## 4 Discussion
Ultimately, for patients with quadriceps weakness and inhibition secondary to a knee injury, we suggest the use of the SBWS executed with \(\rm\theta=45^{\circ}\) and \(\rm C_{GR}\) shifted at the rearfoot because it can lead to enough quadriceps muscle activation for muscle strengthening purposes while minimising the mechanical loading on the knee joint structures. It is worth noting that, given its joint-safety attributes, this exercise can be used in the early stage of rehabilitation programmes as soon as the patient can tolerate partial weight-bearing. Notably, within the different exercise configurations, the TA reached the highest level of activation (about 44% MVIC) among the eight selected muscles. This level was achieved with \(\rm C_{wall}\) shifted at the scapular zone, \(\rm C_{GR}\) at the rearfoot, and the foot placed near the wall (\(d=0.5\)-\(l_{\rm thigh}\)). This result is in line with our previous study [14], which, based on biomechanical modelling and force plate measurements, highlighted that the SBWS can impose high torque demand on the ankle dorsiflexor muscles. The present study definitively confirms that the SBWS may enable effective strengthening of the TA, using body weight as the sole resistance while imposing low stability and balance demand due to the wall support. The activity of the muscles of the rear part of the body (ES, GM, BF, ST, and GL) was maximised in the same exercise condition: feet placed far from the wall (\(d=l_{\rm thigh}\)), \(\rm C_{wall}\) shifted at the scapular zone, and \(\rm C_{GR}\) shifted at the forefoot. However, even in this favourable condition, the GM, BF, and ST reached limited levels of activity given by 6%, 6%, and 10%, respectively. For this reason, the SBWS exercise with the knee at 45\({}^{\circ}\) of flexion cannot be considered effective for hamstring and glute strengthening. In contrast, the GL and ES activity reached levels of 17% and 23% MVIC, respectively. Thus, the SBWS exercise can potentially be used as a safe initial intervention in patients with limited muscle endurance in low back muscles, prior to the execution of more challenging exercises, such as the body-weight supine bridge exercise [26; 27; 28; 29; 30; 31]. The shift in the centre of pressure \(\rm C_{GR}\) of the ground reaction force between rearfoot and forefoot significantly affected the activity of all selected muscles. Overall, this variable had a dominant impact over the muscle activity, compared with the other two variables (Figure 2, Tables 2 and 3). The effect of the \(\rm C_{GR}\) shift was particularly important for muscles (VM, VL, TA, ES, and GL) that reached considerable levels of activity, which may be identified as the target muscles of the exercise. Ultimately, this study highlights that the shift in \(\rm C_{GR}\) between rearfoot and forefoot constitutes a relevant variant of the SBWS exercise. Interestingly, post hoc analysis revealed that the shift in \(\rm C_{wall}\) between the scapular and the pelvic zone did not significantly change the activity of any muscle when the feet were placed near the wall and \(\rm C_{GR}\) was shifted to the rearfoot (Table 3). In this condition, \(\rm C_{GR}\) is located near the wall and the horizontal distance between the body's centre of mass,and C\({}_{\rm GR}\) is minimised. This, in turn, minimises the tendency of gravity to rotate the entire body backward and, consequently, the magnitude of the equilibrating force the wall should exert on the back. Ultimately, this limits the effects of the C\({}_{\rm wall}\) shift. On the contrary, this shift induces its greatest effects when the distance of C\({}_{\rm GR}\) from the wall is maximised, that is, when \(d=l_{\rm thigh}\) and C\({}_{\rm GR}\) shifted at the forefoot. The main limitation of the study is related to the limited number of conditions imposed on the exercise variables.