Multiscale entropy analysis of biological signals

Physical Review E - Statistical, Nonlinear, and Soft Matter Physics

Volumn 71, Issue 2, 2005, 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

CHIRAL; DEFECT STRUCTURES; SPLAY; SUSPENDED FILMS;

CRYSTAL DEFECTS; CRYSTAL ORIENTATION; DISTORTION (WAVES); ELASTICITY; IONS; LAPLACE TRANSFORMS; LIGHT POLARIZATION; MATHEMATICAL MODELS; SUSPENSIONS (FLUIDS); THIN FILMS; VISCOSITY OF LIQUIDS;

SMECTIC LIQUID CRYSTALS;

ADULT; AGED; ALGORITHM; ATRIAL FIBRILLATION; BIOLOGICAL MODEL; CHEMICAL MODEL; CLINICAL TRIAL; COMPUTER ASSISTED DIAGNOSIS; COMPUTER SIMULATION; CONTROLLED CLINICAL TRIAL; CONTROLLED STUDY; DNA SEQUENCE; ELECTROCARDIOGRAPHY; ENTROPY; FEMALE; HEART FAILURE; HUMAN; MALE; MIDDLE AGED; PROCEDURES; REPRODUCIBILITY; SENSITIVITY AND SPECIFICITY;

ADULT; AGED; ALGORITHMS; ATRIAL FIBRILLATION; COMPUTER SIMULATION; DIAGNOSIS, COMPUTER-ASSISTED; ELECTROCARDIOGRAPHY, AMBULATORY; ENTROPY; FEMALE; HEART FAILURE; HUMANS; MALE; MIDDLE AGED; MODELS, BIOLOGICAL; MODELS, CHEMICAL; REPRODUCIBILITY OF RESULTS; SENSITIVITY AND SPECIFICITY; SEQUENCE ANALYSIS, DNA;

EID: 41349087285     PISSN: 15393755     EISSN: 15502376     Source Type: Journal    
DOI: 10.1103/PhysRevE.71.021906     Document Type: Article

References (49)

1. F. Takens, in Dynamical Systems and Turbulence, edited by D. A. Rand and L. S. Young. Lecture Notes in Mathematics Vol. 898 (Springer, Berlin, 1981), p. 366.
2. J.-P. Eckmann and D. Ruelle, Rev. Mod. Phys. 57, 617 (1985).
3. J. Theiler, S. Eubank, A. Longtin, B. Galdrikian, and J. D. Farmer, Physica D 58, 77 (1992).
4. S. M. Pincus, Ann. N.Y. Acad. Sci. 954, 245 (2001), and references therein.
5. P. Grassberger in Information Dynamics, edited by H. Atmanspacher and H. Scheingraber (Plenum, New York, 1991), p. 15.
6. B.-Y. Yaneer, Dynamics of Complex Systems (Addison-Wesley, Reading, Massachusetts, 1997).
7. M. Costa, A. L. Goldberger, and C.-K. Peng, Phys. Rev. Lett. 89, 068102 (2002).
8. M. Costa, A. L. Goldberger, and C.-K. Peng, Comput. Cardiol. 29, 137 (2002).
9. M. Costa and J. A. Healey, Comput. Cardiol. 30, 705 (2003).
10. M. Costa, A. L. Goldberger, and C.-K. Peng, Phys. Rev. Lett. 92, 089804 (2004).
11. M. Costa, C.-K. Peng, A. L. Goldberger, and J. M. Hausdorff, Physica A 330, 53 (2003).
12. C. E. Shannon, Bell Syst. Tech. J. 27, 379 (1948).
13. R. Shaw, Z. Naturforsch. A 36, 80 (1981).
14. P. Grassberger and I. Procaccia, Physica D 56, 189 (1983).
15. P. Grassberger and I. Procaccia, Phys. Rev. A 28, 2591 (1983).
16. F. Takens, in Proceedings of the 13th Colóquio Brasileiro de Matemática (Instituto de Matemática Pura e Aplicada, Rio de Janeiro, 1983).
17. S. M. Pincus, Proc. Nad. Acad. Sci. U.S.A. 88, 2297 (1991).
18. T. M. Cover and J. A. Thomas, Elements of Information Theory (Wiley, New York, 1991), p. 64.
19. S. M. Pincus, I. M. Gladstone, and R. A. Ehrenkranz, J. Clin. Monit. 7, 335 (1991).
20. J. S. Richman and J. R. Moorman, Am. J. Physiol. 278, H2039 (2000).
21. P. Grassberger, T. Schreiber, and C. Schaffrath, Int. J. Bifurcation Chaos Appl. Sci. Eng. 1, 521 (1991).
22. D. P. Feldman and J. P. Cnitchfield, Phys. Lett. A 238, 244 (1998).
23. Y.-C. Zhang, J. Phys. I 1, 971 (1991).
24. A. L. Goldberger, C.-K. Peng, and L. A. Lipsitz, Neurobiol. Aging 23, 23 (2002).
25. A. J. Mandell and M. F. Shlesinger in The Ubiquity of Chaos, edited by S. Krasner (American Association for the Advancement of Science, Washington, D.C., 1990), p. 35.
26. M. P. Paulus, M. A. Geyer, L. H. Gold, and A. J. Mandell, Proc. Natl. Acad. Sci. U.S.A. 87, 723 (1990).
27. H. C. Fogedby, J. Stat. Phys. 69, 411 (1992).
28. V. V. Nikulin and T. Brismar, Phys. Rev. Lett. 92, 089803 (2004).
29. J. E. Mietus, C.-K. Peng, I. Henry, R. L. Goldsmith, and A. L. Goldberger, Heart 88, 378 (2002).
30. The New York Heart Association functional classification is used to characterize patients' limitations from left ventricular failure. Subjects assigned to class I can perform ordinary physical exercise with no limitations. Subjects assigned to class II are comfortable at rest but experience fatigue or shortness of breath when performing ordinary physical exercise. Class III subjects are also comfortable at rest but their ability to exercise is markedly reduced. Class IV comprises those subjects who have symptoms at rest.
31. Time series derived from subjects with atrial fibrillation have statistical properties similar to those of white noise on shorter time scales (≤200 s). For more details, see [45-47].
32. K. K. L. Ho, G. B. Moody, C.-K. Peng, J. E. Mietus, M. G. Larson, D. Levy, and A. L. Goldberger, Circulation 96, 842 (1997).
33. A. Bunde, S. Havlin, J. W. Kantelhardt, T. Penzel, J.-H. Peter, and K. Voigt, Phys. Rev. Lett. 85, 3736 (2000).
34. T. Cavalier-Smith, in The Evolution of Genome Size, edited by T. Cavalier-Smith (Wiley, Chichester, U.K., 1985).
35. J. S. Mattick, BioEssays 25, 930 (2003).
36. J. S. Mattick, EMBO Rep. 2, 986 (2001).
37. C.-K. Peng, S. V. Buldyrev, A. L. Goldberger, S. Havlin, F. Sciortino, M. Simons, and H. E. Stanley, Nature (London) 356, 168 (1992).
38. C.-K. Peng, S. V. Buldyrev, A. L. Goldberger, S. Havlin, R. N. Mantegna, M. Simons, and H. E. Stanley, Physica A 221, 180 (1995).
39. S. V. Buldyrev, A. L. Goldberger, S. Havlin, R. N. Mantegna, M. E. Matsa, C.-K. Peng, M. Simons, and H. E. Stanley, Phys. Rev. E 51, 5084 (1995).
40. B. Audit, C. Thermes, C. Vaillant, Y. d'Aubenton-Carafa, J. F. Muzy, and A. Arneodo, Phys. Rev. Lett. 86, 2471 (2001).
41. B. Audit, C. Vaillant, A. Arneodo, Y. d'Aubenton-Carafa, and C. Thermes, J. Mol. Biol. 316, 903 (2002).
42. L. A. Lettice et al., Proc. Natl. Acad. Sci. U.S.A. 99, 7548 (2002).
43. M. A. Nobrega, I. Ovcharenko, V. Afzal, and E. M. Rubin, Science 302, 413 (2003).
44. i=log N, where N is the total number of data points. Therefore, entropy monotonically increases as the number of symbols increases.
45. J. Hayano, F. Yamasaki, S. Sakata, A. Okada, S. Mukai, and T. Fujinami, Am. J. Physiol. 273, H2811 (1997).
46. W. Zeng and L. Glass, Phys. Rev. E 54, 1779 (1996).
47. 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. Rienzo, G. Manda, G. Parati, A. Pedotti, and A. Zanchetti (Ios Press Inc., Amsterdam, 1999), p. 91.
48. D. E. Lake and R. J. Moorman (private communication).
49. D. E. Lake, J. S. Richman, M. P. Griffin, and J. R. Moorman, Am. J. Physiol. 283, R789 (2002).