{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T03:39:51Z","timestamp":1760240391660,"version":"build-2065373602"},"reference-count":37,"publisher":"MDPI AG","issue":"6","license":[{"start":{"date-parts":[[2019,5,31]],"date-time":"2019-05-31T00:00:00Z","timestamp":1559260800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>Multiscale entropy (MSE) provides information-domain measures of the systems\u2019 complexity. The increasing interest in MSE of the cardiovascular system lies in the possibility of detecting interactions with other regulatory systems, as higher neural networks. However, most of the MSE studies considered the heart-rate (HR) series only and a limited number of scales: actually, an integrated approach investigating HR and blood-pressure (BP) entropies and cross-entropy over the range of scales of traditional spectral analyses is missing. Therefore, we aim to highlight influences of higher brain centers and of the autonomic control on multiscale entropy and cross-entropy of HR and BP over a broad range of scales, by comparing different behavioral states over 24 h and by evaluating the influence of hypertension, which reduces the autonomic control of BP. From 24-h BP recordings in eight normotensive and eight hypertensive participants, we selected subperiods during daytime activities and nighttime sleep. In each subperiod, we derived a series of 16,384 consecutive beats for systolic BP (SBP), diastolic BP (DBP), and pulse interval (PI). We applied a modified MSE method to obtain robust estimates up to time scales of 334 s, covering the traditional frequency bands of spectral analysis, for three embedding dimensions and compared groups (rank-sum test) and conditions (signed-rank test) at each scale. Results demonstrated night-and-day differences at scales associable with modulations in vagal activity, in respiratory mechanics, and in local vascular regulation, and reduced SBP-PI cross-entropy in hypertension, possibly representing a loss of complexity due to an impaired baroreflex sensitivity.<\/jats:p>","DOI":"10.3390\/e21060550","type":"journal-article","created":{"date-parts":[[2019,5,31]],"date-time":"2019-05-31T11:59:56Z","timestamp":1559303996000},"page":"550","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":21,"title":["Information-Domain Analysis of Cardiovascular Complexity: Night and Day Modulations of Entropy and the Effects of Hypertension"],"prefix":"10.3390","volume":"21","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-8775-2605","authenticated-orcid":false,"given":"Paolo","family":"Castiglioni","sequence":"first","affiliation":[{"name":"IRCCS Fondazione Don Carlo Gnocchi, 20148 Milan, Italy"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9402-7439","authenticated-orcid":false,"given":"Gianfranco","family":"Parati","sequence":"additional","affiliation":[{"name":"Istituto Auxologico Italiano, IRCCS, Department of Cardiovascular, Neural and Metabolic Sciences, S.Luca Hospital, 20149 Milan, Italy"},{"name":"Department of Medicine and Surgery, University of Milano-Bicocca, 20126 Milan, Italy"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8924-8234","authenticated-orcid":false,"given":"Andrea","family":"Faini","sequence":"additional","affiliation":[{"name":"Istituto Auxologico Italiano, IRCCS, Department of Cardiovascular, Neural and Metabolic Sciences, S.Luca Hospital, 20149 Milan, Italy"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2019,5,31]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"335","DOI":"10.1007\/BF01619355","article-title":"A regularity statistic for medical data analysis","volume":"7","author":"Pincus","year":"1991","journal-title":"J. Clin. Monit."},{"key":"ref_2","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_3","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_4","doi-asserted-by":"crossref","first-page":"14100","DOI":"10.1073\/pnas.93.24.14100","article-title":"Older males secrete luteinizing hormone and testosterone more irregularly, and jointly more asynchronously, than younger males","volume":"93","author":"Pincus","year":"1996","journal-title":"Proc. Natl. Acad. Sci. USA"},{"key":"ref_5","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_6","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_7","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_8","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":"Physica A"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"817","DOI":"10.1088\/0967-3334\/29\/7\/010","article-title":"Reduced short-term complexity of heart rate and blood pressure dynamics in patients with diabetes mellitus type 1: Multiscale entropy analysis","volume":"29","author":"Trunkvalterova","year":"2008","journal-title":"Physiol. Meas."},{"key":"ref_10","doi-asserted-by":"crossref","unstructured":"Watanabe, E., Kiyono, K., Hayano, J., Yamamoto, Y., Inamasu, J., Yamamoto, M., Ichikawa, T., Sobue, Y., Harada, M., and Ozaki, Y. (2015). Multiscale Entropy of the Heart Rate Variability for the Prediction of an Ischemic Stroke in Patients with Permanent Atrial Fibrillation. PLoS ONE, 10.","DOI":"10.1371\/journal.pone.0137144"},{"key":"ref_11","doi-asserted-by":"crossref","unstructured":"Ho, Y.-L., Lin, C., Lin, Y.-H., and Lo, M.-T. (2011). The Prognostic Value of Non-Linear Analysis of Heart Rate Variability in Patients with Congestive Heart Failure\u2014A Pilot Study of Multiscale Entropy. PLoS ONE, 6.","DOI":"10.1371\/journal.pone.0018699"},{"key":"ref_12","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_13","doi-asserted-by":"crossref","first-page":"231","DOI":"10.3390\/e17010231","article-title":"Multiscale Entropy Analysis of Heart Rate Variability for Assessing the Severity of Sleep Disordered Breathing","volume":"17","author":"Pan","year":"2015","journal-title":"Entropy"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"17552","DOI":"10.1038\/srep17552","article-title":"Complexity of Heart Rate Variability Can Predict Stroke-In-Evolution in Acute Ischemic Stroke Patients","volume":"5","author":"Chen","year":"2015","journal-title":"Sci. Rep."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"11473","DOI":"10.1038\/s41598-018-29961-y","article-title":"Impact of Supratentorial Cerebral Hemorrhage on the Complexity of Heart Rate Variability in Acute Stroke","volume":"8","author":"Chen","year":"2018","journal-title":"Sci. Rep."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"95","DOI":"10.1136\/jnnp-2014-308389","article-title":"Complexity of heart rate variability predicts outcome in intensive care unit admitted patients with acute stroke","volume":"86","author":"Tang","year":"2015","journal-title":"J. Neurol. Neurosurg. Psychiatry"},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"17","DOI":"10.1097\/SHK.0b013e318164e4d0","article-title":"Heart Rate Multiscale Entropy at Three Hours Predicts Hospital Mortality in 3,154 Trauma Patients","volume":"30","author":"Norris","year":"2008","journal-title":"Shock"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"18003","DOI":"10.1209\/0295-5075\/107\/18003","article-title":"Mood states modulate complexity in heartbeat dynamics: A multiscale entropy analysis","volume":"107","author":"Valenza","year":"2014","journal-title":"EPL"},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"1","DOI":"10.3389\/fneur.2018.00769","article-title":"A Heartbeat Away From Consciousness: Heart Rate Variability Entropy Can Discriminate Disorders of Consciousness and Is Correlated With Resting-State fMRI Brain Connectivity of the Central Autonomic Network","volume":"9","author":"Riganello","year":"2018","journal-title":"Front. Neurol."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"R150","DOI":"10.1152\/ajpregu.00076.2016","article-title":"Multiscale entropy analysis of heart rate variability in heart failure, hypertensive, and sinoaortic-denervated rats: classical and refined approaches","volume":"311","author":"Silva","year":"2016","journal-title":"Am. J. Physiol. Regul. Integr. Comp. Physiol."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"e560","DOI":"10.1097\/CCM.0000000000000299","article-title":"A Multiscale Entropy-Based Tool for Scoring Severity of Systemic Inflammation","volume":"42","author":"Vandendriessche","year":"2014","journal-title":"Crit. Care Med."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"237","DOI":"10.1016\/j.artmed.2007.07.012","article-title":"Multiscale analysis of short term heart beat interval, arterial blood pressure, and instantaneous lung volume time series","volume":"41","author":"Angelini","year":"2007","journal-title":"Artif. Intell. Med."},{"key":"ref_23","doi-asserted-by":"crossref","unstructured":"Castiglioni, P., Coruzzi, P., Bini, M., Parati, G., and Faini, A. (2017). Multiscale Sample Entropy of Cardiovascular Signals: Does the Choice between Fixed- or Varying-Tolerance among Scales Influence Its Evaluation and Interpretation?. Entropy, 19.","DOI":"10.3390\/e19110590"},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"1425","DOI":"10.1088\/0967-3334\/32\/9\/006","article-title":"The effect of orthostatic stress on multiscale entropy of heart rate and blood pressure","volume":"32","author":"Turianikova","year":"2011","journal-title":"Physiol. Meas."},{"key":"ref_25","unstructured":"(1996). Heart rate variability: Standards of measurement, physiological interpretation and clinical use. Task Force of the European Society of Cardiology and the North American Society of Pacing and Electrophysiology. Circulation, 93, 1043\u20131065."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"1232","DOI":"10.1038\/s41598-018-37970-0","article-title":"Patterns of cardiovascular variability after long-term sino-aortic denervation in unanesthetized adult rats","volume":"9","author":"Radaelli","year":"2019","journal-title":"Sci. Rep."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"1","DOI":"10.3389\/fphys.2019.00477","article-title":"Closed-Loop Cardiovascular Interactions and the Baroreflex Cardiac Arm: Modulations over the 24 Hours and the Effect of Hypertension","volume":"10","author":"Parati","year":"2019","journal-title":"Front. Physiol."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"158","DOI":"10.1016\/j.physa.2006.10.077","article-title":"Revisiting sample entropy analysis","volume":"376","author":"Govindan","year":"2007","journal-title":"Physica A"},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"R1-38","DOI":"10.1088\/0967-3334\/23\/1\/201","article-title":"Fractal characterization of complexity in temporal physiological signals","volume":"23","author":"Eke","year":"2002","journal-title":"Physiol. Meas."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"80","DOI":"10.2307\/3001968","article-title":"Individual Comparisons by Ranking Methods","volume":"1","author":"Wilcoxon","year":"1945","journal-title":"Biometr. Bull."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"289","DOI":"10.1111\/j.2517-6161.1995.tb02031.x","article-title":"Controlling the False Discovery Rate: A Practical and Powerful Approach to Multiple Testing","volume":"57","author":"Benjamini","year":"1995","journal-title":"J. R. Stat. Soc. Ser. B Stat. Methodol."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"755","DOI":"10.1088\/0967-3334\/36\/4\/755","article-title":"Limits of permutation-based entropies in assessing complexity of short heart period variability","volume":"36","author":"Porta","year":"2015","journal-title":"Physiol. Meas."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"17","DOI":"10.1088\/0967-3334\/34\/1\/17","article-title":"K-nearest-neighbor conditional entropy approach for the assessment of the short-term complexity of cardiovascular control","volume":"34","author":"Porta","year":"2013","journal-title":"Physiol. Meas."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"352","DOI":"10.1007\/BF02441589","article-title":"Relationships between short-term blood-pressure fluctuations and heart-rate variability in resting subjects. I: A spectral analysis approach","volume":"23","author":"Karemaker","year":"1985","journal-title":"Med. Biol. Eng. Comput."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"556","DOI":"10.1161\/01.HYP.24.5.556","article-title":"Cardiovascular autonomic modulation in essential hypertension. Effect of tilting","volume":"24","author":"Radaelli","year":"1994","journal-title":"Hypertension"},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"129","DOI":"10.1042\/cs0970129","article-title":"Broad-band spectral analysis of 24 h continuous finger blood pressure: comparison with intra-arterial recordings","volume":"97","author":"Castiglioni","year":"1999","journal-title":"Clin. Sci."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"391","DOI":"10.1042\/cs0970391","article-title":"Pulse rate variability is not a surrogate for heart rate variability","volume":"97","author":"Constant","year":"1999","journal-title":"Clin. Sci."}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/21\/6\/550\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T12:55:03Z","timestamp":1760187303000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/21\/6\/550"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,5,31]]},"references-count":37,"journal-issue":{"issue":"6","published-online":{"date-parts":[[2019,6]]}},"alternative-id":["e21060550"],"URL":"https:\/\/doi.org\/10.3390\/e21060550","relation":{},"ISSN":["1099-4300"],"issn-type":[{"type":"electronic","value":"1099-4300"}],"subject":[],"published":{"date-parts":[[2019,5,31]]}}}