# Discrimination of Severity of Alzheimer’s Disease with Multiscale Entropy Analysis of EEG Dynamics

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## Abstract

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## 1. Introduction

## 2. Materials and Methods

#### 2.1. Participants

#### 2.2. EEG Recordings and Preprocessing

#### 2.3. Multiscale Entropy (MSE) Algorithm

#### 2.4. Feature Extraction in Linear Discriminant Analysis (LDA)

#### 2.5. Performance Matrix

#### 2.6. Analysis Procedure

- Leave-one-out cross validation (LOOCV) method was used to test the performance of the LDA in differentiating 15 HC and 15 AD2 subjects.
- The expected AD severity indices were obtained by training 15 HC and 15 AD2 subjects using LDA. Then, the models obtained were applied to all the HC, AD1, and AD2 groups to compare their weighted sum values.
- The 69 AD1 subjects were divided into training and validation sets with 54 and 15 subjects, respectively, to obtain the AD severity indices. Then, the models obtained were applied to the 15 HC, 15 AD1, and 15 AD2 subjects to compare their weighted sum values.

## 3. Results

#### 3.1. LOOCV Performance in Differentiating the HC from AD2 Subjects

#### 3.2. AD Severity Index Obtained by Training HC and AD2 Groups

#### 3.3. AD Severity Index Obtained by Training HC and AD1 Groups

## 4. Discussion

## 5. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 1.**(

**a**) The MSE ($\tau $ = 6) vs. the MSE ($\tau $ = 15) of the 30 EEG signals recorded from the T4 electrode. The 15 circle and 15 square symbols are from 15 healthy subjects and 15 patients with moderate to severe AD, respectively. The red dashed line is the differentiating boundary. (

**b**) The weighted sum values of the 30 signals. The red dashed line is the differentiating boundary with threshold value 0.

**Figure 2.**The weighted sum values of the 30 EEG signals recorded from the T4 electrode for the 3S–5S cases. The 15 circle and 15 square symbols are from 15 HC and 15 AD2 subjects, respectively.

**Figure 3.**The differentiating result with the same data as in Figure 1 using simplified weighted sum model as MSE ($\tau $ = 6) − MSE ($\tau $ = 15). The F1 score is 0.933. (

**a**) The MSE ($\tau $ = 6) vs. the MSE ($\tau $ = 15) of the 30 EEG signals recorded from the T4 electrode. The 15 circle and 15 square symbols are from 15 healthy subjects and 15 patients with moderate to severe AD, respectively. The red dashed line is the differentiating boundary. (

**b**) The weighted sum values of the 30 signals. The red dashed line is the differentiating boundary with threshold value 0.134.

**Figure 4.**The weighted sum values of the 45 EEG signals recorded from the optimal electrode for the 3S–5S cases. The 15 circle, 15 diamond, and 15 square symbols are from 15 HC, 15 AD1, and 15 AD2 subjects, respectively.

**Table 1.**Optimal F1 scores of LOOCV in differentiating subjects into the HC and AD2 groups of each electrode obtained using 1–5 MSE scales (labeled as 1S–5S), respectively. Bold highlights the best performances.

Case | 1S | 2S | 3S | 4S | 5S | |
---|---|---|---|---|---|---|

Electrode | ||||||

Fp1 | 0.710 | 0.774 | 0.903 | 0.903 | 0.933 | |

Fp2 | 0.733 | 0.759 | 0.815 | 0.857 | 0.857 | |

F7 | 0.710 | 0.828 | 0.933 | 0.938 | 0.938 | |

F3 | 0.710 | 0.800 | 0.889 | 0.889 | 0.889 | |

Fz | 0.710 | 0.815 | 0.903 | 0.903 | 0.903 | |

F4 | 0.714 | 0.800 | 0.828 | 0.897 | 0.897 | |

F8 | 0.750 | 0.897 | 0.933 | 0.966 | 0.966 | |

T3 | 0.733 | 0.786 | 0.867 | 0.867 | 0.857 | |

C3 | 0.741 | 0.800 | 0.867 | 0.875 | 0.897 | |

Cz | 0.750 | 0.774 | 0.867 | 0.839 | 0.857 | |

F4 | 0.714 | 0.800 | 0.828 | 0.897 | 0.897 | |

F8 | 0.750 | 0.897 | 0.933 | 0.966 | 0.966 | |

T3 | 0.733 | 0.786 | 0.867 | 0.867 | 0.857 | |

C3 | 0.741 | 0.800 | 0.867 | 0.875 | 0.897 | |

Cz | 0.750 | 0.774 | 0.867 | 0.839 | 0.857 | |

C4 | 0.800 | 0.867 | 0.867 | 0.897 | 0.933 | |

T4 | 0.786 | 0.938 | 0.966 | 0.968 | 1.000 | |

T5 | 0.828 | 0.903 | 0.903 | 0.903 | 0.933 | |

P3 | 0.828 | 0.933 | 0.966 | 0.966 | 0.966 | |

Pz | 0.786 | 0.897 | 0.903 | 0.903 | 0.903 | |

P4 | 0.759 | 0.903 | 0.933 | 0.933 | 0.968 | |

T6 | 0.621 | 0.750 | 0.750 | 0.774 | 0.774 | |

O1 | 0.800 | 0.897 | 0.897 | 0.897 | 0.897 | |

O2 | 0.667 | 0.690 | 0.667 | 0.667 | 0.645 |

**Table 2.**Optimal F1 score and corresponding accuracy, precision, recall, specificity, selected electrode, and scales for each of the 1S–5S cases, respectively.

Case | Electrode | Scales | F1 Score | Accuracy | Recall | Precision | Specificity |
---|---|---|---|---|---|---|---|

1S | T5; P3 | {12}; {19} | 0.828 | 0.833 | 0.813 | 0.867 | 0.800 |

2S | T4 | {6, 15} | 0.938 | 0.933 | 0.882 | 1.000 | 0.867 |

3S | T4 | {2, 3, 14} | 0.966 | 0.967 | 1.000 | 0.933 | 1.000 |

4S | T4 | {6, 9, 12, 17} | 0.968 | 0.967 | 0.938 | 1.000 | 0.933 |

5S | T4 | {2, 8, 11, 15, 16} | 1.000 | 1.000 | 1.000 | 1.000 | 1.000 |

Case | Weighted Sum Model |
---|---|

2S | 0.82 · MSE ($\tau $ = 6) − 0.58 · MSE ($\tau $ = 15) − 0.56 |

3S | 0.61 · MSE ($\tau $ = 2) + 0.79 · MSE ($\tau $ = 3) − 0.10 · MSE ($\tau $ = 14) − 0.29 |

4S | 0.43 · MSE ($\tau $ = 6) + 0.54 · MSE ($\tau $ = 9) − 0.67 · MSE ($\tau $ = 12) + 0.25 · MSE ($\tau $ = 17) − 1.13 |

5S | 0.22 · MSE ($\tau $ = 2) + 0.67 · MSE ($\tau $ = 8) − 0.30 · MSE ($\tau $ = 11) − 0.55 · MSE ($\tau $ = 15) + 0.32 · MSE ($\tau $ = 16) − 0.69 |

**Table 4.**Comparison of MSE-based weighted sum values among the HC, AD1, and AD2 groups. (The values are labeled as mean ± SD.)

Group | HC N = 15 | AD1 N = 69 | AD2 N = 15 | |
---|---|---|---|---|

Case | ||||

2S | 0.13 ± 0.12 | 0.05 ± 0.14 | −0.13 ± 010 | |

3S | 0.05 ± 0.04 | 0.00 ± 0.05 | −0.05 ± 0.05 | |

4S | 0.12 ± 0.08 | 0.06 ± 0.11 | −0.12 ± 0.08 | |

5S | 0.09 ± 0.05 | 0.03 ± 0.12 | −0.09 ± 0.05 |

**Table 5.**Optimal F1 score and corresponding accuracy, precision, recall, specificity, selected electrode, and scales for each of the 1S–5S cases.

Case | Electrode | Scales | F1 Score | Accuracy | Recall | Precision | Specificity |
---|---|---|---|---|---|---|---|

3S | F8 | {2, 3, 12} | 0.854 | 0.797 | 0.976 | 0.759 | 0.933 |

4S | F7 | {2, 5, 6, 12} | 0.857 | 0.797 | 0.955 | 0.778 | 0.867 |

5S | F7 | {1, 2, 4, 15, 17} | 0.857 | 0.797 | 0.955 | 0.778 | 0.867 |

Case | Weighted Sum Model |
---|---|

3S | − 0.63 · MSE ($\tau $ = 2) + 0.76 · MSE ($\tau $ = 3) − 0.16 · MSE ($\tau $ = 12) − 0.06 |

4S | − 0.31 · MSE ($\tau $ = 2) + 0.86 · MSE ($\tau $ = 5) − 0.36 · MSE ($\tau $ = 6) − 0.21 · MSE ($\tau $ = 12 − 0.06 |

5S | − 0.10 · MSE ($\tau $ = 1) − 0.47 · MSE ($\tau $ = 2) + 0.78 · MSE ($\tau $ = 4) − 0.40 · MSE ($\tau $ = 15) − 0.05 · MSE ($\tau $ = 17) |

**Table 7.**Comparison of MSE-based weighted sum values among the HC, AD1, and AD2 groups. (The values are labeled as mean ± SD.)

Group | HC N = 15 | AD1 N = 15 | AD2 N = 15 | |
---|---|---|---|---|

Case | ||||

3S | 0.02 ± 0.02 | −0.03 ± 0.04 | −0.07 ± 0.04 | |

4S | 0.28 ± 0.04 | 0.24 ± 0.06 | −0.19 ± 0.03 | |

5S | 0.03 ± 0.08 | −0.05 ± 0.10 | −0.13 ± 0.07 |

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**MDPI and ACS Style**

Hsu, C.F.; Chao, H.-H.; Yang, A.C.; Yeh, C.-W.; Hsu, L.; Chi, S.
Discrimination of Severity of Alzheimer’s Disease with Multiscale Entropy Analysis of EEG Dynamics. *Appl. Sci.* **2020**, *10*, 1244.
https://doi.org/10.3390/app10041244

**AMA Style**

Hsu CF, Chao H-H, Yang AC, Yeh C-W, Hsu L, Chi S.
Discrimination of Severity of Alzheimer’s Disease with Multiscale Entropy Analysis of EEG Dynamics. *Applied Sciences*. 2020; 10(4):1244.
https://doi.org/10.3390/app10041244

**Chicago/Turabian Style**

Hsu, Chang Francis, Hsuan-Hao Chao, Albert C. Yang, Chih-Wei Yeh, Long Hsu, and Sien Chi.
2020. "Discrimination of Severity of Alzheimer’s Disease with Multiscale Entropy Analysis of EEG Dynamics" *Applied Sciences* 10, no. 4: 1244.
https://doi.org/10.3390/app10041244