**4. Results**

The algorithm was tested using the dataset published in our previous study [43]. It contains acquisitions of 25 volunteer subjects; they repeated four times the cycle as defined in the flexion-relaxation test procedure [43]. In each cycle the electromyography signals of four muscles were acquired. Therefore, a total number of 400 events were extracted for the evaluation of the performances using the proposed algorithm for FRP clinical assessment. To identify if the automatic algorithm was taking the correct decision, in terms of FRP identification, a comparison between FRR and VIS method results were presented. VIS method was taken as a benchmark because of, due to its accurate performances, it was commonly adopted in clinical and research applications [20]. The recordings collected in the dataset were evaluated by independent blind teams composed of medical experts. Using VIS method (on the sEMG signals with the superimposed inclination signal), the blind teams provided handwritten reports in which the occurrences of FRP in each cycle have been reported. The results of the VIS method were obtained by summarizing the handwritten reports and in cases of disagreement between the three blind teams, a final decision was reached by the majority. The VIS method results are shown in Table 1, where each event of the dataset is classified by a Positive (P) or a Negative (N) outcome. In events with the positive outcome the blind teams have ascertained the FRP presence in the cycle under examination while in the events with a negative outcome the FRP absence was identified. The VIS method is based on criteria found in the literature: "A clear, sudden reduction in motor activity" [20].

**Table 1.** Results of the VIS method. For each subject, the cycles of each channel are classified as Positive (P) or Negative (N) events.


An ideal algorithm, for FRP detection, should identify the FRP onset in all the events with a positive outcome and it should recognize FRP absence in all the events with a negative outcome. Comparing the results of the VIS method with those obtained by the proposed automatic algorithm for FRP detection is possible to identify four types of events classification:


The information, collected in the dataset, was processed by the proposed algorithm for FRP detection and the results have been shown together with the flexion-extension ratio values calculated in each cycle and channel (Table 2), using Equation (1). Table 3 shows the mean and the SD obtained using the algorithm for computing ratios between full-flexion and extension phase.

Since the number of dataset events was statistically significant, it was possible to derive accuracy, sensitivity, and specificity about the performances of the proposed algorithm using the following equations:

$$A\_c = \frac{TP + TN}{P + N} = \frac{TP + TN}{TP + FP + TN + FN} = \frac{382}{400} = 95.5\% \tag{2}$$

$$S\_c = \frac{TP}{P} = \frac{TP}{TP + FN} = \frac{195}{195 + 3} = 98.5\% \tag{3}$$

$$S\_p = \frac{TN}{N} = \frac{TN}{TN + FP} = \frac{187}{187 + 15} = 92.6\% \tag{4}$$


**Table 2.** Results of the FRR method for all 400 events. Each value contains the event classification and the relative ratio. It was used an *FRRThreshold* = 0.35.

**Table 3.** Mean and standard deviation of the FRR, for Healthy and LBP subjects, obtained using the proposed method.

