# How many steps to reach steady state of postural stability, progression velocity and step length during gait initiation? Effects of ageing and Parkinson's disease

Arnaud Simonet, Arnaud Delafontaine, Paul Fourcade, Eric Yiou

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Arnaud Simonet, Arnaud Delafontaine, Paul Fourcade, Eric Yiou. How many steps to reach steady state of postural stability, progression velocity and step length during gait initiation? Effects of ageing and Parkinson's disease. Neurodegenerative Diseases, 2026, pp.1 - 24. 10.1159/000547017. hal-05475586

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# How Many Steps to Reach Steady State of Postural Stability, Progression Velocity, and Step Length during Gait Initiation? Effects of Ageing and Parkinson's Disease

Arnaud Simonet<sup>a, b</sup> Arnaud Delafontaine<sup>a, c, d</sup> Paul Fourcade<sup>a</sup> Eric Yiou<sup>a</sup>

<sup>a</sup>CIAMS, Université Paris-Saclay, Orsay, France; <sup>b</sup>LADAPT Loiret, Centre de Soins de Suite et de Réadaptation, Amilly, France; <sup>c</sup>Laboratoire d'Anatomie Fonctionnelle, Faculté des Sciences de la Motricité, Université Libre de Bruxelles, Brussels, Belgium; <sup>d</sup>Laboratoire d'Anatomie, de Biomécanique et d'Organogenèse, Faculté de Médecine, Université Libre de Bruxelles, Brussels, Belgium

## Keywords

Steady state walking · Gait initiation · Postural stability · Progression velocity · Step length · Parkinson's disease · Ageing

## Abstract

**Introduction:** This study examined how many steps are required to reach a steady state of postural stability, progression velocity, and step length during gait initiation in healthy young adults, healthy elderly adults, and patients with Parkinson's disease (PD). **Methods:** Healthy young adults (n = 10), healthy elderly adults (n = 11), and PD patients (n = 12) had to initiate gait and walk straight at spontaneous and maximal velocity to the end of an 11-m long room. Mean values and variability of biomechanical indicators of postural stability ("margin of stability" [MoS], "braking index" [BI]), progression velocity (peak anteroposterior centre-of-mass velocity), and step length were computed along five successive steps using a markerless motion capture system. **Results:** The results showed that the number of steps required to reach steady state walking depended on the experimental variable. For the progression velocity, the step length and the BI, two steps were required. For the MoS, one

step was required. PD patients and healthy participants used different strategies to reach steady state of BI, which may expose the former to a high risk of instability in the first step. Interestingly, mean BI and variability of PD patients returned to normal following this first step. **Conclusion:** These findings suggest that rehabilitation programs aiming to improve walking in PD patients at an early stage of the disease (stage 2 on the Hoen and Year scale) may specifically target the first step.

© 2025 The Author(s).
Published by S. Karger AG, Basel

## Introduction

Gait initiation (GI), defined as the transient period between the upright standing posture and steady-state walking [1], is a functional locomotor task classically used in the literature to investigate the posturo-dynamic conditions for stable whole-body progression. However, despite intensive researches on GI (e.g., Yiou et al. [2] for a review), it is still unclear how many steps are required to reach a steady state of postural stability, progression velocity, and step length. It is important to answer this question for both motor control and in the clinical field

<figure><img src="image_2.png" /></figure>

<footnote>karger@karger.com
www.karger.com/ndd</footnote>

<footnote>© 2025 The Author(s).
Published by S. Karger AG, Basel</footnote>

<footnote>This article is licensed under the Creative Commons Attribution 4.0 International License (CC BY) (https://karger.com/Services/OpenAccessLicense). Usage, derivative works and distribution are permitted provided that proper credit is given to the author and the original publisher.</footnote>

<footnote>Correspondence to:
Eric Yiou, eric.yiou@universite-paris-saclay.fr</footnote>
since it may help better understand how posturo-
dynamic conditions are established during GI in both
healthy subjects and neurological participants having
difficulty starting to walk (typically patients with Par-
kinson's disease [PD]). One might assume that more
steps are required to reach this state, exposing patients
more to potential risks of instability and falling.

There is little agreement in the literature regarding the
number of steps required to reach steady-state walking,
probably because authors have based their conclusions
on different biomechanical parameters, experimental
tools, experimental conditions, and populations. For
example, based on electromyography, force-plate data,
walking velocities, and ranges of joint motion, Mann
et al. [3] suggested that healthy young adults (HY) re-
quire “approximately” three steps to reach steady-state
walking. This finding is in agreement with Miller and
Verstraete [4], who investigated the mechanical energy
of GI in a similar population. Based on velocity and
spatiotemporal parameters, Lindemann et al. [5] re-
ported that community-dwelling older persons need to
walk at least 2.5 m to reach a steady state. A recent study
by Strutzenberger et al. [6] further showed that when gait
is initiated on an instrumented ramp at different incli-
nations, steady-state walking speed in healthy partici-
pants was reached by the third step. Contrasting with
these studies, other authors proposed that HY reach
steady-state walking with the very first step [7, 8], a
conclusion based on analysis of the GI progression ve-
locity obtained from a force-plate and/or camera re-
cordings in HY.

It is interesting to note that none of these studies
investigated the number of steps required to reach a
steady state of postural stability, nor did they question
whether this number of steps depends on progression
velocity (spontaneous or maximal) despite the fact that
progression velocity and postural stability could be
controlled by two distinct systems within the basal
ganglia circuitry [9]. As a consequence, the establish-
ment timing of these biomechanical parameters might
differ during GI. In addition, only HY were studied in all
the above-mentioned experiments (with the exception of
Lindemann et al. [5], as stated above). So, although it is
well known that postural stability, progression velocity,
and step length during GI are altered with physiological
ageing [10–13] and, to a greater degree, with PD [9,
14–17], it is not currently known whether these bio-
mechanical parameters worsen or improve in the course
of walking in these populations. So, this study sought to
determine how many steps are required to reach a steady
state of postural stability, progression velocity, and step

length in healthy young adults (HY), healthy elderly
adults (HE), and PD patients. We hypothesized that: (i)
PD patients require more steps than their healthy
counterparts, and HE require more steps than HY, and
that (ii) the number of steps required to reach a steady
state of postural stability, progression velocity, and step
length may differ.

Methods

Participants

Thirty-three adults were divided into three groups: HY, healthy HE, and patients with PD (see Table 1 for participants’ anthropometrical features). Inclusion criteria for healthy participants required ages between 20 and 30 years without any pathologies for the HY group, and between 60 and 80 years without any pathologies for the HE group. For the PD group, participants were aged between 60 and 80 years with a confirmed diagnosis of PD. For the PD patients, the average time since diagnosis was 7.4 ± 2.8 years. Their score on the Hoehn and Yahr Scale was 2.0 ± 0.6 points. The average scores on the Unified Parkinson Disease Rating Scale-III and the Montreal Cognitive Assessment (MoCA) were 33.8 ± 11.7 and 25.7 ± 2.3, respectively. Their Mini-Mental State Exam (MMSE) score was 27.0 ± 1.7. Both the MoCA and the MMSE were used to ensure a comprehensive evaluation of cognitive function. While the MMSE is widely used for general cognitive screening, the MoCA is more sensitive to mild cognitive impairments, particularly in executive functions, which are often affected in PD and other neurological conditions. Using both tools allowed for a broader and more accurate assessment of cognitive status. Exclusion criteria common to all groups included visual, hearing, or orthopaedic problems, as well as cognitive impairments (i.e., a score <25 on the Mini-Mental State Exam and Montreal Cognitive Assessment). Additional exclusion criteria for the HE and PD groups included walking with aids and a medical history of falling. Specific to the PD group were exclusions for freezing gait, identified neurological disorders (other than Parkinson’s), and dementia. PD patients were recorded with their usual levodopa treatment and did not have dyskinesia. All participants provided written consent after being informed of the nature and purpose of the experiment, which was conducted in accordance with the Declaration of Helsinki and approved by the “Comité de Protection des Personnes Ile-de-France XI” under identification number 19028-60429.
<table><caption>**Table 1.** Participants' anthropometrical features</caption><thead><tr><th>Group</th><th>Age, years</th><th>Gender (female/male)</th><th>Body mass, kg</th><th>Height, m</th><th>BMI, kg/m²</th><th>Shoe size (EU)</th></tr></thead><tbody><tr><td>PD (n = 12)</td><td>68.4±5.1</td><td>2/10</td><td>70.5±11.8</td><td>1.70±0.07</td><td>24.5±3.6</td><td>41.3±1.5</td></tr><tr><td>HY (n = 10)</td><td>24.7±0.7</td><td>4/6</td><td>70.2±13.5</td><td>1.70±0.12</td><td>24.7±0.7</td><td>40.3±3.7</td></tr><tr><td>HE (n = 11)</td><td>66.5±3.6</td><td>8/3</td><td>63.9±10.1</td><td>1.65±0.06</td><td>23.4±3.4</td><td>39.3±1.8</td></tr></tbody></table>

PD, patients with Parkinson's disease; HY, healthy young adults; HE, healthy elderly adults.

## Experimental Setup and Procedure

The participants had to initiate gait and walk straight to the end of 11-m long room, stop, and come back quietly in the starting position. The starting position was at the opposite of the room. Gait was initiated at a spontaneous velocity ("spontaneous velocity condition") and at maximal velocity ("maximal velocity condition" [MVC]) with the preferred foot. The preferred foot for gait initiation was consistent across trials and conditions. Participants were instructed to keep a steady-state velocity progression until they may slow down (if necessary [cf. in the "maximal velocity condition"]) approximately 2 m before reaching the end of the room. Visual analysis of each trial by experimented researchers and clinicians showed that these instructions were respected by all participants. With this experimental set-up, participants thus walked approximately 9 m from the starting position before they may start to slow down (cf. Fig. 1). Series of five trials were carried out in each velocity condition. Two blank trials (not recorded) were performed before each series to allow the participants to familiarize themselves with the instructions and the environment. The participants were barefoot and began walking when they felt ready after hearing an auditory signal. Movement analysis was performed using a markerless motion system (MLS) composed of twelve Qualisys Hybrid cameras (Qualisys, Gothenburg, Sweden). This system was calibrated to record body motion on a 6 m distance, which was sufficient to fully catch the five first steps of each trial in the two velocity conditions and the three groups. At the end of the fifth step, participants were thus located approximately 4–5 m from the "slowing down zone." To avoid the effects of fatigue, participants were required to take a 2-min rest between the two velocity conditions, and a 30-s rest between trials. The velocity conditions were randomized across participants to avoid a rank effect.

## Raw Data

The data obtained from the cameras were transferred to Theia software (Theia3D, Kingston, ON, Canada) for reconstruction of the 3D body segment position and the

whole-body centre-of-mass position. Previous studies [18–21] showed that the MLS used in this study was sufficiently reliable to quantify the biomechanical variables of this study described below. Three-dimensional whole-body centre-of-mass velocity was computed according to the following formula applied to the mediolateral, vertical, and anteroposterior directions:

$$V_{\text{CoM}}(t) = [\text{CoM}(t) - \text{CoM}(t_{-1})] \times F \quad (1)$$

where $V_{\text{CoM}}(t)$ and $\text{CoM}(t)$ are the whole-body centre-of-mass velocity and position at the time t, respectively; $\text{CoM}(t_{-1})$ is the centre-of-mass position at the previous frame ($t_{-1}$); F is the sample frequency set at 85 Hz. This frequency corresponds to the limit of the MLS in full HD mode.

The data were filtered with a no-lag low-pass Butterworth order filter with a 15 Hz cut-off frequency [22]. Qualisys Track Manager software was used to synchronize the signals.

## Experimental Variables

### Margin of Stability

The control of postural stability along the mediolateral direction is known to be of utmost importance during locomotion [23, 24]. The concept of "margin of stability" (MoS) was introduced by Hof et al. [23] and used to quantify postural stability along this direction at the time of swing-foot contact, which corresponds to the time of maximal instability. For each step, the MoS was computed as the difference between the position of the mediolateral boundary of the base of stability ($BoS_{ymax}$) and the mediolateral position of the "extrapolated CoM" at foot contact ($yCoM_{FC}$), i.e.,

$$\text{MoS} = \text{BoS}_{ymax} - y\text{CoM}_{\text{FC}} \quad (2)$$

$\text{BoS}_{ymax}$ was computed from the MLS recordings as the mediolateral distance between the two heels at the time of swing-foot contact [25, 26]. $y\text{CoM}_{\text{FC}}$ was calculated as follows:
<figure><img src="image_3.png" /><figcaption>Fig. 1. Experimental set up showing the disposal of the markerless camera and the metrics of the different zones of the walking track.</figcaption></figure>

$$yCoM_{FC} = yCoM_{FC} + [y'CoM_{FC}]/[\omega0] \quad (3)$$

where yCoM<sub>FC</sub> and y'CoM<sub>FC</sub> are the mediolateral centre-of-mass position and velocity at foot contact, respectively; ω<sub>0</sub> is the eigen frequency of the body modelled as an inverted pendulum, calculated as:

$$\omega0 = \sqrt{\frac{g}{l}} \quad (4)$$

where g = 9.81 m/s<sup>2</sup> is the gravitational acceleration and l is the length of the inverted pendulum which, in this study, corresponded to 57.5% of body height [27].

Stability at foot contact is ensured on condition that yCoM<sub>FC</sub> is within the BoS<sub>ymax</sub>, which corresponds to a positive MoS value. A negative MoS value indicates an unstable state.

## Braking Index

Previous studies have shown that, in healthy adults, the trace of the vertical centre-of-mass velocity reaches a downward-oriented peak during GI execution [9, 14]. The trace then reverses direction to reach a value close to zero at the time of foot contact. This time course indicates that the fall of the centre-of-mass is actively braked to soften foot landing and facilitate execution of the next step [28, 29]. The so-called braking index (BI) reflects this ability of the CNS to actively brake this vertical fall of the centre-of-mass under gravity. It is a classic indicator of stability control, computed as follows at each step:

$$BI = [z'CoM_{MIN} - z'CoM_{FC}]/z'CoM_{MIN} \quad (5)$$

Where z'CoM<sub>MIN</sub> is the peak of downward centre-of-mass vertical velocity, and z'CoM<sub>FC</sub> is the vertical centre-of-mass velocity at foot contact (shown in Fig. 2). According to equation (5), BI >0 indicates that the vertical fall of the centre-of-mass is actively braked in anticipation to foot contact. In contrast, BI = 0 indicates that the centre of mass fall is braked by foot contact.

## Progression Velocity

This variable corresponded to the peak of the anteroposterior centre-of-mass velocity [1, 2, 30] (shown in Fig. 2). This peak velocity was reached a few ms after foot contact. It was computed at each step.

## Step Length

This variable corresponded to the distance between the two heels at the time of swing heel strike.

## Coefficient of Variation

For each of the experimental variables above, the dispersion of each step value around the mean was evaluated with a coefficient of variation (CV) computed as follows:

$$CV = [mean]/[standard deviation] \quad (6)$$

We considered that a steady state of progression velocity, postural stability, and step length is reached if both the mean and the CV of the investigated experimental variables reach a constant value in the course of the successive steps.
<figure><img src="image_4.png" /><figcaption>**Fig. 2.** Typical time-course traces of the 3D centre-of-mass velocity recorded with the MLS during the first five steps of walking in the three experimental groups (one trial in the SVC). HY, HE, PD: healthy young adults (a), healthy elderly adults (b), and PD group (c), respectively. CoM, centre-of-mass; AP, ML: anteroposterior and mediolateral direction. FC1, FC2, FC3, FC4, FC5: foot contact for the first, second, third, fourth and fifth step, respectively. t0: onset of biomechanical traces. PV, z'CoMMIN: progression velocity (peak of forward velocity) and negative peak of vertical centre-of-mass velocity. z'CoMFC and y'CoMFC: vertical and mediolateral centre-of-mass velocity at the time of foot contact, respectively. A positive value of these traces indicates a centre-of-mass velocity directed forward (upper panel), upward (middle panel), and toward the swing foot (bottom panel).</figcaption></figure>
SVC

MVC

<figure><img src="image_5.png" /></figure>

<figure><img src="image_6.png" /></figure>

<figure><img src="image_7.png" /></figure>

<figure><img src="image_8.png" /></figure>

(Figure continued on next page.)

## Statistics

For each group and velocity condition, means ± standard deviations (SDs) of the experimental variables were computed over the first five steps of walking on the track. Shapiro test and Mauchly test were performed to ensure the normality of the data and the homogeneity of the variances, respectively. A repeated-measures ANOVA model with two within-subject factors and one between-subject factors was used on each mean value and corresponding CV. The within-subject factors were the step number (five levels: step 1 to step 5) and the velocity condition (two levels: “spontaneous velocity condition” vs. “maximal velocity condition”). The between-subject factor was the group (three levels: healthy young [HY], healthy elderly [HE], and patients with PD). The Tukey post hoc test was used when required. The threshold

of significance was set at *p* < 0.05. The Eta square (η²) was used to assess effect sizes when ANOVA showed a significant effect. The effect sizes were classified as trivial (η² < 0.01), small (0.01–0.06), medium (0.06–0.14), and large (≥0.14).

## Results

### Biomechanical Traces

Typical time-course traces of the 3D centre-of-mass velocity recorded with the markerless system (MLS) during the first five steps of walking (spontaneous velocity condition [SVC]) are shown in Figure 2. Visual analysis shows that the shape of these traces is globally similar across all three experimental groups. Along the anteroposterior direction, the
<figure><img src="image_9.png" /><figcaption>**Fig. 3.** Comparison of the MoS (a), BI (b), progression velocity (c) and step length (d) between the experimental groups and the successive steps in the spontaneous (SVC) and the maximal velocity condition (MVC). HY, HE, PD: healthy young adults (red trace), healthy elderly adults (green trace) and PD group (blue trace), respectively. Reported are mean values (all participants combined) ± 1 SD. **b°**: significant difference in BI between the PD group and both healthy groups (HY and HE) for the first step only in the SVC and MVC with *p* < 0.01 (as revealed by post hoc tests). +++: significant difference of BI between the first step and the four following steps (second, third, fourth, and fifth) in the PD group</figcaption></figure>

in the SVC and MVC with *p* < 0.001. **c***: significant difference of progression velocity between the first step and each of the four following steps (second, third, fourth and fifth) for all groups in the SVC and MVC with *p* < 0.001. ▲▲: significant difference of progression velocity between the PD group and both healthy groups (HY and HE) in the SVC with *p* < 0.01. □□□: significant difference of progression velocity between the PD group and both healthy groups (HY and HE) in the MVC with *p* < 0.001. **d***: significant difference of step length between healthy young group (HY) and PD groups for all steps in SVC and for the first three steps in MVC with *p* < 0.05.

velocity remained positive (i.e., directed forward) and peaked a few milliseconds after each foot contact. Along the vertical direction, the velocity reached a negative peak (downward oriented) a few milliseconds before each foot contact. The trace then reversed to reach a value close to zero, indicating that the fall of the centre-of-mass was actively braked at each step. Along the mediolateral direction, the velocity alternatively reached negative and positive peaks, corresponding to peaks oriented toward the right and left swing leg side.

## Comparison of the Mean Values of Experimental Variables across Steps, Velocity Conditions, and Groups

### Margin of Stability

There was no significant main effect of the group, velocity condition or step number on the mean value of the MoS (shown in Fig. 3a). Similarly, there was no significant two-by-two or triple interaction between factors on this variable.
<figure><img src="image_10.png" /></figure>

(Figure continued on next page.)

## Braking Index

There was a significant main effect of the group (F(2, 286) = 7.29, *p* < 0.001, η² = 0.035) and step number (F(4, 286) = 18.10, *p* < 0.001, η² = 0.17) along with a significant group X step number interaction (F(8, 286) = 5.31, *p* < 0.001, η² = 0.10) on the mean value of the BI. There was no other significant interaction between factors or significant main effect of the velocity condition on this variable. Post hoc tests further showed that the BI was significantly higher in both the HY and the HE group than in the PD group in both velocity conditions, for the first step only (with *p* < 0.01; shown in Fig. 3b). Post hoc tests also showed that the BI was significantly lower in the first step than in the four following steps in the PD group only, and in both velocity conditions (all with *p* < 0.001), with no significant difference between these four steps.

## Progression Velocity

There was a significant main effect of the group (F(2, 286) = 91.41, *p* < 0.001, η² = 0.18), velocity condition (F(1, 286) = 336.12, *p* < 0.001, η² = 0.33) and step number (F(4, 286) = 45.50, *p* < 0.001, η² = 0.18), along with a significant group X velocity condition interaction (F(2, 286) = 17.36, *p* < 0.001, η² = 0.03) on the progression velocity. There was no other significant interaction between factors. As expected, post hoc tests showed that progression velocity was significantly higher in the MVC than in the SVC at each step and for each group (all with *p* < 0.001, not shown in the Fig. 3c). Post hoc tests further showed that progression velocity was significantly higher in both the HY and HE groups than in the PD group for each step in the MVC only (all with *p* < 0.001, shown in Fig. 3c). In the SVC, the progression velocity was significantly higher in both healthy groups than in the
<figure><img src="image_11.png" /><figcaption>**Fig. 4.** Comparison of the variability of the MoS (a), BI (b), progression velocity (c) and step length (d) between the experimental groups and the successive steps in the spontaneous (SVC) and the maximal velocity conditions (MVC). HY, HE, PD: healthy young adults (red trace), healthy elderly adults (green trace) and PD group (blue trace), respectively. Reported are mean values of the CV (all participants</figcaption></figure>

combined) ± 1 SD. **b +++**: significant difference of BI variability between the first step and the four following steps (second, third, fourth and fifth) in all groups in the SVC and MVC with *p* < 0.001 (as revealed by post hoc tests). **d ****: significant difference of step length variability between the first step and the four following steps (all groups pooled together) with *p* < 0.001 (as revealed by post hoc tests).

PD group for the first step only (p < 0.01). This velocity
tended to be slower for the other steps as well (as can be seen
from the Fig. 3), but the difference was not significant. Last,
post hoc tests showed that progression velocity was signifi-
cantly lower in the first step than in the four following steps in
all groups and in both velocity conditions (all with p < 0.001),
with no significant difference between these four steps.

Step Length

There was a significant main effect of the group (F(2, 286) = 33.32, *p* < 0.001, *η*² = 0.17) and velocity condition (F(1, 286) = 20.68, *p* < 0.001, *η*² = 0.05) on the step length, with no significant main effect of step number. There was no significant two-by-two or triple interaction between

factors on this variable. Post hoc further showed that each
step was significantly larger in the HY group than in the PD
group in the SVC. In the MVC, only the first three steps
were significantly larger in the HY group than in the PD
group (all with *p* < 0.05, shown in Fig. 3d).

Comparison of the Variability of Experimental
Variables across Steps, Velocity Conditions, and Groups
Margin of Stability

There was no significant main effect of the group,
velocity condition and step number on the coefficient of
variability (CV) of the MoS (shown in Fig. 4a). Similarly,
there was no significant two-by-two or triple interaction
between factors on this variable.
## Braking Index

There was a significant main effect of the group ($F(2, 286) = 8.17, p < 0.001, \eta^2 = 0.02$) and step number ($F(4, 286) = 127.58, p < 0.001, \eta^2 = 0.61$) along with a significant group X step number interaction ($F(8, 286) = 3.85, p < 0.001, \eta^2 = 0.04$) on the BI CV. There was no other interaction between factors or significant main effect of the velocity condition on this variable. Post hoc tests further showed that the BI CV was significantly higher in the first step than in the four following steps in all groups and in both velocity conditions (all with $p < 0.001$), with no significant difference between these four steps (shown in Fig. 4b).

## Progression Velocity

There was a significant main effect of the velocity condition on the progression velocity CV ($F(1, 286) = 9.60, p < 0.001, \eta^2 = 0.03$). In contrast, there was no significant main effect of the group or step number, and no significant interaction between factors on this variable (shown in Fig. 4c).

## Step Length

There was a significant main effect of the step number ($F(4, 286) = 8.85, p < 0.001, \eta^2 = 0.11$) on the step length CV. In contrast, there was no significant main effect of the group and velocity condition. There was also no significant two-by-two or triple interaction between factors on this variable. Post hoc tests further showed that the step length CV was significantly higher in the first step than in the four following steps (all groups pooled together) in the SVC ($p < 0.001$, shown in Fig. 4d). A similar trend (nonsignificant) was observed in the MVC.

## Discussion

This study examined how many steps are required to reach a steady state of postural stability, progression velocity and step length in HY, healthy HE, and PD patients. To address this question, we proposed that a steady state is reached on condition that both the mean and the variability of the investigated experimental variables reach a stable value in the course of the successive steps.

Visual analysis of the typical time-course traces of the anteroposterior centre-of-mass velocity during the first five steps of walking (shown in Fig. 2) suggested that progression velocity (mean of peak anteroposterior

centre-of-mass velocity) was lower in the first step than in the following steps for all groups and for both velocity conditions, with no apparent difference between the last four steps. Statistical analysis shown in Figure 3 confirmed this visual analysis. The results further showed that the centre-of-mass velocity reached at the end of the first step ($1.19 \pm 0.24$ m/s, mean of all participants and velocity conditions combined) corresponded to 80% of the velocity reached at the end of the following steps ($1.49 \pm 0.27$ m/s, mean of the second, third, fourth, and fifth steps, all participants and velocity conditions combined). This percentage is lower than the 90% value reported by Jian et al. [8], in a study involving only four HY. In contrast to mean progression velocity, our results also showed that the within-participants variability of progression velocity did not change across the five successive steps for all participants and both velocity conditions. So, taken globally, these results suggest that a steady state of progression velocity during walking was reached at the second step, regardless of the velocity condition and the experimental group. This statement contrasts with previous authors who suggested that steady state gait progression velocity is reached in the first step of walking in HY [1, 7]. However, we note that these authors did not use statistics to compare the velocity of the first step (which was the only step recorded) vs. the following steps, but compared the first step with literature data on steady state gait. It is clear that this method, associated with a limited sample of participants ($n = 5$), may not be sufficiently precise to reveal differences of even 20% between successive steps within the same participant.

Our results further showed that the progression velocity was slower in the PD group than in the two heathy groups (the difference was significant for all steps in the MVC and it was significant for the first step in the SVC). These findings are in line with the literature [31–34] and reflect the well-known bradykinesia symptom of PD patients. Moreover, results showed that the mean step length did not change across the five successive steps for all groups and both velocity conditions. In contrast, the step length CV was 50% higher in the first step than in the four following steps pooled together in the SVC, with no significant difference between these last four steps). A similar trend could be seen in the MVC, with a step length CV 36% higher in the first step than in the four following steps (shown in Fig. 4, bottom right panel). The difference was, however, not significant. These finding may suggest that, as for the progression velocity, the step length reached a
steady state at the second step, regardless of the ex-
perimental group.

A slightly different picture emerged when we
considered the BI, a classical biomechanical indicator
of stability control [9, 11, 14, 28, 29]. Indeed, the
results showed that the mean value of this variable was
not significantly different between the first step and the
following steps in both healthy groups and both ve-
locity conditions. Nor was there any difference be-
tween the following steps. In contrast, this variable was
significantly lower in the first step than in each of the
four following steps (with no difference between these
steps) in the PD group and in both velocity conditions.
The difference reached up to 100% (both velocity
conditions combined). In addition, the variability was
significantly higher in the first step than in the four
following steps in all experimental groups (shown in
Fig. 4). The difference reached up to 250% (both ve-
locity conditions and all groups combined). Based on
the assessment of stride characteristics during loco-
motion, movement variability has classically been
associated with reduced gait stability and unsteadiness
in the literature [35]. Thus, our findings suggest that,
as for progression velocity but for different reasons, a
steady state of BI was reached at the second step of
walking, whatever the velocity condition and the ex-
perimental group. However, the PD patients and the
healthy participants used a different strategy to reach
this steady state, with the PD patients having both a
lower BI and higher variability in the first step com-
pared to the following steps, and healthy participants
having only higher variability. In addition, the BI of
the first step was significantly lower in the PD group
than in both healthy groups, a finding that is in line
with the literature on GI [9, 14].

It can be questioned whether this latter finding
could be ascribed to the slower progression velocity of
the first step in the PD group compared to the healthy
groups. According to this hypothesis, the slower
progression velocity of PD patients would make the
centre-of-mass braking less necessary. Results re-
ported in the Figure 3 are, however, not in line with
this hypothesis. In the PD group, the progression
velocity of the first step indeed reached 1.1 ± 0.17 m/s
in the MVC (mean ± SD). This value was very close to
the 1.2 ± 0.20 m/s value reached during the steady state
of the progression velocity in the SVC (mean ± SD of
the last four steps). At this velocity, the BI of PD
patients was 0.9 ± 0.03 (mean ± SD of the last four
steps), a value which was much larger than the mean BI
reached with the first step in the MVC (0.3 ± 0.26). In

other words, it seems that the slower progression
velocity of PD patients compared to the healthy groups
is not a sufficient factor to explain the lower BI of the
first step. These results rather suggest that PD patients
have difficulty to trigger the central mechanisms for
braking their centre of mass fall with the first step of
walking and are therefore particularly prone to in-
stability at this time.

Surprisingly, our results further showed that both the
mean value and the CV of the BI reached similar values
in the PD group and in both healthy groups following the
first step. In other words, all of the above-mentioned
negative effects of PD on the BI observed in the first step
vanished. This original finding suggests that this com-
ponent of postural control returns to normal with the
execution of the second step in the PD group.

The results also showed that neither the mean value
nor the variability of the MoS changed over the course of
the steps in any groups, nor was there any significant
difference across groups. In other words, a steady state of
mediolateral stability at foot contact appears to have
been reached in the first step of walking, with no sig-
nificant effect of PD or ageing, which contrasts markedly
with the above variables. It is admitted that the control of
mediolateral stability during locomotion is of utmost
importance to prevent falls in this direction, which are
known to cause more serious hip fractures compared to
other directions [36-40]. Thus, it might be that the
immediate establishment of this control (i.e., at the first
step) takes priority over establishment of the two other
variables. Priority of this control over progression ve-
locity during GI had previously been reported during GI
performed with experimental unilateral knee joint hy-
pomobility induced by the wearing of an orthosis [41].
The authors showed that, under this constrained con-
dition, participants (HY) were able to develop a postural
strategy to maintain stability at foot contact (evaluated
with the MoS) to the detriment of GI progression ve-
locity. The priority of one variable over another may
depend on the task constraints [42]. Alternatively, a
different timing of the biomechanical variable estab-
lishment during GI may reflect that their control is
exerted by different central structures. Of particular
interest, Chastan et al. [9] investigated the effects of
nigral stimulation on locomotion and postural stability
in PD patients. Their results suggested that ante-
roposterior (length and velocity) and vertical (braking
capacity) GI parameters were controlled by two distinct
systems within the basal ganglia circuitry, representing
locomotion and balance, respectively. They postulated
that the *substantia nigra pars reticulata*, a major basal
ganglia output known to project to pontomesencephalic structures, was involved in balance control during gait. To date, it is not known whether mediolateral GI parameters, such as the MoS in this study, are controlled by other systems or by other parts of the basal ganglia circuitry. Such differences of priority and/or central structures may also potentially explain the discrepancy in the literature regarding the number of steps required to reach so-called steady-state walking since this state might depend on the variable being analysed.

These above statements on the effect of group or step number on postural stability, as evaluated with the MoS, should be taken with caution since, in the present study, this variable was only quantified at the foot contact time, as previously done in the literature (e.g., [2] for a review). This variable was therefore a mechanical measure of instantaneous gait stability and may not reflect global gait stability [43]. Hence, it is not excluded that by taking into account the whole evolution of the MoS trace at each step, a significant effect of the group or step number on postural stability may have been revealed. Such global variable remains, however, to be defined. In addition, it should be emphasized that the MoS is a composite variable, i.e., it includes several biomechanical parameters: the base of support size, the velocity and position of the centre of mass along with anthropometrical features of the participants (cf. Equations 3, 4). It is therefore possible that a same value of MoS be reached with different combinations of these parameters, depending on the step number or the group. Future studies may investigate these different possibilities.

Last, we were surprised to observe that comparing HY to healthy HE showed no significant effect of ageing on any of the experimental variables. This result may be ascribed to a particularly good physical health status of the elderly participants associated with regular physical activity and/or to mitigated physical health of the young adults participants in our study. This aspect was not controlled in the experiment. Similarly, comparing healthy elderly to PD patients showed no significant effect of the disease on the BI from the second step. This result may possibly be ascribed to the early stage of the disease of our patients (stage 2 on the Hoen and Year scale) and/or to the efficiency of their L-Dopa medication.

From a technological point of view, the present results add to the growing evidence from the literature showing that markerless motion systems are relevant to investigate the biomechanics of normal and pathological walking [18–21, 44, 45]. Drawbacks and advantages of these systems compared to other available motion analysis systems (force-plates, cameras with markers, inertial

measurement units, etc.) have been thoroughly discussed in [18, 19]. In brief, these systems enable data collection in ecological conditions by reducing constraints associated with sensors placement under controlled laboratory environments. This approach thus appears particularly well-suited for studying (loco)motor behaviours in experimental settings that closely reflect real-life conditions.

## Limitation

In the present study, the experimental set up was designed to examine the number of steps required to reach a steady state of walking in three groups of participants. It could be criticized that because the distance walked by participants was necessarily limited by the size of the experimental room, participants may have quickly anticipated stopping after a few steps. For this reason, a steady state of walking could in fact not have been reached during the recordings. If true, this statement might be an issue for most studies focussing on the biomechanics of steady state walking because it would imply that experiments should use a walking track of an indetermined minimally length. This constraint obviously does not apply to investigations on a treadmill. To minimize this potential issue as much as possible, participants of the present study were instructed to keep a steady-state velocity progression until they may slow down approximately 2 m before reaching the end of the room. With this experimental set up, participants could thus walk approximately 9 m from the starting position before they may start to slow down. At the end of their last step, participants were located approximately 4–5 m from the “slowing down zone,” and 6–7 m from the end of the room. With such large distances, it can reasonably be thought that participants did not need to brake during the recorded steps to anticipate stopping. As indicated in the methods, this statement was confirmed by visual analysis of each trial by experimented researchers and clinicians. It was further confirmed by the result that the progression velocity and step length of the last four recorded steps reached a constant value in all groups and velocity conditions (as were all the other parameters). It is, however, not excluded that the value of these steady state locomotor parameters be dependent on the distance walked to be covered by the participants on the walking track. Future studies will investigate this hypothesis.

## Conclusions

Results of the present study showed that the number of steps required to reach steady-state walking depends on the experimental variable being investigated, and not
on the sensorimotor state of the participants as initially hypothesized. When considering the progression velocity, the BI and the step length in the course of walking, two steps were required, while when considering the MoS (with the precautions stressed in the discussion) just one step was required. However, the strategy used to reach the steady state of the BI was different in PD patients and in healthy participants, and this strategy could expose the former to a high risk of instability with the first step. After this first step, the indicators of the BI (mean value and variability) of PD patients returned to normal. These findings suggest that rehabilitation programmes aimed at improving dynamic stability in PD patients may target more specifically the first step of walking. It is important to note, however, that the conclusions of this study apply only to PD patients at an early stage of the disease and under L-Dopa medication (cf. Table 1). Future studies are required to determine whether PD patients in an off-medication state and/or in a more advanced state of the disease and with freezing behave similarly. In addition, participants of the present study walked barefoot in laboratory setting conditions, as it is classically done in the literature. It is not excluded that changing the footwear condition (e.g., barefoot, habitual shoes, and habitual shoes with foot orthoses as in [46]), the environmental condition of the experiment (e.g., in a laboratory or in a natural environment) or the size of the experimental room would impact the present results.

## Acknowledgments

The authors thank Kim De Haan for editing the English version of the manuscript.

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## Statement of Ethics

All participants provided written consent after being informed of the nature and purpose of the experiment, which was conducted in accordance with the Declaration of Helsinki and approved by the "Comité de Protection des Personnes Ile-de-France XI" under identification number 19028-60429.

## Conflict of Interest Statement

The authors have no conflicts of interest to declare.

## Funding Sources

This research was funded by the Association Nationale de la Recherche et de la Technologie (CIFRE No. 2020/1053). The APC was funded by the LADAPT Loiret. The funder had no role in the design, data collection, data analysis, and reporting of this study.

## Author Contributions

Conceptualization, methodology, writing – review and editing, validation, funding acquisition, and visualization: E.Y., A.S., A.D., and P.F.; formal analysis, data curation, and writing – original draft preparation: A.S. and E.Y.; software, investigation, and resources: A.S.; supervision and project administration, E.Y. All authors have read and agreed to the published version of the manuscript.

## Data Availability Statement

The data that support the findings of this study are not publicly available due to privacy reasons but are available from the corresponding author upon reasonable request.
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