*2.3. Biomechanical Measurements*

#### 2.3.1. Anthropometric Measurements and Base of Support

For each subject, we measured the following AMs (Table 1): body height, inter anteriorsuperior iliac spine distance, limb length, foot length, body mass, and body mass index. The AMs were recorded over a period of 5 s of standing using eight additional markers, as described in [12]. The AMs were used for the estimation of the CoM of each body segment (SCoM), according to the anthropometric tables and regression equations proposed by [43]. For each trial, the BoS area and BoS width were calculated. We also accounted for feet position asymmetry by measuring the foot alignment, the difference between feet extrarotation angles, and the BoS opening angle [11,12].

**Table 1.** Biomechanical measurements. Abbreviations: AP, anteroposterior; C7, seventh cervical vertebra; CoM, center of mass; CoP, center of pressure; ML, mediolateral; PSIS, posterior superior iliac spine.


laboratory vertical axis (◦ )

Angle between the line connecting the knee and hip centers of rotation and the laboratory vertical axis (◦ ) Angle between the line connecting the knee and ankle centers of rotation and the laboratory vertical axis (◦ ) **Table 1.** *Cont.*


#### 2.3.2. Postural Profile

The standing postural profile was characterized by means of trunk, thigh, and shank sagittal angles (Figure 1) [20] computed shortly before the GI execution (during a 1 s window before the onset of the APAs). The trunk angle was defined as the inclination of the line passing through the markers placed on the middle point between the two posterior superior iliac spines and the seventh cervical vertebra with respect to the vertical axis of the laboratory. The thigh angle was calculated as the angle between the vector connecting the knee and hip center of rotation and the vertical axis of the laboratory. The shank angle was computed between the line connecting the joint centers of the knee and ankle and the vertical axis of the laboratory.

#### 2.3.3. Anticipatory Postural Adjustments and Gait Initiation

GI variables were defined based on the displacement of the CoP, recorded by the force platform. The CoM was estimated as the weighted mean of the SCoM [44]. GI variables were calculated by dedicated algorithms in Matlab ambient (Matlab® R2018b, The MathWorks Inc., Natick, MA, USA) (as in [11,12]). All GI measurements computed in the study are listed and described in Table 1. Briefly, four reference instants were automatically identified on the CoP track and checked by visual inspection using an interactive software: the onset of the APAs, the heel-off of the swing foot (HOSW), the toe-off of the swing foot (TOSW), and the toe-off of the stance foot (TOST). The APA onset (APAONSET) was detected as the instant at which the CoP started moving consistently backward and toward the swing foot; HOSW was defined as the time at which CoP reached the most lateral position toward the swing foot; TOSW was defined as the moment at which the CoP shifted from lateral to anterior motion; and TOST was defined as the last frame of the force platform signal

(Figure 2). The APAs were divided into two periods: the imbalance phase (IMB), from APAONSET to HOSW, and the unloading phase (UNL), from HOSW to TOSW [12,20,40,45]. The following measurements were calculated for both the IMB and UNL periods: duration and anteroposterior and mediolateral CoP displacement, average velocity, and maximal velocity (Table 1). Of note, the mediolateral CoP displacement during the imbalance phase was considered positive when the shift of the CoP was towards the swing foot, while the mediolateral CoP displacement during the unloading phase was considered positive when the CoP was moving towards the stance foot. The IMB and UNL anteroposterior CoP displacement were both defined as positive when the CoP movement was oriented backwards. We additionally defined the stepping phase, from HOSW to the subsequent heel contact of the swing foot, by means of markers placed on the feet. The first step was characterized in terms of step length and average and maximal velocity (Table 1). Velocity and acceleration of the CoM were defined at the end of the IMB and UNL phases and at the instant of TOST. Additionally, the position of the CoM with respect to the CoP and the inclination of the vector connecting the two points in the transversal plane were computed at the end of IMB and UNL and at the TOST (Table 1) [12].

**Figure 1.** Scheme of the postural angles analyzed in the study. The trunk angle was defined as the inclination of the line passing through the markers placed on the middle point between the two posterior superior iliac spines and the seventh cervical vertebra with respect to the vertical axis of the laboratory. The thigh angle was calculated as the angle between the vector connecting the knee and hip center of rotation and the vertical axis of the laboratory. The shank angle was computed between the line connecting the joint centers of the knee and ankle and the vertical axis of the laboratory.

#### 2.3.4. Segmental Centers of Mass

To describe the temporal pattern of segmental movements during GI, we computed the latency of movement onset of the following 16 SCoM: head, chest, abdomen, pelvis, swing arm, stance arm, swing forearm, stance forearm, swing hand, stance hand, swing thigh, stance thigh, swing shank, stance shank, swing foot, and stance foot (similarly to [46]). For each trial, the movement onset latency of each SCoM was computed as the movement time from the onset of the APAs and normalized for the total GI time (from APAONSET to the toe-off of the swing foot). For each subject, we rank-ordered the SCoM onset times and computed the following for each group: (i) the movement time from APAONSET normalized for the total GI time and (ii) the relative frequency of each SCoM onset time to appear as events 1–16 of GI. To improve the readability of the data, we repeated the analysis after

combining the SCoM into six groups (upper trunk: head and chest; lower trunk: abdomen and pelvis; swing arm: swing arm, forearm, and hand; stance arm: stance arm, forearm, and hand; swing leg: swing thigh, shank, and foot; and stance leg: stance thigh, shank, and foot).

#### *2.4. Statistical Analysis*

For each subject, all measurements were averaged over GI trials executed with the same swing foot. Each participant performed at least three GI trials with the same swing foot. Single trials and average values were inspected and outliers were removed from further analyses based on the Mahalanobis distance [47,48].

First, we verified matching between groups for demographic, clinic, BoS, and AM features with a Mann–Whitney U-test (*p*-value set at 0.05). Before comparing the GI measurements across groups, we investigated their relationship with the BoS and AMs with two partial correlation analyses [12]. For each group, we correlated the GI measurements first with the BoS measurements controlling for the AMs, and then with the AMs controlling for the BoS. In agreement with [11], GI variables that significantly correlated (Spearman's ρ > 0.5 and *p*-value < 0.01) with the BoS in at least one group were excluded from further analyses. We opted for this conservative approach because the BoS was freely chosen by the subjects and may have been influenced by both the disease and compensatory mechanisms. The GI variables that correlated (Spearman's ρ > 0.5 and *p*-value < 0.01) with the AMs were instead corrected by means of the decorrelation normalization technique, as described by O'Malley [49]. This correction was applicable as AMs were not influenced by the disease (no patient had camptocormia, skeletal deformities, and so on).

GI variables not dependent on the BoS and decorrelated from the influence of the AMs were then compared between groups using a Dunn's test (*p*-value set at 0.05, adjusted with Bonferroni correction for multiple comparisons).

We then investigated alterations of the initial postural condition. As for the GI measurements, we assessed the correlation of the AMs and the BoS with the postural angles with partial correlation analyses (Spearman's ρ > 0.5 and *p*-value < 0.01), before comparing the postural angles across groups (Dunn's test, *p*-value set at 0.05, adjusted with Bonferroni correction for multiple comparisons).

As we found differences in the postural profiles across groups, we investigated whether altered GI measurements in the PD groups were related to postural changes rather than to impaired motor programming. We performed a partial correlation analysis between the GI outcome measurements and the postural angles correcting for the group variable. We considered a correlation significant when Spearman's ρ > 0.5 and *p*-value < 0.01.

Differences across groups in the SCoM movement onset were analyzed with a Dunn's test (*p*-value < 0.05, adjusted with Bonferroni correction for multiple comparisons).

All statistical analyses, except partial correlation analyses performed in Matlab, were performed with the JMP package (JMP® Pro 14.0.0, SAS Institute Inc., Cary, NC, USA).

#### **3. Results**

Demographic features, AM measurements, and BoS measurements did not significantly differ between groups (Table 2). Clinical data were similar between PDNF and PDF patients (Table 2).

Of note, none of the patients showed freezing episodes during GI recordings. Therefore, our results define primarily the impact of APA alterations and postural features in favoring FOG in PD and not a causal correlation with the occurrence of gait freezing episodes at GI.

#### *3.1. Selection of GI Variables*

The BoS did not correlate with most of the biomechanical measures of the IMB and stepping phases, but did correlate with the UNL. The results are consistent with our previous findings [12]. The GI variables that were independent from the BoS are listed in Table 3. The BoS and the AMs showed no correlations with the trunk, thigh, and shank angles.

**Table 2.** Demographic, clinical, anthropometric, and base of support features. Data are shown as mean (standard deviation). No statistically significant difference was found across groups (Mann– Whitney U-test, *p*-value set at 0.05). Abbreviations: HC, healthy controls; LEDD, levodopa equivalent daily dose; PDF, Parkinson's disease with freezing of gait; PDNF, Parkinson's disease with no freezing of gait; UPDRS-III, Unified Parkinson's Disease Rating scale, part III. Refer to Table 1 for a list of other abbreviations used.


**Table 3.** Gait initiation measurements: comparison between groups. Only biomechanical variables not correlated with the base of support are listed. Data are shown as mean (standard deviation). The mediolateral CoP displacement during imbalance and unloading was considered positive when the shift in the CoP was towards the swing and the stance foot, respectively. The anteroposterior CoP displacement during imbalance and unloading phase were both defined as positive when the CoP movement was oriented backwards. Abbreviations: HC, healthy controls; PDF, Parkinson's disease with freezing of gait; PDNF, Parkinson's disease with no freezing of gait; refer to Table 1 for a list of other acronyms used.



**Table 3.** *Cont.*

Dunn's test, significant *p*-value after Bonferroni correction: # HC vs. PDNF, <sup>+</sup> HC vs. PDF, \* PDNF vs. PDF.
