Multiscale Entropy Analysis of Complex Physiologic Time Series

Physical Review Letters

Volumn 89, Issue 6, 2002, Pages

  Costa, Madalena ^a,b   Goldberger, Ary L ^a   Peng, C K ^a  

^a HARVARD MEDICAL SCHOOL   (United States)

^b UNIVERSITY OF LISBON   (Portugal)

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHMS; ASYMPTOTIC STABILITY; BIOELECTRIC POTENTIALS; BIOLOGICAL ORGANS; CARDIOVASCULAR SYSTEM; COMPUTER SIMULATION; DISEASES; PHYSIOLOGY; PROBABILITY DENSITY FUNCTION; RANDOM PROCESSES; TIME SERIES ANALYSIS; WHITE NOISE;

ATRIAL FIBRILLATION; CARDIAC ARRHYTHMIA; MULTISCALE ENTROPY ANALYSIS; PHYSIOLOGIC TIME SERIES;

STATISTICAL MECHANICS;

ALGORITHM; BIOLOGICAL MODEL; DISEASES; ENTROPY; HEART FAILURE; HEART RATE; HUMAN; PATHOLOGY; PATHOPHYSIOLOGY; PHYSIOLOGY; PROCEDURES; TIME;

ALGORITHMS; DISEASE; ENTROPY; HEART FAILURE; HEART RATE; HUMANS; MODELS, BIOLOGICAL; PATHOLOGY; PHYSIOLOGY; TIME FACTORS;

EID: 1842722362     PISSN: 00319007     EISSN: 10797114     Source Type: Journal    
DOI: 10.1103/PhysRevLett.89.068102     Document Type: Article

References (16)

1. S.M. Pincus, Ann. N.Y. Acad. Sci.ANYAA9 954, 245 (2001), and references therein.
2. A. Porta, S. Guzzetti, N. Montano, R. Furlan, M. Pagani, A. Malliani, and S. Cerutti, IEEE Trans. Biomed. Eng.10.1109/10.959324 48, 1282 (2001);
3. M. Palus, Physica (Amsterdam) 93D, 64 (1996);
4. N. Wessel, A. Schumann, A. Schirdewan, A. Voss, and J. Kurths, Lect. Notes Comput. Sci.LNCSD9 1933, 78 (2000).
5. A.L. Goldberger, C.-K. Peng, and L.A. Lipsitz, Neurobiol. Aging10.1016/S0197-4580(01)00266-4 23, 23 (2002).
6. J.S. Richman and J.R. Moorman, Am. J. Physiol. 278, H2039 (2000).
7. J. Hayano, F. Yamasaki, S. Sakata, A. Okada, S. Mukai, and T. Fujinami, Am. J. Physiol. 273, H2811 (1997).
8. W. Zeng and L. Glass, Phys. Rev. E 54, 1779 (1996).
9. R. Balocchi, C. Carpeggiani, L. Fronzoni, C.-K. Peng, C. Michelassi, J. Mietus, and A.L. Goldberger, in Methodology and Clinical Applications of Blood Pressure and Heart Rate Analysis, edited by M. Di Rienzo, G. Mancia, G. Parati, A. Pedotti, and A. Zanchetti (IOS Press, Amsterdam, 1999), pp.�91–96.
10. For deterministic periodic systems, the KS entropy is zero because any state depends only on the initial conditions. In contrast, this entropy measure is maximum for uncorrelated random processes, since each state is totally independent of the previous ones. J.-P. Eckmann and D. Ruelle, Rev. Mod. Phys.10.1103/RevModPhys.57.617 57, 617 (1985).
11. S.M. Pincus, Proc. Natl. Acad. Sci. U.S.A.PNASA6 88, 2297 (1991). Let (Formula presented) represent a time series of length (Formula presented). Consider the (Formula presented)-length vectors: (Formula presented) and the following definition for the distance between two vectors: (Formula presented). Let (Formula presented) represent the number of vectors (Formula presented) within (Formula presented) of (Formula presented). Therefore, (Formula presented) represents the probability that any vector (Formula presented) is within (Formula presented) of (Formula presented). Define (Formula presented). ApEn is a parameter defined as follows: (Formula presented). For finite (Formula presented), it is estimated by the statistics (Formula presented). Lower values of (Formula presented) reflect more regular time series while higher values are associated with less predictable (more complex) time series.
12. Y.-C. Zhang, J. Phys. I (France)JPGCE8 1, 971 (1991).
13. H.C. Fogedby, J. Stat. Phys. 69, 411 (1992).
14. The term “multiscale entropy” has been employed in a different context in the image processing literature. See, for example, J.-L. Starck, F. Murtagh, and A. Bijaoui, Image Processing and Data Analysis (Cambridge University Press, Cambridge, 1998).
15. MIT-BIH Normal Sinus Rhythm Database and BIDMC Congestive Heart Failure Database available at http://www.physionet.org/physiobank/database/#ecg.
16. A.L. Goldberger, L.A.N. Amaral, J.M. Hausdorff, P.?Ch. Ivanov, C.-K. Peng, and H.E. Stanley, Proc. Natl. Acad. Sci. U.S.A.PNASA6 99 (suppl. 1), 2466 (2002).