### Synopsis

**ASL perfusion fMRI has much less neurovascular effects than BOLD fMRI,
but its application in time-series analysis is still depreciated due to the low
signal-to-noise-ratio (SNR). Robust principal component analysis (RPCA) decomposing
the original data into a smoothly varying low-rank component and a residual
component with sparse signal. In this study, we used RPCA to denoise ASL MRI.
Our results showed that RPCA can markedly increase the sensitivity of ASL
MRI-based functional connectivity analysis. **### Introduction

Functional brain activity has been widely assessed with the
blood-oxygen-level-dependent (BOLD) fMRI. But BOLD signal is relative and
contaminated by neurovascular effects. It can even be offset the target brain
area since the major contribution of BOLD signal change comes from the oxygen
level change in vein. These issues can be greatly avoided by using arterial
spin labeling perfusion fMRI, which directly measures the quantitative cerebral
blood flow (CBF). However, ASL MRI has a low signal-to-noise ratio (SNR) [1], which has greatly hindered a widespread
application of ASL in dynamic functional activity studies. Robust principal
component analysis (RPCA) [2] is a new technique
for feature extraction or data recovering. Sorting all data into a big data
matrix, RPCA decompose split it into a low-rank (L) plus a sparse (S)
component. The L-component represents the slowly varying part and the
S-component carries the temporally uncorrelated dynamic changes. Such process fits
well with ASL signal denoising since ASL signal can be roughly modeled as a
combination of background CBF and random noise plus other physiological noise [3]. The purpose of this study was to evaluate RPCA
(or equivalently L+S decomposition) in ASL fMRI.

### Method

ASL data acquired with a pseudo
continuous ASL sequence were identified from previous study [4] and local database.
Data acquisitions were approved by IRB with signed consent form from all
subjects. 15 old subjects were included. ASL images were
preprocessed using ASLtbx with state-of-art denoising procedures [5,
6]. Each CBF
image volume was then reformatted into a column vector, and all CBF column
vectors were then sorted into a big matrix M (Fig. 1). The inexact augmented
Lagrange multiplier RPCA algorithm [7] and the
code provide by Chen and Ganesh were used to decompose M into the L and S component. The weight on sparse error term in the cost
function was set to be 1/sqrt(number of inner brain voxels). The bottom row of Fig. 1 shows an example of L+S decomposition for one slide of
one timepoint. After decomposition, each L column vector was reshaped back to a
3D L-CBF image. Both the original CBF images and the L-CBF images were
spatially warped into the MNI space using SPM12.
Seed-based
functional connectivity (FC) analyses were performed. The seeds were two regions-of-interest
(ROIs) drawn in right motor cortex (MC) and parietal cortex (PA), respectively
(Fig. 2). The mean CBF values were then extracted from each ROI from all CBF
images. The time series of the mean CBF value was then used as the regressor
for a whole brain simple regression analysis. The correlation coefficient maps
of all subjects were grouped together for a group level statistical analysis. The
same analysis was performed for the original and the L-CBF images separately.

### Results

Fig. 1 shows that the L+M decomposition can extract a good quality baseline
CBF map even from one timepoint. Fig. 3 shows the average CBF map of the M, L,
and S CBF image series. As compared to the original mean CBF map, the mean
L-CBF map presents higher homogeneity and roughly while keeps the same grey
matter/white matter image contrast. Fig.
4 shows the results of FC analysis. The top row was the group level MC-FC
analysis results; the bottom row was PA-FC results. On the left was based on
the original CBF images; on the right was from the L-CBF images. Significance
level was defined by a Bonferroni corrected p=0.05. For both FC, L+S decomposition
greatly improved sensitivity for identifying the contralateral FC. For MC-FC,
L+M showed FC in the middle superior MC as well as in the supplementary motor
area. For PA-FC, L+M showed markedly increased FC in precuneus and several
other brain areas.

### Discussion and conclusion

We showed that L+M decomposition can extract
reasonable CBF map from even one time-point. The mean CBF map after taking the
sparse components out presents reduced inhomogeneity though the global CBF
value also reduced, which may be improved by adjusting the L+S algorithm
parameters though a test-retest study or a simulation study would be needed to
find the optimal parameter values. The most significant improvement of L+M for
ASL is in the time-series analysis, where we showed a remarkably increased
sensitivity for two different seeds-based FC. L+M decomposition may eventually
pave the way of ASL MRI for time series analysis such as FC, functional
connectome analysis, resting state network analysis etc.

### Acknowledgements

This study was supported by Upenn-Pfizer Alliance Fund, Natural Science Foundation of Zhejiang Province Grant LZ15H180001, the Youth 1000 Talent Program ofChina, and Hangzhou Qianjiang Endowed Professor Program.### References

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