Wavelet transform-based mode decomposition for EEG signals under general anesthesia

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Brain, Cognition and Mental Health

Main article text

 

Introduction

Materials & Methods

Algorithm for the EWT and the Hilbert transform

EWT steps

Algorithm for WMD

Anesthesia management and data acquisition

EEG Mode Decomposition for EMD, VMD, EWT, and WMD

Data processing and statistics

Results

Case analysis of the EWT application

Hilbert spectrograms of the IMFs in the EWT and WMD methods

Multiple linear regression models to predict the BIS

Discussion

Conclusions

Supplemental Information

Step-by-step explanation of the EWT algorithm

(A) An initial EEG wave (128 Hz, 0.5 s, 64 data points). (B) mirroring the double expansion of the original EEG wave (128 data points). (C) Fast Fourier transform. 1. Power spectrum, 2. Convolutional integral, and 3. Sorted index by argosoft() function. (D) Creation of Mayer filter bank (mfb-0, mfb-1, and mfb-2). (E) Decomposition in the frequency domain. (F) Inverse Fourier transform. 1. Inverse Fourier transform from the frequency domain to the time domain. 2. Un-mirroring to intrinsic mode functions (IMFs), (G). Decomposition into IMFs in time-domains.

DOI: 10.7717/peerj.18518/supp-1

Construction of the Meyer wavelet filter bank in the EWT

(A) ω = ωii=1,2,...,N (N denotes the number of maxima, and also, the number of filter banks.Assuming the frequency domain [0, π] is divided into N consecutive segments, we need to extract N-1 boundaries excluding 0 and π (This figure shows the case of N = 6). (B) To find the boundary in the EWT, local maxima in the spectrum are found and sorted in descending order, and the boundary is defined as the average between consecutive maxima. Let ω n be the limit between each segment (where ω0 = 0 and ωn = π), and denote each segment by Λn = [ωn−1ωn], then Nn1Λn=[0,π]. (C) A scheme explaining Eqs. (2) and (3). (D) A tight frame constructed by Meyer’ s wavelet with a set of ϕ1(t), ψn(t)Nn=1 explaining (7). φ(): scale function, ψ (): wavelet function, β: beta function β (x) = x4(35 − 84x + 70x2 + 20x3) ((5)), τ : transition phase, ω : the limit between each segment (where ω0 = 0 and ωn = π). BPF, band-pass filter, IMF, intrinsic mode function; LPF, low-pass filter; Mfb, Meyer wavelet filter bank.

DOI: 10.7717/peerj.18518/supp-2

Hilbert spectrograms of the IMFs and the color density spectral arrays (DSAs) in the VMD, EWT, and WMD methods

IMFs 1–6, a summed signal composed of all IMFs (IMF-all, which is the same as the initial EEG), and color DSAs for 30 min before emergence in all ten patients (as screen capture images from the EEG Mode Decompositor software) are shown.

DOI: 10.7717/peerj.18518/supp-3

Multiple linear regression (MLR) analysis between the BIS values and parameters of IMFs

(A) In the in VMD, EWT, or WMD, using 6 median values of the central frequencies and 6 total powers (TPs) as explanatory variables. (B) Using all parameters of the IMFs derived from the VMD+EWT+WMD as explanatory variables. (C) In the three different mode decomposition using only 6 median values of the central frequencies as explanatory variables, and (D) in the three different mode decomposition using only 6 median values of total powers as explanatory variables. The EEG data were obtained from the last 30 min before emergence in ten patients who received sevoflurane general anesthesia. MAE, mean absolute error; RMSE, root mean squared error; freq, central frequency; TP, total power; p < 0.05.

DOI: 10.7717/peerj.18518/supp-4

Tab-separated values of raw EEG data (microvolts) for 30 min before the emergence of GA in ten patients

DOI: 10.7717/peerj.18518/supp-5

Comma-separated values of processed EEG data

BIS index, SEF95, TP, EMGlow, center frequencies of IMFs, and TPs of IMFs for 30 min before the emergence of GA in ten patients.

DOI: 10.7717/peerj.18518/supp-6

The Jupyter Notebook file of Python (ver. 3.8) code for the EWT

DOI: 10.7717/peerj.18518/supp-7

The implementation Processing (ver. 4.0.5) Ewt and Wmd Class codes in Python

DOI: 10.7717/peerj.18518/supp-8

Video, Patient #6, EMD, 30 min before emergence of GA. A video file showing EMD analysis of EEG data for 30 min leading up to emergence in Patient #6

DOI: 10.7717/peerj.18518/supp-9

Video, Patient #6, VMD, 30 min before emergence of GA. A video file showing VMD analysis of EEG data for 30 min leading up to emergence in Patient #6

DOI: 10.7717/peerj.18518/supp-10

Video, Patient #6, EWT, 30 min before emergence of GA. A video file showing EWT analysis of EEG data for 30 min leading up to emergence in Patient #6

DOI: 10.7717/peerj.18518/supp-11

Video, Patient #6, WMD, 30 min before emergence of GA. A video file showing WMD analysis of EEG data for 30 min leading up to emergence in Patient #6

DOI: 10.7717/peerj.18518/supp-12

MLR analysis of the BIS values and the parameters of the IMFs in VMD, the EWT, or WMD

The objective variable was the median value of the BIS from 10 patients and the explanatory variables were the statistically significant median values of the central frequencies and the TPs of the IMFs in A) VMD, B) the EWT, C) WMD, or D) VMD+EWT+WMD. The EEG data were obtained from the last 30 min before emergence in 10 patients who received sevoflurane GA. MAE: mean absolute error; RMSE, root mean squared error; p < 0.05.

DOI: 10.7717/peerj.18518/supp-13

MLR analysis using the BIS values and the parameters of the IMFs in VMD, the EWT, or WMD

The objective variable was the median value of the BIS from 10 patients, and the explanatory variables were (1) the six median values of the central frequencies and (2) the six total powers of the IMFs. The EEG data were obtained from the last 30 min period before emergence in 10 patients who received sevoflurane GA. MAE, mean absolute error; RMSE, root mean squared error; p < 0.05.

DOI: 10.7717/peerj.18518/supp-14

Additional Information and Declarations

Competing Interests

The authors declare there are no competing interests.

Author Contributions

Shoko Yamochi performed the experiments, analyzed the data, authored or reviewed drafts of the article, and approved the final draft.

Tomomi Yamada performed the experiments, analyzed the data, prepared figures and/or tables, authored or reviewed drafts of the article, and approved the final draft.

Yurie Obata performed the experiments, analyzed the data, prepared figures and/or tables, authored or reviewed drafts of the article, and approved the final draft.

Kazuki Sudo performed the experiments, analyzed the data, authored or reviewed drafts of the article, and approved the final draft.

Mao Kinoshita performed the experiments, analyzed the data, authored or reviewed drafts of the article, and approved the final draft.

Koichi Akiyama performed the experiments, analyzed the data, authored or reviewed drafts of the article, and approved the final draft.

Teiji Sawa conceived and designed the experiments, performed the experiments, analyzed the data, prepared figures and/or tables, authored or reviewed drafts of the article, and approved the final draft.

Human Ethics

The following information was supplied relating to ethical approvals (i.e., approving body and any reference numbers):

The Institutional Review Board (IRB) of the Kyoto Prefectural University of Medicine (KPUM) (No. ERB-C-1074).

Data Availability

The following information was supplied regarding data availability:

The raw data and code are available in the Supplemental Files.

The EEG dataset is available at GitHub and Zenodo:

https://github.com/teijisw/EEG_DataSet

– teijisw. (2024). teijisw/EEG_DataSet: Supplementary Dataset of Wavelet Transform-based Mode Decomposition (v.1.0.0). Zenodo. https://doi.org/10.5281/zenodo.13989502.

Funding

The authors received no funding for this work.

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