Dietmar Cordes^{1,2}, Muhammad Kaleem^{3}, Xiaowei Zhuang^{1}, Karthik Sreenivasan^{1}, Zhengshi Yang^{1}, and Virendra Mishra^{1}

^{1}Cleveland Clinic Lou Ruvo Center for Brain Health, LAS VEGAS, NV, United States, ^{2}University of Colorado Boulder, Boulder, CO, United States, ^{3}University of Management & Technology, Lahore, Pakistan

### Synopsis

In this project, high-frequency contributions to
functional connectivity of the Default Mode Network (DMN) are studied. Rather
than relying on user-defined frequency bands, Empirical Mode Decomposition
(EMD) is used to decompose the natural occurring frequency bands of the DMN.
The novelty of our approach lies in the data-adaptive and user-independent
decomposition of fMRI data using EMD, and identification of a resting-state
network based on the frequency characteristics of intrinsic modes in the data,
instead of using wavelet- or windowed-Fourier-transform methods. Results are
shown for multiband MB8 resting-state data of a group of 22 healthy subjects.

### INTRODUCTION

Analysis of functional
networks in resting-state data were traditionally obtained by using
low-pass-filtered data with frequencies in the range 0.01Hz to 0.1Hz^{1}.
Recently, it was argued that high frequencies above 0.1Hz may also contribute
to functional connectivity in resting-state data^{2,3}. To shed more
light on this phenomenon, we acquired 30min resting-state data from 22 subjects
by using a high sampling rate allowing to investigate the frequency content up
to 0.65Hz. Rather than relying on user-defined frequency bands, we use
Empirical Mode Decomposition (EMD)^{4} to study the natural occurring
frequency bands of the DMN. The novelty of our approach lies in the data-adaptive
and user-independent decomposition of fMRI data using EMD, and identification
of resting-state networks based on the frequency characteristics of intrinsic
modes in the data, instead of using wavelet- or windowed-Fourier-transform
methods. ### METHODS

Functional MRI was
performed on 22 (age 18-25) healthy subjects in a 3T Trio Tim Siemens MRI
scanner equipped with a 32channel head coil using multiband EPI with imaging
parameters: MB8, TR 765ms, TE = 30ms, flip 44deg, partial Fourier 7/8 (phase),
FOV = 19.1 x 14.2 cm, 80 slices in oblique axial orientation, resolution 1.65mm
x 1.65mm x 2mm, BW =1724 Hz/pixel (echo spacing = 0.72ms), 2380 time frames
(30min scanning duration). Due to the short TR, no slice-timing correction was
performed. The usual preprocessing steps included field-map-based distortion
correction, realignment, spatial smoothing (8mm), and normalization to the MNI
152 template using ANTS software (http://stnava.github.io/ANTs/). All voxels
were resampled to a 2mm x 2mm x2mm grid. Obtained motion parameters were less
than 0.6mm on average in all directions (and equivalently the parameters for
rotations). Group ICA (based on the FastICA algorithm^{5}) was
performed by stacking all data in the temporal domain to obtain the major
resting-state networks. Using spatial regression of the found DMN network on
the group time series data, the group time series signature of the DMN was
obtained. The DMN group time signature was decomposed using EMD, which allows a
signal being partitioned into its intrinsic modes of oscillation, called
intrinsic mode functions (IMFs), without any assumptions of stationarity or
linearity, or imposition of a priori assumptions on frequencies of interest.
The IMF with index 1 (IMF 1) contains the highest frequencies, and IMF k
contains the lowest frequency components. It has been shown that the frequency
arrangement in IMFs mimics that of a dyadic filter bank. After the group IMFs
were obtained, the corresponding group spatial maps were calculated by
regression of each individual IMF on the original stacked group data. The obtained
group spatial maps resembled the spatial characteristics of each IMF. To obtain
instantaneous frequency characteristics, the Hilbert Huang Transform (HHT) was
applied on each IMF. The spectrum of each IMF was obtained with standard kernel
density estimation algorithm in Matlab to study the frequency characteristics
of each IMF.### RESULTS

Fig.1 shows one slice of the spatial map for
the DMN obtained by group ICA and the decomposition maps of the full data into
maps belonging to 8 IMFs. The DMN can be reliably identified in IMFs 2 to 6. Fig.2
shows the frequency spectra of the obtained IMFs. Note that each IMF
corresponds to a frequency band which partially overlaps with bands from
neighboring IMFs. Peak frequencies and effective range (FWHM) of the first 3 high-frequency
IMFs are given by 0.43Hz (0.64Hz-0.22Hz), 0.16Hz (0.28Hz-0.08Hz), and 0.088Hz (0.122Hz-0.047Hz),
respectively.### DISCUSSION

The frequency range where the DMN could be
reliably identified was found to be in the range 0.01Hz to 0.28Hz covered by
IMFs 2 to 6 for the group data. In the frequency range above 0.28Hz which is
essentially covered by IMF 1, no pattern resembling the DMN could be
identified. IMF 1 appears to be a wide spectrum noise component which may be
used in denoising fMRI data. We found that with increasing frequency range, the
DMN pattern for IMFs 2 to 6 shows only minor changes in the positive (yellow
colored) pattern. Regarding negative changes (blue colored), most changes are
observed in the high frequency range between IMF2 and IMF3. ### CONCLUSION

We have studied the
frequency dependence of the DMN in group fMRI resting-state data using EMD.
Given our sampling rate (TR 0.765s) we were able to show that the DMN could be
reliably found in 5 different frequency bands covered by IMF 2 to IMF 6 which
covered an effective frequency range up to 0.28Hz.### Acknowledgements

The study was supported in parts by National Institute of General Medical
Sciences (grant: P20GM109025) and National Institute of Biomedical Imaging and
Bioengineering (grant: 1R01EB014284).### References

[1] Cordes D, et
al. Frequencies contributing to functional connectivity in the cerebral cortex
in resting-state data. AJNR 2001, 22:1326-1333.

[2] Niazy RK, et
al. Spectral characteristics of resting-state networks. Prog. Brain Res. 2011,
193:259-276.

[3] Chen JE, Glover GH. BOLD
fractional contribution to resting-state functional connectivity above 0.1Hz.
NeuroImage 2014, 107:207-218,

[4] P. Flandrin, et al. Empirical
mode decomposition as a filter bank, IEEE Sig. Proc. Letters 2004, 11(2), 112-114.

[5] Hyvärinen A. Fast and
Robust Fixed-Point Algorithms for Independent Component Analysis. IEEE Transactions on Neural Networks 1999, 10(3):626-634.