## 3 Results
### Effect of HYP on PA and K\({}_{\text{ts}}\) in Children with CP  
Our data indicate that the presence or absence of clinically recognized hamstrings hypertornia affected almost all variables. K\({}_{\text{ts}}\) was affected (Kruskal-Wallis test: H(1,N = 213) = 12.56, \(p\) = 0.0004)) by the presence of hypertornia (as recognized with HYP\({}_{\text{vs}}\)) (Table 1). \begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \hline  & \multicolumn{6}{c}{**Absence of Hypertornia (n = 117)**} & \multicolumn{6}{c}{**Presence of Hypertornia (n = 96)**} & \multicolumn{2}{c}{\(p\)} \\ \hline
**Angle (deg)** & **Mean** & **Median** & **Min** & **Max** & **SD** & **Mean** & **Median** & **Min** & **Max** & **SD** & \\ \hline PA & 39.66 & 40.00 & 5.00 & 70.00 & 14.03 & 42.60 & 40.00 & 10.00 & 80.00 & 12.96 & 0.23 \\ K\({}_{\text{ts}}\) & 15.60 & 14.50 & 0.57 & 51.81 & 9.99 & 20.40 & 19.09 & 2.14 & 52.57 & 11.27 & **\textless{0.001}** \\ \hline \hline \end{tabular}  
* n: number of limbs; SD: standard deviation; bold values denote statistical significance at the \(p\leq\) 0.05 level.
* K\({}_{\text{ts}}\) and PA were affected by the presence of hypertornia (as recognized with HYP\({}_{\text{vt}}\)) as examined with Kruskal–Wallis test: H(1,N = 213) = 16.26694, \(p\) = 0.0001 and H(1,N = 213) = 3.57, \(p\) = 0.05, respectively (Table 2).  
\end{table} 
Table 1: The poplileal angle values (PA) and knee angular position at the end of swing/initial stance (K\({}_{\text{ts}}\)) were larger in the limbs with clinically detected knee flexors hypertornia, but the differences were not statistically significant for PA when hypertornia had been identified using TAS at slow velocities (HYP\({}_{\text{vs}}\)). Figure 3: Knee position at the end of swing/initial stance (K\({}_{\text{ts}}\)) increases with the poplileal angle (PA) according to the equation: K\({}_{\text{ts}}\) = 5.00 + 0.31 \(\times\) PA (r = 0.39; \(p\) < 0.001) in the limbs of patients with CP. Each circle represents the K\({}_{\text{ts}}\) value for the specific PA angle acquired from one single study participant. The PA and K\({}_{\rm ks}\) were larger in the limbs with clinically detected knee flexors hypertonia, but the differences were not statistically significant for PA when hypertonia had been identified using TAS at slow velocities (HYP\({}_{\rm vs}\)). K\({}_{\rm ts}\) were larger (\(p<0.001\)) in the limbs with (\(20.4\pm 11.27^{\circ}\)) than without (\(15.60\pm 9.99^{\circ}\)) knee flexors hypertonia (HYP\({}_{\rm vs}\)). At fast velocity (HYP\({}_{\rm vf}\)), PAs were larger (\(p\leq 0.05\)) in the limbs with (\(42.81\pm 12.66^{\circ}\)) than without (\(38.96\pm 14.38^{\circ}\)) hypertonia and K\({}_{\rm ts}\) were larger (\(p<0.001\)) in the limbs of patients with (\(20.39\pm 11.01^{\circ}\)) than without (\(14.85\pm 9.89^{\circ}\)) knee flexors hypertonia. Probabilities of Inclusion for Hamstring Lengthening Surgery Patients with or without Hypertonia Based on the Values of PA and K\({}_{\rm ts}\)  
The analysis of sensitivity/specificity of K\({}_{\rm ss}\) (Figure 4) to detect the presence of knee flexors hypertonia using ROC analysis (AUC = 0.66, \(p<0.0001\)) (Table 3) indicates that \(13.93^{\circ}\) is the K\({}_{\rm ts}\) cutoff value (sensitivity = 75%, specificity = 51.5%) to detect the absence of knee flexors hypertonia. The probability of absence of hypertonia (as detected with TAS at fast velocities HYP\({}_{\rm vf}\)) decreases for K\({}_{\rm ts}\) larger than \(13.93^{\circ}\).