## 2 Materials and Methods
### Registration and Image Processing Workflow  
In this section, all the steps constituting the proposed image post-processing and alignment protocol for multimodal MR muscle images are described. A concise graphical representation is displayed in Figure 1.  
Figure 1: Image processing and registration pipeline. * As a very first step, all Dicom images obtained from the MRI scanner were converted to Nifti files with dcm2 nii [30]. * A further step was devoted to the generation of quantitative parametric maps at t0 and t1. Fat Fraction and T2 relaxation maps were obtained with an in-house script from the Dixon and the MESE T2 sequences, respectively; T2 maps were calculated voxel-wise fitting a standard mono-exponential decay through a least-square minimization approach [31], whereas Fat Fraction maps were estimated using the regularized field map formulation and graph cut solution [32]. Finally, DTI maps, obtained from the EPI multi-shell sequence, were generated using the ExploreDTI software (v4.8.6, University Medical Center Utrecht, Utrecht, The Netherlands) [33]. All the quantitative maps generation process was carried out in the MATLAB environment. * The headers of the estimated quantitative maps were systematically matched with the corresponding source image headers that were used as a reference. This step ensures the recovery of the correct geometrical orientation for the following registration steps. * To suppress the contribution of the subcutaneous fat, muscle volumes were selected using the semi-automatic segmentation tool of ITK-Snap (v3.8.0) [34] before registration and used as masks to calculate the similarity metric, as shown in Figure 2.
* Finally, the voxels of the images were made isotropic to account for the sampling unevenness to improve the registration performance along the slice direction (final voxel resolution was \(1\times 1\times 1\) mm\({}^{3}\)). The registration pipeline consisted of an intensity-based rigid and elastic deformation. The rigid deformation was chosen for the intra-session registration (i.e., all the maps were coregistered to the corresponding T1-w image), whereas the combination of the rigid and the elastic deformations was chosen for the longitudinal registration (t1 vs t0). Considering their contrast, Signal to Noise Ratio (SNR), and resolution, morphological T1-w images were selected as references for both intra-session (rigid) and longitudinal registration (rigid + elastic). The elastic registration was a classical Free-Form Deformation (FFD) based on cubic B-Splines. Mattes Mutual Information [35] was chosen as a similarity metric and a gradient descent-based optimizer in a multi-resolution strategy was used for both rigid and elastic steps of the registration pipeline. The complete parameter set-up is reported in Table 1.  
The effect of different learning rates--a parameter that determines the step size of the optimizer at each iteration while moving toward a minimum of the loss function--were evaluated and kept stable for each iteration and multi-resolution step. As to the elastic step, different mesh sizes were also evaluated. The mesh size is defined as the number of polynomial patches comprising the finite domain of support, and its relationship with the number of control points in any given dimension is mesh size \(=n_{control\ points}-spline\ order\). Figure 2: An example of the results of the masking step on T1-w MR images in 3 orthogonal views. * The initial rigid roto-translations was performed in three conditions: 1. Native resolution without selecting a mask (NM)
2. Native resolution with mask (M)
3. Isotropic voxels with mask (IM)  
For each condition, we run the registration with five different learning rates: 1 (the default value in simple ITK), 3, 5, 10, and 15. * In a second step, a nonrigid transformation was used, based on b-splines, with a polynomial warping of the third order.