Short overview

HySCO is an academic software for the correction of susceptibility artifacts in diffusion weighted images based on a reversed gradient based acquisition scheme. It is developed by Lars Ruthotto and Jan Modersitzki as an add-on to the registration toolbox FAIR.

HySCO requires the acquisition of a pair of images with reversed phase-encoding gradients that are oppositely affected by distortions. From the so-called "blip-up" and "blip-down" image data, HySCO estimates the field-inhomogeneity by solving a tailored image registration problem that incorporates a physical model of inhomogeneity artifacts in spin-echo MRI.

HySCO's name-giving component is a special non-linear regularization functional, which is inspired by hyperelasticity. It ensures smoothness of the field inhomogeneity and invertibility of the geometrical transformations regardless of the actual choice of regularization parameters.

Fig. 1: HySCO within the ACID-SC toolbox.

Preprocessing

Prior to applying HySCO, the dMRI dataset has to be corrected for intra-subject (between-volume) displacements using ECMOCO: Importantly, apply ECMOCO on the blip-up and blip-down images separately?

Usage

• Reference blip-up image: Select one reference image volume acquired with blip-up phase encoding direction (b=0 image is recommended, because it has higher SNR). Note that the ''true'' blip-up and down directions can be unknown! Just define here one DTI dataset as ''blip-up'' and the other as 'blip-down'. The field inhomogeneity is estimated by minimizing the sum-of-squared difference between this image and the blip-down image chosen below and regularization.

• Reference blip-down image: Select one reference image volume acquired with blip-down phase encoding direction (see above for details).

• Other blip-up images: (optional) Choose ''other image volumes'' acquired with blip-up phase encoding direction. The data is corrected by applying the transformation estimated by the reference blip-up/down data. If an equal number of blip-up and blip-down data is provided as ''other image volumes'', you may also want to disable ''Apply to other images'' (see 7).

• Other blip-down images: (optional) Choose ''other image volumes'' acquired with blip-down phase encoding direction.

• Dimension of phase-encoding: Specify the phase-encoding direction of your data (i.e. the direction in which the susceptibility distortions will be greatest). Default is y-direction.

• Maximal data resolution: Choose the finest discretization level for field inhomogeneity estimation. If set to ''full'' a multi-level strategy with three discretization levels is used, where the resolution on the finest level equals the data resolution. To save computation time, choose ''half''. The multi-level scheme will be stopped after the second level (i.e. half of data resolution) and the inhomogeneity estimate will be interpolated to the data resolution.

• Apply to other images: If set to ''no'' and if the same number of diffusion-weighted images is provided for blip-up and blip-down, the field inhomogeneities are estimated for each set of blip-up/down images separately (This might be useful to correct in addition to susceptibility-induced distortion for the distortions due to nonlinear eddy current fields). To this end, the field-inhomogeneity estimated from the non-diffusion weighted images is used as a starting guess for minimization of the distance between the respective diffusion-weighted image pairs. Optimization is only carried out on the finest discretization level to save computation time.

Output

• Field homogeneity map: Estimated from the pairs of blip-up and blip-down images and saved .

• HySCO corrected blip-up data: saved as a nifti file.

• HySCO corrected blip-down data: saved as a nifti file.

Fig. 2: Illustration of the output of HySCO on a typical SC dMRI dataset. The uncorrected dMRI dataset (here, a b0 image is shown) features susceptibility artifacts manifested as geometric distortions (here: contraction) of the cord in the phase-encoding (anterior-posterior) direction, causing significant misalignment with respect to a reference structural image (see red contour lines). In contrast, the geometric distortion was largely removed in the HySCO-corrected b0 image, greatly improving the overlap with the reference image.

References

Ruthotto, L, Kugel, H, Olesch, J, Fischer, B, Modersitzki, J, Burger, M, and Wolters, C H. Diffeomorphic Susceptibility Artefact Correction of Diffusion-Weighted Magnetic Resonance Images. Physics in Medicine and Biology, 57(18), 5715-5731; 2012.

Ruthotto, L, Mohammadi, S, Heck, C, Modersitzki, J, and Weiskopf, N. HySCO - Hyperelastic Susceptibility Artifact Correction of DTI in SPM. Presented at the Bildverarbeitung fuer die Medizin 2013.

Macdonald, J., Ruthotto, L. Improved Susceptibility Artifact Correction of Echo-Planar MRI using the Alternating Direction Method of Multipliers J Math Imaging Vis 60, 268–282 (2018).

J. Modersitzki: FAIR: Flexible Algorithms for Image Registration. SIAM, Philadelphia, 2009.