jan.
2023. "Application of Multiscale Sample Entropy in Assessing Effects of Exercise Training on Skin Blood Flow Oscillations in People with Spinal Cord Injury" *Entropy* 25, no. 4: 690.
https://doi.org/10.3390/e25040690