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Open AccessArticle

Refined Multiscale Entropy Using Fuzzy Metrics: Validation and Application to Nociception Assessment

1
Department of Electronic Engineering, Universidad de San Buenaventura, Cali 760033, Colombia
2
Department of Automatic Control, Universitat Politècnica de Catalunya, 08028 Barcelona, Spain
3
Center for Biomedical Engineering Research, Universitat Politècnica de Catalunya, 08028 Barcelona, Spain
4
CIBER of Bioengineering, Biomaterials and Nanomedicine (CIBER-BBN), 08028 Barcelona, Spain
5
Research and Development Department, Quantium Medical SL, 08302 Mataró, Spain
6
Department of Biomedical Sciences for Health, University of Milan, 20133 Milan, Italy
7
Department of Cardiothoracic-Vascular Anesthesia and Intensive Care, IRCCS Policlinico San Donato, San Donato Milanese, 20097 Milan, Italy
8
Systems Pharmacology Effect Control & Modeling (SPEC-M) Research Group, Department of Anesthesia, Hospital CLINIC de Barcelona, 08036 Barcelona, Spain
9
Department of Anesthesia and Perioperative Care, University of California San Francisco (UCSF), San Francisco, CA 94143, USA
*
Author to whom correspondence should be addressed.
This paper is an extended version of an abstract presented in the 40th Annual International Conference of the IEEE Engineering in Medicine and Biology Society (EMBC’18), Honolulu, HI, USA, 17–21 July 2018.
Entropy 2019, 21(7), 706; https://doi.org/10.3390/e21070706
Received: 2 July 2019 / Revised: 15 July 2019 / Accepted: 16 July 2019 / Published: 18 July 2019
(This article belongs to the Special Issue Information Dynamics in Brain and Physiological Networks)
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Abstract

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’s 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. View Full-Text
Keywords: fuzzy entropy; conditional entropy; complexity; electroencephalography; pain assessment; refined multiscale entropy; sample entropy; sedation-analgesia fuzzy entropy; conditional entropy; complexity; electroencephalography; pain assessment; refined multiscale entropy; sample entropy; sedation-analgesia
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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).
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Valencia, J.F.; Bolaños, J.D.; Vallverdú, M.; Jensen, E.W.; Porta, A.; Gambús, P.L. Refined Multiscale Entropy Using Fuzzy Metrics: Validation and Application to Nociception Assessment. Entropy 2019, 21, 706.

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