# Fatigue Effects on the Lower Leg Muscle Architecture Using Diffusion Tensor MRI
## 2 Materials and Methods
### Image Analysis and Data Processing  
Regions of interest (ROIs) were drawn in the PD images using a piecewise linear boundary provided by the Osirix software version 9.0, Pixmeo SARL (Bernex, Switzerland) (Figure 2-left). The ROIs were outlined manually according to the anatomical boundaries of the tibialis anterior (TA), gastrocnemius medialis (GM), gastrocnemius lateralis (GL) and soleus (SOL) muscles. All the ROIs were manually drawn by the same operator, with a total of 46-82 contour curves for each muscle on each phase of the protocol (before and after the exercise). The volumes of the individual muscles (V\({}_{\text{m}}\)) were determined by summing the product of the cross-sectional areas of the muscle from each image and the slice thickness (3.9 mm) (Figure 2-right). Moreover, from the PD images, the maximal anatomical cross-sectional area (ACSA\({}_{\text{max}}\)) was determined as the largest cross-section outlined across the whole muscle. Muscle length (L\({}_{\text{m}}\)) was defined as the distance between the muscle's proximal and distal ends. Figure 2: **(Left)** Boundaries of the GM, GL, SOL and TA muscles, which were delimited in the DP images. (Right) Muscles’ volumes computed with the ACSA determined in each slice of each muscle. The three principal axes of the diffusion tensor can be calculated through a diagonalization process, where the eigenvalues and eigenvectors are determined. These parameters give us information regarding the shape and the direction of the diffusion, respectively [25]. Other parameters, derived from these, can be quantified: the fractional anisotropy (FA) and the apparent diffusion coefficient (ADC). The computation of the diffusion tensor imaging results was performed through a custom script that used FSL Tools (FMRIB Analysis Group, Oxford, UK) developed to process the imaging data. This routine included the motion and eddy current correction and the co-registration of the PD images with the diffusion tensor images. Fibers were tracked from the diffusion tensor using the free software Diffusion Toolkit version 0.6.2 and TrackVis version 0.5.2 ([PERSON], [PERSON], [PERSON], Center for Biomedical Imaging, Department of Radiology, Massachusetts General Hospital, Boston, MA, USA). The DTI data was opened in TrackVis and the anatomical image (PD) was superimposed on the DTI. The slice corresponding to the ACSA\({}_{\text{max}}\) of each muscle was chosen to draw the seed ROI necessary for the tracking. Two more ROIs were drawn, four slices above and four slices below, to guarantee the tracking of fibers only from that specific muscle. From the tracked fibers, the following parameters were determined: the average fiber length (L\({}_{\text{f}}\)), defined as the mean value of the length of the fibers calculated through the tracking algorithm in Diffusion Toolkit, and the pennation angle (\(\theta\)), defined as the fiber angle relative to the force-generating axis. It was measured directly in the fiber-tracked images (using Osirix software) by rotating the image in line with the longitudinal axis and positioning it in a plane where it visualized the preferred angular orientation of the fibers (Figure 3). When two or more fiber orientations were visualized, all the angles were determined, and the mean value was used in the results. PCSA is directly proportional to the maximum titanic tension that can be generated by the muscle and represents the sum of the cross-sectional areas of all the muscle fibers within the muscle. It was estimated using Equation (1), which was derived from the work of the pioneer [PERSON] [37] and continued nowadays by [PERSON] [38]. \[\text{PCSA (cm}^{2})=\text{(muscle volume (cm}^{3}))/\text{(fiber length (cm))}\cdot\cos\theta, \tag{1}\]  
The inter-subject variability regarding the shape of the muscles was also investigated.