Cédric Meurée^{1,2,3,4,5}, Pierre Maurel^{2,3,4,5}, Elise Bannier^{2,3,4,5,6}, and Christian Barillot^{2,3,4,5}

Partial volume effects (PVE) are an important limitation of arterial spin labeling (ASL) acquisitions, impacting the validity of quantitative cerebral blood flow (CBF) estimations. This abstract presents a super-resolution algorithm, which includes information of high resolution (HR) structural images to reconstruct HR CBF maps from low resolution ASL series, without increasing the acquisition time. Compared with nearest neighbor, trilinear and 3rd order spline interpolations, the proposed algorithm is found to generate a CBF image closer to the one obtained with a reference HR ASL acquisition. CBF calculations can therefore be improved by using this algorithm, which reduces the PVE.

Introduction

Low (3.5x3.5x5mm^{3}) and high resolution (1.75x1.75x2mm^{3}) 2D pseudo-continuous ASL (pCASL) series with FOV=224x224mm^{2}, TR/TE=4060/12ms, LD=1500ms, PLD=1800ms were acquired on a healthy volunteer on a 3T MR scanner. The protocol also included a 3D MP2RAGE (1x1x1mm^{3} isotropic, FOV=256x256mm^{2}), using the UNI image as an unbiased structural image, and M0 images at the same low and high resolutions as equilibrium magnetization maps (TR=10s, TE=12ms).

An inhouse processing pipeline based on Nipype^{4}, SPM8 and Python functions was used to generate perfusion images from the two raw pCASL series. The series were realigned on the first volume, the perfusion images calculated as the mean of the differences between
control and label images, and the structural and M0 images were
registered on these perfusion maps.

The purpose of super-resolution algorithms is to retrieve a high resolution image $$$x$$$ from a low resolution one $$$y$$$ acquired by the scanner, subject to a decimation operator $$$D$$$, a degradation model $$$H$$$, chosen as a 3D boxcar function^{3}, and noise $$$η$$$ :

$$y = DHx + η$$

In this study, $$$x$$$ represents the high resolution perfusion or M0 image and $$$y$$$ the low resolution one. $$$\hat{x}$$$, the estimation of $$$x$$$, can be obtained by minimizing an optimization function similar to the one proposed in [3] in the context of diffusion images:

$$\hat{x} = argmin_{x}\{ || y-DHx ||^{2}_{2} + \gamma \phi_{S}(x)\}$$

where $$$γ$$$ is a scalar and $$$\phi_{S}$$$ a non-local patch-based regularization term including information from the high resolution structural image $$$x_{struct}$$$.

The proposed algorithm consists therefore in the following steps (figure 1). First, a 3^{rd} order spline interpolation is performed in order to obtain an image with the desired dimensions. Then, iterations between the non-local patch-based regularization and an original data fidelity term (equations 3 and 4) until convergence generate a high resolution image minimizing the optimization problem.

$$ \hat{x}_{i}^{t+1} = \frac{1}{Z_{i}}\sum_{j\in{V_{i}}} \hat{x}_{i}^{t} exp-(\frac{||N(x_{i, struct}) - N(x_{j, struct})||^{2}_{2}}{2\sigma^{2}_{i, struct}} + \frac{||N(\hat{x}_{i}^{t}) - N(\hat{x}_{j}^{t})||^{2}_{2}}{2\sigma^{2}_{i}})$$

$$ \hat{x}^{t+1} = \hat{x}^{t+1} - (DH\hat{x}^{t+1} - y)$$

$$$N(x_{i})$$$ represents the *3x3x3* neighborhood around voxel *i*, $$$\sigma_{i}$$$ the empirical local variance, $$$V_{i}$$$ a 7x7x7 search volume around voxel *i* and $$$Z_{i}$$$ a scaling parameter controlling that the sum of the weights is equal to 1.

This algorithm was applied to the low resolution perfusion and M0 maps, using the MP2RAGE UNI image. The Buxton model was then used to
calculate the CBF maps corresponding to the high resolution acquisition
and the reconstructed images.^{5}

CBF maps were also produced following nearest neighbor, trilinear and 3^{rd} order spline interpolations applied to the perfusion and M0 maps as a matter of comparison.

The perfusion, M0 and CBF images obtained with the different methods are presented in figure 2.

The high resolution CBF image being considered as the reference image, the quality of the reconstructions was evaluated by calculating the PSNR between this reference and the generated images (figure 3).

The PSNR comparing the reference and the CBF map generated using the proposed algorithm is superior to the values obtained using nearest neighbor, trilinear and 3^{rd} order spline interpolations. The contamination of the gray matter (GM) signal by white matter values induced by PV effects at low resolution and nearest neighbor interpolation, and the smoothness resulting from the trilinear and 3^{rd} order spline interpolations, is reduced by using the proposed super-resolution algorithm. This means that the CBF values in the gray matter are closer to the one obtained with the high resolution data.

Ongoing inclusions will raise the number of subjects integrated in the results to be provided at the time of the conference.

1. Asllani I., Borogovac A., Brown T. R., Regression Algorithm Correcting for Partial Volume Effects in Arterial Spin Labeling MRI. Magnetic Resonance in Medicine. 2008;60:1362-1371

2. Petr J., Ferré J.C., Gauvrit J.Y., Barillot C., Denoising Arterial Spin Labeling MRI using Tissue Partial Volume. SPIE Medical Imaging. 2010, San Diego, United States, (pp. 76230L-76230L). International Society for Optics and Photonics.

3. Coupé P., Manjon J. V., Chamberland M., Descoteaux M. Hiba B., Collaborative Patch-Based Super-Resolution for Diffusion-Weighted Images. Neuroimage. 2013;83:245-261

4. Gorgolewski K., Burns C. D., Madison C., Clark D., Halchenko Y. O., Waskom M., Ghosh S. S., Nipype: a Flexible, Lightweight and Extensible Neuroimaging Data Processing Framework in Python. Frontiers in Neuroinformatics. 2011;5:13

5. Buxton R. B., Frank L. R., Wong E. C., Siewert B., Warach S., Edelman R. R., A General Kinetic Model for Quantitative Perfusion Imaging with Arterial Spin Labeling. Magnetic Resonance in Medicine. 1998;40:383-396

Figure 1: Description of the proposed super-resolution algorithm.

Figure 2: First line: high resolution and reconstructed perfusion images obtained from the low resolution ones using nearest neighbor interpolation, trilinear interpolation, 3rd order spline interpolation and the proposed algorithm - second line: high resolution and reconstructed M0 images using the same methods - third line: CBF maps obtained from the high resolution and reconstructed perfusion and M0 maps.

Figure 3: PSNR (db) values calculated on gray
matter, comparing the CBF map obtained from high resolution perfusion
and M0 images to the CBF maps calculated from the reconstructed
perfusion and M0 images.