Spectral analysis of BOLD signal has shown its unique advantages in neuroscience research, such as separating noise from neurophysiological signals ¹ and identifying different components in BOLD signal ². Previous researchers have found that components of interest and meaningful resting-state networks mainly resided in low-frequency BOLD oscillations (<0.1Hz), and were usually contaminated by high-frequency physiological noise. Other studies suggested that the BOLD signal might be a mixture of different frequency components, and these components in different frequency bands might be associated with distinct neurocognitive processes and have different neurophysiological implications ³. Empirical Mode Decomposition (EMD) could be a promising data-driven method to isolate these frequency components. It decomposes the BOLD time series into several rhythms with distinct frequency bands, termed intrinsic mode functions (IMFs) ⁴. However, the neurophysiological basis of the IMFs, and the robustness and stability of EMD method is still unclear. In this study, we attempted to examine the robustness and stability of IMFs by computing the cross session coherence (CSC) of IMFs, and evaluate how the CSC of IMFs in the brain may differ from that in the phantom.

MRI Data Acquisition. The resting-state fMRI data were acquired on a 3.0-Tesla system (Siemens Prisma, Germany). Four healthy adults (ages from 25-26 years old, 2 females) participated in this study. Each participant underwent ten eyes-closed resting-state scanning sessions, the intervals between these sessions randomly ranged from 40 mins to7 days. A gradient echo T2*-weighted EPI sequence was used for acquiring resting-state functional images with the following parameters: TR/TE=2000/30ms, flip angle=80°, matrix size=64×64, FOV=240×240mm, 33 axial slices, thickness/gap=3.5/0.7mm. Each session consists of 240 functional volumes. A 3D T1-weighted MPRAGE image was acquired for each subject, 128 sagittal slices (slice thickness/gap=1.33/0mm, in-plane resolution=256×192, TR/TE=2530/3.39ms, TI=1100ms, flip angle=7°, FOV=256×256mm). The phantom images were acquired with the same parameters.

After preprocessing, the time course of each voxel was normalized by subtracting its own temporal mean and dividing by its own temporal standard deviation. Then, the EMD method decomposed the original signal into a finite set of IMFs. Each IMF occupies a unique frequency range, the first IMF (IMF1) occupies the highest frequencies, and the last (IMF5) occupies the lowest, with the other IMFs in between. The number of IMFs was determined by the intrinsic temporal-spectral characteristics of the original time series. For almost all voxels in the brain, the decomposition of the time course yielded five IMFs, denoted as IMF1 to IMF5, and the frequency range of these five IMFs covers 0-0.25Hz. After acquired five IMFs for each voxel, the resemblance between the power spectrum of the corresponding IMFs of the same brain area in two different sessions (i.e. the voxel with the same MNI coordinates in two sessions) were calculated by using Pearson’s correlation. This correlation coefficient was assigned to this area as the CSC value. Hence we acquired 45 CSC maps for each subject and the phantom. The procedure of calculating CSC is shown in Fig.1

As shown in Fig.2, except IMF1, the values of the CSC of other IMFs in all the voxels in the phantom distributed in a significantly lower range than that in the brain, indicating that the IMFs in brain showed higher stability and consistency across sessions than that in the phantom. Fig.3 and Fig.4 show the spatial distribution of voxels with CSC values higher than a certain threshold in the males’ and females’ brains correspondingly. Fig.5 shows the spatial distribution of the voxels with CSC values higher than a certain threshold (the same threshold used for the human brain) in the phantom. Results showed that high CSC values mainly reside in the white matter for IMF2, while the frequency profiles of some clusters in the grey matter showed higher consistency across different sessions in IMF3, 4 and 5. While the supra-threshold voxels in the phantom are randomly scattered in the whole space without forming any regular clusters.We introduced CSC method to quantify the similarity of the frequency profiles of the resting-state BOLD signals in different sessions, and examined the robustness and stability of EMD method. Our results demonstrated that the spectral profile of the IMFs in brain showed higher cross-session consistency, robustness, and stability than that in the phantom, which suggested that different frequency components of BOLD signal in the brain might be associated with distinct intrinsic neuronal oscillations rather than random noise.