Neurovascular coupling in eye-open-eye-close task and resting state: Spectral correspondence between concurrent EEG and fMRI

Neurovascular coupling serves as an essential neurophysiological mechanism in functional neuroimaging, which is generally presumed to be robust and invariant across different physiological states, encompassing both task engagement and resting state. Nevertheless, emerging evidence suggests that neurovascular coupling may exhibit state dependency, even in normal human participants. To investigate this premise, we analyzed the cross-frequency spectral correspondence between concurrently recorded electroencephalography (EEG) and functional magnetic resonance imaging (fMRI) data, utilizing them as proxies for neurovascular coupling during the two conditions: an eye-open-eye-close (EOEC) task and a resting state. We hypothesized that given the state dependency of neurovascular coupling, EEG-fMRI spectral correspondences would change between the two conditions in the visual system. During the EOEC task, we observed a negative phase-amplitude-coupling (PAC) between EEG alpha-band and fMRI visual activity. Conversely, in the resting state, a pronounced amplitude-amplitude-coupling (AAC) emerged between EEG and fMRI signals, as evidenced by the spectral correspondence between the EEG gamma-band of the midline occipital channel (O z ) and the high-frequency fMRI signals (0.15 – 0.25 Hz) in the visual network. This study reveals distinct scenarios of EEG-fMRI spectral correspondence in healthy participants, corroborating the state-dependent nature of neurovascular coupling.


Introduction
Brain functionality can be assessed through various neuroimaging techniques that detect a wide range of physiological information and target the underlying neuronal activity.Renowned techniques such as electroencephalogram (EEG) (Berger, 1929;Buzsáki et al., 2012), magnetoencephalography (MEG) (Cohen, 1972(Cohen, , 1968)), functional near-infrared spectroscopy (fNIRS) (Ferrari et al., 1985), functional transcranial doppler sonography (fTCD) (Aaslid et al., 1982), and functional magnetic resonance imaging (fMRI) (Ogawa et al., 1990) offer invaluable insights into brain functionality.In particular, fMRI provides spatial information on regional brain activity and has been employed in diverse neuroscience fields, from, for example, cognitive psychology (Friston et al., 1997) to the study of psychiatric disorder (Phillips et al., 1997) and neurological diseases (Seeley et al., 2007).The fMRI signal, grounded in the blood-oxygenation level dependent (BOLD) principle, captures both neuronal activity and the local cerebral hemodynamic fluctuations due to their closely intertwined spatial and temporal dynamics in a healthy brain (Kim and Ogawa, 2012).Specifically, neuronal activity induces vasodilation and subsequent hyperemia, resulting in increased blood oxygenation (Attwell and Iadecola, 2002).When performing cognitive tasks, increases in neuronal local field potential lead a series of regional hemodynamic responses, composed of cerebral blood flow, cerebral blood volume, and cerebral oxygenation, formulating a complex process termed neurovascular coupling (Iadecola, 2004).
Neurovascular coupling is the cornerstone that enables fMRI to map neural activities indirectly across various psychophysiological conditions, not only during task engagement but also in an intrinsic or resting state (Biswal et al., 1995;Girouard and Iadecola, 2006;Greicius et al., 2003;Iadecola, 2004;Michels et al., 2010;Raichle et al., 2001).Despite the proliferation of fMRI studies, two presumptions warrant further investigation.First, the assumed constancy of neurovascular coupling in fMRI research is challenged by literature, suggesting its sensitivity to baseline physiology, with potential alterations in clinical pathophysiological conditions (Murta et al., 2017;Pak et al., 2017).Even in non-clinical settings, disparities in EEG and fMRI indices across different sleep stages (Wu et al., 2019) suggest that neurovascular coupling (reflected by the EEG-fMRI correspondence relation) may be condition-dependent, rather than time-invariant or universally consistent.Second, although EEG provides high temporal resolution and fMRI offers a lower one (Nunez and Srinivasan, 2006;Ogawa et al., 1992), most EEG-fMRI studies have relied on traditional correlation analyses between single fMRI time courses (with or without deconvolution of hemodynamic response function [HRF]) and EEG spectral power within a certain frequency band (generated from the envelope amplitude of delta, theta, alpha, beta, and gamma bands) (Mantini et al., 2007;Mo et al., 2013;Scheeringa et al., 2011).This approach is in line with the traditional phase-amplitude coupling (PAC) approach, wherein the phase of low-frequency signal (i.e., fMRI, commonly less than 1 Hz) is synchronized with the envelope of the high-frequency signal (i.e., EEG, commonly exceeding 1 Hz) within a specific frequency band.However, the PAC concept assumes that fMRI signal fluctuation is driven by the phase of high-frequency EEG signals.While this presumption may hold for task-induced brain activity, it may not be effective for assessing the underlying neurovascular relationship during resting state, as the resting-state fMRI signals could be complex, encompassing multiple distinctive neurophysiological sources.An alternative model for EEG-fMRI spectral coupling might involve amplitude-amplitude coupling (AAC), or a combination of both PAC and AAC, in the resting state.In the AAC perspective, the EEG spectral power in each frequency bin could exhibit amplitude modulations with the fMRI spectral power across its frequency range, even though the commonly applied frequency range in EEG signals (typical range: 1-40 Hz) is much higher than the low-frequency range of fMRI signals (typical range: 0.01 to 0.10 Hz).Based on the above-mentioned considerations, we hypothesize that the two different neurophysiological conditions (task engagement and resting state) lead to distinctive patterns of EEG-fMRI spectral correspondence (PAC and AAC).
To further illustrate the two spectral correspondence patterns, PAC was firstly introduced to investigate the relationship between EEG and fMRI signals during task engagements (Leicht et al., 2016;Michels et al., 2010;Murta et al., 2017;Omidvarnia et al., 2017;Uji et al., 2018).Past PAC studies demonstrated correlations between specific frequency bands of the EEG signal and single fMRI waveforms (without frequency decomposition) while performing the cognitive tasks, but different EEG frequency bands may lead to either positive or negative correlations with the fMRI signal, suggesting that the fMRI signals are differentially coupled with EEG signals at different frequency bands (Omidvarnia et al., 2017).For instance, in a working memory task, the fMRI signal alone showed positive correlations with alpha/high-beta/gamma and negative correlations with theta/alpha/low-beta EEG signals (Michels et al., 2010).During motor tasks, high-gamma EEG activity and fMRI time courses were positively correlated in the motor cortex (Uji et al., 2018).In a finger-tapping task, alpha/beta and gamma EEG demonstrated negative and positive coupling with the fMRI signal, respectively (Murta et al., 2017).The relationship between gamma-band EEG and fMRI waveforms was weak during auditory stimuli in a high-risk psychosis group (Leicht et al., 2016).In summary, PAC identifies the nonlinear frequency modulation between the phase of high-frequency signal (i.e., EEG) and the amplitude of low-frequency target signal (i.e., fMRI) with specific timings and periodicity, and PAC has been considered a general scenario for EEG-fMRI relationship under the assumption of static neurovascular coupling.
Beyond the task-based fMRI studies, neurovascular coupling during the resting state (i.e., task-free condition) has also been analyzed with conventional PAC approach.For instance, in a resting state, EEG alpha power and fMRI-based functional connectivity presented either negative (Chang et al., 2013) or positive relations (Mo et al., 2013) in the default-mode network (DMN).This correlation analysis directly inherits the PAC approach from task-based studies.However, resting-state brain signals may not follow the PAC relationship for two plausible reasons.First, since the neurons at rest are firing sparsely and in a nonstationary manner (Shoham et al., 2006), unlike the assembled neuronal activities in task engagements, the absence of specific onset times and fluctuation periodicity confers a higher level of uncertainty in both amplitude and frequency domains on the resting-state brain signals, as shown in time-frequency maps in the literature (Chang and Glover, 2010;Hsu et al., 2022).Second, the fMRI signals in the resting state may contain a variety of spectral sources, unlike the single source of BOLD contrast in task condition, as supported by past literature (Song et al., 2022;Thompson and Fransson, 2015;Wu et al., 2012).Meanwhile, different EEG frequency bands may contribute distinctively to the fMRI signals (Laufs et al., 2003;Mantini et al., 2007).Therefore, the multiple fMRI signal sources in the resting state may interact simultaneously with multiple EEG frequency bands in a nonstationary manner.The two factorsunknown timing and multiple sourcesin the resting-state fMRI signals indicate a complexity that surpasses the PAC concept, leading us to propose AAC as an alternative scenario for discerning the EEG-fMRI spectral correspondence in the resting state.
Previous research has also identified a possible AAC relationship between frequency bands of EEG signal and fMRI spectral components during task engagements, such as in auditory and visual oddball tasks (Walz et al., 2013) and tonic alertness (Sadaghiani et al., 2012), but AAC has seldom been introduced to resting-state fMRI signals (Hsu et al., 2022).Technically, AAC seeks the amplitude modulations across the observable spectra of two concurrent signals (Jirsa and Müller, 2013), which is only feasible through fine-grained time-frequency decomposition using techniques such as the short-time Fourier transform (STFT), wavelet, or Hilbert-Huang transform (HHT) (Cordes et al., 2021;Hsu et al., 2022;Thompson and Fransson, 2015).Considering the intrinsic characteristics of non-linearity and non-stationarity in both EEG and fMRI signals, we employed the HHT methods for estimating AAC, which provides the highest resolution in time-frequency decompositions and is best suited for analyzing the spectral correspondence between simultaneously recorded EEG and fMRI signals (Hsu et al., 2022).This technique highlights the potential for similar research methods to be applied to exploring neurovascular coupling in EEG-fMRI studies during the resting state.
In this study, we explored the macro-scale neurovascular coupling through the EEG-fMRI spectral correspondence (PAC or AAC) within the visual network under the two conditions: the first is the task-like eyeopen-eye-close (EOEC) condition, notable for the prominent changes in EEG alpha power, and the second is the resting state.We sought to verify whether EEG-fMRI spectral correspondence is more suitably characterized by AAC as compared to the conventional PAC, in pursuit of condition-dependent neurovascular coupling.

PAC and AAC through HHT
Unlike the Fourier transform, which is based on the sinusoidal signals decomposition, the HHT method adaptively decomposes input signals to generate high-resolution time-frequency maps through the following three steps (Huang et al., 1998): (1) data decomposition into a set of intrinsic mode functions (IMFs) that preserve the physical meaning of the original dataset, (2) calculation of the instantaneous frequency within these IMFs, and (3) representation of the spectral information in a Hilbert-based time-frequency map via Hilbert spectral analysis (HSA).Using these nonstationary and nonlinear HHT processes, spectral correspondence for both AAC and PAC can be discerned through the combination of generated IMFs or time-frequency maps.In PAC, the single waveform of the target low-frequency signal (e.g., fMRI) correlates highly with each temporal waveform of the time-frequency map from the high-frequency signal (e.g., EEG).Here, we have utilized IMFs to replace the single fMRI signal for enhanced sensitivity in both task-based simulation and real data (Lin et al., 2016).Conversely, AAC spectral correspondence is achieved through cross-correlation analysis between the two time-frequency maps from both low-frequency and high-frequency signals by collapsing the temporal dimension.
To delineate the cross-frequency features, we employed the ensemble empirical mode decomposition (EEMD) method to extract IMFs from both EEG and fMRI signals.EEMD entails a strategy of repeatedly adding a specific level of white noise to the signal, recursively decomposing the signal, and then generating averaging the IMFs to mitigate the mode-mixing issue present in the original EMD, with further details referenced in Lin et al. (2016).Following EEMD, we disregarded the IMFs representing linear trends, and all remaining IMFs were utilized to compute the HSA for the time-frequency distribution of the signal, applicable to both simulation and real data.In spectral coupling, PAC is reflected by the cross-frequency correlations between IMFs of the fMRI signals and the HSA of the EEG signals, while the AAC scenario is assessed by the correlations between the HSA maps for both fMRI and EEG signals.A schematic diagram illustrating both PAC and AAC analyses is presented in Fig. 1a.

Simulations for PAC and AAC
Applying the HHT to EEG-fMRI spectral coupling analysis is a novel approach, and its sensitivity has yet to be tested.To address this gap, we performed three simulations of fMRI and EEG signals featuring both PAC and AAC to explore various aspects of the method (see Fig. 1b).The PAC and AAC analyses were then applied to two simulations representing plausible EEG-fMRI relationships to evaluate the sensitivity of HHT in assessing neurovascular coupling.
1. Simulation 1 featured a block-design task paradigm (single source) to emulate the EEG/fMRI signals during an eye-open-eye-close (EOEC) task, with a 30-second stimulus onset followed by a 30-second stimulus offset over three cycles, targeting a frequency of 0.0167 Hz.Here, a PAC phenomenon in the EEG-fMRI spectral coupling was expected.2. Simulation 2 utilized a mixed task paradigm (two-source) combining jittered events (10-to-30-second event stimuli onset and offset over nine cycles, targeting a frequency of 0.05 Hz) with a block design (15-second stimulus onset and a variable 20-to-180-second stimulus offset over two cycles, targeting a frequency of 0.011 Hz).This was to mimic the multiple-source resting-state EEG/fMRI signals, where a mixed coupling consisting of both AAC and PAC was anticipated.
The simulated fMRI signals were created by convolving the respective paradigms with canonical HRF (Lindquist et al., 2009), resulting in a sampling rate of 0.5 Hz.Simultaneously, the EEG signals were simulated by convolving the specific paradigms with an 8-Hz sinusoidal fluctuation (alpha band) at a 100-Hz sampling rate.Furthermore, to assess sensitivity, the fMRI and EEG signals were generated with varying levels of white noise (0 %, 20 %, 40 %, 60 %, 80 %, and 100 %) in the two simulations to determine the EEG-fMRI spectral correspondence.For optimal HHT decomposition, all simulated fMRI signals underwent fourfold up-sampling, and the EEMD analysis was repeated 100 times for each simulation.

Experiment procedures
Fourteen young participants (7 females; mean age = 25.6 ± 3.9) were recruited for this study.All participants were right-handed, free from any metal devices in their bodies (such as dental braces), without a history of psychiatric or neurological disorders, and not currently taking psychoactive medications.The experimental procedures were conducted in compliance with the guidelines and regulations set forth by the Research Ethics Committee of Taipei Medical University  (201512ES054).Written informed consent was obtained from all participants prior to the study.

Simultaneous EEG-fMRI recordings
To examine neurovascular coupling during both task-performed and task-free conditions, EEG data were acquired concurrently with fMRI scans.Two conditions were designed: an EOEC task and a resting state.In the EOEC session, the experiment was performed in three blocks, each block comprising a 30-second eye-open period followed by a 30-second eye-close interval, totaling 3 min (90 measurements).During the resting session, participants were instructed to keep their eyes open (to prevent sleep), maintain a steady head position, stay awake, and refrain from engaging in specific thought processes for 5 min scan (150 measurements).All the resting scans were conducted prior to the EOEC task.
The experiments were performed using a 3T Tim Trio MRI scanner (Siemens, Erlangen, Germany) in National Yang Ming Chiao Tung University.Upon arrival, each participant was seated in an armchair for setup and preparation before the EEG-fMRI recordings.A 32-channel EEG cap was fitted before functional scanning.Scalp EEG data, with a reference between the C z and F z electrodes, were captured using an MR compatible 32-channel 10/20 EEG system (BrainProducts, Germany) at a sampling frequency of 5 kHz.To verify changes in alpha power, participants were asked to keep eyes open for 30 s and then closed for another 30 s before entering the scan room.Functional imaging was acquired with gradient-echo planer imaging (GE-EPI) sequence with a 64×64 matrix; field of view (FOV) of 22×22 cm; 32 slices with 3.4 mm thickness aligned with the anterior commissure-posterior commissure (AC-PC) line; TR/TE = 2000/30 ms; and flip angle = 78 • .Physiological parameters, including respiratory and pulse rate, were monitored and recorded using a pressure belt and a pulse oximeter equipped with infrared sensor (MR-compatible Physiologic Monitoring Unit, Siemens, Germany).These parameters were later used as nuisance regressors in post-processing to mitigate their effects on resting-state functional connectivity.Additionally, high-resolution T 1 -weighted anatomical images were acquired for each subject for spatial normalization (MPRAGE with 256×256×176 matrix size; 1 × 1 × 1 mm 3 in-plane resolution; 900 ms inversion time; TR/TE = 1900/2.27ms; flip angle = 8 • ).

Data processing for both EEG and fMRI
The EEG data were preprocessed using BrainVision Analyzer 2.02 (BrainProducts, Germany) and the EEGLAB toolkit (Delorme and Makeig, 2004) (https://sccn.ucsd.edu/eeglab).In BrainVision Analyzer, gradient artifacts were removed via template subtraction (Allen et al., 2000), and signals were resampled to 250 Hz.Cardiobalistogram artifacts were removed by subtracting the average pulse artifact fluctuation from each channel (Allen et al., 1998).Using EEGLAB, the data underwent band-pass filter with a Butterworth zero-phase filter from 0.03 to 40 Hz and were re-referenced to the average.The EEG signals were then segmented into 2-second epochs (matching the timing of TR in each volume/measurement of the fMRI scan), and the EEG epochs with prominent motion artifacts (amplitude > 100 μV) were discarded with the removal of the corresponding fMRI volume (after preprocessing) to preserve the timing consistency for both EEG and fMRI signals.Artifacts related to eye-blinking and physiological noise were manually removed after a temporal fast independent component analysis (FAST-ICA) decomposition.The spectral power of the EEG was subsequently segmented into frequency bands: delta (1-4 Hz), theta (4-8 Hz), alpha (8-13 Hz), beta (13-30 Hz), and gamma (> 30 Hz).
The fMRI data were preprocessed using Statistical Parametric Mapping package (SPM12, Wellcome Institute of Cognitive Neurology, UK) and Analysis of Functional NeuroImages (AFNI) (Cox and Hyde, 1997;Cox and Jesmanowicz, 1999).Artifact Detection Tools (ART, https:// www.nitrc.org/projects/artifact_detect/,part of the CONN software) (Whitfield-Gabrieli and Nieto-Castanon, 2012;Nieto-Castanon, 2020) were used to identify spikes and correct motion for each dataset.All functional dataset showed head motion below 3.4 mm in translation (in any direction) and 1 • of rotation, with framewise displacement less than 0.2 mm.For resting-state fMRI datasets, additional preprocessing steps such as quadratic detrend and RETROICOR (artifact removal of heart-rate and respiration) were applied, and nuisance regression was performed to remove motion, white matter, and cerebrospinal fluid signal influences using AFNI.Notably, no filtering was applied to the resting-state fMRI datasets to preserve the full observable fMRI spectrum.Preprocessed functional images were coregistered to individual anatomical image and normalized to the standard MNI brain template using nonlinear alignment and resampled to a 2-mm isotropic voxel size.Normalized images were spatially smoothed with a Gaussian kernel of 6-mm full width at half maximum (FWHM) to accommodate any anatomical variability across participants.The fMRI data in the EOEC task was high-pass filtered (cutoff frequency: 128 s) and then analyzed using the general linear model by fitting the EOEC task paradigm convolved with the canonical HRF (Allen et al., 1998).After generating the group-level activation map of the EOEC task, the fMRI time courses were extracted for further spectral correspondence analyses with EEG signals.

Spectral correspondence between EEG and fMRI
To determine the cross-frequency coupling between EEG and fMRI in the EOEC task, the O z -channel EEG signal and corresponding fMRI time courses extracted from the activated primary visual cortex (Supplementary Fig. S1) were subjected to the HHT analyses (generating IMFs via EEMD and generating the fine-grained time-frequency maps through HSA, as shown in Fig. 1).In the PAC approach, the temporal correlation analysis was conducted between each of the fMRI-based IMF and each temporal waveform from the EEG-based time-frequency map, resulting in a spectral correspondence map (IMF number × EEG spectrum).In the AAC approach, the temporal correlations were calculated between each pair of the temporal waveforms from the two time-frequency maps of EEG and fMRI by collapsing temporal information for spectral correspondence (fMRI spectrum × EEG spectrum).Pearson correlation coefficients were then converted into z-values for the following statistical comparison.In the resting condition, for probing the EEG-fMRI crossfrequency coupling between different brain areas, we selected EEG signals from the 4 midline channels (F z , C z , PO z , and O z, corresponding to the frontal, central, parieto-occipital, and occipital lobes, respectively), and the fMRI waveforms extracted from corresponding spherical ROIs (6-mm radius) based on the 10-20 EEG electrode system to match the spatial locations (Rojas et al., 2018) (Fig. 1a).One-sample t-test was conducted in the group-level PAC/AAC spectral correspondence (correlation) maps to assess any cross-frequency coupling deviant away from 0 (two-tailed) with Bonferroni-corrected p < 0.05 (also notifying the thresholding of uncorrected p < 0.05 in the resulting figures for more information).Moreover, to further explore the EEG-fMRI coupling across the visual network in the resting state, we compared the PAC/AAC spectral correspondence between the EEG-O z signals and the fMRI signals of 3 prescribed spherical ROIs (6-mm radius) in the visual network (center of the seed location: [− 2,− 48,60], [− 14,− 84,36], and [0,− 96,12]), where the regions of the visual network were calculated by one-sample t-test from the resting-state functional connectivity map, seeding at the primary visual cortex (3dClustSim-corrected p < 0.05 with autocorrelation function and cluster size > 50 voxels).%, with complete results for varying noise levels presented in Supplementary Figure S2.In Simulation 1, PAC correspondence was observed between the simulated EEG signal (x-axis; 5-20 Hz) and the 4th to 6th IMF (0.008-0.031Hz) of the simulated fMRI signal (y-axis; target frequency: 0.0167 Hz) across different noise levels.However, AAC results showed comparable spectral correspondence at the 0 % noise level but diluted with stronger noise level.In Simulation 2, PAC correspondence showed high precision that the simulated EEG signal (8 Hz) had high correlations with the 3rd to 7th IMFs (0.002-0.063Hz) of the fMRI signals (target frequencies: 0.011 and 0.05 Hz), corresponding to the two simulated sources, across all noise levels.AAC correspondence depicted the two-source spectral relationship with blurred artifacts at 0 % noise, but this correspondence weakened with increasing noise.

EEG-fMRI spectral coupling in the EOEC task
The group-level brain activation map for the EOEC task is displayed in Fig. S1 and Table S1.Fig. 3 presents the group results of PAC and AAC between EEG-O z signals and the fMRI signals from the activated cluster in the occipital lobe.The PAC spectral correspondence (Fig. 3, upper panel) revealed a significant negative correlation between EEG alpha band and the fMRI 5th IMF (0.008-0.016Hz) during the EOEC task (Bonferroni-corrected p < 0.05).However, in the AAC analysis (Fig. 3, lower panel), no spectral correspondence passed the statistical testing with multiple comparison (Bonferroni-corrected p < 0.05).

Discussions
We probed the complexities of neurovascular coupling through the spectral correspondences between concurrent EEG and fMRI signals.
Through the simulations with the designed signals, we demonstrated the characteristics of HHT-based spectral correspondence maps for both PAC and AAC.In the real dataset, we observed unique patterns of EEG-fMRI spectral correspondence across the two conditions, the EOEC task and resting state, in the same healthy participants.In the EOEC task, there was a significant PAC spectral correspondence between the EEG alpha band and the corresponding fMRI signal.Conversely, in the resting state, the AAC spectral correspondence was more pronounced, particularly between EEG gamma band and high-frequency fMRI signals (> 0.15 Hz) across midline brain regions and within the visual network.The distinctive EEG-fMRI spectral correspondences between the EOEC task and the resting state highlight the dynamicity nature of neurovascular coupling, which varies with the neurophysiological state, even among individuals without neurological abnormalities.
Traditionally, analyses of concurrent EEG and fMRI have operated under the assumption that fluctuations in the fMRI signal follow the envelope of specific EEG frequency bands (i.e., PAC).Consequently, previous research has often reported relationships between EEG frequency bands and resting-state fMRI signals without distinct frequency identification, leading to both negative (Chang et al., 2013) and positive relation (Mo et al., 2013) between alpha power and functional connectivity on default-mode network (DMN).This is because the typical fMRI signals for functional connectivity analysis fall in a low frequency range less than 0.10 Hz compared with the canonical frequency of neuronal firing rates or electrophysiology, where such low frequency signals were not considered with neurophysiological information.However, fMRI signals exhibit its own specific frequency bands that correlate with specific functionality (Gohel and Biswal, 2015;Hiltunen et al., 2014;Keinänen et al., 2018;Yuan et al., 2012), as exhibited in regional frequency distinctions (Wu et al., 2008;Wu and Chao, 2012) and the identified three distinct frequency bands through graph theory (Thompson and Fransson, 2015).Therefore, considering that both EEG and fMRI possess spectral signature indicative of brain functions, it is reasonable to speculate that these modalities may interact in a cross-frequency manner (i.e., PAC or AAC), particularly in resting-state signals where source identification is challenging.Moreover, the assessment of PAC or AAC spectral correspondence between EEG and fMRI signals necessitates the adaptive, nonlinear, and nonstationary analysis capabilities of the HHT.The discerned PAC patterns during the EOEC task and AAC patterns during the resting state could arise from the inherent nature of brain signals, which often manifest as multiple intertwined sources with nonstationary dynamics (Gultepe and He, 2013).Consequently, the current study provides insights for further research into neurovascular coupling across both active task engagements and resting state.

PAC vs. AAC
PAC has traditionally been used to explore cross-frequency relationships within a single modality (Jensen and Colgin, 2007), proving valuable for identifying phases that modulate the amplitude of specific frequency bands (Tort et al., 2009).This method has been instrumental in dissecting the temporal dynamics of neurophysiological signals associated with cognitive processes (Canolty et al., 2006).When applied across different modalities, PAC enables to uncover previously unrecognized patterns and relationships, thus enhancing our comprehension of the dynamic nature of neurophysiological activities (Cohen, 2014).Specifically, PAC facilitates insight into how fluctuation in one frequency within a modality correspond to changes in another during various cognitive and neural processes (Buzsáki and Draguhn, 2004).Conversely, AAC is typically employed to examine correlation between the amplitudes of different frequency bands within neural signals (Cohen, 2014).This approach allows for the investigation of the cooperative dynamics across multiple frequency bands, which underpin complex neural processes (Bruns and Eckhorn, 2004).A unique feature of AAC is its ability to determine the relationship between the amplitudes of two signals across different frequency band, potentially reflecting the degree of coordination or interaction between or within neural network, contingent on the frequency bands analyzed (Onslow et al., 2011).While PAC provides insights into the timing relationships between neural oscillations, AAC provides information of the intensity relationship between brain rhythms (Bruns and Eckhorn, 2004;Canolty and Knight, 2010).In the context of task performance EEG-fMRI investigations, PAC is particularly suitable due to the discernible target timing and periodicity, providing evidence of a tight relationship between the phase of one rhythm and the amplitude of another (Canolty et al., 2006).For resting state studies, AAC provides an alternative perspective, focusing on amplitude relationships across frequency bands or the overall power within these bands (Cohen, 2014).Leveraging from AAC, we could determine the EEG and fMRI relationship given multiple time-varying signal sources in the resting state.In short, PAC and AAC are spectral correspondence analyses used for distinctive neurophysiological scenarios, such as the EOEC task and the resting state observed in this study.
As noted in Fig. 2, we conducted two simulations to validate the effectiveness of the spectral correspondence map (PAC and AAC) using the HHT analysis.With predefined target timing and periodicity, the PAC approach effectively detected spectral correspondence at the intended frequency.However, the target information could be spread into multiple adjacent IMFs (the mode-splitting problem), in which the blurriness with less spectral specificity could not differentiate multiple sources.Remarkably, even with 100 % noise, the sensitivity of spectral correspondence in PAC remained intact due to the exclusion of the IMFs with extreme frequency ranges.In contrast, the AAC approach demonstrated high precision in mapping spectral correspondence, capturing multiple sources at target frequencies effectively without blurriness, albeit only at the 0 % noise level.Actually, in each HSA, the power of 1-D waveform is redistributed into a fine-grained 2-D time-frequency map, resulting in diminished signal power.Consequently, the PAC approach requires only one round of HSA (applied to EEG data), whereas the AAC approach necessitates two rounds of HSA (for both EEG and fMRI data).This leads to the AAC approach being more sensitive to noise interference.This increased noise level might also be the reason why the AAC approach demonstrates weaker correlation coefficients compared with the PAC approach.In summary, both PAC and AAC approaches are effective in probing EEG-fMRI spectral correspondence, yet they exhibit varying sensitivities to the noise level in the spectral correspondence maps.Future investigations employing spectral correspondence analysis should proceed with caution, particularly when utilizing HHT for EEG-fMRI investigations.

PAC between EEG and fMRI in the task condition
Along the history of neuroimaging, PAC has been a prevalent method  for detecting association across in EEG frequency bands.The complex and distributed alpha system, which characterized by various generators and functions, extends to other inherent EEG frequencies, including delta, theta, and gamma oscillations (Bas ¸ar et al., 2001).For instance, when performing memory tasks, the quantity of task items is determined by the number of gamma cycles that fit within a single theta cycle (Herrmann et al., 2016;Lisman and Idiart, 1995).This cross-frequency coupling between theta and gamma oscillations has been further supported by multiple electrophysiological studies (Canolty et al., 2006;Demiralp et al., 2007;Mormann et al., 2005).The integration among EEG frequency bands, particularly regarding oscillation modulations and cognitive processes, may reveal inherent causal associations.The concept of synchronizations between EEG frequency bands and fMRI signal fluctuations has been extended to resting-state researches (Mantini et al., 2007), with neural dynamics suggesting that high-and low-frequency synchronization independently contribute to the BOLD-fMRI signal (Scheeringa et al., 2011).This coupling is further validated in study of alpha oscillations relation to tonic alertness (Sadaghiani et al., 2012).Consequently, the PAC spectral correspondence in this study adhered to the same concept, with the exception of decomposing fMRI signals into multiple IMFs using EEMD analysis.This method serves a dual purpose: (1) to generate a PAC-based spectral correspondence map via multiple IMFs with different frequencies for comparison with the AAC-based spectral correspondence map, and (2) to enhance sensitivity by focusing on IMFs within the target frequency, as indicated in our previous research (Lin et al., 2016).
In the EOEC task, the decomposed EEG spectral power, as represented in the time-frequency map, demonstrated a linear correlation with the fMRI-generated IMFs.This correlation was evident in the PAC spectral correspondence (Fig. 3).Previous literature had indicated that PAC increases during resting state and decreases during movement execution (Miller et al., 2012;Yanagisawa et al., 2012), and a negative correlation between the EEG power in alpha-and gamma-bands and BOLD signals during finger-tapping tasks (Murta et al., 2017).Our findings align with previous studies, demonstrating a negative PAC correlation between alpha-band EEG and relatively low-frequency BOLD signal during EOEC task.The alpha-band EEG, associated with wakeful relaxation states with eyes closed and selective attention processes (Foxe and Snyder, 2011), presents competitive or inhibitory interaction with the low-frequency BOLD signal in the visual areas.This suggests that the EOEC task enhances alpha-band EEG presentation while concurrently suppressing brain activation in the visual cortex.Thus, we adopted the EOEC task as the target frequency to validate the effectiveness of PAC spectral correspondence in the EEG-fMRI coupling in Fig. 3, highlighting that PAC was more effective than AAC in this specific task.

AAC between EEG and fMRI in the resting state
In the resting state, the cross-frequency correlations were conducted and observed linear correlations between the decomposed EEG spectral power and the decomposed fMRI spectral power (AAC), rather than the fMRI IMFs (PAC).We originally conjectured AAC for the resting state brain signals because of several reasons.First, resting-state fMRI data is well-known comprised of multiple spatially distributed functional networks (Doucet et al., 2011;Hacker et al., 2017), and these networks are spontaneously intertwined with each other through the graph-theory analysis (Whitfield-Gabrieli and Nieto-Castanon, 2012), which partly supports that every fMRI waveform could contain multiple sources.Second, beyond the time-varying features of the resting-state fMRI signals, Gultepe and He demonstrated the distinction of signal characteristics between networks, where the task-positive networks tend to contain nonlinear signals and the task-negative networks contains mostly linear signals (Gultepe and He, 2013).Considering the complicated spatiotemporal features of nonstationarity, nonlinearity, and multiple sources underlying the resting-state brain signals, the PAC method, by treating single fMRI waveform as the target, could be a simplified form to disentangle the EEG-fMRI spectral coupling.Facing the technical challenges, the HHT-based time-frequency decompositions (Huang et al., 1998) for both EEG and fMRI would be a more suitable strategy than the traditional linear decomposition methods to investigate the EEG-fMRI spectral coupling.Align with our expectation, the Figs. 4 and 5 appear to present prominent AAC spectral correspondences between the resting-state EEG and fMRI data.
The understanding of high-frequency BOLD-fMRI signals remains comparatively limited due to the traditional focus on low-frequency BOLD-fMRI signals when probing spontaneous brain activity and functional connectivity (Biswal et al., 1995;Fox and Raichle, 2007).Nevertheless, recent research suggests that high-frequency BOLD fluctuations might be associated with specific functions of brain regions, including perception, motor control, and cognitive processing (Baria et al., 2011;Gohel and Biswal, 2015;Zuo et al., 2010).This high-frequency fMRI signals may reflect more localized neuronal activities (Scheeringa et al., 2011), offering a more directly linkage to localized neuronal activity rather than the broader systemic factors like global blood supply or regulatory mechanisms (He and Liu, 2012).Furthermore, a recent study found high-frequency BOLD oscillation during deep sleep, indicating localized slow wave activity, particularly in the posterior cortices (Song et al., 2022).This emerging evidence reinforces the significance of high-frequency fMRI signals, which exhibit a positive correlation with gamma-band EEG activity, as shown in this work (Figs. 4 and 5).This association may have a critical role in the spontaneous activities of large-scale brain networks and higher-order cognitive functions.Furthermore, high-frequency fMRI signals may have different neurophysiological origins compared to low-frequency fMRI signals, suggesting their varied functional roles in the resting state (Gohel and Biswal, 2015).With the increasing availability of data acquisition with higher sampling rates, it is advisable to explore a broader frequency range.This approach could enhance the likelihood of unraveling the complex neurophysiological mechanisms underlying neurovascular coupling.

Limitations
This study presents a several key considerations and limitations.First, a major limitation was the low fMRI sampling rate, which restricted the observable frequency range and induces aliasing issues, i. e., the low-frequency contamination from the high-frequency physiological signals.Henceforth, our PAC/AAC findings could be partially contaminated by the aliased signals at higher frequency than the Nyquist frequency of fMRI (0.25 Hz with 2 s of TR).Future studies could mitigate aliasing issue by employing advanced techniques like the simultaneous multislice (SMS) technique to shorten the TR and avoid the aliasing.Secondly, the EOEC task was limited to three minutes to prevent participants falling asleep during nighttime EEG-fMRI data collection.Despite the limited duration, the degree of freedom in the first-level GLM remained to be 81, and both EEG alpha change and fMRI signal change were stable across each participant.Longer acquisition times would be beneficial for EEG-fMRI coupling investigation for future research to enhance statistical power.Thirdly, the complexities of simultaneous EEG-fMRI acquisition led to a small sample size of 14 participants, potentially impacting the generalizability of the findings.Further test-retest reliability assessments warranted to verify the robustness of these results.Nevertheless, unlike the cross-sectional studies requiring abundant sample size, this study focused on the within-group comparisons of neurovascular coupling, identifying consistent patterns or differences under varying conditions.Despite the limited sample size, the ability to draw these comparisons significantly strengthen the robustness of the results and contributes a valuable foundation for future research endeavors in this field.

Conclusion
Phase-amplitude coupling (PAC) measures the timing relationships between different neural oscillations, while amplitude-amplitude coupling (AAC) assesses the intensity relationships between various brain rhythms.We hypothesized that the EEG-fMRI coupling might shift between PAC and AAC under different conditions.Through simultaneous EEG-fMRI recordings among 14 normal human participants, we carried out the EEG-fMRI spectral correspondence in both EOEC task and resting state.We demonstrated a negative PAC relationship between EEG-O z alpha-band oscillations and corresponding fMRI signals during the EOEC task.Conversely, in the resting state, an AAC relationship emerged between EEG-O z gamma-band and high-frequency fMRI signals (0.15-0.25 Hz) within the visual network.The distinctive results between EOEC and resting state suggest that EEG-fMRI spectral correspondence may vary depending on cognitive or physiological conditions, rather than representing a consistent, state-independent relationship.Furthermore, our discovery of neurovascular coupling in the resting state underscores the importance of high-frequency BOLD-fMRI fluctuations, which potentially originate from distinct neurophysiological sources that differ from those of the low-frequency fMRI signals.This observation warrants further investigations to fully understand these diverse roles.

Fig. 1 .
Fig. 1.Schematic diagram of generating AAC and PAC spectral correspondence using the HHT analysis.(a) Demonstration of decomposing EEG and fMRI signals into IMFs and then transformed into HSA time-frequency maps.(b) The procedures of PAC (IMF-HSA) and AAC (HSA-HSA) in the 2 simulations for EEG-fMRI coupling.

Fig. 2
Fig.2illustrates the group-level PAC and AAC patterns derived from simulated EEG and fMRI signals across noise levels of 0 %, 60 %, and 100

Fig. 4
Fig. 4 displays the group results of PAC and AAC in the resting state, with spectral correspondence calculated between EEG signals from the four midline channels and the fMRI time courses from the corresponding spherical ROIs.The resting state showed no significant PAC correlation between EEG and fMRI signals across the four selected channel.Conversely, AAC analyses revealed several significant EEG and fMRI spectral coupling in high-frequency ranges (Bonferroni corrected p < 0.05).In F z , EEG gamma band showed positive correlation with fMRI signal of 0.150-0.175Hz and showed negative correlation with fMRI signal of 0.200-0.225Hz.In C z , EEG gamma band showed positive correlation with fMRI signal of 0.125-0.150Hz.In PO z , EEG theta band showed positive correlation with fMRI signal of 0.200-0.225Hz.In O z , EEG beta band showed negative correlation with fMRI signal of 0.025-0.050,and EEG gamma band showed positive correlation with fMRI signal of 0.175-0.225Hz.

Fig. 2 .
Fig. 2. Spectral correspondence of PAC and AAC in the two simulations.Simulation 1 was designed with single signal source (targeting frequency: 8 Hz in EEG and 0.0167 Hz in fMRI) for simulating task engagement, and the Simulation 2 was designed with dual sources (targeting frequency: 0.011/0.05Hz in fMRI and 8 Hz in EEG) for simulating resting-state signals.By collapsing the time information, the PAC correspondence was shown with blurriness in both X and Y dimensions, but not much affected across different noise levels.In contrast, the AAC results showed high precision spectral correspondence between simulated EEG and fMRI signals; however, the spectral correspondence could be weakened by the enhanced noise level.

Fig. 3 .
Fig. 3.The EEG-fMRI spectral correspondence in the eye-open-eye-close (EOEC) task.Significant correlations were found between EEG-O z alpha (negative correlation) and beta (positive correlation) bands and the fMRI 5th IMF (0.008-0.016Hz) in the block-designed EOEC task.Instead, AAC does not show significant correspondence after multiple comparison.The red or blue squares denote positive and negative correlations with uncorrected p < 0.05, respectively, where the asterisk (*) represents Bonferroni-corrected p < 0.05.

Fig. 4 .
Fig. 4. The EEG-fMRI spectral correspondence of midline channels in the resting state.AAC shows multiple significant spectral correspondence, in which mostly occurs in relatively high-frequency range for both EEG (β and γ band) and fMRI signals (0.175-0.225Hz).However, no significant PAC was demonstrated between resting EEG and fMRI signals among the four midline channels.The red or blue squares denote positive and negative correlations with uncorrected p < 0.05, respectively, where the asterisk (*) represents Bonferroni-corrected p < 0.05.

Fig. 5 .
Fig. 5.The EEG-fMRI spectral coupling of the visual network in the resting state.In AAC, the EEG-O z gamma band show positive correlations with the relatively high-frequency fMRI signals (0.175-0.225Hz) in the resting state.The EEG-O z beta band shows negative correlation with typical resting-state fMRI frequency below 0.1 Hz.No significant PAC was exhibited between the EEG-O z signals and the fMRI signals of the 3 prescribed ROIs from the visual network in the resting state.The red or blue squares denote positive and negative correlations with uncorrected p < 0.05, respectively, where the asterisk (*) represents Bonferroni-corrected p < 0.05.