ROUGH DRAFT authorea.com/9562

# Introduction

Magnetic susceptibility is dimensionless proportionality constant that indicates the degree of magnetization of a material in response to an applied magnetic field (wikipedia). As the name suggests, Susceptibility Weighted(SW) MR imaging is a method of brain imaging in which the intensity of a particular voxel is proportional to the magnetic susceptibility of the underlying tissue. Because de-oxygenated venous blood is rich in iron content than neighbouring tissues, the magnetic property is also substantially different which is why SW images are used for a good understanding of the distibution of veins in the brain.

In our experiment full-brain volumetric images (512x512x500) in NIfTI format were recorded with a Philips MR scanner at 3 Tesla using a 3D Presto FFE sequence (0.43x0.43x0.3 mm voxel size). Facial features have been removed from these images for de-identification. Separate phase and magnitude images are provided. The next section gives the details of 2 methods used for processing the SW images thus acquired.

Susceptibility Weighted Magnitude Image

Susceptibility Weighted Phase Image

## Method 1

This image processing method considers both the magnitude volume and the phase volume of SW images. Before the steps of processing are described its worthwhile to take a closer look at what the magnitude volume and phase volume of the MR images actually are(Ying ). Generally complex MR image acquisition can be expressed as:

$I = |I|*exp(\phi)$

where $$|I|$$ is the magnitude part and $$\phi$$ is the phase component of the image. The phase image conveys several important information like field inhomogeniety, venous blood flow etc. But extracting the phase image from the measured complex image is non-trivial, because the any phase component beyond the range of $$-(\pi, \pi]$$ is wrapped back into the principal value range. So when the phase image is generated from the scanner it undergoes the Phase Wrapping process, as mentioned above. The phase image provided here is in true sense a phase wrapped image in which the Wrapped Phase is defined as:

$\psi = W(\phi)$

where $$W$$ is the wrapping operator. So for further image processing, we need to determine the true phase information which can be obtained by unwrapping the provided phase image. This image processing method consists of the following steps.(Liu )

• Step 1: Phase Unwrapping Phase unwrapping is performed by FSL PRELUDE tool. Slicewise phase unwrapping is performed, which is a quicker process but 3D volume wise phase is much slower but very robust.

• Step 2: Spatial High Pass Filtering Spatial High pass filtering of the phase unwrapped images is performed by subtracting the spatially smoothed image from the original image. For spatial smoothing, a gaussian kernel is used and as a rule of thumb, the sigma of the kernel is taken as 3*voxel dimension. In this case it is approximated ~1.3mm.

• Step 3: Voxelwise Product of Magnitude and Phase Unwrapped Image The spatially high pass filtered phase unwrapped image is multiplied with the magnitude image in FSL, to generate a volume in which the veins are represented as white voxels. A binary mask for veins can be generated by restricting the volume thus generated to a particular ROI, normalizing and scaling to a predetermined intensity range.