## 4 Discussion  
This study provides a quantitative biomechanical analysis of the static wall squat with all relevant exercise variants: (1) the distance of the heels from the wall (more precisely, the horizontal distance \(d\) of the ankle from the hip); (2) the whole set of possible body configurations at each distance \(d\), which are determined by the corresponding values of the knee angle \(\theta_{\text{knee}}\); (3) a voluntary shift between the rearfoot and forefoot of the centre of pressure \(x_{\text{GR}}\) of the ground reaction force; (4) a voluntary shift between the scapular and pelvic zone of the centre of pressure \(y_{\text{wall}}\) of the force exerted by the wall on the back. Figure 2 highlights that the ankle and hip angles corresponding to a given degree of knee flexion can be readily modulated by changing the distance \(d\). For example, placing the feet at progressively greater distance from the wall, while keeping the knee angle unchanged, yields a progressive increase in hip flexion. This information is relevant, because high levels of hip flexion are mechanically linked with posterior pelvic tilt and lumbar spine flexion (hip-lumbo-pelvic rhythm) [16]. Decrease of the lumbar lordosis beyond the neutral zone [17] should be avoided in weight bearing condition. Furthermore, a limitation in ankle dorsiflexion mobility can considerably limit the maximum degree of knee flexion when the feet are placed near the wall due to the mechanical constraint imposed by the wall. Higher values of \(d\) are advisable with this limitation. Figure 6: Dependence of the tibiofemoral shear force \(\varphi_{\text{TF, shear}}\) on the knee angle \(\theta_{\text{knee}}\) for different values of the horizontal ankle-to-hip distance \(d\) (\(d\) = 0.2, 0.3, 0.4, 0.5 m), two positions of the centre of pressure \(y_{\text{wall}}\) of the force exerted by the wall on the back (scapular support, \(y_{\text{wall}}=y_{\text{shoulder}}\), and pelvic support, \(y_{\text{wall}}=y_{\text{hip}}\)), and two positions of the centre of pressure \(x_{\text{GR}}\) of the ground reaction force (\(x_{\text{GR}}\) at rearfoot, \(x_{\text{GR}}=x_{\text{ankle}}\), and \(x_{\text{GR}}\) at forefoot, \(x_{\text{GR}}=x_{\text{ankle}}+13\) cm). Positive values of \(\varphi_{\text{TF, shear}}\) reflect a posterior (PCL loading) tibial pull, whereas negative values reflect an anterior (ACL loading) tibial pull. \(\varphi_{\text{TF, shear}}\) has been plotted only at knee angles where a knee-extension muscle torque is developed (\(\tau_{\text{knee}}>0\)), and under the condition that \(\tau_{\text{knee}}\) is produced by the quadriceps in absence of hamstring cococontraction. Thus, negative values of \(\varphi_{\text{TF, shear}}\) represent the maximum theoretic limit of anterior TF force that may occur in the wall-squat exercise. Figures 3-5 highlight that the knee, hip, and ankle muscle torque (\(\tau_{\text{knee}}\), \(\tau_{\text{hip}}\), \(\tau_{\text{ankle}}\)) can be finely modulated by changing the values of \(d\), \(\theta_{\text{knee}}\), \(y_{\text{wall}}\), and \(x_{\text{GR}}\). Considerable levels of hip-extension muscle torque \(\tau_{\text{hip}}\) are only reached by shifting the point of application of the wall force towards the scapular zone and placing the feet at a greater distance from the wall. With the additional conditions \(\theta_{\text{knee}}\sim 80^{\circ}\) and \(x_{\text{GR}}=x_{\text{ankle}}+13\) cm, \(\tau_{\text{hip}}\) takes its maximum value of about 130 Nm. This torque level is relevant, given that the average maximal-effort hip extensor torque (measured isokinetically at \(30^{\circ}\)/s and averaged over the whole range of hip motion) developed by healthy males is about 180 Nm [16]. Notably, the corresponding value of knee-extension muscle torque \(\tau_{\text{knee}}\) is about 30 Nm. Thus, the bodyweight wall squat, when adequately managed, may constitute an effective strengthening exercise for the hip (and lumbar spine) extensor muscles with negligible involvement of the knee muscles.