A pathophysiological model of gait captures the details of the impairment of pace/rhythm, variability and asymmetry in Parkinsonian patients at distinct stages of the disease

Locomotion in people with Parkinson’ disease (pwPD) worsens with the progression of disease, affecting independence and quality of life. At present, clinical practice guidelines recommend a basic evaluation of gait, even though the variables (gait speed, cadence, step length) may not be satisfactory for assessing the evolution of locomotion over the course of the disease. Collecting variables into factors of a conceptual model enhances the clinical assessment of disease severity. Our aim is to evaluate if factors highlight gait differences between pwPD and healthy subjects (HS) and do it at earlier stages of disease compared to single variables. Gait characteristics of 298 pwPD and 84 HS able to walk without assistance were assessed using a baropodometric walkway (GAITRite®). According to the structure of a model previously validated in pwPD, eight spatiotemporal variables were grouped in three factors: pace/rhythm, variability and asymmetry. The model, created from the combination of three factor scores, proved to outperform the single variables or the factors in discriminating pwPD from HS. When considering the pwPD split into the different Hoehn and Yahr (H&Y) stages, the spatiotemporal variables, factor scores and the model showed that multiple impairments of gait appear at H&Y stage 2.5, with the greatest difference from HS at stage 4. A contrasting behavior was found for the asymmetry variables and factor, which showed differences from the HS already in the early stages of PD. Our findings support the use of factor scores and of the model with respect to the single variables in gait staging in PD.

Gait protocol and analysis of spatiotemporal data. Spatiotemporal gait variables of HS and pwPD were acquired using an electronic walkway (GAITRite ® , CIR Systems, Sparta, NJ, USA) 46 . Participants were asked to walk barefoot on the walkway at a comfortable speed with the standard instruction "walk along the walkway at your normal speed". The walk started 2 m before the 4.60 m walkway, to compensate for problems with gait initiation 47 , and stopped 2 m after the walkway to compensate for speeding up/slowing down at the end. During the trials, patients were allowed to use their usual walking aid, if they needed it. Subjects repeated the trial four times 48 . Since the gait variables of the first trial differed significantly from the other three, the first trial was considered as a familiarisation trial and not included in the analysis 38 . Therefore, we considered only the 2nd, 3rd and 4th trials, with a total of 21-24 steps. This ensured a good inter-trial reliability 38,49 . Data processing. Based on the recorded footfalls, for each walking trial the GAITRite ® walkway automatically calculates 46 gait variables, of which 36 separately for each foot (making a total of 82 variables). First of all, Construction of the gait model and factor scores. The model was originally confirmed in a sample of pwPD 38 and subsequently applied in a sample of HS 42 . In this study, we used the model in both cohorts to verify its discriminating power in identifying the progression of gait impairment over the different H&Y stages with respect to HS. In particular, the eight gait variables from both pwPD and HS, selected a priori from the model of Arcolin et al. 38 , were used and a new exploratory factor analysis (EFA), which is necessary for creating the model, was conducted using the methods previously reported 38 . After determining the number of factors to be considered, the variables were distributed into factors based on the EFA matrix. This represents the correlations between the variables and factors: correlation coefficients ≥ 0.40 were considered relevant for a given factor 50 . By replicating the EFA of Arcolin et al. 38 and using the spatio-temporal variables of both pwPD and HS, we expected to allocate the eight gait variables into three factors (pace/rhythm, variability and asymmetry). This permitted the generation of the three factor scores and of the model, the comparison between HS and the overall sample of pwPD, and between HS and the pwPD at the different H&Y stages. After EFA, we computed the factor scores, one for each factor of the gait model. Using the weighted sum score (WSS) method, factor scores were calculated by transforming the eight gait variables into z-scores and then aggregating them based on the EFA results (for a detailed description see the Supplementary Material) 51 . Higher scores indicate greater gait impairment. In order to combine the three factor scores (pace/rhythm, variability and asymmetry) into an overall score of the full gait model, we performed a logistic regression analysis (see below).

Comparison of pwPD with HS.
We assessed the ability of each gait variable, factor score and score of the all-inclusive model to correctly detect subjects belonging to each of the two cohorts (pwPD and HS) through Receiver Operating Characteristic (ROC) curves. We used the area under the ROC curve (AUC) and its 95% Confidence Interval (95% CI) to assess the diagnostic performance of each variable and factor and the model. The AUC ranges between 0.5 (no diagnostic accuracy beyond chance) to 1.0 (perfect diagnostic accuracy): an area > 0.90 indicates high accuracy, 0.70-0.90 moderate accuracy, 0.50-0.70 low accuracy and < 0.50 a chance result 52 . To describe the accuracy of the ROC curve, we also reported the sensitivity and specificity of the cutoff values at which the pair of sensitivity and specificity values was maximised, hence the point that maximises the discrimination between true-positive rate and false-positive rate. In fact, sensitivity is the number of true positive decisions/the number of actually positive cases, while specificity is the number of true negative decisions/the number of actually negative cases. We then calculated the accuracy, which is the proportion of subjects correctly classified at that cutoff (both true positives and true negatives) to the total number of subjects. Where not specified, text and tables report the results as mean ± SD, while the Figures report the mean ± standard error (SE). The differences in the factor scores between HS and pwPD at the various H&Y stages were assessed by one-way analysis of variance (ANOVA). When ANOVA gave a significant result (p < 0.05), the post hoc Fisher's Least Significant Difference test was used to assess differences between the variables evaluated for each group and the Bonferroni correction was applied. A logistic regression analysis was performed to provide the score of the model. The STATA command "logit" was used with the factor scores of pace/rhythm, variability and asymmetry as independent variables and the condition (HS or PD) as dependent variable. We used the "roctab" command of STATA to obtain the nonparametric estimation of the ROC curve and the AUC values for gait variables and factor scores. Conversely, for the model of gait we used the "lroc" command after logistic regression analysis. AUCs were compared with the STATA command "roccomp" and χ 2 test was used to calculate the statistical difference between AUCs. All statistical analyses were performed using the STATA R13.0 software package.

Results
The two cohorts: pwPD and HS. Of 359 pwPD screened for eligibility, 61 (17%) did not meet the inclusion criteria and were excluded. The remaining 298 (139 women and 159 men, mean age 70.0 years) formed the pwPD cohort (Table 1). Stratified by the modified H&Y stage of severity, patients were classified at: stage 1, n = 7; stage 1.5, n = 27; stage 2, n = 60; stage 2.5, n = 99; stage 3, n = 93; stage 4, n = 12. Disease duration ranged from 6 months to 26 years, with a mean of 7.6 years, and correlated with the levodopa equivalent daily dosage (r = 0.58, p < 0.0005) (Fig. 1). Ninety-one participants commonly used a walking aid in daily life, but only 42 of these (walker, n = 20; cane, n = 22) made use of it during gait assessment on the baropodometric walkway. Of these, 12 were at H&Y stage 2.5, 23 at stage 3 and 7 at stage 4.
Regarding the HS group, 96 healthy subjects were screened for eligibility, of which 12 (13%) not meeting the inclusion criteria were excluded, leaving 84 participants (44 women and 40 men, mean age 71.5 years), who constituted the HS cohort. Clinical characteristics of pwPD and HS are reported in Table 1. No significant differences were found between groups for gender, age and body mass index. The score of MMSE was slightly lower in pwPD than in HS. Table 2 shows the mean values of the eight variables for both the pwPD and the HS cohorts. All gait variables differed significantly between HS and the overall sample of pwPD. PwPD had a reduced gait speed and longer step time and double support time compared to HS. The mean value of the double support time was 32% and 21% of the gait cycle in pwPD and HS, respectively. Variability and asymmetry variables were greater in pwPD than in HS. www.nature.com/scientificreports/ The ability of the gait variables, separately considered, to discriminate between pwPD and HS was assessed by ROC analysis (Table 3). Three variables showed moderate ability to discriminate between pwPD and HS: gait speed, step length CV and swing time CV. The remaining 5 variables (step time, double support time, step velocity CV, step time asymmetry and swing time asymmetry) had AUC values between 0.50 and 0.70, corresponding to low discriminative accuracy. Of note, gait speed, step length CV and swing time CV had the highest AUC value (0.73, 0.72 and 0.70, respectively), with similar accuracy in correctly classifying pwPD from HS (around 67%).

Discriminating power of gait variables.
Exploratory factor analysis (EFA) of the model and ability of factor scores to discriminate between pwPD and HS. The EFA results on the correlation of each variable with the three factors are shown in the Supplementary Material. Despite our heterogeneous sample (containing both HS and pwPD), the distribution of variables of both cohorts into factors was the same as for the model presented by Arcolin et al. 38 . The pace/rhythm factor included three variables (gait speed, step time, and double support time), the variability factor four variables (step velocity CV, step length CV, swing time CV and gait speed) while the asymmetry factor contained two variables (step time asymmetry and swing time asymmetry) (see Supplementary Material).
The three factor scores in isolation, created for each of the three identified factors (see Supplementary Material), showed a low to moderate ability to discriminate between pwPD and HS (Fig. 2, Table 3). The pace/rhythm and the asymmetry factors had a low ability to correctly classify pwPD and HS (AUC = 0.65 and AUC = 0.66, respectively), while the variability factor showed the highest ability to discriminate between pwPD and HS (AUC = 0.77). The logistic regression model, created by combining the three factor scores, proved to have a good ability to discriminate pwPD from HS (Fig. 2, Table 3). The AUC of the model (= 0.81) was larger with respect to the AUCs of each single factor in isolation (for pace/rhythm and asymmetry, p < 0.0005; for variability, p < 0.05).
Variables and factor scores split by H&Y stage in comparison to HS. Variables, factor scores and the model, after evaluating their ability to discriminate HS from the overall cohort of pwPD, were then evaluated for each stage of pwPD severity ( Supplementary Fig. S1). The largest difference in the scores of the three factors was found between HS and pwPD at stages 2.5, 3 and 4, in spite of the obvious larger variance in stage 4 compared to the others. www.nature.com/scientificreports/ A radar chart was used to represent the evolution of the gait variables across the six stages of H&Y (Fig. 3). In order to compare pwPD and HS, the data were transformed into z-scores based on the means and SDs of HS (e.g., z-score pace/rhythm factor = (pace/rhythm factor of pwPD − mean pace/rhythm factor of HS)/SD pace/ rhythm factor of HS). The chart shows that much as for the factor scores mentioned before, major differences with respect to HS emerged for pwPD at or above H&Y stage 2.5, except for step time asymmetry and asymmetry factor, which differed from HS also at H&Y stage 1.5 (p < 0.05). While for some variables and factors the differences with respect to HS increased gradually with the progression of H&Y stages, differences in double support time, step length variability and velocity, variability factor and the model increased disproportionately. The gait speed was the only variable which showed a different behaviour. While the other variables and factor scores increased with the progression of PD, at H&Y stages 2.5, 3 and 4 patients walk slowly. Hence, as the reference value (zero in the radar chart, corresponding to the dotted circle) is HS, the increase of the other variables and factor scores was expressed by positive values. On the contrary, the z-score of gait speed of pwPD become negative at H&Y stage 2.5 and higher.
Gait impairment progression across H&Y stages in comparison to HS. The effect size (ES) of the differences between pwPD and HS for the 8 gait variables, 3 factors and the gait model are shown in Fig. 4. All variables were sensitive to gait impairment in PD. The pace/rhythm variables (first three columns on the left) showed an increased amplitude of the differences between pwPD and HS as PD severity increased (from bottom to top of the panel). The values of the three variability parameters became worse as the disease progressed. The difference between HS and pwPD became explicit from stage 2.5 onwards, with the ES showing the highest value at stage 4. Small differences emerged also in the first stages in step length and step velocity CV. The two asymmetry variables were moderately different between pwPD and HS already at the first two stages of the modified H&Y scale. The differences were non-significant at stage 2 but then progressively increased in the higher stages. The ES of the differences for each of the three factors was broadly similar to that of the single constituent variables. Finally, the ES of the differences (pwPD vs. HS) for the model ranged from large to huge as H&Y stage increased. The combination of the three factor scores in the model detected a strong difference in gait features between HS and pwPD at all stages of the modified H&Y scale.
By scanning Fig. 4 from left to right, one can see that pwPD at stages 1 and 1.5 showed just a light to moderate change with respect to HS in the variability and asymmetry variables and for the pace/rhythm and variability factors, whereas the step time asymmetry and the asymmetry factor obviously highlighted the weight of asymmetry in the these initial PD stages, with large differences with respect to HS at stages 1 and 1.5. At H&Y stage 2, pwPD began showing an initial impairment in gait speed, but overall were not much different from pwPD at stages 1 and 1.5, except, remarkably, for the gait asymmetry variables and factor. It seems that larger differences start appearing at stage 2.5 and higher, becoming huge at stage 4. www.nature.com/scientificreports/

Discussion
This study has compared the gait characteristics of pwPD with those of HS and identified the gait changes in relation to the disease progression, focusing not only on the single gait variables, but also on factors (groups of variables) and on a model incorporating the distinct factors of gait. Our results show that the model applied here, based on non-redundant variables, can be used with confidence in the clinical setting as a reliable marker of gait quality in PD. One can also use the model to classify the disease as it progresses, matching the patient's score with that of their corresponding H&Y stage. Our findings indicate that the gait variables considered in isolation have a moderate ability to discriminate pwPD from HS, with the best discriminative ability found in gait speed, but their discriminative power increases when they are collected together in the factor score or in the model. Further, when considering pwPD stratified by H&Y stage, it emerges that multiple impairment signs appear at stage 2.5, while at the earlier stages of disease both the asymmetry variables and the asymmetry factor highlight differences between patients and HS. Accuracy of the model in differentiating PD from HS. The gait features included in this study were selected according to a validated model of gait. This was created from a sample of pwPD with H&Y stage ranging from 1 to 4. We found that, by using only 8 gait characteristics from three independent gait domains (pace/ rhythm, variability and asymmetry), we were able to achieve a good identification of gait impairment in PD.
The accuracy of the model is higher than that of the single variables. Previous studies have tried to describe gait of pwPD using different methods, such as vertical ground reaction force 55 , inertial measurement units 56 , tri-axial accelerometer 41 and instrumented insoles 22 . All these studies were based on a small number of patients, did not take into account the entire spectrum of disease severity, and extracted numerous variables that are not always easily interpretable from a clinical point of view. Besides, the use of wearable technologies does not seem to increase the ability to differentiate the pwPD and HS correctly based on the data simply collected from sensorized mats 57 .
Recently, Rehman et al. 58 assessed gait of more than 100 pwPD with a GAITRite® walkway and, using a machine learning approach, tried to highlight the group of spatiotemporal variables that best differentiated pwPD from HS. They identified six variables (step velocity, step length, step time, step length variability, step width and step width variability) that reached an accuracy ranging between 73 and 97%. Compared to our study, the main differences are the lack of asymmetry variables in Rehman et al. 's work 58 and the absence of variables related to step width in our model. We do not believe that "step width" is of major clinical importance to warrant its inclusion in the model due to: (a) the low correlation values of step width with the other variables, as also in Rehman et al. 58 , (b) its low discriminative ability in discriminating pwPD from HS in our dataset where the AUC was 0.60 (not shown in results), and (c) the absence of significant differences in the mean step width between pwPD and HS, as in Roemmich et al. 59 and as recently stated in a meta-analysis 21 . Conversely, asymmetry is an essential feature in the evaluation of PD gait, since alterations in step time asymmetry are associated with a shorter time to diagnosis 19 and bear high relevance for characterising de novo pwPD 60 .
Nevertheless, three of the 6 variables identified by Rehman et al. 58 are the same as those included in our model, which may explain the similar value of accuracy. Of note, both studies seem to consolidate the importance of assessing the variability domain in addition to the pace/rhythm variables. In fact, our findings underline that, among the factors, variability has the greatest accuracy in differentiating pwPD from HS.
Pace/rhythm. Gait speed, step time and double support time, belonging to the pace/rhythm factor, showed differences between pwPD and HS which became greater as the disease progressed. The difference is not significant in the first few H&Y stages, but grows from large to huge between stages 2.5 and 4. Gait speed, which is the most frequently reported variable in the studies investigating gait of pwPD 10,21 , appeared to be one of best variables for discriminating gait of PD from HS. Nevertheless, the main difference in gait speed between these two populations appears from stage 2.5 onwards. These results support previous findings based on a large cohort of HS according to which gait speed is not a significant predictor of PD conversion 19 and are in line with other studies that reported no difference in the mean gait speed of patients with early PD compared to HS [61][62][63] . Recently, Keloth et al. 64 also noted that the double-support interval increased with the severity of PD, but the increase was modest and not significant at stage 3. This is in line with our results, since we found medium differences at stages 2.5 and 3, while huge differences were found at stage 4.
With respect to the above-mentioned variables of pace/rhythm factor, step time had the lowest ability to discriminate pwPD from HS. In fact, only patients with more advanced stages of PD showed moderate to large differences in step time compared to HS. This result is not surprising given the numerous studies showing that gait cadence is not usually altered in PD [65][66][67] or increased as a compensatory mechanism for the step length reduction 65,66 . More in general, pace/rhythm factor showed the lowest ability to differentiate pwPD from HS compared to the other factors and to the model. The sensitivity of pace/rhythm factor in assessing disease progression became large only on reaching H&Y stage 3.
Variability. Gait abnormalities in pwPD include increased stride-to-stride variability, a fluctuation in the value of spatial or temporal variables, or both from one stride to the next 23 . Variability is a reliable marker of gait 9,68,69 , and it shows a similar reliability in pwPD and HS 70 . The variability factor has a good discriminative ability between pwPD and HS and increases with the progression of the disease 14 . Overall, variability compared to pace/ rhythm factor shows a stronger difference between pwPD and HS than pace/rhythm from stages 2 to 3. In detail, there were only small differences between pwPD and HS in the CVs at H&Y stages ≤ 2, but at stage 2.5 moderate differences emerged in the CV of step velocity and large differences in the CV of swing time and step length. www.nature.com/scientificreports/ Further, the model shows that, in addition to gait speed, the variability of swing time and step length are the first variables in the progression of the disease that crucially show a large difference compared to HS when pwPD reach stage 2.5. A huge difference compared to HS is obvious in patients at stage 4, showing that variability increases progressively as the condition deteriorates. It has been proposed that gait speed and gait variability are linked to different cortical networks 71 which probably have a different action on the brain stem nuclei controlling gait and whose progressive deterioration may have different tempos.
Asymmetry. In PD, there is substantial asymmetry of clinical signs 72 . Usually, asymmetry is present from the onset of the disease and may persist in the more severe cases 73 . Gait asymmetry in pwPD is connected to uncoordinated activity in the leg muscles 26 , is normally present in the lower limbs 74 , but can affect the upper limbs as well 75 . We found that the two markers of temporal asymmetry (step time and swing time asymmetry), collapsed together in the asymmetry factor, had moderate ability to identify pwPD from HS, not superior to the variability factor. Nevertheless, it is interesting to note that both the swing time and, in particular, the step time asymmetry are an early sign of the disease. This is in keeping with the conclusion of Del Din et al. 19 , who posited that higher step time variability and gait asymmetry may allow an earlier diagnosis of PD. In particular, they found that step time asymmetry, which in our study was the most sensitive single measure in the early stages of PD, strongly predicts the risk of PD.
In early PD, the difference with respect to healthy gait for both step time and swing time asymmetry, while not large, is here significant. This difference noticeably diminishes with the progression of the disease, and becomes non-significant at H&Y stage 2, when the signs of the disease became bilateral. However, our analysis highlights a definite increase in the temporal gait asymmetries of pwPD compared to healthy gait also at stages 2.5, 3 and, in particular, a large difference at H&Y stage 4, indicating that asymmetry is not only a marker of early PD, but a major sign accompanying the progress of gait impairment and possibly predisposing to freezing of gait 74 .
Interestingly, this increase in temporal gait asymmetries related to the disease progression is underscored by the asymmetry factor and by the model. Thus, our results strongly support the use of factors in addition to the single gait measures, even if not superior to the step time asymmetry. An accurate assessment of asymmetry would thus appear important in clinical practice, since this aspect may be successfully treated with a specific rehabilitation intervention 76 , even if some authors have found that only spatial but not temporal asymmetry improves with rehabilitation in pwPD at stage 1 to 3 77 .
Clinimetric value of the modified H&Y scale. The original H&Y scale was the first rating scale to describe the progression of PD 78 , providing an overall indication of the stage of disease and progression of symptoms and disability 79,80 . It correlates with dopaminergic loss and with other scales targeting motor abnormality, disability, quality of life, and has a strong clinimetric performance for motor assessment 43,79,81 . Originally created with 5 levels, the modified version added two intermediate stages, 1.5 and 2.5, to better capture the progression of PD, and this version has been adopted by many researchers 15,45,82 .
With our model, it is possible to establish how powerful a certain gait marker is (be it a variable or factor of the model, or the model itself as a whole) in assessing the extent of the differences between HS and pwPD at each stage. From our results, the addition of the intermediate stage 2.5 in the modified H&Y scale seems more than justified. The differences between pwPD and HS are similar at stages 1 and 1.5, showing that gait worsening does not become significant during these early phases of PD 83,84 . Factor scores and most of the variables of pwPD begin diverging clearly from those of HS only between stages 2 and 2.5. Recent findings show that dopaminergic loss and deficits in gait and postural control occur between the H&Y stages 2 and 3 85 . The modified H&Y scale with the 2.5 stage gives the opportunity of a finer view at a critical point, because the transition from H&Y 2 to 3 marks a pivotal milestone in the progression of PD, when gait and balance disorders cause disability in many everyday activities 86 . In fact, our study shows that the critical changes appear between stages 2 and 2.5 rather than between 2 and 3.
Finally, the increase in the factor scores and in the score of the model was disproportionate in pwPD at stage 4, and this strongly reflects the aggravation of locomotion as the disease worsens. Of note, the worsening of the gait variables in pwPD at stage 4 was not attributable to the appearance of freezing of gait since the trials in which our patients showed episodes of freezing of gait on the electronic walkway were not considered in the analysis.

Limitations.
In this cross-sectional study the distribution of pwPD across the severity stages was not even since most of our patients suffered from mild to moderate PD. However, a sizeable number of less and more severely affected patients was contained in our cohort. In particular, the patients at stage 4 were not so numerous since many of them could not walk without assistance, while the selection criteria excluded all pwPD at H&Y stage 5. Spatiotemporal parameters and gait variability were not stratified across age groups in the healthy subject cohort. Analysis of the magnitude of the ES between pwPD and HS was not done for matched ages, because the primary criterion was the H&Y stage. However, a post-hoc appraisal showed that the pwPD within each stage had a mean age not different from that of the entire HS cohort, except for stage 1 and 1.5. In this regard, a recent article showed that gait-related changes with respect to age appear to be significant in HS but not in pwPD 87 . This limitation is mitigated by the demonstration that gait variability measures remain stable over time and are not influenced by age in HS 88 .

Conclusions
Efforts to regularly update classification on PD gait, including data on critical markers of disability, are important for evidence-based care planning and resource allocation. This cross-sectional study, based on a large cohort of pwPD, showed that our model holds when applied to a mixed population of pwPD and HS and that the accuracy www.nature.com/scientificreports/ to differentiate PD from HS increases by grouping the variables into factors and into a model. The asymmetry factor and the model, compared to the single variables, highlight gait differences between pwPD and HS at earlier stages of PD. Further, the model emphasizes significant deviations from a monotonous trend in the gait variables, meaning that not all spatiotemporal variables evolve concurrently. For example, changes in step asymmetry are markers of early PD, while changes in double-support time and swing time variability obtrude at H&Y stage 2-2.5. Overall, the data suggest that the gait pattern worsens in the course of the disease, as more and more brain cells die and the neuronal networks lose more and more capacities 89 , but this progression is definitely different for the individual variables, conveying the suggestion that separate neural networks selectively control distinct gait processes. The asymmetry factor is the strongest predictor of PD even when the variability and pace/rhythm factors hardly help. Conversely, there is no clear-cut threshold in the modified H&Y scale, beyond which gait variables would show abnormal values. The scores of the variables, factors and model clearly separate the gait features of pwPD and HS, so that the model can be safely used to compare gait between the two cohorts. Although some differences between PD and healthy gait emerges for each of the modified H&Y stages, they become stronger for patients in the upper levels of the scale. Further, our findings support the clinimetric value of the modified H&Y scale that includes 0.5 increments, because several variables start showing a difference compared to HS at 2.5 points of the H&Y scale, and the magnitude of these differences changes at 3.0. The model and its factors are appropriate to assess the complexity of the gait impairment in pwPD, and identify the spatiotemporal variables that become abnormal at a certain stage of the modified H&Y scale. Any improvement in our knowledge of the nature and aggravation of gait quality in pwPD is welcome for the clinician, in the view of selecting the best treatment options 90,91 and improving the differential diagnosis from other neurodegenerative diseases 92 . Recently, Rennie et al. 93 demonstrated that a highly challenging balance and gait training significantly impacts pace and rhythm aspects of gait in pwPD. The assessment of different gait domains helps frame the effects of rehabilitation in a coherent context and might help identify the best treatment at different stages of disease.
The results obtained in this study are comparable with and extend those yielded by the preliminary validation study 38,42 , thus showing that the present model is a valid instrument to check gait impairment and their correspondence with severity in PD. The simple application of the scheme describing the most relevant structural features of gait in PD makes the model an attractive and useful tool for clinical practice and research. Future investigations have to assess if the model is valid in longitudinal studies 17 and confirm that the model not only faithfully represents the commonest pattern of progression in the PD walking disability, but also helps stage individual patients with PD and fine-tune the treatment based on these gait markers.

Data availability
The datasets generated during and/or analysed during the current study are available from the corresponding author (I.A.) on reasonable request.