Variational Mode Decomposition Analysis of Electroencephalograms during General Anesthesia: Using the Grey Wolf Optimizer to Determine Hyperparameters
Abstract
:1. Introduction
2. Materials and Methods
2.1. Anesthesia Management and Data Acquisition
2.2. Algorithm for VMD and the Hilbert Transform
- 1.
- The first step computes the analytic signal associated with each IMF according to the Hilbert transform (Formula (1)).
- 2.
- The second step involves demodulating the analytic signal to the baseband by multiplying it with an exponential function, which is adjusted to the respective estimated central frequency .
- 3.
- The third step estimates the bandwidth by using the Gaussian smoothness of the demodulated signal, which involves calculating the squared L2 norm of the slope of the demodulated analytic signal. It then computes the associated analytic signal using the Hilbert transform to obtain the one-sided frequency spectrum of each intrinsic mode uk.
Algorithm 1. Optimization Concept for VMD [14]. | |
initialization repeat for Update for all | |
(5) | |
Update | |
(6) | |
end for Dual ascent for all | |
(7) | |
until convergence: | |
(8) |
2.3. Grey Wolf Optimizer
2.4. The Fitness Function: Envelope Entropy
3. Results
3.1. Convergence Status of K, PF, and Fitness Values in GWO
3.2. Temporal Changes in the K, PF, and Fitness Values According to the GWO
3.3. VMD Analysis under GWO Support during the Three Phases of General Anesthesia
4. Discussion
5. Conclusions
Supplementary Materials
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Acknowledgments
Conflicts of Interest
References
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K | PF | Fitness | |||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|
Patient | Patient | Patient | |||||||||||
#1 | #2 | #3 | Mean ± SD | #1 | #2 | #3 | Mean ± SD | #1 | #2 | #3 | Mean ± SD | ||
Converge value | 2.35 | 2.7 | 2.8 | 2.6 ± 0.2 | 3178 | 2918 | 2315 | 2804 ± 443 | −9.8769 | −9.8156 | −9.7289 | −9.8071 ± 0.07 | |
Iteration | % | % | % | ||||||||||
1 | 143 | 117 | 133 | 131 ± 13 | 78 | 73 | 108 | 86 ± 19 | 99.9248 | 99.9940 | 99.7606 | 99.8361 ± 0.0829 | |
2 | 149 | 113 | 120 | 127 ± 19 | 82 | 80 | 120 | 94 ± 23 | 99.8326 | 99.8327 | 99.7607 | 99.8562 ± 0.0662 | |
3 | 143 | 111 | 104 | 119 ± 21 | 96 | 82 | 145 | 108 ± 33 | 99.8325 | 99.8346 | 99.8927 | 99.8946 ± 0.0610 | |
4 | 149 | 111 | 100 | 120 ± 26 | 96 | 82 | 138 | 106 ± 29 | 99.8346 | 99.8346 | 99.9371 | 99.9141 ± 0.0610 | |
5 | 143 | 111 | 96 | 117 ± 24 | 100 | 90 | 144 | 111 ± 29 | 99.9729 | 99.8346 | 99.9370 | 99.9200 ± 0.0708 | |
6 | 121 | 100 | 96 | 106 ± 14 | 91 | 89 | 133 | 104 ± 24 | 99.9902 | 99.9881 | 99.9370 | 99.9802 ± 0.0678 | |
7 | 121 | 100 | 93 | 105 ± 15 | 91 | 89 | 130 | 104 ± 23 | 99.9902 | 99.9881 | 99.9677 | 99.9820 ± 0.0155 | |
8 | 106 | 100 | 95 | 100 ± 6 | 97 | 95 | 125 | 106 ± 17 | 99.9939 | 99.9909 | 99.9733 | 99.9860 ± 0.0125 | |
9 | 100 | 100 | 93 | 98 ± 4 | 100 | 100 | 118 | 106 ± 10 | 100.000 | 100.000 | 99.9733 | 99.9945 ± 0.0111 | |
10 | 100 | 100 | 93 | 98 ± 4 | 100 | 100 | 112 | 104 ± 7 | 100.000 | 100.000 | 99.9910 | 99.9970 ± 0.0096 | |
11 | 100 | 100 | 98 | 99 ± 1 | 100 | 100 | 103 | 101 ± 2 | 100.000 | 100.000 | 99.9970 | 99.9990 ± 0.0052 | |
12 | 100 | 100 | 98 | 99 ± 1 | 100 | 100 | 103 | 101 ± 2 | 100.000 | 100.000 | 99.9976 | 99.9992 ± 0.0017 | |
13 | 100 | 100 | 100 | 100 ± 0 | 100 | 100 | 101 | 100 ± 1 | 100.000 | 100.000 | 99.9986 | 99.9995 ± 0.0014 | |
14 | 100 | 100 | 100 | 100 ± 0 | 100 | 100 | 101 | 100 ± 1 | 100.000 | 100.000 | 99.9988 | 99.9996 ± 0.0008 | |
15 | 100 | 100 | 100 | 100 ± 0 | 100 | 100 | 101 | 100 ± 1 | 100.000 | 100.000 | 99.9988 | 99.9996 ± 0.0007 | |
16 | 100 | 100 | 100 | 100 ± 0 | 100 | 100 | 101 | 100 ± 0 | 100.000 | 100.000 | 99.9989 | 99.9996 ± 0.0007 | |
17 | 100 | 100 | 100 | 100 ± 0 | 100 | 100 | 101 | 100 ± 0 | 100.000 | 100.000 | 99.9990 | 99.9997 ± 0.0006 | |
18 | 100 | 100 | 100 | 100 ± 0 | 100 | 100 | 100 | 100 ± 0 | 100.000 | 100.000 | 100.000 | 100.0000 ± 0.000 | |
19 | 100 | 100 | 100 | 100 ± 0 | 100 | 100 | 100 | 100 ± 0 | 100.000 | 100.000 | 100.000 | 100.0000 ± 0.000 | |
20 | 100 | 100 | 100 | 100 ± 0 | 100 | 100 | 100 | 100 ± 0 | 100.000 | 100.000 | 100.000 | 100.0000 ± 0.000 |
K | PF | Fitness | |||||||
---|---|---|---|---|---|---|---|---|---|
Before Emergence | After Emergence | Before Emergence | After Emergence | Before Emergence | After Emergence | ||||
Patient | Mean ± SD | Mean ± SD | p-Value | Mean ± SD | Mean ± SD | p-Value | Mean ± SD | Mean ± SD | p-Value |
#1 | 2.3 ± 0.7 | 2.5 ± 1.0 | 0.525 | 2722 ± 1792 | 3190 ± 1914 | 0.309 | −5.7779 ± 0.0898 | −9.4826 ± 0.4004 | <0.001 * |
#2 | 2.4 ± 0.8 | 3.0 ± 1.4 | 0.014 * | 2881 ± 1678 | 3071 ± 1772 | 0.675 | −9.7762 ± 0.0728 | −9.6799± 0.2341 | 0.016 * |
#3 | 2.6 ± 1.0 | 2.8 ± 1.4 | 0.624 | 2271 ± 1834 | 2271 ± 1922 | 0.107 | −9.7607 ± 0.0714 | −9.6886 ± 0.1563 | 0.008 * |
Mean | 2.4 ± 0.8 | 2.7 ± 1.3 | 0.016 * | 2625 ± 1768 | 2844 ± 1869 | 0.989 | −8.4383 ± 0.0780 | −9.6170± 0.2636 | <0.001 * |
SD | 0.2 ± 0.1 | 0.3 ± 0.2 | 316 ± 81 | 500 ± 84 | 2.3039 ± 0.0103 | 0.1165 ± 0.1247 |
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Kushimoto, K.; Obata, Y.; Yamada, T.; Kinoshita, M.; Akiyama, K.; Sawa, T. Variational Mode Decomposition Analysis of Electroencephalograms during General Anesthesia: Using the Grey Wolf Optimizer to Determine Hyperparameters. Sensors 2024, 24, 5749. https://doi.org/10.3390/s24175749
Kushimoto K, Obata Y, Yamada T, Kinoshita M, Akiyama K, Sawa T. Variational Mode Decomposition Analysis of Electroencephalograms during General Anesthesia: Using the Grey Wolf Optimizer to Determine Hyperparameters. Sensors. 2024; 24(17):5749. https://doi.org/10.3390/s24175749
Chicago/Turabian StyleKushimoto, Kosuke, Yurie Obata, Tomomi Yamada, Mao Kinoshita, Koichi Akiyama, and Teiji Sawa. 2024. "Variational Mode Decomposition Analysis of Electroencephalograms during General Anesthesia: Using the Grey Wolf Optimizer to Determine Hyperparameters" Sensors 24, no. 17: 5749. https://doi.org/10.3390/s24175749