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Sample entropy, a complexity measure that quantifies the new pattern generation rate of time series, has been widely applied to physiological signal analysis. It can effectively reflect the pattern complexity of one-dimensional sequences, such as the information contained in amplitude or period features. However, the traditional method usually ignores the interaction between amplitude and period in time series, such as electroencephalogram (EEG) signals. To address this issue, in this study, we propose a new method to describe the pattern complexity of waveform in a two-dimensional space. In this method, the local peaks of the signals are first extracted, and the variation range and the duration time between the adjacent peaks are calculated as the instantaneous amplitude and period. Then the amplitude and period sequences are combined into a two-dimensional sequence to calculate the sample entropy based on the amplitude and period information. In addition, in order to avoid the influence of the different units in the two dimensions, we use the Jaccard distance to measure the similarity of the amplitude-period bi-vectors in the waveforms, which is different from the one-dimensional method. The Jaccard distance is defined as the ratio of the different area to the combined area of two rectangles containing the amplitude-period bi-vectors in the Cartesian coordinate system. To verify the effectiveness of the method, we construct five sets of simulative waveforms in which the numbers of patterns are completely equal in one-dimensional space of amplitude or period but the numbers in two-dimensional space are significantly different (P0.00001). Simulation results show that the two-dimensional sample entropy could effectively reflect the different complexities of the five signals (P0.00001), while the sample entropy in one-dimensional space of amplitude or period cannot do. The results indicate that compared with the one-dimensional sample entropy, the two-dimensional sample entropy is very effective to describe and distinguish the complexity of interactive patterns based on amplitude and period features in waveforms. The entropy is also used to analyze the resting state EEG signals between well-matched depression patient and healthy control groups. Signals in three separated frequency bands (Theta, Alpha, Beta) and ten brain regions (bilateral: frontal, central, parietal, temporal, occipital) are analyzed. Experimental results show that in the Alpha band and in the left parietal and occipital regions, the two-dimensional sample entropy in depression is significantly lower than that in the healthy group (P0.01), indicating the disability of depression patients in generation of various EEG patterns. These features might become potential biomarkers of depressions.
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Keywords:
- sample entropy /
- two-dimension /
- electroencephalogram /
- major depressive disorder
[1] Pincus S M 1991 Proc. Natl. Acad. Sci. USA 88 2297
[2] Richman J S, Moorman J R 2000 Am. J. Physiol.-Heart C. 278 2039
[3] Bruce E N, Bruce M C, Vennelaganti S 2009 J. Clin. Neurophysiol. 26 257
[4] Zhu L, Deng J, Wu J H, Zhou N R 2015 Acta Phys. Sin. 64 184302 (in Chinese) [朱莉, 邓娟, 吴建华, 周南润2015物理学报64 184302]
[5] Lei M, Meng G, Zhang W M, Sarkar N 2016 Acta Phys. Sin. 65 108701 (in Chinese) [雷敏, 孟光, 张文明, Nilanjan Sarkar 2016物理学报65 108701]
[6] Alcaraz R, Rieta J J 2010 Biomed. Signal. Proces. 5 1
[7] Kim D J, Jeong J, Chae J H, Park S, Kim S Y, Go H J, Paik I H, Kim K S, Choi B 2000 Psychiat. Res-Neuroim. 98 177
[8] Lee Y J, Zhu Y S, Xu Y H, Shen M F, Zhang H X, Thakor N V 2001 Clin. Neurophysiol. 112 1288
[9] Li Y J, Tong S B, Liu D, Gai Y, Wang X Y, Wang J J, Qiu Y H, Zhu Y S 2008 Clin. Neurophysiol. 119 1232
[10] Ahmadlou M, Adeli H, Adeli A 2012 Int. J. Psychophysiol. 85 206
[11] Bachmann M, Lass J, Suhhova A, Hinrikus H 2013 Comput. Math. Method. M. 2013 251638
[12] Zavala-Yoe R, Ramirez-Mendoza R, Cordero L M 2015 Springerplus 4 437
[13] Abasolo D, Hornero R, Espino P, Alvarez D, Poza J 2006 Physiol. Meas. 27 241
[14] Takahashi T, Cho R Y, Mizuno T, Kikuchi M, Murata T, Takahashi K, Wada Y 2010 Neuroimage 51 173
[15] Okazaki R, Takahashi T, Ueno K, Takahashi K, Higashima M, Wada Y 2013 J. Affect. Disorders 150 389
[16] Li X L, Li D, Liang Z H, Voss L J, Sleigh J W 2008 Clin. Neurophysiol. 119 2465
[17] Zhang T, Chen W Z, Li M Y 2016 Acta Phys. Sin. 65 038703 (in Chinese) [张涛, 陈万忠, 李明阳2016物理学报65 038703]
[18] Lin P F, Tsao J, Lo M T, Lin C, Chang Y C 2015 Entropy 17 560
[19] Ahmed M U, Mandic D P 2011 Phys. Rev. E 84 061918
[20] Orzechowska A, Filip M, Galecki P 2015 Med. Sci. Monitor 21 3643
[21] Pampallona S, Bollini P, Tibaldi G, Kupelnick B, Munizza C 2004 Arch. Gen. Psychiat. 61 714
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[1] Pincus S M 1991 Proc. Natl. Acad. Sci. USA 88 2297
[2] Richman J S, Moorman J R 2000 Am. J. Physiol.-Heart C. 278 2039
[3] Bruce E N, Bruce M C, Vennelaganti S 2009 J. Clin. Neurophysiol. 26 257
[4] Zhu L, Deng J, Wu J H, Zhou N R 2015 Acta Phys. Sin. 64 184302 (in Chinese) [朱莉, 邓娟, 吴建华, 周南润2015物理学报64 184302]
[5] Lei M, Meng G, Zhang W M, Sarkar N 2016 Acta Phys. Sin. 65 108701 (in Chinese) [雷敏, 孟光, 张文明, Nilanjan Sarkar 2016物理学报65 108701]
[6] Alcaraz R, Rieta J J 2010 Biomed. Signal. Proces. 5 1
[7] Kim D J, Jeong J, Chae J H, Park S, Kim S Y, Go H J, Paik I H, Kim K S, Choi B 2000 Psychiat. Res-Neuroim. 98 177
[8] Lee Y J, Zhu Y S, Xu Y H, Shen M F, Zhang H X, Thakor N V 2001 Clin. Neurophysiol. 112 1288
[9] Li Y J, Tong S B, Liu D, Gai Y, Wang X Y, Wang J J, Qiu Y H, Zhu Y S 2008 Clin. Neurophysiol. 119 1232
[10] Ahmadlou M, Adeli H, Adeli A 2012 Int. J. Psychophysiol. 85 206
[11] Bachmann M, Lass J, Suhhova A, Hinrikus H 2013 Comput. Math. Method. M. 2013 251638
[12] Zavala-Yoe R, Ramirez-Mendoza R, Cordero L M 2015 Springerplus 4 437
[13] Abasolo D, Hornero R, Espino P, Alvarez D, Poza J 2006 Physiol. Meas. 27 241
[14] Takahashi T, Cho R Y, Mizuno T, Kikuchi M, Murata T, Takahashi K, Wada Y 2010 Neuroimage 51 173
[15] Okazaki R, Takahashi T, Ueno K, Takahashi K, Higashima M, Wada Y 2013 J. Affect. Disorders 150 389
[16] Li X L, Li D, Liang Z H, Voss L J, Sleigh J W 2008 Clin. Neurophysiol. 119 2465
[17] Zhang T, Chen W Z, Li M Y 2016 Acta Phys. Sin. 65 038703 (in Chinese) [张涛, 陈万忠, 李明阳2016物理学报65 038703]
[18] Lin P F, Tsao J, Lo M T, Lin C, Chang Y C 2015 Entropy 17 560
[19] Ahmed M U, Mandic D P 2011 Phys. Rev. E 84 061918
[20] Orzechowska A, Filip M, Galecki P 2015 Med. Sci. Monitor 21 3643
[21] Pampallona S, Bollini P, Tibaldi G, Kupelnick B, Munizza C 2004 Arch. Gen. Psychiat. 61 714
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