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      Entropy Measures in Analysis of Head up Tilt Test Outcome for Diagnosing Vasovagal Syncope

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          Abstract

          The paper presents possible applications of entropy measures in analysis of biosignals recorded during head up tilt testing (HUTT) in patients with suspected vasovagal syndrome. The study group comprised 80 patients who developed syncope during HUTT (57 in the passive phase of the test (HUTT(+) group) and 23 who had negative result of passive phase and developed syncope after provocation with nitroglycerine (HUTT(−) group)). The paper focuses on assessment of monitored signals’ complexity (heart rate expressed as R-R intervals (RRI), blood pressure (sBP, dBP) and stroke volume (SV)) using various types of entropy measures (Sample Entropy (SE), Fuzzy Entropy (FE), Shannon Entropy (Sh), Conditional Entropy (CE), Permutation Entropy (PE)). Assessment of the complexity of signals in supine position indicated presence of significant differences between HUTT(+) versus HUTT(−) patients only for Conditional Entropy (CE(RRI)). Values of CE(RRI) higher than 0.7 indicate likelihood of a positive result of HUTT already at the passive phase. During tilting, in the pre-syncope phase, significant differences were found for: (SE(sBP), SE(dBP), FE(RRI), FE(sBP), FE(dBP), FE(SV), Sh(sBP), Sh(SV), CE(sBP), CE(dBP)). HUTT(+) patients demonstrated significant changes in signals’ complexity more frequently than HUTT(−) patients. When comparing entropy measurements done in the supine position with those during tilting, SV assessed in HUTT(+) patients was the only parameter for which all tested measures of entropy (SE(SV), FE(SV), Sh(SV), CE(SV), PE(SV)) showed significant differences.

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          A Mathematical Theory of Communication

          C. Shannon (1948)
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            Approximate entropy as a measure of system complexity.

            Techniques to determine changing system complexity from data are evaluated. Convergence of a frequently used correlation dimension algorithm to a finite value does not necessarily imply an underlying deterministic model or chaos. Analysis of a recently developed family of formulas and statistics, approximate entropy (ApEn), suggests that ApEn can classify complex systems, given at least 1000 data values in diverse settings that include both deterministic chaotic and stochastic processes. The capability to discern changing complexity from such a relatively small amount of data holds promise for applications of ApEn in a variety of contexts.
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              Physiological time-series analysis using approximate entropy and sample entropy.

              Entropy, as it relates to dynamical systems, is the rate of information production. Methods for estimation of the entropy of a system represented by a time series are not, however, well suited to analysis of the short and noisy data sets encountered in cardiovascular and other biological studies. Pincus introduced approximate entropy (ApEn), a set of measures of system complexity closely related to entropy, which is easily applied to clinical cardiovascular and other time series. ApEn statistics, however, lead to inconsistent results. We have developed a new and related complexity measure, sample entropy (SampEn), and have compared ApEn and SampEn by using them to analyze sets of random numbers with known probabilistic character. We have also evaluated cross-ApEn and cross-SampEn, which use cardiovascular data sets to measure the similarity of two distinct time series. SampEn agreed with theory much more closely than ApEn over a broad range of conditions. The improved accuracy of SampEn statistics should make them useful in the study of experimental clinical cardiovascular and other biological time series.
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                Author and article information

                Journal
                Entropy (Basel)
                Entropy (Basel)
                entropy
                Entropy
                MDPI
                1099-4300
                16 December 2018
                December 2018
                : 20
                : 12
                : 976
                Affiliations
                [1 ]Department of Theoretical Foundations of Bio-Medical Science and Medical Informatics, Collegium Medicum, Nicolaus Copernicus University, 85-067 Bydgoszcz, Poland
                [2 ]Department of Emergency Medicine, Wroclaw Medical University, 02-091 Wroclaw, Poland
                [3 ]1st Department of Cardiology, Medical University of Warsaw, 02-091 Warsaw, Poland
                [4 ]Department of Cardiology and Internal Diseases, Collegium Medicum, Nicolaus Copernicus University, 85-067 Bydgoszcz, Poland
                Author notes
                [* ]Correspondence: buszko@ 123456cm.umk.pl ; Tel.: +48-52-585-3428
                Author information
                https://orcid.org/0000-0001-8234-2773
                Article
                entropy-20-00976
                10.3390/e20120976
                7512576
                45c90baa-9e4c-4696-aae6-ade000f1cab5
                © 2018 by the authors.

                Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license ( http://creativecommons.org/licenses/by/4.0/).

                History
                : 21 November 2018
                : 12 December 2018
                Categories
                Article

                sample entropy,permutation entropy,fuzzy entropy,shannon entropy,conditional entropy,vasovagal syndrome,head up tilt test

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