Kenneth Wengler^{1,2} and Xiang He^{2}

Pseudo-continuous
arterial spin labeling (pCASL) with segmented 3D-GRASE acquisition is widely
accepted as the optimal ASL technique. However, the method suffers from
blurring along the partition direction caused by point spread function (PSF)
broadening. In this study, a PSF deconvolution method for pCASL images with
3D-GRASE acquisition is developed and evaluated in simulations and in-vivo
experiments. The deconvolution method greatly reduces the effects of the PSF
and recover the perfusion signal for segmentation factors of at least 2_{PAR}
x 2_{PE}. The proposed deconvolution method improves the accuracy of
cerebral blood flow quantification and facilitates the use of lower
segmentation factors.

The effect of image blurring along the PAR direction in 3D-GRASE images can be modeled by convolution of the true image with the PSF. Non-blind deconvolution was applied iteratively according to,

$$D^{i+1}=\min\left[\parallel P\ast D^{i}-B\parallel_2^2+\lambda^{2}\parallel D^{i}-R \parallel_2^2+\lambda^{2}\parallel w\left(\nabla D^{i}\right)\parallel_2^2\right]\qquad.$$

Where *D* is the deblurred image, *P* is the point spread function, *B* is the measured image, *λ* is the
regularization parameter determined by the L-curve method, *R* is a local smoothness constraint, and *w* is related to structural gradient to preserve anatomical integrity.

PSF’s for
segmentation factors of 1_{PAR }x 2_{PE}, 2_{PAR }x 2_{PE},
3_{PAR} x 2_{PE}, and 4_{PAR} x 2_{PE} were
estimated using extended phase graphs^{4}. Pseudo-diffusion effect from
intravascular tagged water signal (~30% ^{5}) was accounted for by
augmented EPG^{6}.

A numerical perfusion phantom was generated based on high resolution brain MPRAGE images with CBF values of 60 and 20 ml/100g/min assigned for GM and WM respectively. The deconvolution method was assessed through simulations at different levels of signal to noise ratio (SNR). Dispersion was calculated as the standard deviation of CBF in GM and estimation bias was calculated as,

$$Bias=\left[\overline{CBF}_{GM}^{True}-\overline{CBF}_{GM}^{Est}\right]\div \overline{CBF}_{GM}^{True}\times100\% \qquad.$$

Six subjects were
recruited for this IRB approved study. All experiments were performed on 3T
Siemens scanners. High resolution MPRAGE images with voxel size of 1x1x1 mm^{3}
were acquired for brain structure. A segmentation factor of 2 on PE was adopted
for all 3D-GRASE images. Segmentation factors on PAR direction were 1, 2, 3,
and 4. Other MR parameters were: TR of 4 seconds; 80x64x40 matrix; 3 mm
isotropic resolution; RF flip angle of 120°; labeling time of 1600 ms; post-labeling
delay of 1500 ms. Reference images were acquired for each segmentation factor
with a TR of 8 seconds. The total acquisition times were kept at 6 minutes.

ASL images were
realigned, coreregistered, and smoothed using ASLtbx^{7}. GM, WM, and
CSF probability maps were generated using SPM12. Deconvolution was applied on
the difference image using PSFs with and without pseudo-diffusion effect.

Fig. 1 displays the
CBF maps from simulations. Deconvolution nearly eliminated the blurring
artifact and recovered the perfusion map for segmentation factors of 2_{PAR} x
2_{PE} and greater. For segmentation factor of 1_{PAR }x 2_{PE},
deconvolution only partially resolved the blurring. The bias and dispersion for
different segmentation factors and SNR levels is shown in Fig. 2. Deconvolution
reduced CBF bias for all segmentation factors, and brings it within the
physiological noise level of ASL studies except for 1_{PAR} x 2_{PE}
segmentation. As expected, bias showed little dependency on SNR and the
deconvolution slightly increases the dispersion of CBF quantification.

Fig. 3 displays the
typical result from a volunteer subject. The proposed method reduces the
blurring along the PAR direction and significantly improves the GM/WM contrast
ratio (Fig. 4). These results indicate that for segmentation factors of at
least 2_{PAR} x 2_{PE}, the proposed deconvolution method is
capable of reconstituting the perfusion signal. This is further supported by
the mean GM CBF estimated across all six subjects (Fig. 5). Comparing deconvolution
using PSF with and without pseudo-diffusion, the underestimation of GM CBF is
still significant until very high segmentation factors are adopted. This is
consistent with the notion that PSF with pseudo-diffusion is much broader than
conventional PSF due to T1/T2 relaxation. Meanwhile, deconvolution with the
pseudo-diffusion effect further improves the GM/WM contrast ratio as
demonstrated in Fig 4.

1. Detre, John A., et al. "Applications of arterial spin labeled MRI in the brain." Journal of Magnetic Resonance Imaging 35.5 (2012): 1026-1037.

2. Alsop, David C., et al. "Recommended implementation of arterial spin-labeled perfusion MRI for clinical applications: A consensus of the ISMRM perfusion study group and the European consortium for ASL in dementia." Magnetic resonance in medicine 73.1 (2015): 102-116.

3. Vidorreta, Marta, et al. "Evaluation of segmented 3D acquisition schemes for whole-brain high-resolution arterial spin labeling at 3 T." NMR in Biomedicine27.11 (2014): 1387-1396.

4. Weigel, Matthias. "Extended phase graphs: Dephasing, RF pulses, and echoes-pure and simple." Journal of Magnetic Resonance Imaging 41.2 (2015): 266-295.

5. St Lawrence, Keith S., et al. "A two-stage approach for measuring vascular water exchange and arterial transit time by diffusion-weighted perfusion MRI." Magnetic resonance in medicine 67.5 (2012): 1275-1284.

6. He, Xiang, et al. Diffusion Sensitivity of ASL Perfusion with 3D-GRASE Readout. International Society of Magnetic Resonance in Medicine 23rd Annual Meeting, (2015): Toronto.

7. Wang, Ze, et al. "Empirical optimization of ASL data analysis using an ASL data processing toolbox: ASLtbx." Magnetic resonance imaging 26.2 (2008): 261-269.