## 2 Materials and Methods
### Data Analysis
#### 2.3.2 Image Quality  
Probe-skin contact loss might occur due to sweating, the cyclic motion of the legs, and the impact forces from the ground. Accordingly, the duration percentage of probe-skin contact was quantified for all acquisitions. In case the transducer lost complete contact with the skin, a black ultrasound image was observed with a bright, white, hyper-echoic line-shaped artifact present near the transducer position, resulting from the high acoustic impedance between the ultrasound transducer and air causing total reflection (Figure 3A). Hence, contact loss was empirically defined as a frame containing a black area of at least 80% of the image. The field-of-view stability was evaluated utilizing the complex wavelet structural similarity index method (CW-SSIM). The CW-SSIM is a full-reference method based on human vision, which compares the structures visible within an image to those of a chosen reference image. The similarity between the images is computed using the brightness (mean pixel intensity), contrast (variance), and image structures (covariance) [34]. The CW-SSIM has been shown to be an adequate comparison method for ultrasound data [35], since it compares the detail images of the highest decomposition level. Accordingly, the method (a) disregards noise and ultrasound speckle, (b) predominantly compares the principal image features, and (c) adopts the benefit of the relatively higher precision with which lower frequencies can be determined. Moreover, small rigid rotations and translations, and modest image brightness alterations have no effect on the CW-SSIM index. For example, a brightness modification of 10% leads to a CW-SSIM index reduction from its maximum value 1 to minimally 0.996 [34]. The CW-SSIM index will decrease to approximately zero in case the image structures are completely different and will be equal to one in case the images compared are identical. Figure 2: The workflow of the muscle architecture detection. **(1)** The original image (**2**) is decomposed into five oriented detail images with four orientations. Level 2–4 and level 5 are used for fascicles and aponeuroses detection, respectively. For both, the structure orientation perpendicular to the ultrasound beam is used. **(3)** Subsequently, a threshold is applied to the detail images of the aponeuroses and fascicles. **(4)** In the aponeuroses detail image, the edges of the anterior and posterior aponeurosis adhering to the muscle are identified, respectively. **(5)** Only the region between these aponeuroses is selected for fascicles detection. **(6)** The detected aponeuroses and fascicles super imposed onto the original image. Prior to the CW-SSIM analysis, the images were decomposed as previously described, using six levels and 16 orientations. For each of the 16 oriented detail images of level six, the local CW-SSIM indices are computed using:  
\[S(c_{I},c_{II}) =\frac{2|\sum c_{I,i}\ c_{II,i}^{*}|}{\sum|c_{I,i}|^{2}+\sum|c_{II,i }|^{2}}, \tag{1}\]  
with \(c_{I}=\{c_{I,i}|i=1,...,N\}\) and \(c_{II}=\{c_{II,i}|i=1,...,N\}\) the local wavelet coefficients acquired from the same spatial location in the oriented detail image of the reference image and the image it is being compared to, and \(c^{*}\) the complex conjugate of \(c\)[34]. These local CW-SSIM indices are combined into a single index per oriented detail image using a \(7\times 7\) Gaussian filter. The standard deviation of the Gaussian was defined as a quarter of the size of the detail image [34]. Subsequently, the mean of the CW-SSIM indices of the oriented detail images is obtained, resulting in the final CW-SSIM index describing the similarity between the two images. In this study, the CW-SSIM indices over time were obtained by calculating a representative CW-SSIM index. The representative CW-SSIM indices were calculated from the ten second ultrasound clips, which were obtained after every kilometer ran by the athlete. Ten randomly chosen reference frames of first and the previous acquisition were compared to all frames of an ultrasound clip.