## 4 Discussion  
The goal of this study was to investigate the association of lower limb symmetry during the multi-joint task of vertical hopping performed by males who had undergone an ACLR on average two years before, and the duration of their postoperative physiotherapy was under the supervision of a specialist. The main finding of the study was that double-leg vertical hop landing limb symmetry in patients an average of two years after ACLR was correlated with postoperative physiotherapy supervision duration. The longer the postoperative physiotherapy supervision was, the higher the vGRF BM value obtained in the ACL-reconstructed limb and the higher the LSI value during the double-leg vertical hop landing. There was also a significant, although weak, association  
Figure 6: A significant positive correlation indicated that a higher limb symmetry index of vGRF BM during the double-leg vertical hop landing is associated with a longer duration of postoperative physiotherapy supervision in patients after ACLR. Figure 7: A statistically significant but weak positive correlation indicated that the higher limb symmetry index of vGRF BM during the single-leg vertical hop landing is associated with a longer duration of postoperative physiotherapy supervision in patients after ACLR. between the single-leg vertical hop landing limb symmetry and the postoperative physiotherapy supervision duration. In the present study, in patients whose postoperative physiotherapy was supervised for less than six months, the vGRF BM was significantly worse during the hop landing for the ACL-reconstructed limb compared to the contralateral one, and compared to the patients who underwent supervised physiotherapy for six months or more, and also compared to healthy individuals. Those findings indicate the long-term consequences of postoperative physiotherapy supervision that lasted less than six months. Generally, there is no uniform terminology regarding unsupervised postoperative physiotherapy after ACLR, as the amount of physiotherapy input attained with so-called non-supervised or partially supervised physiotherapy is unclear. According to the opinion of some authors discussing the issue in the past, a minimally supervised postoperative physiotherapy procedure is cost saving [10] and can result in successful ACL rehabilitation [7; 10; 35; 36]. This opinion has been changing [11; 12]. There are studies indicating better outcomes in terms of speed and agility in patients eight months postoperatively, who underwent a physiotherapeutic procedure at a rehabilitation center and were directly supervised by a physiotherapist for at least six months after ACLR, compared to the patients with a shorter postoperative physiotherapy supervision [12]. In other studies, in patients following supervised physiotherapy for less than six months postoperatively, the two-legged landing limb symmetry was worse than that in the patients receiving fully supervised physiotherapy for at least six months, and worse than that in healthy individuals, indicating that fully supervised postoperative physiotherapy is more effective for improving two-legged vertical jump landing limb symmetry eight months after ACLR [27]. The present study confirms the influence of the postoperative physiotherapy supervision for at least six months postoperatively on the landing limb symmetry in patients after ACLR. Supervision by a specialist during the final stages of physiotherapy after ACLR, and practicing strength, power, complex movement patterns, running, and endurance training [32], seems to be crucial to restore, in particular, two-legged vertical hop landing limb symmetry two years postoperatively. Patients after knee surgery need to continue a specific program for reducing proprioceptive deficits in the long term, as returning to sports activity is not sufficient for reducing such deficits [37; 38].