Multiscale entropy analysis of biological signals
Abstract
Traditional approaches to measuring the complexity of biological signals fail to account for the multiple time scales inherent in such time series. These algorithms have yielded contradictory findings when applied to real-world datasets obtained in health and disease states. We describe in detail the basis and implementation of the multiscale entropy (MSE) method. We extend and elaborate previous findings showing its applicability to the fluctuations of the human heartbeat under physiologic and pathologic conditions. The method consistently indicates a loss of complexity with aging, with an erratic cardiac arrhythmia (atrial fibrillation), and with a life-threatening syndrome (congestive heart failure). Further, these different conditions have distinct MSE curve profiles, suggesting diagnostic uses. The results support a general "complexity-loss" theory of aging and disease. We also apply the method to the analysis of coding and noncoding DNA sequences and find that the latter have higher multiscale entropy, consistent with the emerging view that so-called "junk DNA" sequences contain important biological information.
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MSE analysis has been used to provide insights into the complexity and periodicity of signals over a range of timescales since the method was proposed by Costa et at [31].
“MSE analysis has been used to provide insights into the complexity and periodicity of signals over a range of timescales since the method was proposed by Costa et at [31].”
From Predicting depressive symptom severity through individuals’ nearby Bluetooth device count data collected by mobile phones: preliminary longitudinal study (2021) · cites this paper as [31]
Cites
A Mathematical Theory of Communication
Shannon, C. E. (1948) · Bell System Technical Journal · doi:10.1002/j.1538-7305.1948.tb01338.x · Cited by 88,486 · see citing works
Elements of Information Theory
Cover, T. M., & Thomas, J. A. (2001) · Wiley eBooks · doi:10.1002/0471200611 · Cited by 37,139 · see citing works
Approximate entropy as a measure of system complexity.
Pincus, S. M. (1991) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.88.6.2297 · Cited by 5,811 · see citing works
Measuring the strangeness of strange attractors
Grassberger, P., & Procaccia, I. (1983) · Physica D Nonlinear Phenomena · doi:10.1016/0167-2789(83)90298-1 · Cited by 5,697 · see citing works
Ergodic theory of chaos and strange attractors
Eckmann, J., & Ruelle, D. P. (1985) · Reviews of Modern Physics · doi:10.1103/revmodphys.57.617 · Cited by 4,989 · see citing works
Testing for nonlinearity in time series: the method of surrogate data
Theiler, J. P., Eubank, S., Longtin, A., Galdrikian, B., & Farmer, J. D. (1992) · Physica D Nonlinear Phenomena · doi:10.1016/0167-2789(92)90102-s · Cited by 3,759 · see citing works
Multiscale Entropy Analysis of Complex Physiologic Time Series
Costa, M., Goldberger, A. L., & Peng, C.-K. (2002) · Physical Review Letters · doi:10.1103/physrevlett.89.068102 · Cited by 3,207 · see citing works
Self-citationDynamical Systems and Turbulence
Takens, F. (1981) · Medical Entomology and Zoology · Cited by 2,098 · see citing works
Estimation of the Kolmogorov entropy from a chaotic signal
Grassberger, P., & Procaccia, I. (1983) · Physical Review A · doi:10.1103/physreva.28.2591 · Cited by 1,456 · see citing works
Long-range correlations in nucleotide sequences
Peng, C., Buldyrev, S. V., Goldberger, A. L., Havlin, S., Sciortino, F., Simons, M., & Stanley, E. (1992) · Nature · doi:10.1038/356168a0 · Cited by 1,410 · see citing works
Self-citationWhat is physiologic complexity and how does it change with aging and disease?
Goldberger, A. L., Peng, C., & Lipsitz, L. A. (2002) · Neurobiology of Aging · doi:10.1016/s0197-4580(01)00266-4 · Cited by 875 · see citing works
Self-citationNon‐coding RNAs: the architects of eukaryotic complexity
Mattick, J. S. (2001) · EMBO Reports · doi:10.1093/embo-reports/kve230 · Cited by 848 · see citing works
(1998) · Choice Reviews Online · doi:10.5860/choice.35-6275a · Cited by 822 · see citing works
Strange Attractors, Chaotic Behavior, and Information Flow
Shaw, R. (1981) · Zeitschrift für Naturforschung A · doi:10.1515/zna-1981-0115 · Cited by 803 · see citing works
A regularity statistic for medical data analysis
Pincus, S. M., Gladstone, I. M., & Ehrenkranz, R. A. (1991) · Journal of Clinical Monitoring and Computing · doi:10.1007/bf01619355 · Cited by 785 · see citing works
Scanning Human Gene Deserts for Long-Range Enhancers
Nobrega, M. A., Ovcharenko, I., Afzal, V., & Rubin, E. M. (2003) · Science · doi:10.1126/science.1088328 · Cited by 608 · see citing works
Long-range correlation properties of coding and noncoding DNA sequences: GenBank analysis
Buldyrev, S. V., Goldberger, A. L., Havlin, S., Mantegna, R. N., Matsa, M. E., Peng, C., Simons, M., & Stanley, E. (1995) · Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics · doi:10.1103/physreve.51.5084 · Cited by 589 · see citing works
Self-citationChallenging the dogma: the hidden layer of non‐protein‐coding RNAs in complex organisms
Mattick, J. S. (2003) · BioEssays · doi:10.1002/bies.10332 · Cited by 568 · see citing works
Correlated and Uncorrelated Regions in Heart-Rate Fluctuations during Sleep
Armin Bunde, A., Havlin, S., Kantelhardt, J. W., Penzel, T., Peter, J.-H., & Voigt, K. (2000) · Physical Review Letters · doi:10.1103/physrevlett.85.3736 · Cited by 545 · see citing works
NONLINEAR TIME SEQUENCE ANALYSIS
Grassberger, P., Schreiber, T., & Schaffrath, C. (1991) · International Journal of Bifurcation and Chaos · doi:10.1142/s0218127491000403 · Cited by 534 · see citing works
Multiscale entropy analysis of human gait dynamics
Costa, M. D., Peng, C., Goldberger, A. L., & Hausdorff, J. M. (2003) · Physica A Statistical Mechanics and its Applications · doi:10.1016/j.physa.2003.08.022 · Cited by 508 · see citing works
Self-citationHo, K. K. L., Moody, G. B., Peng, C.-K., Mietus, J. E., Larson, M. G., Levy, D., & Goldberger, A. L. (1997) · Circulation · doi:10.1161/01.cir.96.3.842 · Cited by 489 · see citing works
Self-citationDisruption of a long-range cis-acting regulator for Shh causes preaxial polydactyly
Lettice, L. A., Horikoshi, T., Heaney, S. J. H., van Baren, M. J., van der Linde, H. C., Breedveld, G. J., Joosse, M., Akarsu, N. A., Oostra, B. A., Endo, N., et al. (2002) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.112212199 · Cited by 458 · see citing works
Measures of statistical complexity: Why?
Feldman, D. P., & Crutchfield, J. P. (1998) · Physics Letters A · doi:10.1016/s0375-9601(97)00855-4 · Cited by 438 · see citing works
Assessing Serial Irregularity and Its Implications for Health
Pincus, S. M. (2001) · Annals of the New York Academy of Sciences · doi:10.1111/j.1749-6632.2001.tb02755.x · Cited by 401 · see citing works
The pNNx files: re-examining a widely used heart rate variability measure
Mietus, J. E., Peng, C., Henry, I., Goldsmith, R. L., & Goldberger, A. L. (2002) · Heart · doi:10.1136/heart.88.4.378 · Cited by 263 · see citing works
Self-citationStatistical properties of DNA sequences
Peng, C., Buldyrev, S. V., Goldberger, A. L., et al. (1995) · Physica A Statistical Mechanics and its Applications · doi:10.1016/0378-4371(95)00247-5 · Cited by 173 · see citing works
Self-citationMultiscale entropy to distinguish physiologic and synthetic RR time series
Costa, M. D., Goldberger, A. L., & Peng, C. (2003) · Computers in cardiology · doi:10.1109/cic.2002.1166726 · Cited by 161 · see citing works
Self-citationComplexity and 1/f noise. A phase space approach
Zhang, Y. (1991) · Journal de Physique I · doi:10.1051/jp1:1991180 · Cited by 143 · see citing works
Long-Range Correlations in Genomic DNA: A Signature of the Nucleosomal Structure
Audit, B., Thermes, C., Vaillant, C., et al. (2001) · Physical Review Letters · doi:10.1103/physrevlett.86.2471 · Cited by 135 · see citing works
Comment on “Multiscale Entropy Analysis of Complex Physiologic Time Series”
Nikulin, V. V., & Brismar, T. (2004) · Physical Review Letters · doi:10.1103/physrevlett.92.089803 · Cited by 100 · see citing works
Audit, B., Vaillant, C., Arnéodo, A., d’Aubenton-Carafa, Y., & Thermes, C. (2002) · Journal of Molecular Biology · doi:10.1006/jmbi.2001.5363 · Cited by 95 · see citing works
Long-Range Correlations in Genomic DNA
Arnéodo, A., Audit, B., Muzy, J., et al. (2001) · Technische Universität Dortmund Eldorado (Technische Universität Dortmund) · doi:10.17877/de290r-6399 · Cited by 87 · see citing works
Paulus, M. P., Geyer, M. A., Gold, L. H., & Mandell, A. J. (1990) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.87.2.723 · Cited by 85 · see citing works
On the phase space approach to complexity
Fogedby, H. C. (1992) · Journal of Statistical Physics · doi:10.1007/bf01053799 · Cited by 81 · see citing works
Statistical properties of heartbeat intervals during atrial fibrillation
Zeng, W.-Z., & Glass, L. (1996) · Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics · doi:10.1103/physreve.54.1779 · Cited by 31 · see citing works
Costa, Goldberger, and Peng Reply:
Costa, M. D., Goldberger, A. L., & Peng, C. (2004) · Physical Review Letters · doi:10.1103/physrevlett.92.089804 · Cited by 25 · see citing works
Self-citationMethodology and clinical applications of blood pressure and heart rate analysis.
Rienzo, D. (1999) · PubMed · Cited by 12 · see citing works
Flagged first, then by citations
Cited by
Sorted by citations
Increased Brain Signal Variability Accompanies Lower Behavioral Variability in Development
McIntosh, A. R., Kovacevic, N., & Itier, R. J. (2008) · PLoS Computational Biology · doi:10.1371/journal.pcbi.1000106 · Cited by 431 · see citing works
Heart rate variability: are you using it properly? Standardisation checklist of procedures
Catai, A. M., Pastre, C. M., Godoy, M. F. D., Silva, E. D., Takahashi, A. C. D. M., & Vanderlei, L. C. M. (2020) · Brazilian Journal of Physical Therapy · doi:10.1016/j.bjpt.2019.02.006 · Cited by 423 · see citing works
Atypical EEG complexity in autism spectrum conditions: A multiscale entropy analysis
Catarino, A., Churches, O., Baron-Cohen, S., Andrade, A., & Ring, H. (2011) · Clinical Neurophysiology · doi:10.1016/j.clinph.2011.05.004 · Cited by 271 · see citing works
Ekstrom, A. D., Arnold, A. E. G. F., & Iaria, G. (2014) · Frontiers in Human Neuroscience · doi:10.3389/fnhum.2014.00803 · Cited by 263 · see citing works
On the use of approximate entropy and sample entropy with centre of pressure time-series
Montesinos, L., Castaldo, R., & Pecchia, L. (2018) · Journal of NeuroEngineering and Rehabilitation · doi:10.1186/s12984-018-0465-9 · Cited by 172 · see citing works
Ahmad, S., Tejuja, A., Newman, K. D., Zarychanski, R., & Seely, A. J. (2009) · Critical Care · doi:10.1186/cc8132 · Cited by 151 · see citing works
Fuentemilla, L., Barnes, G. R., Düzel, E., & Levine, B. (2014) · NeuroImage · doi:10.1016/j.neuroimage.2013.08.029 · Cited by 114 · see citing works
Nobukawa, S., Yamanishi, T., Kasakawa, S., Nishimura, H., Kikuchi, M., & Takahashi, T. (2020) · Frontiers in Psychiatry · doi:10.3389/fpsyt.2020.00255 · Cited by 89 · see citing works
Riganello, F., Larroque, S. K., Bahri, M. A., Heine, L., Martial, C., Carrière, M., Charland-Verville, V., Aubinet, C., Vanhaudenhuyse, A., Chatelle, C., et al. (2018) · Frontiers in Neurology · doi:10.3389/fneur.2018.00769 · Cited by 70 · see citing works
Dynamic entropy-based pattern learning to identify emotions from EEG signals across individuals
Lu, Y., Wang, M., Wu, W., Han, Y., Zhang, Q., & Chen, S. (2020) · Measurement · doi:10.1016/j.measurement.2019.107003 · Cited by 73 · see citing works
Zhang, Y., Folarin, A. A., Sun, S., Cummins, N., Ranjan, Y., Rashid, Z., Conde, P., Stewart, C., Laiou, P., Matcham, F., et al. (2021) · JMIR mHealth and uHealth · doi:10.2196/29840 · Cited by 68 · see citing works
Galaska, R., Makowiec, D., Dudkowska, A., Koprowski, A., Chlebus, K., Wdowczyk‐Szulc, J., & Rynkiewicz, A. (2008) · Annals of Noninvasive Electrocardiology · doi:10.1111/j.1542-474x.2008.00215.x · Cited by 49 · see citing works
Norris, P. R., Canter, J. A., Jenkins, J. M., Moore, J. H., Williams, A. E., & Morris, J. A. (2009) · Annals of Surgery · doi:10.1097/sla.0b013e3181b8fb1f · Cited by 40 · see citing works
Bertrand, J.-A., McIntosh, A. R., Postuma, R. B., Kovacevic, N., Latreille, V., Panisset, M., Chouinard, S., & Gagnon, J.-F. (2016) · Brain Connectivity · doi:10.1089/brain.2015.0390 · Cited by 36 · see citing works
Multi-Scale Permutation Entropy for Audio Deepfake Detection
Wang, C., He, J., Yi, J., Tao, J., Zhang, C. Y., & Zhang, X. (2024) · ICASSP 2024 - 2024 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP) · doi:10.1109/icassp48485.2024.10448095 · Cited by 31 · see citing works
Bauer, C. M., Kankaanpää, M. J., Meichtry, A., Rissanen, S. M., & Suni, J. H. (2019) · Journal of Electromyography and Kinesiology · doi:10.1016/j.jelekin.2019.06.008 · Cited by 24 · see citing works
Dreszer, J., Grochowski, M., Lewandowska, M., Nikadon, J., Gorgol, J., Bałaj, B., Finc, K., Duch, W., Kałamała, P., Chuderski, A., et al. (2020) · Human Brain Mapping · doi:10.1002/hbm.25162 · Cited by 23 · see citing works
Hierarchical fusion of visual and physiological signals for emotion recognition
Fang, Y., Rong, R., & Huang, J. (2021) · Multidimensional Systems and Signal Processing · doi:10.1007/s11045-021-00774-z · Cited by 17 · see citing works
Bouny, P., Arsac, L. M., Pratviel, Y., Boffet, A., Touré Cuq, E., & Deschodt-Arsac, V. (2022) · Brain Sciences · doi:10.3390/brainsci12060794 · Cited by 6 · see citing works
EEG complexity as a biomarker for autism spectrum disorder risk
Bosl, W., Tierney, A., Tager-Flusberg, H., & Nelson, C. (2011) · BMC Medicine · doi:10.1186/1741-7015-9-18 · Cited by 485 · see citing works
- Authors
- Costa, M., Goldberger, A. L., & Peng, C.-K.
- Affiliations
- Beth Israel Deaconess Medical Center (US)
- Venue
- Physical Review E
- Publisher
- American Physical Society (APS)
- Published
- 2005-02-18
- Volume
- 71
- Issue
- 2
- Pages
- 021906-021906
- ISSN
- 1539-3755 (ISSN-L)
- 1550-2376
- OpenAlex
- W2059851411
- Cited by
- 2,482
- References
- 38
- Citations by year
- 2026: 94 · 2025: 129 · 2024: 131 · 2023: 171 · 2022: 173 · 2021: 206 · 2020: 211 · 2019: 228 · 2018: 180 · 2017: 150 · 2016: 134 · 2015: 120 · 2014: 130 · 2013: 96 · 2012: 70
- FWCI
- 20.05
- Type
- journal article
- Language
- en
- Open access
- closed
- Locations
- Physical Review E (publishedVersion)
- PubMed (publishedVersion)
- Funders
- Centers for Disease Control and Prevention (H75-CCH119124)
- National Center for Research Resources (P41RR013622, P41 RR13622)
- Eunice Kennedy Shriver National Institute of Child Health and Human Development (R01HD039838, R01-HD39838)
- Topics
- Health Sciences › Medicine › Cardiology and Cardiovascular Medicine › Heart Rate Variability and Autonomic Control
- Social Sciences › Economics, Econometrics and Finance › Economics and Econometrics › Complex Systems and Time Series Analysis
- Life Sciences › Biochemistry, Genetics and Molecular Biology › Molecular Biology › Fractal and DNA sequence analysis
- Keywords
- multiscale entropy, heart rate variability, atrial fibrillation, congestive heart failure, aging, non-coding DNA, junk DNA, time series analysis
- MeSH terms
- Adult, Aged, Algorithms, Atrial Fibrillation, Computer Simulation, Diagnosis, Computer-Assisted, Female, Heart Failure, Humans, Male, Middle Aged, Models, Biological, Models, Chemical, Sensitivity and Specificity, Reproducibility of Results, Electrocardiography, Ambulatory, Sequence Analysis, DNA, Entropy
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