Bispectrum-based Cross-frequency Functional Connectivity: A Study of Alzheimer’s Disease

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 first use of cross-bispectrum to reconstruct 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. An increase of within-band FC in AD is observed in low-frequency bands using both methods. Bispectrum also detects multiple cross-frequency differences, mainly increased FC in AD in delta-theta coupling. An increased importance of low-frequency coupling and decreased importance of high-frequency coupling is observed in AD. Integration properties of AD networks are more vulnerable than HC, while the segregation property is maintained in AD. Moreover, the segregation property of {gamma} is less vulnerable in AD, suggesting the shift of importance from high-frequency activity towards low-frequency components. The results highlight the importance of studying nonlinearity and including cross-frequency FC in characterising AD. Moreover, the results demonstrate the advantages and limitations of using bispectrum to reconstruct FC networks.