# Using Multiscale Entropy to Assess the Efficacy of Local Cooling on Reactive Hyperemia in People with a Spinal Cord Injury

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## Abstract

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## 1. Introduction

## 2. Methods

#### 2.1. Participants

#### 2.2. Data Collection

#### 2.3. Data Analysis

#### 2.3.1. Modified Sample Entropy

#### 2.3.2. Multiscale Entropy Method

#### 2.3.3. Multiscale Entropy of SBF Data

#### 2.4. Relative Wavelet Amplitude of BFO

#### 2.5. Statistical Analysis

## 3. Results

## 4. Discussion

## 5. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 1.**Sacral skin blood flow (SBF) responses to a surface pressure of 60 mmHg without skin temperature changes (

**A**), pressure with cooling (

**B**), and pressure with heating (

**C**) in a participant with a spinal cord injury (SCI). p.u., perfusion unit.

**Figure 2.**Multiscale entropy ${E}_{ms}(m,r,\tau ,N)$ of the simulated signals, where ${s}_{0.01}$, ${s}_{0.03}$, and ${s}_{0.1}$ represent $\mathrm{sin}(2\pi \cdot 0.01t)$, $\mathrm{sin}(2\pi \cdot 0.03t)$, and $\mathrm{sin}(2\pi \cdot 0.1t)$ sampled at 32 Hz, respectively. The length of the signals is $N$ = 9600, corresponding to a 5-min period. In the computation of ${E}_{ms}$, the parameters $m$ = 2 and $r$ = 0.2 × SD were used.

**Figure 3.**${E}_{ms}(m,r,\tau ,N)$ of blood flow oscillations (BFO) associated with endothelial, neurogenic, and myogenic activities in able-bodied (AB) controls during baseline and hyperemia. Data are represented as mean ± standard error. (

**A**) Under pressure-induced hyperemia, ${E}_{ms}$ tended to be higher at large scales compared to baseline, but the differences did not reach a significant level (p > 0.05, Wilcoxon signed-rank test). (

**B**) During pressure with cooling-induced hyperemia, ${E}_{ms}$ was significantly lower at all scales (p < 0.05) compared to baseline. (

**C**) During pressure with heating-induced hyperemia, ${E}_{ms}$ was significantly higher at the scales $\tau $ = 21–73 (p < 0.05) compared to baseline.

**Figure 4.**${E}_{ms}(m,r,\tau ,N)$ of BFO associated with endothelial, neurogenic, and myogenic activities in people with SCI during baseline and hyperemia. Data are represented as mean ± standard error. (

**A**) During pressure-induced hyperemia, ${E}_{ms}$ was slightly higher at large scales compared to baseline (p > 0.05, Wilcoxon signed-rank test). (

**B**) During pressure with cooling-induced hyperemia, ${E}_{ms}$ was lower at the scales $\tau \ge $ 23 (p = 0.06) compared to baseline. (

**C**) During pressure with heating-induced hyperemia, ${E}_{ms}$ was significantly higher at the scales $\tau $ = 31–35 compared to baseline (p < 0.05); at the scales $\tau $ = 37–65, ${E}_{ms}$ during hyperemia was also higher compared to baseline (p = 0.06).

**Figure 5.**Relative wavelet amplitudes (${A}_{r}$) of endothelia, neurogenic, and myogenic oscillations in AB controls and people with SCI during baseline and reactive hyperemia. Data are represented as mean ± standard error. The stars represent p < 0.05 (Wilcoxon signed-rank test). (

**A**,

**B**) The condition of pressure with no temperature change. (

**C**,

**D**) Pressure with cooling. (

**E**,

**F**) Pressure with heating.

**Figure 6.**Comparisons of wavelet amplitude spectrum between filtered SBF signals (containing only endothelial, neurogenic, and myogenic oscillations) from an AB control and surrogate time series. For each segment of the SBF signals during baseline and hyperemia, 30 surrogate time series were generated. The spectra of the surrogate time series are presented as mean ± SD. (

**A**) Under pressure with cooling. (

**B**) Under pressure with heating.

**Figure 7.**Comparisons of ${E}_{ms}(m,r,\tau ,N)$ between the filtered SBF signals and surrogate time series (the wavelet amplitude spectra are shown in Figure 6). For each segment of the SBF signals during baseline and hyperemia, ${E}_{ms}$ was computed for 30 surrogate time series and the results are presented as mean ± SD. (

**A**) Under pressure with cooling. (

**B**) Under pressure with heating.

Pressure with No Temperature Change | Pressure with Cooling | Pressure with Heating | ||||
---|---|---|---|---|---|---|

Baseline | Hyperemia | Baseline | Hyperemia | Baseline | Hyperemia | |

AB | 84.4 ± 8.2 | 77.4 ± 18.7 | 77.5 ± 12.2 | 84.3 ± 9.5 | 80.5 ± 15.4 | 64.7 ± 10.3 |

SCI | 78.9 ± 12.0 | 62.4 ± 17.3 | 67.3 ± 14.3 | 56.7 ± 25.5 | 79.8 ± 12.4 | 67.2 ± 12.0 |

© 2019 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Liao, F.; Yang, T.D.; Wu, F.-L.; Cao, C.; Mohamed, A.; Jan, Y.-K.
Using Multiscale Entropy to Assess the Efficacy of Local Cooling on Reactive Hyperemia in People with a Spinal Cord Injury. *Entropy* **2019**, *21*, 90.
https://doi.org/10.3390/e21010090

**AMA Style**

Liao F, Yang TD, Wu F-L, Cao C, Mohamed A, Jan Y-K.
Using Multiscale Entropy to Assess the Efficacy of Local Cooling on Reactive Hyperemia in People with a Spinal Cord Injury. *Entropy*. 2019; 21(1):90.
https://doi.org/10.3390/e21010090

**Chicago/Turabian Style**

Liao, Fuyuan, Tim D. Yang, Fu-Lien Wu, Chunmei Cao, Ayman Mohamed, and Yih-Kuen Jan.
2019. "Using Multiscale Entropy to Assess the Efficacy of Local Cooling on Reactive Hyperemia in People with a Spinal Cord Injury" *Entropy* 21, no. 1: 90.
https://doi.org/10.3390/e21010090