Cross-Frequency Multilayer Network Analysis with Bispectrum-based Functional Connectivity: A Study of Alzheimer's Disease

Dominik Klepl, Fei He, Min Wu, Daniel J Blackburn, Ptolemaios G Sarrigiannis

Research output: Contribution to journalArticlepeer-review

3 Citations (Scopus)
33 Downloads (Pure)


Alzheimer's disease (AD) is a neurodegenerative disorder known to affect functional connectivity (FC) across many brain regions. Linear FC measures have been applied to study the differences in AD by splitting neurophysiological signals, such as electroencephalography (EEG) recordings, into discrete frequency bands and analysing them in isolation from each other. We address this limitation by quantifying cross-frequency FC in addition to the traditional within-band approach. Cross-bispectrum, a higher-order spectral analysis approach, is used to measure the nonlinear FC and is compared with the cross-spectrum, which only measures the linear FC within bands. This work reports the reconstruction of a cross-frequency FC network where each frequency band is treated as a layer in a multilayer network with both inter- and intra-layer edges. Cross-bispectrum detects cross-frequency differences, mainly increased FC in AD cases in δ-θ coupling. Overall, increased strength of low-frequency coupling and decreased level of high-frequency coupling is observed in AD cases in comparison to healthy controls (HC). We demonstrate that a graph-theoretic analysis of cross-frequency brain networks is crucial to obtain a more detailed insight into their structure and function. Vulnerability analysis reveals that the integration and segregation properties of networks are enabled by different frequency couplings in AD networks compared to HCs. Finally, we use the reconstructed networks for classification. The extra cross-frequency coupling information can improve the classification performance significantly, suggesting an important role of cross-frequency FC. The results highlight the importance of studying nonlinearity and including cross-frequency FC in characterising AD.

Original languageEnglish
Pages (from-to)77-88
Number of pages12
Early online date29 Apr 2023
Publication statusPublished - 15 Jun 2023

Bibliographical note

2023 The Author(s). Published by Elsevier Ltd on behalf of IBRO. This is an open access article under the CC BY license (


The EEG data was funded by a grant from the Alzheimer’s Research UK (ARUK-PPG20114B-25). The views expressed are those of the author(s) and not necessarily those of the NHS, the NIHR or the Department of Health.


  • Alzheimer’s disease
  • bispectrum
  • cross-frequency coupling
  • EEG
  • functional connectivity
  • graph theory


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