Multiscale detrended cross-correlation coefficient: estimating coupling in non-stationary neurophysiological signals

Orestis Stylianou; Gianluca Susi; Martin Hoffmann; Isabel Suárez-Méndez; David López-Sanz; Michael Schirner; Petra Ritter

doi:10.3389/fnins.2024.1422085

Multiscale detrended cross-correlation coefficient: estimating coupling in non-stationary neurophysiological signals

Front Neurosci. 2024 Nov 13:18:1422085. doi: 10.3389/fnins.2024.1422085. eCollection 2024.

Authors

Orestis Stylianou^{1

2

3}, Gianluca Susi^{4

5}, Martin Hoffmann^{1

2}, Isabel Suárez-Méndez^{4

5}, David López-Sanz^{5

6}, Michael Schirner^{1

2

7

8

9}, Petra Ritter^{1

2

7

8

9}

Affiliations

¹ Berlin Institute of Health at Charité, Universitätsmedizin Berlin, Berlin, Germany.
² Charité-Universitätsmedizin Berlin, Corporate Member of Freie Universität Berlin and Humboldt Universität zu Berlin, Department of Neurology with Experimental Neurology, Berlin, Germany.
³ Department of Surgery, Immanuel Clinic Rüdersdorf, University Clinic of Brandenburg Medical School, Berlin, Germany.
⁴ Department of Structure of Matter, Thermal Physics and Electronics, Complutense University of Madrid, Madrid, Spain.
⁵ Center for Cognitive and Computational Neuroscience, Complutense University of Madrid, Madrid, Spain.
⁶ Department of Experimental Psychology, Cognitive Processes and Speech Therapy, Complutense University of Madrid, Madrid, Spain.
⁷ Bernstein Focus State Dependencies of Learning & Bernstein Center for Computational Neuroscience, Berlin, Germany.
⁸ Einstein Center for Neuroscience Berlin, Berlin, Germany.
⁹ Einstein Center Digital Future, Berlin, Germany.

Abstract

The brain consists of a vastly interconnected network of regions, the connectome. By estimating the statistical interdependence of neurophysiological time series, we can measure the functional connectivity (FC) of this connectome. Pearson's correlation (r _P) is a common metric of coupling in FC studies. Yet r _P does not account properly for the non-stationarity of the signals recorded in neuroimaging. In this study, we introduced a novel estimator of coupled dynamics termed multiscale detrended cross-correlation coefficient (MDC₃). Firstly, we showed that MDC₃ had higher accuracy compared to r _P and lagged covariance using simulated time series with known coupling, as well as simulated functional magnetic resonance imaging (fMRI) signals with known underlying structural connectivity. Next, we computed functional brain networks based on empirical magnetoencephalography (MEG) and fMRI. We found that by using MDC₃ we could construct networks of healthy populations with significantly different properties compared to r _P networks. Based on our results, we believe that MDC₃ is a valid alternative to r _P that should be incorporated in future FC studies.

Keywords: brain networks; functional connectivity; functional connectome; non-stationary signals; statistical interdependence.

Grants and funding

The author(s) declare that financial support was received for the research, authorship, and/or publication of this article. P.R. acknowledges support by Digital Europe TEF-Health 101100700, EU H2020 Virtual Brain Cloud 826421, Human Brain Project SGA2 785907; Human Brain Project SGA3 945539, ERC Consolidator 683049; German Research Foundation SFB 1436 (project ID 425899996); SFB 1315 (project ID 327654276); SFB 936 (project ID 178316478); SFB-TRR 295 (project ID 424778381); SPP Computational Connectomics RI 2073/6–1, RI 2073/10–2, RI 2073/9–1; PHRASE Horizon EIC grant 101058240; Berlin Institute of Health & Foundation Charité, Johanna Quandt Excellence Initiative; ERAPerMed Pattern-Cog, the Virtual Research Environment at the Charité Berlin – a node of EBRAINS Health Data Cloud.