{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,15]],"date-time":"2026-05-15T05:51:59Z","timestamp":1778824319991,"version":"3.51.4"},"reference-count":54,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2022,2,16]],"date-time":"2022-02-16T00:00:00Z","timestamp":1644969600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Bioengineering"],"abstract":"<jats:p>Background: Several methods have been proposed to estimate complexity in physiological time series observed at different time scales, with a particular focus on heart rate variability (HRV) series. In this frame, while several complexity quantifiers defined in the multiscale domain have already been investigated, the effectiveness of a multiscale Kolmogorov\u2013Sinai (K-S) entropy has not been evaluated yet for the characterization of heartbeat dynamics. Methods: The use of the algorithmic information content, which is estimated through an effective compression algorithm, is investigated to quantify multiscale partition-based K-S entropy on publicly available experimental HRV series gathered from young and elderly subjects undergoing a visual elicitation task (Fantasia). Moreover, publicly available HRV series gathered from healthy subjects, as well as patients with atrial fibrillation and congestive heart failure in unstructured conditions have been analyzed as well. Results: Elderly people are associated with a lower HRV complexity and a more predictable cardiovascular dynamics, with significantly lower partition-based K-S entropy than the young adults. Major differences between these groups occur at partitions greater than six. In case of partition cardinality greater than 5, patients with congestive heart failure show a minimal predictability, while atrial fibrillation shows a higher variability, and hence complexity, which is actually reduced by the time coarse-graining procedure. Conclusions: The proposed multiscale partition-based K-S entropy is a viable tool to investigate complex cardiovascular dynamics in different physiopathological states.<\/jats:p>","DOI":"10.3390\/bioengineering9020080","type":"journal-article","created":{"date-parts":[[2022,2,16]],"date-time":"2022-02-16T20:26:41Z","timestamp":1645043201000},"page":"80","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":7,"title":["A Multiscale Partition-Based Kolmogorov\u2013Sinai Entropy for the Complexity Assessment of Heartbeat Dynamics"],"prefix":"10.3390","volume":"9","author":[{"given":"Andrea","family":"Scarciglia","sequence":"first","affiliation":[{"name":"Bioengineering and Research Centre \u201cE. Piaggio\u201d, and Department of Information Engineering, School of Engineering, University of Pisa, 56122 Pisa, Italy"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9030-7601","authenticated-orcid":false,"given":"Vincenzo","family":"Catrambone","sequence":"additional","affiliation":[{"name":"Bioengineering and Research Centre \u201cE. Piaggio\u201d, and Department of Information Engineering, School of Engineering, University of Pisa, 56122 Pisa, Italy"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1421-6510","authenticated-orcid":false,"given":"Claudio","family":"Bonanno","sequence":"additional","affiliation":[{"name":"Department of Mathematics, University of Pisa, 56127 Pisa, Italy"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6574-1879","authenticated-orcid":false,"given":"Gaetano","family":"Valenza","sequence":"additional","affiliation":[{"name":"Bioengineering and Research Centre \u201cE. Piaggio\u201d, and Department of Information Engineering, School of Engineering, University of Pisa, 56122 Pisa, Italy"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2022,2,16]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"579","DOI":"10.1007\/BF01053745","article-title":"Embedology","volume":"65","author":"Sauer","year":"1991","journal-title":"J. Stat. Phys."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"189","DOI":"10.1016\/0167-2789(83)90298-1","article-title":"Measuring the strangeness of strange attractors","volume":"9","author":"Grassberger","year":"1983","journal-title":"Phys. D"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"346","DOI":"10.1103\/PhysRevLett.50.346","article-title":"Characterization of strange attractors","volume":"50","author":"Grassberger","year":"1983","journal-title":"Phys. Rev. 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