# Consciousness Detection in a Complete Locked-in Syndrome Patient through Multiscale Approach Analysis

^{1}

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## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Dataset

#### 2.2. Sample Entropy

#### 2.3. Permutation Entropy

#### 2.4. Poincaré Plot

_{1}) and the SD along the diagonal line (SD

_{2}) were measured, as shown in Figure 4. Its mathematical expression is as follows: SDX is the standard deviation of time series, and SDSD is the standard deviation of the succeeding difference of time series.

#### 2.5. Multiscale Approach

_{1}, b

_{2}, …, b

_{i}was created by separating the original time series a

_{1}, a

_{2}, …, a

_{i+3}into non-overlapping windows of a scale of 4 and then averaging the time series in each window.

## 3. Results

#### 3.1. Multiscale Approach

_{1}of the Poincaré plots to extract a cleaner result from all approaches.

#### 3.2. Multiscale Sample Entropy

#### 3.3. Multiscale Permutation Entropy

#### 3.4. Multiscale Poincaré (MSP) Plots

_{1}represents the instantaneous variability, and SD

_{2}shows the ECoG voltage variability of the 30 s recoding time window. We show the 24 h results of SD

_{1}and SD

_{2}in Figure 10 and Figure 11.

_{1}and SD

_{2}of the MSP plots for 24 h are shown in Figure 10 and Figure 11. The result of SD

_{1}was the average of all 59 usable channels, and SD

_{2}was the average of 52 usable channels. The trend of SD

_{1}and SD

_{2}was similar to MSE. The distributions of MSP plots during the experiment had the high-peaked and heavy-tailed characteristics, which are different from the flat-topped characteristic of MSE and MPE. The kurtosis of MSE distribution was leptokurtic, and the MSE and MPE distributions were platykurtic. Considering the preparation during the experiment, we raised the threshold to the average of the upper half of the sorted data during the experiment. With a threshold value of SD

_{1}at 4.36, the ground truth periods at 16:04–16:22 and 16:56–17:04 exceeded the threshold. Using this consciousness level threshold, the periods between 10:22–10:44, 11:24–12:14, 01:08–02:46, 03:10–03:44 and 04:46–05:04 could be labelled as periods of consciousness. Both SD

_{1}and SD

_{2}showed similar trends, but the result of SD

_{1}was clearer, so we will use it to compare it with the other methods.

## 4. Discussion

## 5. Conclusions

## Supplementary Materials

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 2.**Channel locations of the electrocorticography (ECoG) electrode array. (

**Left**): channel names, with the functional channels shown in yellow and the ground channel (S032) and reference channel (G102) in orange. (

**Right**): the position of the implanted ECoG grid electrodes.

**Figure 3.**Example of permutation entropy estimation. (

**a**) Time series X = (12, 9, 7, 6, 10, 5, 13). (

**b**) The six possible permutation patterns for m = 3. (

**c**) The relative frequency of all possible ordinal patterns for n = 3 for this time series, P (2,1,3) = 0.4, P (2,3,1) = 0.2 and P (3,2,1) = 0.4.

**Figure 4.**The Poincaré plot (time delay = 1), standard deviation perpendicular to the diagonal line (SD

_{1}) and standard deviation along the diagonal line (SD

_{2}) describing the fitted ellipse of the ECoG voltage dispersion along the minor and major axis.

**Figure 7.**The results of multiscale sample entropy (MSE) (scale = 4) for 24 h. The period of the experiment is indicated by the grey block. The threshold value is indicated by a red horizontal line. The periods of presumed consciousness are indicated by the high values of MSE, shown in red blocks. To avoid the plot being too crowded, we marked the predicted conscious periods, which are predicted conscious periods of more than 6 min for every 10 min overlapping time window.

**Figure 8.**The results of multiscale permutation entropy (MPE) (scale = 4) for 24 h. The period of the experiment is indicated by the grey block. The threshold value is shown by a red horizontal line. The periods of consciousness as presumed by the high values of MPE are indicated in the yellow blocks. To avoid the plot being too crowded, we marked the predicted conscious periods, which are predicted conscious periods of more than 8 min in every 12 min overlapping time window.

**Figure 9.**The Poincaré plot. (

**Left**): 30 s during the experiment. (

**Right**): the other 30 s during the day.

**Figure 10.**The SD

_{1}of the multiscale Poincaré (MSP) plots (scale = 4) for 24 h. The period of the experiment is indicated by the grey block. The threshold value is indicated by a red horizontal line. The presumed periods of consciousness, as indicated by high values of SD

_{1}, are shown in blue blocks. To avoid the plot being too crowded, we marked the predicted conscious periods which were more than 6 min for every 10 min overlapping time window.

**Figure 12.**The result of the majority decision of the three methods is indicated by the dark red block. The period of the experiment is shown in the grey block. The state of consciousness identified by the different methods is enclosed by magenta (MSE), yellow (multiscale permutation entropy (MPE)), and blue (multiscale Poincaré (MSP)) blocks.

**Figure 13.**The statistical results (Z-test) for (

**a**) MSE, (

**b**) MPE, and (

**c**) MSP over 24 h. The period of the experiment is shown in green. Significant differences are identified by * p < 0.05 and ** p < 0.01 in respect to the values from the proven communication time.

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**MDPI and ACS Style**

Wu, S.-J.; Nicolaou, N.; Bogdan, M.
Consciousness Detection in a Complete Locked-in Syndrome Patient through Multiscale Approach Analysis. *Entropy* **2020**, *22*, 1411.
https://doi.org/10.3390/e22121411

**AMA Style**

Wu S-J, Nicolaou N, Bogdan M.
Consciousness Detection in a Complete Locked-in Syndrome Patient through Multiscale Approach Analysis. *Entropy*. 2020; 22(12):1411.
https://doi.org/10.3390/e22121411

**Chicago/Turabian Style**

Wu, Shang-Ju, Nicoletta Nicolaou, and Martin Bogdan.
2020. "Consciousness Detection in a Complete Locked-in Syndrome Patient through Multiscale Approach Analysis" *Entropy* 22, no. 12: 1411.
https://doi.org/10.3390/e22121411