## 4 Discussion  
In the present study, a reliable pipeline for multimodal muscle MRI registration was presented. A quantitative assessment of the effects of various parameters of a multi-step registration approach was evaluated and open-source registration software, based on Python and SimpleITK, was developed to apply the proposed processing and registration protocol. The main findings of the paper can be summarized as follows:  
* Rigid transformation is not sufficient to achieve a good registration performance in muscle MRI, and a second deformable step is needed. * In the first rigid step, the use of a masking strategy alone is not sufficient to obtain good results. Furthermore, the performances are poorly depending on the learning rates of the gradient descent optimizer and a larger learning rate is preferable to speed up the process. * Regarding the deformable transformation step, working with an isotropic voxel in combination with a masking strategy leads to better accuracy, and larger learning rates are preferable. Based on the three accuracy indexes, measuring both overlap and distance between contours, we found that rigid transformation, alone, can produce results acceptable enough to avoid registration failures since the overall DSI was \(>0.7\) and the MSD \(<5\) mm. A DSI \(<0.7\) and an MSD \(>5\) mm were previously reported as the thresholds for considering registration failures [29; 44]. To achieve a good level of performance (DSI \(>0.8\) and MSD \(<1\) mm), though, we found that a non-rigid transformation step is needed. This is particularly evident in the case of individual muscles with smaller volumes, which had lower DSI and higher MSD associated with a larger variability among subjects. The HD metric did not show significant differences and seems to be scarcely discriminating among different conditions. The elastic alignment is necessary to recover deformation that can occur in different sessions, whereas the rigid registration is adequate to recover the intra-session deformation as qualitatively shown in this paper. Previous studies, clinical investigations [27; 28], and atlas validations for muscle MRI registration and segmentation [29; 45; 46] highlighted the need to employ a deformable transformation after a rigid or affine one since skeletal muscles are prone to shape and volume variations, even in short periods, due to position, athletic training [47], atrophy induced by microgravity, bed rest, casts, leg braces or intrinsic pathologies [48], and temperature [49]. However, the lack of technical details and quantitative accuracy assessment is a weakness of the previous papers. In our pipeline, we proposed to work with images having isotropic voxels. In fact, resolution of upper and lower limb MRI acquisition is generally highly anisotropic along the axial direction, this increases the partial volume effect [50; 51] and, therefore, it affects the registration results. Our results showed that voxels isotropization has a slight but not statistically significant effect on rigid registration performances. On the other hand, we found that non-rigid registration carried out on images with isotropic voxels performed systematically better compared to images with native resolution. Interestingly, we also found that in the sub-optimal NM group the anisotropic mesh has the worst performances for both learning rates. Therefore, the resulting under-sampling along one direction most likely affects the non-rigid registration output, probably because the optimizer is more likely to reach a local minimum with an uneven sampling, and the loss of information along the more anisotropic direction compromises the intensity matching. The masking approach used to focus the registration specifically on the muscle tissue without considering the confounding contribution of the surrounding tissues (such as subcutaneous fat) is effective if used in combination with the isotropic voxel condition.