Putamen

The real and imaginary data from the scanner were combined to form the complex data, and then separated into magnitude and phase. The resulting magnitude images were used to obtain the mask of the brain tissue using the BET tool in FSL (FMRIB, University of Oxford) (38 ). The background phase was then removed using the proposed HARPERELLA method. Briefly, the Laplacian of the phase was calculated using Eqs. [1–4], with zero padding to increase the numerical accuracy. Values outside the brain were set to zero while large Laplacian values near the boundary of the brain (<3 voxels from the boundary of the brain) were also considered inaccurate and set to zero. The phase Laplacian values outside the brain were then estimated with Eq. [3], using a spherical kernel radius (R) of 10 mm. This equation is solved using the preconditioned LSQR method, an iterative linear equation solver in Matlab. The Laplacian values for the whole FOV were then obtained by combining the Laplacian values inside the brain with the calculated Laplacian values outside the brain. Eventually, the background removed phase was calculated using Eq. [6] followed by zero filling areas outside the brain.
The phase processed by HARPERELLA was compared with other state of the art phase processing methods. In contrast to the Laplacian-based phase unwrapping in HARPERELLA, we first performed 3D phase unwrapping of the total phase using the algorithm developed by Abdul-Rahman et al. (34 ). The first background phase removal method compared is a SHARP method with a variable radius of spherical kernel at the brain boundary (16 (link)), referred to as V-SHARP for short. The second one is the method of Projection onto the Dipole Field (PDF) developed by Liu et al (29 (link)). All susceptibility maps were computed using the LSQR method (6 (link)). The anatomical structures in the susceptibility maps were segmented manually using a Matlab-based ROI tool as described previously (39 (link)). The selected ROIs include 6 iron rich gray matter nuclei, namely putamen, globus pallidus, caudate nuclei, red nuclei, substantia nigra, dentate nuclei, and 3 subcortical white matter regions, namely internal commissure, splenium of corpus callosum and optic radiation. All algorithms were implemented in Matlab R2011b (Mathworks, Natick, MA).