{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,5]],"date-time":"2025-11-05T06:56:02Z","timestamp":1762325762940,"version":"build-2065373602"},"reference-count":39,"publisher":"MDPI AG","issue":"11","license":[{"start":{"date-parts":[[2023,11,20]],"date-time":"2023-11-20T00:00:00Z","timestamp":1700438400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Korea government (MSIT)","award":["2021-0-00034"],"award-info":[{"award-number":["2021-0-00034"]}]},{"name":"Research Grant of Kwangwoon University","award":["2021-0-00034"],"award-info":[{"award-number":["2021-0-00034"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>Heart rate variability (HRV) is used as an index reflecting the adaptability of the autonomic nervous system to external stimuli and can be used to detect various heart diseases. Since HRVs are the time series signal with nonlinear property, entropy has been an attractive analysis method. Among the various entropy methods, dispersion entropy (DE) has been preferred due to its ability to quantify the time series\u2019 underlying complexity with low computational cost. However, the order between patterns is not considered in the probability distribution of dispersion patterns for computing the DE value. Here, a multiscale cumulative residual dispersion entropy (MCRDE), which employs a cumulative residual entropy and DE estimation in multiple temporal scales, is presented. Thus, a generalized and fast estimation of complexity in temporal structures is inherited in the proposed MCRDE. To verify the performance of the proposed MCRDE, the complexity of inter-beat interval obtained from ECG signals of congestive heart failure (CHF), atrial fibrillation (AF), and the healthy group was compared. The experimental results show that MCRDE is more capable of quantifying physiological conditions than preceding multiscale entropy methods in that MCRDE achieves more statistically significant cases in terms of p-value from the Mann\u2013Whitney test.<\/jats:p>","DOI":"10.3390\/e25111562","type":"journal-article","created":{"date-parts":[[2023,11,20]],"date-time":"2023-11-20T01:54:12Z","timestamp":1700445252000},"page":"1562","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["Multiscale Cumulative Residual Dispersion Entropy with Applications to Cardiovascular Signals"],"prefix":"10.3390","volume":"25","author":[{"given":"Youngjun","family":"Kim","sequence":"first","affiliation":[{"name":"Department of Electronics and Communications Engineering, Kwangwoon University, Seoul 01897, Republic of Korea"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8292-7093","authenticated-orcid":false,"given":"Young-Seok","family":"Choi","sequence":"additional","affiliation":[{"name":"Department of Electronics and Communications Engineering, Kwangwoon University, Seoul 01897, Republic of Korea"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2023,11,20]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"216","DOI":"10.1016\/j.bspc.2018.03.003","article-title":"A Survey on ECG Analysis","volume":"43","author":"Uysal","year":"2018","journal-title":"Biomed. Signal Process. Control"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"203","DOI":"10.1007\/BF00364139","article-title":"Is the Normal Heart a Periodic Oscillator?","volume":"58","author":"Babloyantz","year":"1988","journal-title":"Biol. Cybern."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"48761","DOI":"10.1109\/ACCESS.2020.2978930","article-title":"Multiscale Distribution Entropy Analysis of Heart Rate Variability Using Differential Inter-Beat Intervals","volume":"8","author":"Lee","year":"2020","journal-title":"IEEE Access"},{"key":"ref_4","doi-asserted-by":"crossref","unstructured":"Lee, D.-Y., and Choi, Y.-S. (2018). Multiscale Distribution Entropy Analysis of Short-Term Heart Rate Variability. Entropy, 20.","DOI":"10.3390\/e20120952"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"2357","DOI":"10.1007\/s11071-020-05934-7","article-title":"Multiscale Cumulative Residual Distribution Entropy and Its Applications on Heart Rate Time Series","volume":"101","author":"Mao","year":"2020","journal-title":"Nonlinear Dyn."},{"key":"ref_6","first-page":"1131","article-title":"A New Kernel-Width Adaptation Method for Minimum Error Entropy","volume":"46","author":"Yong","year":"2021","journal-title":"J. Korean Inst. Commun. Inf. Sci."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"49","DOI":"10.1016\/0025-5564(88)90057-0","article-title":"Dimensional Analysis of Heart Rate Variability in Heart Transplant Recipients","volume":"90","author":"Zbilut","year":"1988","journal-title":"Math. Biosci."},{"key":"ref_8","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_9","doi-asserted-by":"crossref","unstructured":"Holzinger, A., and Jurisica, I. (2014). Interactive Knowledge Discovery and Data Mining in Biomedical Informatics: State-of-the-Art and Future Challenges, Springer. Lecture Notes in Computer Science.","DOI":"10.1007\/978-3-662-43968-5"},{"key":"ref_10","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_11","doi-asserted-by":"crossref","first-page":"1553","DOI":"10.3390\/e14081553","article-title":"Permutation Entropy and Its Main Biomedical and Econophysics Applications: A Review","volume":"14","author":"Zanin","year":"2012","journal-title":"Entropy"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"174102","DOI":"10.1103\/PhysRevLett.88.174102","article-title":"Permutation Entropy: A Natural Complexity Measure for Time Series","volume":"88","author":"Bandt","year":"2002","journal-title":"Phys. Rev. Lett."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"610","DOI":"10.1109\/LSP.2016.2542881","article-title":"Dispersion Entropy: A Measure for Time-Series Analysis","volume":"23","author":"Rostaghi","year":"2016","journal-title":"IEEE Signal Process. Lett."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"88","DOI":"10.1063\/1.166090","article-title":"Quantitative Analysis of Heart Rate Variability","volume":"5","author":"Kurths","year":"1995","journal-title":"Chaos"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"161","DOI":"10.1016\/0167-2789(91)90229-3","article-title":"Symbolic Dynamics and Characterization of Complexity","volume":"51","author":"Hao","year":"1991","journal-title":"Phys. D Nonlinear Phenom."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"81","DOI":"10.1016\/S0022-0736(95)80021-2","article-title":"Improved Analysis of Heart Rate Variability by Methods of Nonlinear Dynamics","volume":"28","author":"Voss","year":"1995","journal-title":"J. Electrocardiol."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"1220","DOI":"10.1109\/TIT.2004.828057","article-title":"Cumulative Residual Entropy: A New Measure of Information","volume":"50","author":"Rao","year":"2004","journal-title":"IEEE Trans. Inf. Theory"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"1931","DOI":"10.1016\/j.jspi.2006.06.035","article-title":"On the Dynamic Cumulative Residual Entropy","volume":"137","author":"Asadi","year":"2007","journal-title":"J. Stat. Plan. Inference"},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"201","DOI":"10.1007\/s11263-006-0011-2","article-title":"Non-Rigid Multi-Modal Image Registration Using Cross-Cumulative Residual Entropy","volume":"74","author":"Wang","year":"2007","journal-title":"Int. J. Comput. Vis."},{"key":"ref_20","doi-asserted-by":"crossref","unstructured":"Pickering, M.R., Xiao, Y., and Jia, X. (2008, January 17\u201319). Registration of Multi-Sensor Remote Sensing Imagery by Gradient-Based Optimization of Cross-Cumulative Residual Entropy. Proceedings of the Algorithms and Technologies for Multispectral, Hyperspectral, and Ultraspectral Imagery XIV, Orlando, FL, USA.","DOI":"10.1117\/12.777016"},{"key":"ref_21","doi-asserted-by":"crossref","unstructured":"Ma, Z., and Chu, T. (2013, January 23\u201324). The BCG Signal Feature Extraction and Recognition Based on the Cumulative Residual Entropy. Proceedings of the 2013 2nd International Symposium on Instrumentation and Measurement, Sensor Network and Automation (IMSNA), Toronto, ON, Canada.","DOI":"10.1109\/IMSNA.2013.6743330"},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"417","DOI":"10.1007\/s11517-012-1010-9","article-title":"SEMG-Based Hand Motion Recognition Using Cumulative Residual Entropy and Extreme Learning Machine","volume":"51","author":"Shi","year":"2013","journal-title":"Med. Biol. Eng. Comput."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"068102","DOI":"10.1103\/PhysRevLett.89.068102","article-title":"Multiscale Entropy Analysis of Complex Physiologic Time Series","volume":"89","author":"Costa","year":"2002","journal-title":"Phys. Rev. Lett."},{"key":"ref_24","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 Stat. Nonlin. Soft. Matter Phys."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"379","DOI":"10.1002\/j.1538-7305.1948.tb01338.x","article-title":"A Mathematical Theory of Communication","volume":"27","author":"Shannon","year":"1948","journal-title":"Bell Syst. Tech. J."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"E215","DOI":"10.1161\/01.CIR.101.23.e215","article-title":"PhysioBank, PhysioToolkit, and PhysioNet: Components of a New Research Resource for Complex Physiologic Signals","volume":"101","author":"Goldberger","year":"2000","journal-title":"Circulation"},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"230","DOI":"10.1109\/TBME.1985.325532","article-title":"A Real-Time QRS Detection Algorithm","volume":"3","author":"Pan","year":"1985","journal-title":"IEEE Trans. Biomed. Eng."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"6077","DOI":"10.1016\/j.eswa.2010.02.118","article-title":"Bearing Fault Diagnosis Using Multi-Scale Entropy and Adaptive Neuro-Fuzzy Inference","volume":"37","author":"Zhang","year":"2010","journal-title":"Expert Syst. Appl."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"061918","DOI":"10.1103\/PhysRevE.84.061918","article-title":"Multivariate Multiscale Entropy: A Tool for Complexity Analysis of Multichannel Data","volume":"84","author":"Ahmed","year":"2011","journal-title":"Phys. Rev. E"},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"5865","DOI":"10.1016\/j.physa.2013.07.075","article-title":"Modified Multiscale Entropy for Short-Term Time Series Analysis","volume":"392","author":"Wu","year":"2013","journal-title":"Phys. A Stat. Mech. Its Appl."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"7926","DOI":"10.3390\/e17127849","article-title":"Multiscale Entropy Analysis of Center-of-Pressure Dynamics in Human Postural Control: Methodological Considerations","volume":"17","author":"Gow","year":"2015","journal-title":"Entropy"},{"key":"ref_32","doi-asserted-by":"crossref","unstructured":"Ahmed, M.U., Chanwimalueang, T., Thayyil, S., and Mandic, D.P. (2016). A Multivariate Multiscale Fuzzy Entropy Algorithm with Application to Uterine EMG Complexity Analysis. Entropy, 19.","DOI":"10.3390\/e19010002"},{"key":"ref_33","doi-asserted-by":"crossref","unstructured":"Azami, H., Ab\u00e1solo, D., Simons, S., and Escudero, J. (2017). Univariate and Multivariate Generalized Multiscale Entropy to Characterise EEG Signals in Alzheimer\u2019s Disease. Entropy, 19.","DOI":"10.3390\/e19010031"},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"20200265","DOI":"10.1098\/rsta.2020.0265","article-title":"Advanced Computation in Cardiovascular Physiology: New Challenges and Opportunities","volume":"379","author":"Valenza","year":"2021","journal-title":"Phil. Trans. R. Soc. A"},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"99","DOI":"10.1016\/j.ins.2018.07.063","article-title":"Computer-Aided Diagnosis of Atrial Fibrillation Based on ECG Signals: A Review","volume":"467","author":"Hagiwara","year":"2018","journal-title":"Inf. Sci."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"150","DOI":"10.21595\/jme.2022.22897","article-title":"The Discriminant Statistic Based on MPE-MWPE Relationship and Non-Uniform Embedding","volume":"10","author":"Petrauskiene","year":"2022","journal-title":"J. Meas. Eng."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"1306","DOI":"10.1161\/CIRCULATIONAHA.106.180200","article-title":"Recommendations for the Standardization and Interpretation of the Electrocardiogram","volume":"115","author":"Kligfield","year":"2007","journal-title":"Circulation"},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"177","DOI":"10.1111\/j.1542-474X.1997.tb00325.x","article-title":"An Analysis of the Time-Relations of Electrocardiograms","volume":"2","author":"Bazett","year":"1997","journal-title":"Ann. Noninvasive Electrocardiol."},{"key":"ref_39","doi-asserted-by":"crossref","unstructured":"Ziaukas, P., Alabdulgader, A., Vainoras, A., Navickas, Z., and Ragulskis, M. (2017). New Approach for Visualization of Relationships between RR and JT Intervals. PLoS ONE, 12.","DOI":"10.1371\/journal.pone.0174279"}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/25\/11\/1562\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T21:25:57Z","timestamp":1760131557000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/25\/11\/1562"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,11,20]]},"references-count":39,"journal-issue":{"issue":"11","published-online":{"date-parts":[[2023,11]]}},"alternative-id":["e25111562"],"URL":"https:\/\/doi.org\/10.3390\/e25111562","relation":{},"ISSN":["1099-4300"],"issn-type":[{"type":"electronic","value":"1099-4300"}],"subject":[],"published":{"date-parts":[[2023,11,20]]}}}