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Analysis of the human gait rhythm in Neurodegenerative disease: A multifractal approach using Multifractal detrended cross correlation analysis

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  • Chatterjee, Sucharita

Abstract

In this paper the human gait rhythm of the healthy individuals and the patients suffering from a neurological disorder, Amyotrophic lateral sclerosis (ALS) disease has been studied applying a non-linear technique, Multifractal detrended cross correlation analysis (MF-DXA). The autocorrelation and cross correlation of the stride-interval fluctuations between the left foot and the right foot were studied. The results obtained reflect the fact that the degree of multifractality (W) and the degree of correlation (γ) are greater for the Control group compared to the diseased group. It is evident that the gait pattern of an individual becomes less steady and temporarily more disorganized in neural diseases due to the neuronal deterioration. The results obtained from the autocorrelation study for the left and the right foot are almost identical. It was also observed that the study of the autocorrelation is not always enough to distinguish between the Controlled and the diseased group. The study of the cross correlation between the left and the right foot can then help to recognize the diseased group. The present analysis shows that the cross correlation between the stride-interval fluctuations between the left and the right foot was greater for the healthy individuals compared to the patients with neurodegenerative disease.

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  • Chatterjee, Sucharita, 2020. "Analysis of the human gait rhythm in Neurodegenerative disease: A multifractal approach using Multifractal detrended cross correlation analysis," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 540(C).
    • Handle: RePEc:eee:phsmap:v:540:y:2020:i:c:s0378437119317765
    DOI: 10.1016/j.physa.2019.123154
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    as
    1. Kar, Alpa & Chatterjee, Sucharita & Ghosh, Dipak, 2019. "Multifractal detrended cross correlation analysis of Land-surface temperature anomalies and Soil radon concentration," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 521(C), pages 236-247.
    2. Todd Zorick & Mark A Mandelkern, 2013. "Multifractal Detrended Fluctuation Analysis of Human EEG: Preliminary Investigation and Comparison with the Wavelet Transform Modulus Maxima Technique," PLOS ONE, Public Library of Science, vol. 8(7), pages 1-7, July.
    3. Yuan, Ying & Zhuang, Xin-tian & Liu, Zhi-ying, 2012. "Price–volume multifractal analysis and its application in Chinese stock markets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(12), pages 3484-3495.
    4. Wen-Jie Xie & Zhi-Qiang Jiang & Gao-Feng Gu & Xiong Xiong & Wei-Xing Zhou, 2015. "Joint multifractal analysis based on the partition function approach: Analytical analysis, numerical simulation and empirical application," Papers 1509.05952, arXiv.org.
    5. Buldyrev, S.V. & Dokholyan, N.V. & Goldberger, A.L. & Havlin, S. & Peng, C.-K. & Stanley, H.E. & Viswanathan, G.M., 1998. "Analysis of DNA sequences using methods of statistical physics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 249(1), pages 430-438.
    6. He, Ling-Yun & Chen, Shu-Peng, 2010. "Are developed and emerging agricultural futures markets multifractal? A comparative perspective," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(18), pages 3828-3836.
    7. Wang, Yudong & Wei, Yu & Wu, Chongfeng, 2010. "Cross-correlations between Chinese A-share and B-share markets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(23), pages 5468-5478.
    8. Chen, Shu-Peng & He, Ling-Yun, 2010. "Multifractal spectrum analysis of nonlinear dynamical mechanisms in China’s agricultural futures markets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(7), pages 1434-1444.
    9. Wang, Gang-Jin & Xie, Chi, 2013. "Cross-correlations between Renminbi and four major currencies in the Renminbi currency basket," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(6), pages 1418-1428.
    10. Ghosh, Dipak & Dutta, Srimonti & Chakraborty, Sayantan, 2014. "Multifractal detrended cross-correlation analysis for epileptic patient in seizure and seizure free status," Chaos, Solitons & Fractals, Elsevier, vol. 67(C), pages 1-10.
    11. Dutta, Srimonti & Ghosh, Dipak & Chatterjee, Sucharita, 2016. "Multifractal detrended Cross Correlation Analysis of Foreign Exchange and SENSEX fluctuation in Indian perspective," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 463(C), pages 188-201.
    12. Hausdorff, Jeffrey M. & Ashkenazy, Yosef & Peng, Chang-K. & Ivanov, Plamen Ch. & Stanley, H.Eugene & Goldberger, Ary L., 2001. "When human walking becomes random walking: fractal analysis and modeling of gait rhythm fluctuations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 302(1), pages 138-147.
    13. Zhi-Qiang Jiang & Wei-Xing Zhou, 2011. "Multifractal detrending moving average cross-correlation analysis," Papers 1103.2577, arXiv.org, revised Mar 2011.
    14. Zhuang, Xiaoyang & Wei, Yu & Zhang, Bangzheng, 2014. "Multifractal detrended cross-correlation analysis of carbon and crude oil markets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 399(C), pages 113-125.
    15. Blesić, S. & Milošević, S. & Stratimirović, Dj. & Ljubisavljević, M., 1999. "Detrended fluctuation analysis of time series of a firing fusimotor neuron," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 268(3), pages 275-282.
    16. Ma, Feng & Wei, Yu & Huang, Dengshi, 2013. "Multifractal detrended cross-correlation analysis between the Chinese stock market and surrounding stock markets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(7), pages 1659-1670.
    17. Dutta, Srimonti & Ghosh, Dipak & Samanta, Shukla, 2016. "Non linear approach to study the dynamics of neurodegenerative diseases by Multifractal Detrended Cross-correlation Analysis—A quantitative assessment on gait disease," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 448(C), pages 181-195.
    18. Yuan, Ying & Zhuang, Xin-tian & Jin, Xiu, 2009. "Measuring multifractality of stock price fluctuation using multifractal detrended fluctuation analysis," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 388(11), pages 2189-2197.
    19. Dutta, Srimonti & Ghosh, Dipak & Samanta, Shukla, 2014. "Multifractal detrended cross-correlation analysis of gold price and SENSEX," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 413(C), pages 195-204.
    20. Norouzzadeh, P. & Jafari, G.R., 2005. "Application of multifractal measures to Tehran price index," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 356(2), pages 609-627.
    21. Kantelhardt, Jan W. & Zschiegner, Stephan A. & Koscielny-Bunde, Eva & Havlin, Shlomo & Bunde, Armin & Stanley, H.Eugene, 2002. "Multifractal detrended fluctuation analysis of nonstationary time series," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 316(1), pages 87-114.
    22. Longfeng Zhao & Wei Li & Andrea Fenu & Boris Podobnik & Yougui Wang & H. Eugene Stanley, 2017. "The q-dependent detrended cross-correlation analysis of stock market," Papers 1705.01406, arXiv.org, revised Jun 2017.
    23. Wei-Xing Zhou, 2008. "Multifractal detrended cross-correlation analysis for two nonstationary signals," Papers 0803.2773, arXiv.org.
    24. Kantelhardt, Jan W. & Rybski, Diego & Zschiegner, Stephan A. & Braun, Peter & Koscielny-Bunde, Eva & Livina, Valerie & Havlin, Shlomo & Bunde, Armin, 2003. "Multifractality of river runoff and precipitation: comparison of fluctuation analysis and wavelet methods," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 330(1), pages 240-245.
    25. El Alaoui, Marwane & Benbachir, Saâd, 2013. "Multifractal detrended cross-correlation analysis in the MENA area," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(23), pages 5985-5993.
    26. Shang, Pengjian & Lu, Yongbo & Kamae, Santi, 2008. "Detecting long-range correlations of traffic time series with multifractal detrended fluctuation analysis," Chaos, Solitons & Fractals, Elsevier, vol. 36(1), pages 82-90.
    27. Jaroslaw Kwapien & Pawel Oswiecimka & Stanislaw Drozdz, 2015. "Detrended fluctuation analysis made flexible to detect range of cross-correlated fluctuations," Papers 1506.08692, arXiv.org, revised Nov 2015.
    28. Kaushik Matia & Yosef Ashkenazy & H. Eugene Stanley, 2003. "Multifractal Properties of Price Fluctuations of Stocks and Commodities," Papers cond-mat/0308012, arXiv.org.
    29. S. Shadkhoo & G. R. Jafari, 2009. "Multifractal detrended cross-correlation analysis of temporal and spatial seismic data," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 72(4), pages 679-683, December.
    30. He, Ling-Yun & Chen, Shu-Peng, 2011. "Multifractal Detrended Cross-Correlation Analysis of agricultural futures markets," Chaos, Solitons & Fractals, Elsevier, vol. 44(6), pages 355-361.
    31. Wang, Yudong & Liu, Li & Gu, Rongbao, 2009. "Analysis of efficiency for Shenzhen stock market based on multifractal detrended fluctuation analysis," International Review of Financial Analysis, Elsevier, vol. 18(5), pages 271-276, December.
    32. Cao, Guangxi & Xu, Longbing & Cao, Jie, 2012. "Multifractal detrended cross-correlations between the Chinese exchange market and stock market," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(20), pages 4855-4866.
    33. Dutta, Srimonti & Ghosh, Dipak & Samanta, Shukla & Dey, Santanu, 2014. "Multifractal parameters as an indication of different physiological and pathological states of the human brain," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 396(C), pages 155-163.
    34. Zebende, G.F., 2011. "DCCA cross-correlation coefficient: Quantifying level of cross-correlation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(4), pages 614-618.
    35. Lu, Xinsheng & Tian, Jie & Zhou, Ying & Li, Zhihui, 2013. "Multifractal detrended fluctuation analysis of the Chinese stock index futures market," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(6), pages 1452-1458.
    36. Norouzzadeh, P. & Rahmani, B., 2006. "A multifractal detrended fluctuation description of Iranian rial–US dollar exchange rate," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 367(C), pages 328-336.
    37. Benbachir, Saâd & El Alaoui, Marwane, 2011. "A Multifractal Detrended Fluctuation Analysis of the Moroccan Stock Exchange," MPRA Paper 49003, University Library of Munich, Germany.
    38. He, Ling-Yun & Chen, Shu-Peng, 2011. "Nonlinear bivariate dependency of price–volume relationships in agricultural commodity futures markets: A perspective from Multifractal Detrended Cross-Correlation Analysis," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(2), pages 297-308.
    39. Vassoler, R.T. & Zebende, G.F., 2012. "DCCA cross-correlation coefficient apply in time series of air temperature and air relative humidity," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(7), pages 2438-2443.
    40. Pal, Mayukha & Madhusudana Rao, P. & Manimaran, P., 2014. "Multifractal detrended cross-correlation analysis on gold, crude oil and foreign exchange rate time series," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 416(C), pages 452-460.
    41. Gao-Feng Gu & Wei-Xing Zhou, 2010. "Detrending moving average algorithm for multifractals," Papers 1005.0877, arXiv.org, revised Jun 2010.
    42. Xi-Yuan Qian & Ya-Min Liu & Zhi-Qiang Jiang & Boris Podobnik & Wei-Xing Zhou & H. Eugene Stanley, 2015. "Detrended partial cross-correlation analysis of two nonstationary time series influenced by common external forces," Papers 1504.02435, arXiv.org, revised Apr 2015.
    43. Hajian, S. & Movahed, M. Sadegh, 2010. "Multifractal Detrended Cross-Correlation Analysis of sunspot numbers and river flow fluctuations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(21), pages 4942-4957.
    44. Kantelhardt, Jan W & Koscielny-Bunde, Eva & Rego, Henio H.A & Havlin, Shlomo & Bunde, Armin, 2001. "Detecting long-range correlations with detrended fluctuation analysis," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 295(3), pages 441-454.
    45. Sadegh Movahed, M. & Hermanis, Evalds, 2008. "Fractal analysis of river flow fluctuations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(4), pages 915-932.
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