{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T03:42:33Z","timestamp":1760240553870,"version":"build-2065373602"},"reference-count":29,"publisher":"MDPI AG","issue":"7","license":[{"start":{"date-parts":[[2019,7,18]],"date-time":"2019-07-18T00:00:00Z","timestamp":1563408000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Departamento Administrativo de Ciencia, Tecnolog\u00eda e Innovaci\u00f3n","award":["1232-807-64083"],"award-info":[{"award-number":["1232-807-64083"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>The refined multiscale entropy (RMSE) approach is commonly applied to assess complexity as a function of the time scale. RMSE is normally based on the computation of sample entropy (SampEn) estimating complexity as conditional entropy. However, SampEn is dependent on the length and standard deviation of the data. Recently, fuzzy entropy (FuzEn) has been proposed, including several refinements, as an alternative to counteract these limitations. In this work, FuzEn, translated FuzEn (TFuzEn), translated-reflected FuzEn (TRFuzEn), inherent FuzEn (IFuzEn), and inherent translated FuzEn (ITFuzEn) were exploited as entropy-based measures in the computation of RMSE and their performance was compared to that of SampEn. FuzEn metrics were applied to synthetic time series of different lengths to evaluate the consistency of the different approaches. In addition, electroencephalograms of patients under sedation-analgesia procedure were analyzed based on the patient\u2019s response after the application of painful stimulation, such as nail bed compression or endoscopy tube insertion. Significant differences in FuzEn metrics were observed over simulations and real data as a function of the data length and the pain responses. Findings indicated that FuzEn, when exploited in RMSE applications, showed similar behavior to SampEn in long series, but its consistency was better than that of SampEn in short series both over simulations and real data. Conversely, its variants should be utilized with more caution, especially whether processes exhibit an important deterministic component and\/or in nociception prediction at long scales.<\/jats:p>","DOI":"10.3390\/e21070706","type":"journal-article","created":{"date-parts":[[2019,7,19]],"date-time":"2019-07-19T03:14:41Z","timestamp":1563506081000},"page":"706","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":5,"title":["Refined Multiscale Entropy Using Fuzzy Metrics: Validation and Application to Nociception Assessment"],"prefix":"10.3390","volume":"21","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-2997-2121","authenticated-orcid":false,"given":"Jos\u00e9 F.","family":"Valencia","sequence":"first","affiliation":[{"name":"Department of Electronic Engineering, Universidad de San Buenaventura, Cali 760033, Colombia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jose D.","family":"Bola\u00f1os","sequence":"additional","affiliation":[{"name":"Department of Electronic Engineering, Universidad de San Buenaventura, Cali 760033, Colombia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2031-3261","authenticated-orcid":false,"given":"Montserrat","family":"Vallverd\u00fa","sequence":"additional","affiliation":[{"name":"Department of Automatic Control, Universitat Polit\u00e8cnica de Catalunya, 08028 Barcelona, Spain"},{"name":"Center for Biomedical Engineering Research, Universitat Polit\u00e8cnica de Catalunya, 08028 Barcelona, Spain"},{"name":"CIBER of Bioengineering, Biomaterials and Nanomedicine (CIBER-BBN), 08028 Barcelona, Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Erik W.","family":"Jensen","sequence":"additional","affiliation":[{"name":"Research and Development Department, Quantium Medical SL, 08302 Matar\u00f3, Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6720-9824","authenticated-orcid":false,"given":"Alberto","family":"Porta","sequence":"additional","affiliation":[{"name":"Department of Biomedical Sciences for Health, University of Milan, 20133 Milan, Italy"},{"name":"Department of Cardiothoracic-Vascular Anesthesia and Intensive Care, IRCCS Policlinico San Donato, San Donato Milanese, 20097 Milan, Italy"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8802-6237","authenticated-orcid":false,"given":"Pedro L.","family":"Gamb\u00fas","sequence":"additional","affiliation":[{"name":"Systems Pharmacology Effect Control &amp; Modeling (SPEC-M) Research Group, Department of Anesthesia, Hospital CLINIC de Barcelona, 08036 Barcelona, Spain"},{"name":"Department of Anesthesia and Perioperative Care, University of California San Francisco (UCSF), San Francisco, CA 94143, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2019,7,18]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"266","DOI":"10.1109\/TNSRE.2007.897025","article-title":"Characterization of surface EMG signal based on fuzzy entropy","volume":"15","author":"Chen","year":"2007","journal-title":"IEEE Trans. Neural Syst. Rehabil. Eng."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"61","DOI":"10.1016\/j.medengphy.2008.04.005","article-title":"Measuring complexity using FuzzyEn, ApEn, and SampEn","volume":"31","author":"Chen","year":"2009","journal-title":"Med. Eng. Phys."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"338","DOI":"10.1016\/S0019-9958(65)90241-X","article-title":"Fuzzy sets","volume":"8","author":"Zadeh","year":"1965","journal-title":"Inf. Control"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"2871","DOI":"10.1016\/j.asoc.2010.11.020","article-title":"Complexity analysis of the biomedical signal using fuzzy entropy measurement","volume":"11","author":"Xie","year":"2011","journal-title":"Appl. Soft Comput."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"64","DOI":"10.1186\/s12938-015-0063-z","article-title":"Analysis of short-term heart rate and diastolic period variability using a refined fuzzy entropy method","volume":"14","author":"Ji","year":"2015","journal-title":"Biomed. Eng. Online"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"1320","DOI":"10.7150\/ijbs.19462","article-title":"Complexity Change in Cardiovascular Disease","volume":"13","author":"Chen","year":"2017","journal-title":"Int. J. Biol. Sci."},{"key":"ref_7","doi-asserted-by":"crossref","unstructured":"Xie, H., and Guo, T. (2018, January 4\u20137). Fuzzy entropy spectrum analysis for biomedical signals de-noising. Proceedings of the 2018 IEEE International Conference on Biomedical & Health Informatics (BHI), Las Vegas, NV, USA.","DOI":"10.1109\/BHI.2018.8333367"},{"key":"ref_8","doi-asserted-by":"crossref","unstructured":"Ahmed, M.U., Chanwimalueang, T., Thayyil, S., and Mandic, D. (2017). A Multivariate Multiscale Fuzzy Entropy Algorithm with Application to Uterine EMG Complexity Analysis. Entropy, 19.","DOI":"10.3390\/e19010002"},{"key":"ref_9","doi-asserted-by":"crossref","unstructured":"Girault, J.M., and Heurtier, A.H. (2018). Centered and Averaged Fuzzy Entropy to Improve Fuzzy Entropy Precision. Entropy, 20.","DOI":"10.3390\/e20040287"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"1032","DOI":"10.1109\/TFUZZ.2017.2666789","article-title":"Inherent Fuzzy Entropy for the Improvement of EEG Complexity Evaluation","volume":"26","author":"Cao","year":"2016","journal-title":"IEEE Trans. Fuzzy Syst."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"2202","DOI":"10.1109\/TBME.2009.2021986","article-title":"Refined multiscale entropy: Application to 24-h Holter recordings of heart period variability in healthy and aortic stenosis subjects","volume":"56","author":"Valencia","year":"2009","journal-title":"IEEE Trans. Biomed. Eng."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"325","DOI":"10.1088\/0967-3334\/34\/3\/325","article-title":"Ischemic risk stratification by means of multivariate analysis of the heart rate variability","volume":"34","author":"Valencia","year":"2013","journal-title":"Physiol. Meas."},{"key":"ref_13","doi-asserted-by":"crossref","unstructured":"Bari, V., Valencia, J.F., Vallverd\u00fa, M., Girardengo, G., Marchi, A., Bassani, T., Caminal, P., Cerutti, S., George, A.L., and Brink, P.A. (2014). Multiscale complexity analysis of the cardiac control identifies asymptomatic and symptomatic patients in long QT syndrome type 1. PLoS ONE, 9.","DOI":"10.1371\/journal.pone.0093808"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"7768","DOI":"10.3390\/e17117768","article-title":"A Refined Multiscale Self-Entropy Approach for the Assessment of Cardiac Control Complexity: Application to Long QT Syndrome Type 1 Patients","volume":"17","author":"Bari","year":"2015","journal-title":"Entropy"},{"key":"ref_15","doi-asserted-by":"crossref","unstructured":"Valencia, J.F., Melia, U., Vallverd\u00fa, M., Borrat, X., Jospin, M., Jensen, E.W., Porta, A., Gamb\u00fas, P.L., and Caminal, P. (2016). Assessment of Nociceptive Responsiveness Levels during Sedation-Analgesia by Entropy Analysis of EEG. Entropy, 18.","DOI":"10.3390\/e18030103"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"021906","DOI":"10.1103\/PhysRevE.71.021906","article-title":"Multiscale entropy analysis of biological signals","volume":"71","author":"Costa","year":"2005","journal-title":"Phys. Rev. E"},{"key":"ref_17","doi-asserted-by":"crossref","unstructured":"Riihijarvi, J., Wellens, M., and Mahonen, P. (2009, January 19\u201325). Measuring Complexity and Predictability in Networks with Multiscale Entropy Analysis. Proceedings of the EEE INFOCOM 2009, Rio de Janeiro, Brazil.","DOI":"10.1109\/INFCOM.2009.5062023"},{"key":"ref_18","unstructured":"Wen, H. (2014). A Review of the H\u00e9non Map and Its Physical Interpretations, School of physics, Georgia Institute of Technology."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"656","DOI":"10.1136\/bmj.2.5920.656","article-title":"Controlled sedation with alphaxalone-alphadolone","volume":"2","author":"Ramsay","year":"1974","journal-title":"Br. Med. J."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"547","DOI":"10.1016\/j.medengphy.2013.11.014","article-title":"Filtering and thresholding the analytic signal envelope in order to improve peak and spike noise reduction in EEG signals","volume":"36","author":"Melia","year":"2014","journal-title":"Med. Eng. Phys."},{"key":"ref_21","first-page":"H2039","article-title":"Physiological time-series analysis using approximate entropy and sample entropy","volume":"278","author":"Richman","year":"2000","journal-title":"Am. J. Physiol."},{"key":"ref_22","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_23","doi-asserted-by":"crossref","first-page":"011114","DOI":"10.1103\/PhysRevE.64.011114","article-title":"Effect of trends on detrended fluctuation analysis","volume":"64","author":"Hu","year":"2001","journal-title":"Phys. Rev. E"},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"903","DOI":"10.1098\/rspa.1998.0193","article-title":"The empirical mode decomposition and the Hilbert spectrum for nonlinear and non-stationary time series analysis","volume":"454","author":"Huang","year":"1998","journal-title":"Proc. R. Soc. Lond. Ser. A"},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"114","DOI":"10.1016\/j.csda.2011.05.015","article-title":"Trend filtering via empirical mode decompositions","volume":"58","author":"Moghtaderi","year":"2013","journal-title":"Comput. Stat. Data Anal."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"112","DOI":"10.1109\/LSP.2003.821662","article-title":"Empirical mode decomposition as a filter bank","volume":"11","author":"Flandrin","year":"2004","journal-title":"IEEE Signal Process. Lett."},{"key":"ref_27","unstructured":"Flandrin, P., Gon\u00e7alves, P., and Rilling, G. (2004, January 6\u201310). Detrending and denoising with empirical mode decompositions. Proceedings of the EUSIPCO 2004, Vienna, Austria."},{"key":"ref_28","unstructured":"Rilling, G., Flandrin, P., and Gon\u00e7alves, P. (2005, January 23\u201323). Empirical mode decomposition, fractional Gaussian noise, and Hurst exponent estimation. Proceedings of the IEEE International Conference on Acoustics, Speech, and Signal Processing 2005, Philadelphia, PA, USA."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"38","DOI":"10.1097\/00000542-199601000-00005","article-title":"Measuring the performance of anesthetic depth indicators","volume":"84","author":"Smith","year":"1996","journal-title":"Anesthesiology"}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/21\/7\/706\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T13:07:14Z","timestamp":1760188034000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/21\/7\/706"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,7,18]]},"references-count":29,"journal-issue":{"issue":"7","published-online":{"date-parts":[[2019,7]]}},"alternative-id":["e21070706"],"URL":"https:\/\/doi.org\/10.3390\/e21070706","relation":{},"ISSN":["1099-4300"],"issn-type":[{"type":"electronic","value":"1099-4300"}],"subject":[],"published":{"date-parts":[[2019,7,18]]}}}