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The Shannon entropy Hk in symbolic dynamics analysis of time series has less data demand and can be complemented easily, and therefore is applied to heart rate variability (HRV) analysis. However, the criterion has not been established as to the parameter α, which is used during the transformation into symbols. Like all other physiological signals, great differences between individuals as well as nonstationarity are usual in HRV. Therefore, to achieve a robust and consistent analysis, the parameter α should be considered together with the mean and standard error of the series. In this paper, the integrative effects on Hk of the three parameters were studied firstly in simulation time series, and it was suggested that under certain conditions, the clusters of Hk approach a convergent upper boundary named Hk-up, which reflects the intrinsic dynamics of the time series. Then, in the heart beat interval series analysis of 15 subjects, the abilities of Hk-up to alleviate the impacts brought by both difference between individuals and nonstationarity were testified.
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Keywords:
- symbolic dynamics /
- entropy /
- heart rate variability
[1] Camm A J, Malik M, Bigger J T, Breithardt G, Cerutti S, Cohen R J, Coumel P, Fallen E L, Kennedy H L, Kleiger R E, Lombardi F, Malliani A, Moss A J, Rottman J N, Schmidt G, Schwartz P J, Singer D H 1996 Eur. Heart J. 17 354
[2] Kleiger R E, Stein P K, Bigger J T 2005 A. N. E. 10 88
[3] Ivanov P C, Chen Z, Hu K, Stanley H E 2004 Physica A 344 685
[4] Kleiger R E, Miller J P, Bigger J T, Moss A J 1987 Am. J. Cardiol. 59 256
[5] Malik M, Farell T, Camm A J 1990 Am. J. Cardiol. 66 1049
[6] Huikuri H V, Makikallio T H, Airaksinen K E J, Seppanen T, Puukka P, Raiha I J, Sourander L B 1998 Circulation 97 2031
[7] Stein P K, Kleiger R E 1999 Annu. Rev. Med. 50 249
[8] Zhuang J J, Ning X B, Zou M, Sun B, Yang X 2008 Acta Phys. Sin. 57 2805 (in Chinese) [庄建军、宁新宝、邹 鸣、孙 飙、杨 希 2008 物理学报 57 2805]
[9] Li C, Tang D K, Fang Y, Sun J T, Ding G H, Poon C S, Wu G Q 2009 Acta Phys. Sin. 58 1348 (in Chinese) [李 程、汤大侃、方 勇、孙锦涛、丁光宏、Poon C S、吴国强 2009 物理学报 58 1348]
[10] Ning X B, Bian C H, Wang J, Chen Y 2006 Chin. Sci. Bull. 51 385
[11] Wessel N, Riedl M, Kurths J 2009 Chaos 19 028508
[12] Kurths J, Voss A, Saparin P, Witt A, Kleiner H J, Wessel N 1995 Chaos 5 88
[13] Wessel N, Ziehmann C, Kurths J, Meyerfeldt U, Schirdewan A, Voss A 2000 Phys. Rev. E 61 733
[14] Liu X F, Yu W L 2008 Acta Phys. Sin. 57 2587 (in Chinese) [刘小峰、俞文莉 2008 物理学报 57 2587]
[15] Li J, Ning X B, Wu W, Ma X F 2005 Chin. Phys. 14 2428
[16] Bian C H, Ma Q L, Si J F, Wu X H, Shao J, Ning X B, Wang D J 2009 Chin.Sci. Bull. 54 4610
[17] Huang X L, Cui S Z, Ning X B, Bian C H 2009 Acta Phys. Sin. 58 8160 (in Chinese) [黄晓林、崔胜忠、宁新宝、卞春华 2009 物理学报 58 8160]
[18] Kobayashi M, Musha T 1982 IEEE Trans. Biomed. Eng. 29 456
[19] Peng C K, Havlin S, Stanley H E, Goldberger A L 1995 Chaos 5 82
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[1] Camm A J, Malik M, Bigger J T, Breithardt G, Cerutti S, Cohen R J, Coumel P, Fallen E L, Kennedy H L, Kleiger R E, Lombardi F, Malliani A, Moss A J, Rottman J N, Schmidt G, Schwartz P J, Singer D H 1996 Eur. Heart J. 17 354
[2] Kleiger R E, Stein P K, Bigger J T 2005 A. N. E. 10 88
[3] Ivanov P C, Chen Z, Hu K, Stanley H E 2004 Physica A 344 685
[4] Kleiger R E, Miller J P, Bigger J T, Moss A J 1987 Am. J. Cardiol. 59 256
[5] Malik M, Farell T, Camm A J 1990 Am. J. Cardiol. 66 1049
[6] Huikuri H V, Makikallio T H, Airaksinen K E J, Seppanen T, Puukka P, Raiha I J, Sourander L B 1998 Circulation 97 2031
[7] Stein P K, Kleiger R E 1999 Annu. Rev. Med. 50 249
[8] Zhuang J J, Ning X B, Zou M, Sun B, Yang X 2008 Acta Phys. Sin. 57 2805 (in Chinese) [庄建军、宁新宝、邹 鸣、孙 飙、杨 希 2008 物理学报 57 2805]
[9] Li C, Tang D K, Fang Y, Sun J T, Ding G H, Poon C S, Wu G Q 2009 Acta Phys. Sin. 58 1348 (in Chinese) [李 程、汤大侃、方 勇、孙锦涛、丁光宏、Poon C S、吴国强 2009 物理学报 58 1348]
[10] Ning X B, Bian C H, Wang J, Chen Y 2006 Chin. Sci. Bull. 51 385
[11] Wessel N, Riedl M, Kurths J 2009 Chaos 19 028508
[12] Kurths J, Voss A, Saparin P, Witt A, Kleiner H J, Wessel N 1995 Chaos 5 88
[13] Wessel N, Ziehmann C, Kurths J, Meyerfeldt U, Schirdewan A, Voss A 2000 Phys. Rev. E 61 733
[14] Liu X F, Yu W L 2008 Acta Phys. Sin. 57 2587 (in Chinese) [刘小峰、俞文莉 2008 物理学报 57 2587]
[15] Li J, Ning X B, Wu W, Ma X F 2005 Chin. Phys. 14 2428
[16] Bian C H, Ma Q L, Si J F, Wu X H, Shao J, Ning X B, Wang D J 2009 Chin.Sci. Bull. 54 4610
[17] Huang X L, Cui S Z, Ning X B, Bian C H 2009 Acta Phys. Sin. 58 8160 (in Chinese) [黄晓林、崔胜忠、宁新宝、卞春华 2009 物理学报 58 8160]
[18] Kobayashi M, Musha T 1982 IEEE Trans. Biomed. Eng. 29 456
[19] Peng C K, Havlin S, Stanley H E, Goldberger A L 1995 Chaos 5 82
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