## 4 Discussion  
The first aim of the present study was to establish the association between popliteal angle (PA) and knee angle at the end of the swing phase in walking (Kts) in children with CP. We found a weak correlation between clinically obtained values of PA and Kts that suggests an association between them. Figure 5: The results of ROC analysis (AUC = 0.587, \(p\) = 0.022) indicate that the value of popliteal angle (PA = 30\({}^{\circ}\)) generates the cutoff value (sensitivity = 89.07%, specificity = 25.44%) to detect the absence of knee flexors hypertonia. For PA \(\geq\) 30\({}^{\circ}\), the probability of absence of hypertonia decreases. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline  & **AUC** & **Cutoff** & **Sensitivity** & **Specificity** & \(p\) \\  & & **(deg)** & **(\%)** & **(\%)** & **(\%)** \\ \hline Kts (HYP\({}_{\rm vs}\)) & 0.641 & 16.68 & 61.46 & 64.96 & **0.000395** \\ Kts (HYP\({}_{\rm vf}\)) & 0.660 & 13.93 & 75.00 & 51.48 & **0.000055** \\ PA (HYP\({}_{\rm vs}\)) & 0.562 & 30.00 & 90.20 & 24.43 & 0.102084 \\ PA (HYP\({}_{\rm vf}\)) & 0.587 & 30.00 & 89.08 & 25.44 & **0.021889** \\ \hline \hline \end{tabular} The strength of the impact was evaluated with the area under the sensitivity/specificity curve (AUC) where I means the strongest and 0.5 no impact with a statistical significance of the \(p\)-value. Bold values denote statistical significance at the \(p\leq\) 0.05 level.  
\end{table} 
Table 3: The cutoff values of popliteal angle (PA) and knee angle at the end of swing/initial stance (Kts) during gait to detect the presence of knee flexors hypertonia based on two clinical tests: TAS at slow (HYP\({}_{\rm vs}\)) and TAS fast (HYP\({}_{\rm vf}\)) velocities. The differences between the conditions in which the clinical and instrumental data had been collected could be responsible for 15% of the variance of K\({}_{\rm ts}\) due to PA. Taking into consideration that an increase in PA is related to an increase in K\({}_{\rm ts}\) according to the equation K\({}_{\rm ts}\) = 5.00 + 0.31 \(\times\) PA (r = 0.39; \(p\) < 0.001) it can be estimated that a decrease in PA by 10\({}^{\circ}\) can lead to 3\({}^{\circ}\) improvement of knee position in walking. The value of the estimation can be tested using the data from pre- and post-surgery if available. We found that the presence or absence of hannstrings hypertonia (clinically detected with TAS at slow and fast velocities) affected the majority of variables (Tables 1 and 2). This suggests the contribution of hannstrings hypertonia to the increased values of PA and to an increased knee flexion at the end of swing (Aim 2). The values of PA and knee position at the end of swing were larger (from 11% to 39% when means were considered) in limbs with, rather than without, hypertonia. It had been previously acknowledged that the lack of knee extension at the end of swing may be related not only to hannstrings muscle shortness [26; 27], but also to hannstrings muscle hypertonia and/or selective motor control impairment in a patient with CP [27; 28; 29; 30; 31]. Modelling data also suggest that other factors beyond hannstrings muscle shortness seem to affect knee position at the end of swing [32; 33]. The associations between hannstrings spasticity, PA, and knee position at the end of swing remain debatable [34; 35; 36; 37]. Both the presence [34; 35; 36] and absence [4; 37] of such relationships have been previously reported. Muscle activation, also triggered by stretch reflexes leading to an increased resistance (hypertonia), is commonly reported in patients with CP [38]. It has been reported that PAs were larger when hannstrings were activated than when they were silent in the limbs of patients with CP [1; 11; 12; 39]. Our data provide another argument to support the impact of hannstrings muscle spastic hypertonia on the increased PA values and an increased knee flexion at the end of swing phase of walking.