## 4 Discussion
The strength of the impact of each of the factors requires further studies to better customize the treatment to individual patients' needs. The application of ROC analysis allows the determination of the probabilities of inclusion for hannstring lengthening surgery for patients with or without hypertonia based on the cutoff values of PA and K\({}_{\rm ts}\). The results of ROC analysis not only conforms with another method that had been used in a previous aims to show that both K\({}_{\rm ts}\) and PA can be used to differentiate patients' limbs with the presence or absence of clinically tested hypertonia (Table 3), but also allows us to establish the cutoff values for such differentiation. We found that K\({}_{\rm ts}\) = 13.93\({}^{\circ}\) (AUC = 0.66, \(p\) < 0.0001) generates the cutoff value (sensitivity = 75%, specificity = 51.5%) to detect the absence of knee flexors hypertonia. For K\({}_{\rm ts}\)\(\geq\) 13.93\({}^{\circ}\) the probability of absence of hypertonia decreases rapidly (as detected with TAS at fast velocities) (Figure 4). The value of PA = 30\({}^{\circ}\) (AUC = 0.587, \(p\) = 0.022) generates the cutoff value (sensitivity = 89.07%, specificity = 25.44%) to detect the absence of knee flexors hypertonia. The probability of absence of hypertonia decreases for PA \(\geq\) 30\({}^{\circ}\) (Figure 5). In addition, we found that the pathologically decreased knee extension at the end of swing K\({}_{\rm ts}\)\(\geq\) 10\({}^{\circ}\)[22; 23] can be predicted with 69.7% of sensitivity and 56.3% of specificity when PA = 40\({}^{\circ}\) with rapidly increasing sensitivity for PA > 40\({}^{\circ}\). To our knowledge, our study provides original, analytically obtained cutoff values of PA and K\({}_{\rm ts}\) during gait to detect the presence of knee flexors hypertonia based on two clinical tests: TAS at slow and TAS at fast velocities (HYP\({}_{\rm vs}\), HYP\({}_{\rm vf}\), respectively) (Table 3). The value of such analysis is supported by an effort to establish the criteria for knee flexors lengthening surgery based on the values of clinically tested PA and K\({}_{\rm ts}\), obtained during gait analysis, especially since it has been reported that they are affected as results of surgeries [5; 11; 12; 15; 40]. However, the improvement of knee position at the end of swing after hannstring lengthening was not always successful despite the fact of a decreasing value of PA [5; 11; 12; 14; 15; 31; 40]. It has been recently suggested that indications for hannstring lengthening surgery should focus on instrumented gait analysis data supplemented only by the results of clinical tests in ambulatory children with CP [41]. It has been advocated that the lack of extension especially K\({}_{\text{ts}}\)\(>30^{\circ}\) at the end of swing/initial stance should be used as a main criterion for the hamstring lengthening surgery. Our data do not question this criterion; however, we would like to emphasize that in 98% of ambulatory individuals with CP, K\({}_{\text{ts}}\)\(\geq 30^{\circ}\) indicates the coexistence of hypertonia (Figure 4). It seems that the interaction between muscle shortness and hypertonia should be considered before hamstring lengthening surgery [37] because the presence of hypertonia might influence the selection of appropriate treatment [42]. Theoretically, a hamstring lengthening surgery in the presence of muscle shortening and the absence of hypertonia should increase the knee extension range of the motion and result in both decrease in PA and knee flexion at the end of swing. Moreover, as a result of hamstring lengthening surgery the length of the muscle at certain positions is shorter, the knee flexors moment of force is smaller [43; 44] and the stretch reflex activation also decreases with decreased muscle length as was found in human spasticity by [PERSON] et al. in 1971. Thus, in both cases, the so-called muscle lengthening surgery could be beneficial to the normalization of the value of PA and functional improvement.