**5. Discussion**

The results of the VIS method (Table 1) and FRR method (Table 2) have shown that a subset of subjects exhibited FRP in all cycles and in all muscles, and it was indicated with *IDFRP= (ID1, ID2, ID3, ID8, ID12, ID17, ID18, ID20, ID21)*. The other subjects manifested FRP only in some cycles, some muscles or they didn't manifest FRP in any muscles. The reason for different patterns may lie in muscle fatigue [56], fear, or other features that vary from subject to subject (since there are many variables involved; the patient's report is useful for deepening the topic). Comparing the results of the VIS method with those obtained by the proposed algorithm is possible to carry out the performance evaluation, which is summarized in Table 2. Taking into account only the results related to the subgroup of healthy subjects indicated with *IDHEALTHY*= (*ID2, ID3, ID6, ID7, ID8, ID12, ID16, ID17, ID18, ID20, ID21, ID22, ID25*). The proposed FRR algorithm shows no False Negative, so:

$$S\_{\varepsilon}^{HEALTHY} = \frac{TP}{P} = \frac{TP}{TP + FN} = \frac{147}{147 + 0} = 100\% \tag{5}$$

$$S\_p^{HEALTHY} = \frac{TN}{N} = \frac{TN}{TN + FP} = \frac{51}{51 + 10} = 84\% \tag{6}$$

This means that the ability of the FRR method, Equation (1), to discriminate FRP presence, compared to the VIS method, in the healthy subgroup (with a total number of 147 events) is equal to 100% (Equation (5)). In the literature, Alison et al. [20] reported a sensibility of 100% evaluating other types of FRR methods on 24 events collected in an acquisition campaign that involved only healthy subjects. Therefore, we have obtained similar performance comparing our results with those reported by Alison in the same type of subset but using a greater number of events. While as reported in Equation (6), the proposed FRR algorithm is less performing to discriminate FRP absence in the healthy subgroup (with a total number of 61 events).

We can do similar considerations taking into account only the results related to the subgroup of LBP subjects indicated with *IDLBP* = (*ID1, ID4, ID5, ID9, ID10, ID11, ID13, ID14, ID15, ID19, ID23, ID24*). The proposed algorithm shows:

$$S\_{\varepsilon}^{LBP} = \frac{TP}{P} = \frac{TP}{TP + FN} = \frac{48}{48 + 3} = 94.1\% \tag{7}$$

$$S\_p^{LBP} = \frac{TN}{N} = \frac{TN}{TN + FP} = \frac{136}{136 + 5} = 96.5\% \tag{8}$$

This means that the ability of the FRR method, Equation (1), to discriminate FRP presence, compared to the VIS method, in LBP subgroup (with a total number of 51 events) is equal to 94.1% (Equation (7)). While as reported in Equation (8), the proposed FRR algorithm is more performing to discriminate FRP absence in the LBP subgroup (with a total number of 141 events).

Summarizing, in this study we have extended the evaluation of the FRP taking subjects healthy and with LBP, producing 400 events, and evaluating the performances of the proposed algorithm on the entire group of subjects. The results are illustrated in Table 2, and the performances are indicated in Equations (2)–(4). The table shows that this algorithm correctly recognized 195 of the 198 events with FRP and 187 of the 202 events without FRP. Only 15 False Positives and three False Negatives occurred on a total of 400 events. FNs can occur in events where the end of a phase does not exactly coincide with the end of the sEMG pattern for that phase. Then the sEMG pattern excess enters in the

new phase and it alters the average value, changing the FRR. FPs can occur in events where the FRP is absent and the sEMG activity is moderate and very variable during the full flexion phase. In these cases, the FRR value does not exceed the nominal threshold as the mean value during the full flexion phase is not big enough compared to the activity during the extension.

As shown in equations Equations (2)–(4), the algorithm has therefore accuracy of 95.5%, a sensitivity of 98.5%, and a specificity of 92.6%. Comparing sensitivity Equation (3) and specificity Equation (4) results is clear that the algorithm discriminates very well subjects with FRP while it's more difficult to identify subjects without FRP. Furthermore, as reported in Equation (6), this reduced specificity is mainly caused by healthy subjects who have not FRP.

Most cases of FPs had a value very near to the threshold level (*FRRThreshold*) used to make the decision; often, when the *FRRi*<sup>C</sup> value is near the threshold it can take a different decision compared to the VIS method (the closer FRR gets to the threshold, the greater the uncertainty of the decision), which makes the detection a non-trivial problem.
