{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,11]],"date-time":"2026-02-11T19:11:33Z","timestamp":1770837093128,"version":"3.50.1"},"reference-count":28,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2015,2,20]],"date-time":"2015-02-20T00:00:00Z","timestamp":1424390400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>Depth of anaesthesia (DoA) is an important measure for assessing the degree to which the central nervous system of a patient is depressed by a general anaesthetic agent, depending on the potency and concentration with which anaesthesia is administered during surgery. We can monitor the DoA by observing the patient\u2019s electroencephalography (EEG) signals during the surgical procedure. Typically high frequency EEG signals indicates the patient is conscious, while low frequency signals mean the patient is in a general anaesthetic state. If the anaesthetist is able to observe the instantaneous frequency changes of the patient\u2019s EEG signals during surgery this can help to better regulate and monitor DoA, reducing surgical and post-operative risks. This paper describes an approach towards the development of a 3D real-time visualization application which can show the instantaneous frequency and instantaneous amplitude of EEG simultaneously by using empirical mode decomposition (EMD) and the Hilbert\u2013Huang transform (HHT). HHT uses the EMD method to decompose a signal into so-called intrinsic mode functions (IMFs). The Hilbert spectral analysis method is then used to obtain instantaneous frequency data. The HHT provides a new method of analyzing non-stationary and nonlinear time series data. We investigate this approach by analyzing EEG data collected from patients undergoing surgical procedures. The results show that the EEG differences between three distinct surgical stages computed by using sample entropy (SampEn) are consistent with the expected differences between these stages based on the bispectral index (BIS), which has been shown to be quantifiable measure of the effect of anaesthetics on the central nervous system. Also, the proposed filtering approach is more effective compared to the standard filtering method in filtering out signal noise resulting in more consistent results than those provided by the BIS. The proposed approach is therefore able to distinguish between key operational stages related to DoA, which is consistent with the clinical observations. SampEn can also be viewed as a useful index for evaluating and monitoring the DoA of a patient when used in combination with this approach.<\/jats:p>","DOI":"10.3390\/e17030928","type":"journal-article","created":{"date-parts":[[2015,2,20]],"date-time":"2015-02-20T10:33:12Z","timestamp":1424428392000},"page":"928-949","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":18,"title":["Instantaneous 3D EEG Signal Analysis Based on Empirical Mode Decomposition and the Hilbert\u2013Huang Transform Applied to Depth of Anaesthesia"],"prefix":"10.3390","volume":"17","author":[{"given":"Mu-Tzu","family":"Shih","sequence":"first","affiliation":[{"name":"Department of Mechanical Engineering, and Innovation Center for Big Data and Digital Convergence, Yuan Ze University, Taoyuan, Chung-Li 32003, Taiwan"}]},{"given":"Faiyaz","family":"Doctor","sequence":"additional","affiliation":[{"name":"Department of Computing, Faculty of Engineering & Computing, Coventry University, Coventry, CV15FB, UK"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6849-8453","authenticated-orcid":false,"given":"Shou-Zen","family":"Fan","sequence":"additional","affiliation":[{"name":"Department of Anesthesiology, College of Medicine, National Taiwan University, Taipei 100, Taiwan"}]},{"given":"Kuo-Kuang","family":"Jen","sequence":"additional","affiliation":[{"name":"National Chung-Shan Institute of Science and Technology, Taoyuan, Longtan 32500, Taiwan"}]},{"given":"Jiann-Shing","family":"Shieh","sequence":"additional","affiliation":[{"name":"Department of Mechanical Engineering, and Innovation Center for Big Data and Digital Convergence, Yuan Ze University, Taoyuan, Chung-Li 32003, Taiwan"},{"name":"Center for Dynamical Biomarkers and Translational Medicine, National Central University,  Chung-Li 32001, Taiwan"}]}],"member":"1968","published-online":{"date-parts":[[2015,2,20]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"782","DOI":"10.1097\/ACO.0b013e3283326986","article-title":"Depth of anesthesia","volume":"22","author":"Kent","year":"2009","journal-title":"Curr. Opin. Anaesthesiol."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"715","DOI":"10.1097\/00000542-200003000-00016","article-title":"Approximate entropy as an electroencephalographic measure of anesthetic drug effect during anesthesia","volume":"92","author":"Bruhn","year":"2000","journal-title":"Anaesthesiology"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"187","DOI":"10.1053\/j.sane.2006.09.001","article-title":"Monitoring consciousness: EEG-based measures of anesthetic depth","volume":"25","author":"Mashour","year":"2006","journal-title":"Semin. Anesth. Perioper. Med. Pain."},{"key":"ref_4","doi-asserted-by":"crossref","unstructured":"Wang, R., Gu, F., and Shen, E. (2008). Advances in Cognitive Neurodynamics ICCN 2007, Springer.","DOI":"10.1007\/978-1-4020-8387-7"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"3458","DOI":"10.3390\/e15093458","article-title":"Analysis of EEG via multivariate empirical mode decomposition for depth of anesthesia based on sample entropy","volume":"15","author":"Wei","year":"2013","journal-title":"Entropy"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"903","DOI":"10.1098\/rspa.1998.0193","article-title":"The empirical mode decomposition and Hilbert spectrum for nonlinear and non-stationary time series analysis","volume":"454","author":"Huang","year":"1998","journal-title":"Proc. R. Soc. Lond. A"},{"key":"ref_7","doi-asserted-by":"crossref","unstructured":"Na\u00eft-Ali, A. (2009). Advanced Biosignal Processing, Springer.","DOI":"10.1007\/978-3-540-89506-0"},{"key":"ref_8","doi-asserted-by":"crossref","unstructured":"Martis, R.J., Acharya, U.R., Tan, J.H., Petznick, A., Yanti, R., Chua, C.K., Ng, E.Y., and Tong, L. (2012). Application of empirical mode decomposition (EMD) for automated detection of epilepsy using EEG signals. Int. J. Neural Syst., 22.","DOI":"10.1142\/S012906571250027X"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"2666","DOI":"10.1109\/JSEN.2013.2257742","article-title":"Empirical mode decomposition vs. wavelet decomposition for the extraction of respiratory signal from single-channel ECG: A comparison","volume":"13","author":"Labate","year":"2013","journal-title":"IEEE Sens. J."},{"key":"ref_10","doi-asserted-by":"crossref","unstructured":"Looney, D., Goverdovsky, V., Kidmose, P., and Mandic, D.P. (2014, January 4\u20139). Subspace denoising of EEG artefacts via multivariate EMD. Florence, Italy.","DOI":"10.1109\/ICASSP.2014.6854491"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"2297","DOI":"10.1073\/pnas.88.6.2297","article-title":"Approximate entropy as a measure of system complexity","volume":"88","author":"Pincus","year":"1991","journal-title":"Proc. Natl. Acad. Sci. USA"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"359","DOI":"10.5405\/jmbe.820","article-title":"Comparison of EEG approximate entropy and complexity measures of depth of anaesthesia during inhalational general anaesthesia","volume":"31","author":"Fan","year":"2011","journal-title":"J. Med. Biol. Eng."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"880","DOI":"10.1111\/j.1399-6576.2012.02676.x","article-title":"Measuring the effects of sevoflurane on electroencephalogram using sample entropy","volume":"56","author":"Shalbaf","year":"2012","journal-title":"Acta Anaesthesiol. Scand."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"1097","DOI":"10.1056\/NEJMoa0707361","article-title":"Anesthesia awareness and the bispectral index","volume":"358","author":"Avidan","year":"2008","journal-title":"New Engl. J. Med."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"1757","DOI":"10.1016\/S0140-6736(04)16300-9","article-title":"Bispectral index monitoring to prevent awareness during anaesthesia: The B-Aware randomized trial","volume":"363","author":"Myles","year":"2004","journal-title":"Lancet"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"3325","DOI":"10.3390\/e15093325","article-title":"Application of multivariate empirical mode decomposition and sample entropy in EEG signals via neutral networks for interpreting depth of anesthesia","volume":"15","author":"Huang","year":"2013","journal-title":"Entropy"},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"2607","DOI":"10.1016\/j.ymssp.2006.12.004","article-title":"Bearing fault diagnosis using FFT of intrinsic mode functions in Hilbert\u2013Huang transform","volume":"21","author":"Rai","year":"2007","journal-title":"Mech. Syst. Signal Process."},{"key":"ref_18","doi-asserted-by":"crossref","unstructured":"Safieddine, D., Kachenoura, A., Albera, L., Birot, G., Karfoul, A., Pasnicu, A., Biraben, A., Wendling, F., Senhadji, L., and Merlet, I. (2012). Removal of muscle artifact from EEG data: Comparison between stochastic (ICA and CCA) and deterministic (EMD and wavelet-based) approaches. EURASIP J. Adv. Signal Process., 127.","DOI":"10.1186\/1687-6180-2012-127"},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"7140","DOI":"10.1016\/j.physleta.2008.10.049","article-title":"Measuring time series regularity using nonlinear similarity-based sample entropy","volume":"372","author":"Xie","year":"2008","journal-title":"Phys. Lett. A"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"H2039","DOI":"10.1152\/ajpheart.2000.278.6.H2039","article-title":"Physiological time-series analysis using approximate entropy and sample entropy","volume":"278","author":"Richman","year":"2000","journal-title":"Am. J. Physiol. Heart Circ. Physiol."},{"key":"ref_21","unstructured":"Howell, D.C. (2012). Statistical Methods for Psychology, Cengage Learning. [8th]."},{"key":"ref_22","unstructured":"Glantz, S.A. (1997). Primer of Biostatistics, McGraw-Hill. [4th]."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"1142","DOI":"10.4304\/jcp.7.5.1142-1146","article-title":"Study on fault detection of rolling element bearing based on translation-invariant denoising and Hilbert\u2013Huang transform","volume":"7","author":"Xu","year":"2012","journal-title":"J. Comput."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"1843","DOI":"10.1109\/TPWRS.2007.907542","article-title":"An improved Hilbert\u2013Huang method for analysis of time-varying waveforms in power quality","volume":"22","author":"Senroy","year":"2007","journal-title":"IEEE T. Power Syst."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"1283","DOI":"10.1097\/00000542-200412000-00007","article-title":"Comparative evaluation of the Datex-Ohmeda S\/5 Entropy Module and the Bispectral Index monitor during propofol-remifentanil anesthesia","volume":"101","author":"Schmidt","year":"2004","journal-title":"Anesthesiology"},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"593","DOI":"10.1023\/A:1012216600170","article-title":"Bispectral index (BIS) and burst suppression: Revealing a part of the BIS algorithm","volume":"16","author":"Bruhn","year":"2000","journal-title":"J. Clin. Monit. Comput."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"105","DOI":"10.1016\/S0034-7094(12)70109-5","article-title":"Bispectral index and other processed parameters of electroencephalogram: An update","volume":"62","author":"Nunes","year":"2012","journal-title":"Rev. Bras. Anestesiol."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"154","DOI":"10.1111\/j.0001-5172.2004.00322.x","article-title":"Description of the Entropy\u2122 algorithm as applied in the Datex-Ohmeda S\/5\u2122 Entropy Module","volume":"48","author":"Maja","year":"2004","journal-title":"Acta Anaesthesiol. Scand."}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/17\/3\/928\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T20:42:52Z","timestamp":1760215372000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/17\/3\/928"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2015,2,20]]},"references-count":28,"journal-issue":{"issue":"3","published-online":{"date-parts":[[2015,3]]}},"alternative-id":["e17030928"],"URL":"https:\/\/doi.org\/10.3390\/e17030928","relation":{},"ISSN":["1099-4300"],"issn-type":[{"value":"1099-4300","type":"electronic"}],"subject":[],"published":{"date-parts":[[2015,2,20]]}}}