{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,13]],"date-time":"2026-02-13T14:29:54Z","timestamp":1770992994523,"version":"3.50.1"},"reference-count":26,"publisher":"MDPI AG","issue":"17","license":[{"start":{"date-parts":[[2024,9,4]],"date-time":"2024-09-04T00:00:00Z","timestamp":1725408000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Department of Anesthesiology, Kyoto Prefectural University of Medicine"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>Frequency analysis via electroencephalography (EEG) during general anesthesia is used to develop techniques for measuring anesthesia depth. Variational mode decomposition (VMD) enables mathematical optimization methods to decompose EEG signals into natural number intrinsic mode functions with distinct narrow bands. However, the analysis requires the a priori determination of hyperparameters, including the decomposition number (K) and the penalty factor (PF). In the VMD analysis of EEGs derived from a noninterventional and noninvasive retrospective observational study, we adapted the grey wolf optimizer (GWO) to determine the K and PF hyperparameters of the VMD. As a metric for optimization, we calculated the envelope function of the IMF decomposed via the VMD method and used its envelope entropy as the fitness function. The K and PF values varied in each epoch, with one epoch being the analytical unit of EEG; however, the fitness values showed convergence at an early stage in the GWO algorithm. The K value was set to 2 to capture the \u03b1 wave enhancement observed during the maintenance phase of general anesthesia in intrinsic mode function 2 (IMF-2). This study suggests that using the GWO to optimize VMD hyperparameters enables the construction of a robust analytical model for examining the EEG frequency characteristics involved in the effects of general anesthesia.<\/jats:p>","DOI":"10.3390\/s24175749","type":"journal-article","created":{"date-parts":[[2024,9,4]],"date-time":"2024-09-04T08:46:22Z","timestamp":1725439582000},"page":"5749","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["Variational Mode Decomposition Analysis of Electroencephalograms during General Anesthesia: Using the Grey Wolf Optimizer to Determine Hyperparameters"],"prefix":"10.3390","volume":"24","author":[{"given":"Kosuke","family":"Kushimoto","sequence":"first","affiliation":[{"name":"Department of Anesthesiology, Graduate School of Medical Science, Kyoto Prefectural University of Medicine, Kyoto 602-8566, Japan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0764-3917","authenticated-orcid":false,"given":"Yurie","family":"Obata","sequence":"additional","affiliation":[{"name":"Department of Anesthesiology, Yodogawa Christian Hospital, Osaka 533-0024, Japan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Tomomi","family":"Yamada","sequence":"additional","affiliation":[{"name":"Department of Anesthesiology, Graduate School of Medical Science, Kyoto Prefectural University of Medicine, Kyoto 602-8566, Japan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9478-8764","authenticated-orcid":false,"given":"Mao","family":"Kinoshita","sequence":"additional","affiliation":[{"name":"Department of Anesthesiology, Graduate School of Medical Science, Kyoto Prefectural University of Medicine, Kyoto 602-8566, Japan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5113-9633","authenticated-orcid":false,"given":"Koichi","family":"Akiyama","sequence":"additional","affiliation":[{"name":"Department of Anesthesiology, Kindai University, Higashiosaka 577-8502, Japan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9558-9011","authenticated-orcid":false,"given":"Teiji","family":"Sawa","sequence":"additional","affiliation":[{"name":"Hospital of Kyoto Prefectural University of Medicine, Kyoto 602-8566, Japan"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2024,9,4]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"295","DOI":"10.1213\/ANE.0000000000006860","article-title":"Depth of anesthesia and nociception monitoring: Current state and vision for 2050","volume":"138","author":"Morisson","year":"2024","journal-title":"Anesth. 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