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Towards a more precise and comprehensive characterization of the relationship between EEG alpha rhythm and thalamic BOLD signal
SeyedMohammad Shams1,2, Pierre LeVan3, and J. Jean Chen1,2

1Rotman Research Institute at Baycrest, North York, ON, Canada, 2Department of Medical Biophysics, University of Toronto, Toronto, ON, Canada, 3Department of Radiology, University Medical Center Freiburg, Freiburg, Germany

### Synopsis

In this study, the relationship between EEG alpha band power and the BOLD signal is examined in the thalamus. We overcome previous limitations in temporal resolution by using fast fMRI (MREG) acquisitions. We also consider a wider range of lags between EEG and BOLD signals than previous studies. In addition, cross correlations between alpha EEG and fMRI signals from all voxels in the thalamus region of all subjects are automatically classified using clustering to reveal consistent spatial-temporal patterns in the relationships between EEG alpha activity and BOLD signals in different parts of thalamus.

### Introduction

The relationships between fMRI time series and the alpha rhythm in the thalamus have been studied using predetermined fixed time lags between EEG rhythms and BOLD signals directly by imposing a fixed delay1,2 or indirectly by convolving EEG fluctuations with an HRF3,4. The resulting correlations are then thresholded to determine regional specific relationships between the fMRI and EEG2-4. The results of these studies are somewhat inconsistent, highly sensitive to the predefined EEG-BOLD time lags, and the precise region of interest. It is well known that the thalamic alpha-BOLD relationship cannot be characterized by a fixed delay, as alpha rhythm both originates from and feeds back to the thalamus5. In this study, we explore the relationship between BOLD and EEG rhythm as a function of lags (cross correlation function). This is enhanced by our use of ultra-fast fMRI acquisitions to reveal spatial patterns in (alpha) EEG-fMRI associations.

### Materials and Methods

Data acquisition: Six healthy volunteers (mean age 32, 4 male) participated in this study. Simultaneous EEG and fast fMRI (MREG sequence; 20 min, TR = 0.1s, TE = 36 ms, and FA = 25°) recordings were acquired with Siemens 3T TIM Trio scanner and a 256-channel MR-compatible EEG (EGI; sampling rate 1000 Hz) while the subjects were at rest with open eyes. Also, a high-resolution T1-weighted was acquired for each subject .

FMRI data processing: The fast fMRI data were motion corrected, spatially smoothed with a Gaussian kernel of 4 mm FWHM, and registered to anatomical data using FSL software (www.fmrib.ox.ac.uk/fsl). To obtain the thalamus BOLD signals, brain region segmentation was performed using FreeSurfer (http://surfer.nmr.mgh.harvard.edu/). Finally, extracted BOLD signals were temporally band pass filtered between [0.01, 0.2] Hz.

EEG data processing: (1) gradient switching and cardiac ballistic effects were corrected using template subtraction method, and the residual effects were removed using ICA; (2) the data were down sampled to 200 Hz and re-referenced to common average reference; (3) using a short-time Fourier Transform (1-sec sliding Hanning window with step = 100 msec), we generated the power spectrogram for each channel separately; (4), alpha band fluctuations for each TR epoch was obtained by averaging the spectrogram power in the 8 to 12 Hz band, and then across all channels to obtain the alpha global field power (GFP); (5) the overall alpha rhythm for each subject was convolved with the canonical HRF (gamma PDF that peaks at 5 sec).

Lag Dependent Relationship: Since the correlation merely provides instantaneous zero-lag dependencies between two signals, we opted for the cross-correlation function (CCF) is to characterize the dependency between EEG alpha rhythm and BOLD signals6,

$$CCF(\tau)=\frac{1}{T-\tau}\sum_{t=1}^T x_t^*y_{t+\tau}$$

where 𝑥t and 𝑦t denote the HRF-convolved EEG alpha rhythm and BOLD signal at time t, respectively. To compensate the delay imposed by convolving with HRF, the convolved EEG alpha GFPs were shifted precisely shifted by the delay introduced by gamma PDF ($x_t^*$).

Across voxels, these cross-correlation time series (CCF time series) exhibited quite different temporal patterns in terms of peak time, strength, and more importantly the sign of correlations. Then, to determine common temporal CCF patterns across all subjects, the CCFs from all thalamic voxels of all subjects were placed in an observation matrix and parcellated using k-means clustering. This resulted in different categories of CCFs. The voxels belonging to each CCF category are then mapped in each subject’s native space (to avoid atlas normalization).

### Results

The clustering resulted in three main categories of CCFs, shown in Figure 1. The resultant clusters overlaid on the individual anatomical maps are shown in Figure 2. The CCFs can be distinguished by the weighting and occurrence time of their positive and negative peaks. Moreover, Figure 3 shows the percentage of the thalamic voxels that are categorized into each CCF cluster for each subject.

### Discussion

In this study, aided by fast fMRI data, we examine the dynamics of the relationship between the time variations of alpha global field power (GFP) amplitude and the fMRI signals in the thalamus without any prior assumptions in terms of the delay between two modalities. The results clearly show that the thalamus can be segmented into three subregions with different temporal associations with alpha EEG. Both polarities in correlation are observed in the 10s delay range, in agreement with previous work3. However, the correlations are not static as previous presumed, but can switch polarity as a function of time. Taking into the account the whole correlation time series results in different clusters from previously reported.

### Acknowledgements

No acknowledgement found.

### References

1 Munck, J. C. de, S. I. Gonçalves, L. Huijboom, J. P. A. Kuijer, P. J. W. Pouwels, R. M. Heethaar, and F. H. Lopes da Silva. 2007. “The Hemodynamic Response of the Alpha Rhythm: An EEG/fMRI Study.” NeuroImage 35 (3): 1142–51.

2 Yuan, Han, Vadim Zotev, Raquel Phillips, and Jerzy Bodurka. 2013. “Correlated Slow Fluctuations in Respiration, EEG, and BOLD fMRI.” NeuroImage 79 (October): 81–93.

3 Liu, Zhongming, Jacco A. de Zwart, Bing Yao, Peter van Gelderen, Li-Wei Kuo, and Jeff H. Duyn. 2012. “Finding Thalamic BOLD Correlates to Posterior Alpha EEG.” NeuroImage 63 (3): 1060–69.

4 Scheeringa, René, Karl Magnus Petersson, Andreas Kleinschmidt, Ole Jensen, and Marcel C. M. Bastiaansen. 2012. “EEG α Power Modulation of fMRI Resting-State Connectivity.” Brain Connectivity 2 (5): 254–64.

5 Kropotov, Juri D. 2016. “Chapter 2.2 - Alpha Rhythms.” In Functional Neuromarkers for Psychiatry, edited by Juri D. Kropotov, 89–105. San Diego: Academic Press.

6 Davey CE, Grayden DB, Egan GF, and Johnston LA, 2013 “Filtering induces correlation in fMRI resting state data,” NeuroImage, 64: 728–740

### Figures

Figure 1. Three dominant lag-dependent cross-correlation patterns (CCFs) between EEG alpha rhythm and the thalamic BOLD signal.

Figure 2. Thalamus clustering based on CCF in subjects 1-6. These parcellations have been shown in each subject native’s space. Clusters 1, 2, and 3 are coded with blue, white and red, respectively.

Figure 3. The percentage of the thalamus voxels categorized into each CCF-cluster for each subject, separately.

Proc. Intl. Soc. Mag. Reson. Med. 27 (2019)
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