*5.3. Discriminant Kinematic Parameter Selection and Validation*

The Spearman correlation values between selected parameters and UPDRS scores, and the Mann-Whitney U test values concerning their significance in discriminating PD and HC subjects are shown in Tables 5–8 for the LA, AC, Po and PSCOM tasks, respectively. We remark that, for PSCOM task, the Spearman correlation was evaluated respect to the PSPIGD subscale scores. For the correct application of the U test, only the data of the second acquisition session were considered. The results in the tables show that all the selected parameters correlate with UDRS score (|ρ > 0.3|, *p* < 0.05). Furthermore, they are all significant for Mann-Whitney test (*p* < 0.05), even though at different significance levels. The mean values of the selected parameters respect to the UPDRS severity classes are shown in the radar graphs of Figure 8 for all the tasks.

**Table 5.** Parameters of the LA task: discriminant power and correlation with UPDRS scores.


<sup>a</sup> Significance level *p* < 0.05.



<sup>a</sup> Significance level *p* < 0.05.

### **Table 7.** Parameters of the Po task: discriminant power and correlation with UPDRS scores.


<sup>a</sup> Significance level *p* < 0.05.


**Table 8.** Parameters of the PSCOM task: discriminant power and correlation with UPDRS scores.

<sup>a</sup> Significance level *p* < 0.05; <sup>b</sup> The Spearman correlation was evaluated respect to the PSPIGD subscale scores.

**Figure 8.** Radar graphs of the mean values of the normalized kinematic parameters of HC and UPDRS severity classes for the lower limbs and postural tasks: (**a**) Leg Agility (LA); (**b**) Arising from Chair (AC); (**c**) Posture (Po); **(d)** Postural Instability (PSCOM); (**e**) Legend for the radar plots. See Section 5.3 for further details of the graph representation.

The parameters have been represented such that an increasing values indicate a worsening of the performance, highlighted by a corresponding expansion of the related graph. For this reason, the parameters of Tables 5–8 are represented in Figure 8 directly (with the original parameter name) or inversely (with an overscore on the original parameter name), depending if the parameter value increases or decreases when the severity of the impairment increases.

Furthermore, with reference to Section 4.5, the parameters are scaled in such a way that the parameter values corresponding to the best performance (*p*i PD Norm = *p*i HC ) are represented on the innermost circle (i.e., value = 0) and those corresponding to the worst one (*p*i PD Norm MAX, or 1/*p*i PD Norm MIN, depending on the parameter) are represented on the outermost circle (i.e., value = 1).

Finally, it should be noted that almost all the parameters are able to discriminate the different UPDRS classes for the LA, AC, Po and PSCOM tasks, pointing out the increasing severity of motor impairment by the corresponding increasing of their values. The graphs are encapsulated and do not overlap, which means that a monotonic increase of the parameter value corresponds to an increase (and so a worsening) of the UPDRS score.

The Pearson correlation analysis of the CoM movements, as measured by our system and by the optoelectronic system, shows that they are correlated both in the Antero-Posterior (AP) and in Medio-Lateral (ML) components (Table 4). These values confirm the feasibility of Kinect in the accurate estimation of center of mass movements. In Figure 9a, an example of CoM trajectories as measured at the same time by the two systems is shown; the trajectory of center of mass resembles the gold reference one, even if a scale factor is present. Figure 9b shows an example of the two phases of PSCOM task: in particular, the CoM trajectory measured by the optoelectronic system while a PD subject is performing the Phase1 (solid cyan line) and the Phase2 (solid red line) respectively. In Figure 9c, the same movement as measured by our system is shown.

**Figure 9.** (**a**) Example of CoM trajectory of a PD subject represented in the Antero-Posterior (AP) and Medio-Lateral (ML) components during the Po task, as measured by our system (green line) and by optoelectronic system (black line); (**b**) Details of the trajectories during the first (cyan line) and second phase (red line) of PSCOM task with the respective centroids (black dots) as measured by optoelectronic system; and (**c**) as measured at the same time by our system.

In both figures, the secondary motor task (during which the PD subject is trying to improve and then maintain a straighter posture) clearly increases the body sway along the AP direction, supporting the hypothesis of a performance degradation for PD subjects respect to HC in this context. The shapes of trajectories are quite similar: this confirms the feasibility of our system in acquiring the body CoM in agreement with the gold standard. Again, there is a mild scaling and an offset between the centroids of the trajectories measured by the two systems: this is probably due to the different landmark positions of the body skeleton models considered and to the different algorithms used to estimate the CoM position. Nevertheless, we remark that the CoM parameters we chose are independent from these biases. Furthermore, they convey useful information which well correlates with clinical evaluations, discriminating between PD from HC subjects, as indicated in Table 9. This is evident for almost all the PD subjects, on AP and/or ML directions; on the contrary, this is negligible for HC subjects, as confirmed by the values in the second and third column of Table 9. Furthermore, the differences of the CoM parameters (Phase2 respect to Phase1) between PD and HC subjects are significant at level p < 0.05, both for the U test and for the T test (column 5 and 6, Table 9).


**Table 9.** Average differences of CoM parameters between Phase1 and Phase2 of the Po task for HC and PD subjects.

<sup>a</sup> Significance level *p* < 0.05.
