{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,5]],"date-time":"2026-05-05T16:56:45Z","timestamp":1778000205229,"version":"3.51.4"},"reference-count":32,"publisher":"MDPI AG","issue":"10","license":[{"start":{"date-parts":[[2020,9,24]],"date-time":"2020-09-24T00:00:00Z","timestamp":1600905600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["61601263"],"award-info":[{"award-number":["61601263"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100000923","name":"Australian Research Council","doi-asserted-by":"publisher","award":["DP190101248"],"award-info":[{"award-number":["DP190101248"]}],"id":[{"id":"10.13039\/501100000923","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>The complexity of a heart rate variability (HRV) signal is considered an important nonlinear feature to detect cardiac abnormalities. This work aims at explaining the physiological meaning of a recently developed complexity measurement method, namely, distribution entropy (DistEn), in the context of HRV signal analysis. We thereby propose modified distribution entropy (mDistEn) to remove the physiological discrepancy involved in the computation of DistEn. The proposed method generates a distance matrix that is devoid of over-exerted multi-lag signal changes. Restricted element selection in the distance matrix makes \u201cmDistEn\u201d a computationally inexpensive and physiologically more relevant complexity measure in comparison to DistEn.<\/jats:p>","DOI":"10.3390\/e22101077","type":"journal-article","created":{"date-parts":[[2020,9,25]],"date-time":"2020-09-25T01:39:33Z","timestamp":1600997973000},"page":"1077","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":7,"title":["Modified Distribution Entropy as a Complexity Measure of Heart Rate Variability (HRV) Signal"],"prefix":"10.3390","volume":"22","author":[{"given":"Radhagayathri","family":"Udhayakumar","sequence":"first","affiliation":[{"name":"School of Information Technology, Deakin University, 75 Pigdons Road, Waurn Ponds, Geelong, VIC 3216, Australia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Chandan","family":"Karmakar","sequence":"additional","affiliation":[{"name":"School of Information Technology, Deakin University, 75 Pigdons Road, Waurn Ponds, Geelong, VIC 3216, Australia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4684-4909","authenticated-orcid":false,"given":"Peng","family":"Li","sequence":"additional","affiliation":[{"name":"Division of Sleep and Circadian Disorders, Brigham and Women\u2019s Hospital, Harvard Medical School, Boston, MA 02115, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2981-7957","authenticated-orcid":false,"given":"Xinpei","family":"Wang","sequence":"additional","affiliation":[{"name":"School of Control Science and Engineering, Shandong University, Jinan 250100, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Marimuthu","family":"Palaniswami","sequence":"additional","affiliation":[{"name":"Department of Electrical &amp; Electronic Engineering, The University of Melbourne, Melbourne, VIC 3010, Australia"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2020,9,24]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"220","DOI":"10.1126\/science.6166045","article-title":"Power spectrum analysis of heart rate fluctuation: A quantitative probe of beat-to-beat cardiovascular control","volume":"213","author":"Akselrod","year":"1981","journal-title":"Science"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"1031","DOI":"10.1007\/s11517-006-0119-0","article-title":"Heart rate variability: A review","volume":"44","author":"Acharya","year":"2006","journal-title":"Med. Biol. Eng. Comput."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"85","DOI":"10.5271\/sjweh.15","article-title":"Heart rate variability in health and disease","volume":"21","author":"Estela","year":"1995","journal-title":"Scand. J. Work. Environ. Health"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"S2","DOI":"10.1186\/1471-2105-15-S6-S2","article-title":"Selection of entropy-measure parameters for knowledge discovery in heart rate variability data","volume":"15","author":"Mayer","year":"2014","journal-title":"BMC Bioinform."},{"key":"ref_5","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_6","doi-asserted-by":"crossref","first-page":"24","DOI":"10.1186\/1475-925X-3-24","article-title":"Heart rate analysis in normal subjects of various age groups","volume":"3","author":"Acharya","year":"2004","journal-title":"Biomed. Eng. Online"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"195","DOI":"10.1111\/j.1749-6632.1987.tb48733.x","article-title":"Applications of nonlinear dynamics to clinical cardiology","volume":"504","author":"Goldberger","year":"1987","journal-title":"Ann. N. Y. Acad. Sci."},{"key":"ref_8","first-page":"277","article-title":"Methods derived from nonlinear dynamics for analysing heart rate variability","volume":"367","author":"Voss","year":"2009","journal-title":"Philos. Trans. Math. Phys. Eng."},{"key":"ref_9","doi-asserted-by":"crossref","unstructured":"Zhang, Q., and Dai, X. (2019, January 22\u201326). Entropy-based iterative learning estimation for stochastic non-linear systems and its application to neural membrane potential interaction. Proceedings of the 2019 1st International Conference on Industrial Artificial Intelligence (IAI), Shenyang, China.","DOI":"10.1109\/ICIAI.2019.8850800"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"376","DOI":"10.1109\/TAC.2019.2914257","article-title":"Rbfnn-based minimum entropy filtering for a class of stochastic nonlinear systems","volume":"65","author":"Yin","year":"2020","journal-title":"IEEE Trans. Autom. Control"},{"key":"ref_11","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_12","first-page":"H1643","article-title":"Physiological time-series analysis: What does regularity quantify?","volume":"266","author":"Pincus","year":"1994","journal-title":"Am. J. Physiol."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"349","DOI":"10.1007\/s10439-012-0668-3","article-title":"The appropriate use of approximate entropy and sample entropy with short data sets","volume":"41","author":"Yentes","year":"2013","journal-title":"Ann. Biomed. Eng."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"53","DOI":"10.1016\/j.physa.2003.08.022","article-title":"Multiscale entropy analysis of human gait dynamics","volume":"330","author":"Costa","year":"2003","journal-title":"Phys. Stat. Appl."},{"key":"ref_15","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_16","doi-asserted-by":"crossref","first-page":"77","DOI":"10.1007\/s11517-014-1216-0","article-title":"Assessing the complexity of short-term heartbeat interval series by distribution entropy","volume":"53","author":"Li","year":"2015","journal-title":"Med. Biol. Eng. Comput."},{"key":"ref_17","doi-asserted-by":"crossref","unstructured":"Karmakar, C., Udhayakumar, R.K., and Palaniswami, M. (2015, January 25\u201329). Distribution entropy (disten): A complexity measure to detect arrhythmia from short length rr interval time series. Proceedings of the 2015 37th Annual International Conference of the IEEE Engineering in Medicine & Biology Society (EMBC), Milan, Italy.","DOI":"10.1109\/EMBC.2015.7319565"},{"key":"ref_18","doi-asserted-by":"crossref","unstructured":"Udhayakumar, R.K., Karmakar, C., Li, P., and Palaniswami, M. (2015, January 25\u201329). Effect of data length and bin numbers on distribution entropy (disten) measurement in analyzing healthy aging. Proceedings of the 2015 37th Annual International Conference of the IEEE Engineering in Medicine & Biology Society (EMBC), Milan, Italy.","DOI":"10.1109\/EMBC.2015.7320218"},{"key":"ref_19","doi-asserted-by":"crossref","unstructured":"Castiglioni, P., and Di Rienzo, M. (2008, January 14\u201317). How the threshold r influences approximate entropy analysis of heart-rate variability. Proceedings of the 2008 Computers in Cardiology, Bologna, Italy.","DOI":"10.1109\/CIC.2008.4749103"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"720","DOI":"10.3389\/fphys.2017.00720","article-title":"Stability, consistency and performance of distribution entropy in analysing short length heart rate variability (hrv) signal","volume":"8","author":"Karmakar","year":"2017","journal-title":"Front. Physiol."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"945","DOI":"10.1016\/S0006-3495(91)82309-8","article-title":"Aging and the complexity of cardiovascular dynamics","volume":"59","author":"Kaplan","year":"1991","journal-title":"Biophys. J."},{"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":"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_24","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_25","doi-asserted-by":"crossref","first-page":"45","DOI":"10.1109\/51.932724","article-title":"The impact of the mit-bih arrhythmia database","volume":"20","author":"Moody","year":"2001","journal-title":"IEEE Eng. Med. Biol. Mag."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"72","DOI":"10.1046\/j.1475-097X.2003.00466.x","article-title":"Poincare plot indexes of heart rate variability capture dynamic adaptations after haemodialysis in chronic renal failure patients","volume":"23","author":"Claudia","year":"2003","journal-title":"Clin. Physiol. Funct. Imaging"},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"537","DOI":"10.1007\/s11517-012-1022-5","article-title":"Risk stratification of cardiac autonomic neuropathy based on multi-lag tone-entropy","volume":"51","author":"Karmakar","year":"2013","journal-title":"Med. Biol. Eng. Comput."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"149","DOI":"10.1081\/CEH-48742","article-title":"Fractal and complexity measures of heart rate variability","volume":"27","author":"Perkiomaki","year":"2005","journal-title":"Clin. Exp. Hyp."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"2079","DOI":"10.1161\/01.CIR.100.20.2079","article-title":"Altered complexity and correlation properties of r-r interval dynamics before the spontaneous onset of paroxysmal atrial fibrillation","volume":"100","author":"Vikman","year":"1999","journal-title":"Circulation"},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"1005","DOI":"10.1016\/S0735-1097(96)00243-4","article-title":"Abnormalities in beat to beat complexity of heart rate dynamics in patients with a previous myocardial infarction","volume":"28","author":"Makikallio","year":"1996","journal-title":"J. Am. Coll. Cardiol."},{"key":"ref_31","doi-asserted-by":"crossref","unstructured":"Shi, B., Zhang, Y., Yuan, C., Wang, S., and Li, P. (2017). Entropy analysis of short-term heartbeat interval time series during regular walking. Entropy, 19.","DOI":"10.3390\/e19100568"},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"22","DOI":"10.1186\/s40101-016-0113-7","article-title":"The physiological basis and measurement of heart rate variability in humans","volume":"35","author":"Draghici","year":"2016","journal-title":"J. Physiol. Anthropol."}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/22\/10\/1077\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T10:13:26Z","timestamp":1760177606000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/22\/10\/1077"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,9,24]]},"references-count":32,"journal-issue":{"issue":"10","published-online":{"date-parts":[[2020,10]]}},"alternative-id":["e22101077"],"URL":"https:\/\/doi.org\/10.3390\/e22101077","relation":{},"ISSN":["1099-4300"],"issn-type":[{"value":"1099-4300","type":"electronic"}],"subject":[],"published":{"date-parts":[[2020,9,24]]}}}