IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v160y2022ics0960077922004325.html
   My bibliography  Save this article

Sources of multifractality of the brain rs-fMRI signal

Author

Listed:
  • Guan, Sihai
  • Wan, Dongyu
  • Yang, Yanmiao
  • Biswal, Bharat

Abstract

Based on the multifractal methodology, we examine how complexity in the dynamics of biological systems can be understood. The possible sources of multifractality have been determined by comparing the multifractal indexes obtained on the original, shuffle, Fourier transform surrogate (FTsurrogate), and iterative amplitude adjusted Fourier transform (iAAFT) time series. This paper shows that the rs-fMRI signal is multifractality. The multifractality is due to the fat-tail probability distribution, long-range dependence (LRD), and the excluded hidden structures. Although the excluded hidden structures also contribute to the sources of the multifractality, it is mainly composed of the fat-tail probability distribution and LRD, especially the fat-tail probability distribution. Specifically, the shuffle, FTsurrogate, and iAAFT series, those three series still display a multifractal behavior. However, based on the shuffle series, we know that the trend of change in the curve of fluctuation functions with q is significantly weakened, indicating that the probability distribution is not the only source of the multifractalionality of the rs-fMRI signal. In addition, the multifractal properties of the shuffle series are not as strong as the original series. The FTsurrogate and iAAFT series also are as powerful multifractals as the original. For the original series, the multifractal spectrum is an asymmetric bell shape, indicating that the multifractal spectrum is on the right. This means that the multifractality of the rs-fMRI signal in this scale range is determined by the multifractal properties of large and small fluctuations. The fat-tailed probability distribution, LRD, and excluded hidden structure are generated by the power-law distributions, scale-free temporal dynamics, and the highly structured dynamical activity in space and time (which means latent variables and connectivity patterns). This study implies that the study on the sources of multifractalionality may also discover new insights into the dynamic mechanism of spontaneous brain activity.

Suggested Citation

  • Guan, Sihai & Wan, Dongyu & Yang, Yanmiao & Biswal, Bharat, 2022. "Sources of multifractality of the brain rs-fMRI signal," Chaos, Solitons & Fractals, Elsevier, vol. 160(C).
    • Handle: RePEc:eee:chsofr:v:160:y:2022:i:c:s0960077922004325
    DOI: 10.1016/j.chaos.2022.112222
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077922004325
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2022.112222?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Arneodo, A. & Bacry, E. & Muzy, J.F., 1995. "The thermodynamics of fractals revisited with wavelets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 213(1), pages 232-275.
    2. Gui, Jun & Zheng, Zeyu & Fu, Dianzheng & Fu, Yang & Liu, Zhi, 2021. "Long-term correlations and multifractality of toll-free calls in China," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 567(C).
    3. Yang, Liansheng & Zhu, Yingming & Wang, Yudong, 2016. "Multifractal characterization of energy stocks in China: A multifractal detrended fluctuation analysis," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 451(C), pages 357-365.
    4. Yang, Yan-Hong & Xie, Wen-Jie & Li, Ming-Xia & Jiang, Zhi-Qiang & Zhou, Wei-Xing, 2017. "Statistical properties of user activity fluctuations in virtual worlds," Chaos, Solitons & Fractals, Elsevier, vol. 105(C), pages 271-278.
    5. 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.
    6. Rak, Rafał & Grech, Dariusz, 2018. "Quantitative approach to multifractality induced by correlations and broad distribution of data," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 508(C), pages 48-66.
    7. Telesca, Luciano & Lovallo, Michele & Kanevski, Mikhail, 2016. "Power spectrum and multifractal detrended fluctuation analysis of high-frequency wind measurements in mountainous regions," Applied Energy, Elsevier, vol. 162(C), pages 1052-1061.
    8. Salat, Hadrien & Murcio, Roberto & Arcaute, Elsa, 2017. "Multifractal methodology," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 473(C), pages 467-487.
    9. Zhang, Xie & Liu, Hongzhi & Zhao, Yifei & Zhang, Xingchen, 2019. "Multifractal detrended fluctuation analysis on air traffic flow time series: A single airport case," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 531(C).
    10. Sarker, Alivia & Mali, Provash, 2021. "Detrended multifractal characterization of Indian rainfall records," Chaos, Solitons & Fractals, Elsevier, vol. 151(C).
    11. Stanley, H.E. & Amaral, L.A.N. & Goldberger, A.L. & Havlin, S. & Ivanov, P.Ch. & Peng, C.-K., 1999. "Statistical physics and physiology: Monofractal and multifractal approaches," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 270(1), pages 309-324.
    12. Xi-Nian Zuo & Ting Xu & Michael Peter Milham, 2019. "Harnessing reliability for neuroscience research," Nature Human Behaviour, Nature, vol. 3(8), pages 768-771, August.
    13. Rafal Rak & Dariusz Grech, 2018. "Quantitative approach to multifractality induced by correlations and broad distribution of data," Papers 1805.11909, arXiv.org.
    14. Mikail Rubinov & Olaf Sporns & Jean-Philippe Thivierge & Michael Breakspear, 2011. "Neurobiologically Realistic Determinants of Self-Organized Criticality in Networks of Spiking Neurons," PLOS Computational Biology, Public Library of Science, vol. 7(6), pages 1-14, June.
    15. R. Chialvo, Dante, 2004. "Critical brain networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 340(4), pages 756-765.
    16. Mali, Provash & Mukhopadhyay, Amitabha, 2014. "Multifractal characterization of gold market: A multifractal detrended fluctuation analysis," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 413(C), pages 361-372.
    17. Bhardwaj, Shivam & Chandrasekhar, E. & Seemala, Gopi K. & Gadre, Vikram M., 2020. "Characterization of ionospheric total electron content data using wavelet-based multifractal formalism," Chaos, Solitons & Fractals, Elsevier, vol. 134(C).
    18. Zhang, Xin & Yang, Liansheng & Zhu, Yingming, 2019. "Analysis of multifractal characterization of Bitcoin market based on multifractal detrended fluctuation analysis," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 523(C), pages 973-983.
    19. 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.
    20. Juan Luis Lopez & Jesus Guillermo Contreras, 2013. "Performance of multifractal detrended fluctuation analysis on short time series," Papers 1311.2278, arXiv.org.
    21. Mukli, Peter & Nagy, Zoltan & Eke, Andras, 2015. "Multifractal formalism by enforcing the universal behavior of scaling functions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 417(C), pages 150-167.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Tajmirriahi, Mahnoosh & Rabbani, Hossein, 2024. "Linear multifractional stable motion for modeling of fluid-filled regions in retinal optical coherence tomography images," Chaos, Solitons & Fractals, Elsevier, vol. 180(C).

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Olivares, Felipe & Zanin, Massimiliano, 2022. "Corrupted bifractal features in finite uncorrelated power-law distributed data," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 603(C).
    2. Li, Xing, 2021. "On the multifractal analysis of air quality index time series before and during COVID-19 partial lockdown: A case study of Shanghai, China," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 565(C).
    3. Sarker, Alivia & Mali, Provash, 2021. "Detrended multifractal characterization of Indian rainfall records," Chaos, Solitons & Fractals, Elsevier, vol. 151(C).
    4. Gui, Jun & Zheng, Zeyu & Fu, Dianzheng & Fu, Yang & Liu, Zhi, 2021. "Long-term correlations and multifractality of toll-free calls in China," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 567(C).
    5. Santos, Fábio Sandro dos & Nascimento, Kerolly Kedma Felix do & Jale, Jader da Silva & Stosic, Tatijana & Marinho, Manoel H.N. & Ferreira, Tiago A.E., 2021. "Mixture distribution and multifractal analysis applied to wind speed in the Brazilian Northeast region," Chaos, Solitons & Fractals, Elsevier, vol. 144(C).
    6. Pawe{l} O'swik{e}cimka & Stanis{l}aw Dro.zd.z & Mattia Frasca & Robert Gk{e}barowski & Natsue Yoshimura & Luciano Zunino & Ludovico Minati, 2020. "Wavelet-based discrimination of isolated singularities masquerading as multifractals in detrended fluctuation analyses," Papers 2004.03319, arXiv.org.
    7. Marcin Wk{a}torek & Stanis{l}aw Dro.zd.z & Jaros{l}aw Kwapie'n & Ludovico Minati & Pawe{l} O'swik{e}cimka & Marek Stanuszek, 2020. "Multiscale characteristics of the emerging global cryptocurrency market," Papers 2010.15403, arXiv.org, revised Mar 2021.
    8. Schadner, Wolfgang, 2022. "U.S. Politics from a multifractal perspective," Chaos, Solitons & Fractals, Elsevier, vol. 155(C).
    9. Akash P. POOJARI & Siva Kiran GUPTHA & G Raghavender RAJU, 2022. "Multifractal analysis of equities. Evidence from the emerging and frontier banking sectors," Theoretical and Applied Economics, Asociatia Generala a Economistilor din Romania / Editura Economica, vol. 0(3(632), A), pages 61-80, Autumn.
    10. Liu, Hongzhi & Zhang, Xingchen & Zhang, Xie, 2020. "Multiscale multifractal analysis on air traffic flow time series: A single airport departure flight case," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 545(C).
    11. Schadner, Wolfgang, 2021. "On the persistence of market sentiment: A multifractal fluctuation analysis," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 581(C).
    12. Mukli, Peter & Nagy, Zoltan & Eke, Andras, 2015. "Multifractal formalism by enforcing the universal behavior of scaling functions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 417(C), pages 150-167.
    13. Sierra-Porta, D. & Domínguez-Monterroza, Andy-Rafael, 2022. "Linking cosmic ray intensities to cutoff rigidity through multifractal detrented fluctuation analysis," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 607(C).
    14. Fernández-Martínez, M. & Sánchez-Granero, M.A. & Casado Belmonte, M.P. & Trinidad Segovia, J.E., 2020. "A note on power-law cross-correlated processes," Chaos, Solitons & Fractals, Elsevier, vol. 138(C).
    15. Sun, Xiaoqin & She, Dongli & Sanz, Ernesto & Martín-Sotoca, Juan J. & Tarquis, Ana M. & Gao, Lei, 2023. "Multifractal analysis on CT soil images: Fluctuation analysis versus mass distribution," Chaos, Solitons & Fractals, Elsevier, vol. 176(C).
    16. Telli, Şahin & Chen, Hongzhuan, 2020. "Multifractal behavior in return and volatility series of Bitcoin and gold in comparison," Chaos, Solitons & Fractals, Elsevier, vol. 139(C).
    17. Wu, Liang & Chen, Lei & Ding, Yiming & Zhao, Tongzhou, 2018. "Testing for the source of multifractality in water level records," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 508(C), pages 824-839.
    18. Delbianco, Fernando & Tohmé, Fernando & Stosic, Tatijana & Stosic, Borko, 2016. "Multifractal behavior of commodity markets: Fuel versus non-fuel products," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 457(C), pages 573-580.
    19. Lahmiri, Salim, 2017. "Multifractal analysis of Moroccan family business stock returns," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 486(C), pages 183-191.
    20. Zhang, Shuchang & Guo, Yaoqi & Cheng, Hui & Zhang, Hongwei, 2021. "Cross-correlations between price and volume in China's crude oil futures market: A study based on multifractal approaches," Chaos, Solitons & Fractals, Elsevier, vol. 144(C).

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:chsofr:v:160:y:2022:i:c:s0960077922004325. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Thayer, Thomas R. (email available below). General contact details of provider: https://www.journals.elsevier.com/chaos-solitons-and-fractals .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.