## Introduction

Two examples of unilateral lower limb reflexes that are purported to support safe locomotion are limb withdrawal reflexes during the stance phase31 and stumble correction reflexes during the swing phase32 of gait (i.e., quick removal of the limb if an unsafe object is stepped upon during the stance phase or contacted during the swing phase). It has also been suggested that interlimb reflexes (as evidenced by responses in the contralateral limb following perturbation of the ipsilateral limb) support gait stability control33,34,35,36,37. Note that these studies have used a variety of methods to perturb the lower limbs, including direct nerve stimulation, single joint perturbations and perturbations that have a whole-body effect, which may result in very different responses and adaptations. Such stumbling and interlimb reflexes have also been observed38,39 and have been shown to adapt38,40 following repeated simulated trip perturbations in infants prior to independent walking, indicating that adaptation of these reflexes can occur in a feedback-driven manner, without substantial supraspinal influence. That is not to say that supraspinal structures do not influence balance control in human adults, as there is ample evidence to the contrary36,41,42,43,44,45,46,47,48, but our knowledge of the supraspinal influence on reactive gait stability control during unexpected mechanical perturbations, specifically, is currently limited.

Despite evidence of feedback-driven adaptation in these reflexes during specific stimulation or joint level perturbations and in gait stability control following whole-body mechanical perturbations, whether or not this translates to the retention, savings and interlimb transfer of adaptations in reactive gait stability following mechanical, whole-body perturbations such as slips and trips has not, to our knowledge been addressed in the literature. There is evidence to suggest that humans can at least partly retain reactive adaptations in gait stability over different time periods of months to years8,9,10,49. However, no study has examined savings and the interlimb transfer of reactive gait adaptations to standardised, controlled whole-body (mechanical) perturbations. As these processes are of both fundamental and clinical relevance for understanding human locomotor control, further research into these processes is warranted.

Here we assess the reactive adaptation of gait in response to unexpected, repeated gait perturbations in young healthy adults, how this adaptation is retained after 1 month, and if savings and interlimb transfer of these adaptations can be observed. To achieve this in as controlled and as precise a manner as possible, we use new methods to decrease inter-individual differences in gait stability via a normalisation of walking speed based on gait stability and by perturbing gait with a treadmill belt acceleration standardised to the stability-normalised walking speed50 (preprint version). Thereby, we account for the effects of walking speed on gait stability control and measurement that we have previously outlined5,50,51. The margin of stability (MoS)52 was used to assess gait stability as it is a valid measure of the mechanical stability of the body configuration during large balance perturbations53,54. It was hypothesised that healthy young adults would demonstrate reactive adaptation of gait following repeated gait perturbations, that these adaptations would be partly retained 1 month later, that evidence of savings in both the acute response to a single perturbation and in the recovery behaviour over multiple perturbations would be found, and that the adaptation to repeated perturbations to one lower limb would transfer and benefit gait stability following perturbations to the contralateral lower limb, as the recovery requires a bipedal response that may be generalisable.

The results of the current study show that young healthy adults can adapt their gait in a reactive, feedback-driven manner and reduce the number of steps required to recover balance following unexpected perturbations to gait and retain these adaptations over a 1-month period. Combined retention and savings led to further improvements in reactive stability control during the second measurement 1 month later. Evidence of interlimb transfer of reactive gait adaptations was inconclusive. Our findings suggest that young healthy adults utilise retention and savings in reactive gait adaptations to benefit stability, but that improvements in stability following perturbations to the untrained limb may not be exclusively due to interlimb transfer of adaptations.

## Results

### Study overview

In order to test our hypotheses, 18 healthy young adult participants were subjected to 10 unilateral treadmill belt accelerations during walking on 1 day, as shown in Fig. 1 (see Methods for details). The participants returned approximately 1 month later (28.4 ± 3.4 days) and repeated the perturbation protocol, although the participants were only aware that they would complete a “walking balance challenge” and were told that it could be different on the second day. The gait perturbation protocol was conducted at a stability-normalised walking speed based on trials of unperturbed walking at various speeds for each individual, to ensure that all participants were walking at comparable stability levels50. The stability-normalised walking speeds ranged from 1.22 m s−1 to 1.51 m s−1 with a mean ± SD of 1.33 ± 0.07 m s−1. In order to quantify stability, we determined the anteroposterior MoS at the moment of foot touchdown as defined by Hof et al.52, adapted for a reduced kinematic model based on Süptitz et al.55. Representative data from one participant during a perturbation and during fast walking is shown in Fig. 2, alongside schematic representations of the body configuration at specific time points, to illustrate how the components of the MoS are affected by different walking conditions.

In the following results, data are presented as median and 95% confidence intervals unless otherwise stated. Day 1 values are represented by filled symbols, Day 2 values by empty symbols. Perturbations to the right leg are represented by squares and perturbations to the left leg by circles. Perturbations of the same number (i.e., Pert1R) are represented by the same colours. The data used to create each figure can be found in Supplementary Data 1.

### Reactive gait adaptations to repeated perturbations

The two-way repeated-measures analysis of variances (ANOVAs) revealed significant perturbation number and step effects and significant perturbation number by step interactions on the MoS for Day 1 (F[3,51] = 7.117, P = 0.0004; F[9,153] = 39.05, P < 0.0001; and F[27, 459] = 2.788, P < 0.0001, respectively) and Day 2 (F[3,51] = 14.69, P < 0.0001; F[9,153] = 49.11, P < 0.0001; and F[27,459] = 5.943, P < 0.0001, respectively). Tukey’s multiple comparisons tests revealed that MoS during Base and Pre were not significantly affected by perturbation number (0.30 < P < 0.99; see Supplementary Table 1). Regarding the adaptation of gait on Day 1, the participants were able to return to MoS Base values after five and four post-perturbation steps for Pert2L and Pert9L, respectively, indicated by MoS values significantly different to Base for Post1-5 and Post1-4, respectively (Fig. 3; for detailed multiple comparisons results, see Supplementary Table 2). On Day 2, further adaptation across the left leg perturbations was seen as Pert9L required only two recovery steps for participants to regain stability, compared with four steps during Pert2L, indicated by MoS values significantly different to Base for Post1-2 and Post1-4, respectively (Fig. 3; Supplementary Table 3).

### Retention of reactive adaptations in gait

Regarding retention of the Day 1 adaptations to perturbations of the left leg after 1 month, Pert2L on Day 2 resulted in participants requiring the same number of recovery steps (four) before returning to MoS Base as during Pert9L on Day 1 (Fig. 4 and Supplementary Tables 2 and 3). A direct comparison of Day 1 Pert9L vs. Day 2 Pert2L revealed a significant perturbation number by step interaction (F[9,153] = 2.696, P = 0.0061) and the post-hoc comparisons revealed significant differences for Post3 only (P = 0.0002; Fig. 4).

### Interlimb transfer and savings of gait adaptations

The adaptation to perturbations applied to the left leg did not appear to transfer to stability recovery following perturbations to the right leg on Day 1, as no significant differences were found between Pert1R and Pert10R for any step (Fig. 5; also see Supplementary Table 4) and the number of steps needed post-perturbation to return to MoS Base was the same during Pert1R and Pert10R (Fig. 5; also see Supplementary Table 2). However, Pert1R on Day 2 required one step less in order to recover to MoS Base, compared with Day 1 Pert1R and Pert10R (Fig. 5 and Supplementary Table 3). In contrast, the adaptation to perturbations applied to the left leg on Day 2 did appear to transfer and benefit stability recovery following perturbations to the right leg, as significant differences were found between Pert1R and Pert10R for Post2-5 (Fig. 5; also see Supplementary Table 5), although the number of steps needed post-perturbation to return to MoS Base was the same (four) during Pert1R and Pert10R (Fig. 5; also see Supplementary Table 3). To further investigate the results regarding interlimb transfer of reactive adaptations in gait, post-hoc analyses were conducted (see below).

The presence of savings was unclear, due to the almost complete retention of adaptations on Day 2 (Pert2L Day 2 vs. Pert9L Day 1; Figs. 3 and 4; Supplementary Tables 2 and 3). Post-hoc analyses were conducted to further investigate savings (see below).

### Post-hoc analyses of savings and interlimb transfer

As full retention was seen in the number of steps to recover to MoS Base in Day 2 Pert2L, compared with Day 1 Pert9L, it was unclear from the pre-planned analysis if savings in the recovery response were present. To investigate the possible presence of savings in the acute recovery response, Pert2L from each day was analysed in a two-way repeated-measures ANOVA with day and step as factors, with Bonferroni’s test for multiple comparisons. This analysis revealed evidence of savings, as the rate of recovery to MoS Base was significantly faster (savings), with significant post-hoc differences between Pert2L on Days 1 and 2 at Post4 and Post5 (Fig. 6a and Supplementary Table 6). To further investigate savings in the overall recovery response, two-way repeated-measures ANOVAs with step and perturbation number as factors with Bonferroni’s test for multiple comparisons were conducted for all perturbations on Day 1 and Day 2, and revealed that the number of steps required to reach MoS baseline after the perturbations plateaued at four steps from the third perturbation onwards on Day 1, while on Day 2, as little as two steps where required by the sixth perturbation (Fig. 6b and Supplementary Table 7). The numbers of steps to return to MoS baseline are summarised in Fig. 6b, and the full results of these ANOVAs can be found in Supplementary Table 7.

The pre-planned analysis appeared to reveal evidence of interlimb transfer on Day 2, but not Day 1. In order to explore these findings further, we calculated the number of steps required to reach consistently positive MoS values following Pert1R, Pert2L, Pert9L and Pert10R on each day, for each individual. A two-way repeated-measures ANOVA with day and perturbation number as factors with Bonferroni’s test for multiple comparisons revealed significant day (F[1,17] = 8.951, P = 0.0082) and perturbation number (F[3,51] = 15.79, P < 0.0001) effects on the number of steps to reach positive MoS (Fig. 7). Regarding interlimb transfer, Pert10R on Day 2 required significantly fewer steps for participants to reach positive MoS values compared with Pert1R on Day 2 (P = 0.0016) and Pert10R on Day 1 (P = 0.0016; Fig. 7).

To determine if the apparent interlimb transfer of adaptations in stability on Day 2 (see Figs. 5 and 7) were purely due to transfer, or partly due to a practice effect of the right leg, a two-way repeated-measures ANOVA with step and perturbation number as factors with Bonferroni’s test for multiple comparisons were conducted for the fourth perturbation to each leg: Day 1 Pert5L and Day 2 Pert10R, respectively. No significant effect of perturbation number was found. However, during Day 1 Pert5L, three steps were needed to return to baseline MoS, whereas during Day 2 Pert10R, five steps were needed (Fig. 8).

## Discussion

An interesting outcome on Day 1 was that some participants demonstrated an increase, rather than a decrease in stability at Post1 during Pert2L (see Fig. 9 for the individual values). With repetition of the perturbations, participants adapted towards a decrease in stability (Pert9L, Fig. 9), which was maintained on Day 2. At first glance, this change does not appear logical; why would participants decrease their stability with practice? On closer inspection of the data and of the video recordings, it appears that some individuals created a large increase in the base of support with a large anterior step, to prevent a forward loss of balance, resulting in an increase in the MoS. However, as the treadmill was moving at a fixed speed, participants then had to “catch up” with the treadmill belt. This strategy appears to initially prioritise stability control and neglect the secondary task of continuing walking.

Our results showed that young healthy adults are capable of almost fully retaining reactive adaptations in gait over a period of 1 month. Previous work has repeatedly demonstrated partial retention of reactive gait adaptations in healthy adults8,9,10,49. The reasons why our participants demonstrate almost full retention are unclear, but could be related to the nature of the perturbation, the normalisation procedure or awareness of the task. What we can conclude from these results is that young adults do not necessarily need frequent or consecutive exposure to unexpected gait perturbations to improve their reactive gait stability. This finding aligns with one recent study that showed that older adults need only one overground slip perturbation to trigger beneficial, long-lasting adaptations in stability control49.

In contrast to our hypothesis, no interlimb transfer of adaptations in reactive gait stability appeared to occur on Day 1. This result was surprising for two reasons. First, although the perturbations were applied to one leg specifically, multiple recovery steps are needed following such perturbations to control balance (i.e., both legs are necessary for recovery), as well as upper body control and counter rotations63. Therefore, we suspected that the response during and immediately following each perturbation (i.e., the first recovery step) may be limb specific, due to different requirements for braking and propulsion similar to previous suggestions for slip recovery64, but that the following alterations in gait would be generalisable and could consequently benefit stability control. Second, as opposed to most previous studies on interlimb transfer in gait (of which one has shown that adaptations transfer across limbs65 while others have not2,66,67), our paradigm required reactive adaptation to repeated, unexpected perturbations, not feedforward correction of errors during continuous perturbation. Abrupt, as opposed to gradual, gait perturbations provide a substantial amount of error feedback that can aid participants’ gait adaptation3,68,69 and savings70. Based on this evidence, we reasoned that the adaptations in stability control seen after the perturbations of the left leg may be transferred to aid recovery from perturbation to the right leg. One previous study that did analyse interlimb transfer of adaptations in reactive gait stability found that participants could only transfer pre-perturbation adaptations (predictive, not reactive) in gait between limbs64, but their analysis only included the first recovery step and the perturbation was not standardised, meaning that the exact impact of the perturbation to each limb may have slightly differed. Regarding the improvements in stability observed following the two perturbations to the right leg on Day 2, we cannot conclusively say, based on the current data, whether or not these were due to interlimb transfer of adaptations. Our post-hoc analysis seems to suggest that a practice effect may have contributed to these findings (Fig. 8), but not all of the first four perturbations to each limb occurred on the same day, limiting the conclusions that can be drawn.

As can be seen in our results, individual responses to the perturbations varied. It could be argued that individual variability within and between participants may therefore influence the analysis and that by averaging repeated trials, a clearer picture of the effect of the perturbations could be gained. However, as the effects of these perturbations are so strong, we do not feel that this variability compromises the study. Analysing these initial single trials could be considered a strength in terms of ecological validity, as the variation in responses is more representative of what is seen in daily life following real, truly unexpected perturbations to gait71.

The participants in the current study were not given any details about the nature of the perturbations, but we did consider the possibility that performance on Day 2 could be influenced by prior knowledge and experience of the task acquired on Day 1. Even though no measurable changes in gait stability during baseline walking were found in the current study, previous studies have demonstrated the beneficial effects of increased awareness of perturbations on stability recovery performance following trips72,73. For the eight perturbations to the left leg, the plateau of recovery steps required for re-stabilisation on Day 1 was quickly improved upon on Day 2 (Figs. 6b and 7). It is unclear if this was due to independent or combined effects of retention, savings or increased task awareness, but we can conclude that for this form of gait perturbation, “complete” adaptation on first exposure does not necessarily represent the participant’s best task performance, which has implications for perturbation-based balance training programmes.

In conclusion, we have shown that young healthy adults are capable of adapting their gait in a reactive, feedback-driven manner to control stability and reduce the number of steps to reach positive and baseline values of MoS, and that they can fully retain these adaptations over a 1-month period. On re-exposure to the perturbations, a combination of retention and savings led to further improvements in reactive stability control above those made 1 month before. In contrast to our expectations, evidence of interlimb transfer of reactive gait adaptations was inconclusive. Our results show that humans utilise retention and savings in reactive gait adaptations to benefit stability, but that interlimb transfer may not be exclusively responsible for improvements following perturbations to the untrained limb. These findings broaden our understanding of reactive gait adaptability and have implications for future studies on gait stability and adaptability, as well as for falls prevention interventions.

## Methods

### Participants

Eighteen healthy adults participated in this study (eight males, 10 females; age: 24.4 ± 2.5 years; height: 174.9 ± 7.4 cm; weight: 74.6 ± 15.2 kg). The participants had no self-reported history of walking difficulties, dizziness or balance problems, and had no known neuromuscular condition or injury that could affect balance or walking. Informed consent was obtained and the study was conducted in accordance with the Declaration of Helsinki. The study protocol was approved by the Maastricht University Medical Centre medical ethics committee (NL58205.068.16).

### Setup and procedures

The Computer Assisted Rehabilitation Environment Extended (CAREN; Motekforce Link, Amsterdam, The Netherlands) was used for this study, which included a dual-belt force plate-instrumented treadmill (Motekforce Link, Amsterdam, The Netherlands; 1000 Hz), a 12-camera motion capture system (100 Hz; Vicon Motion Systems, Oxford, UK) and a virtual environment that provided optic flow during walking. Three high definition video cameras also recorded video footage of the measurements. A safety harness system connected to an overhead frame was used at all times. Five retroreflective markers were attached to anatomical landmarks (C7, left and right trochanter and left and right hallux) and the three-dimensional coordinates of these markers were tracked by the motion capture system. Each session began with walking familiarisation trials at 0.4 m s−1 up to 1.8 m s−1. Sixty seconds were used for each speed. Participants were then given sufficient rest (approximately 2 min) before continuing with the measurements.

The procedures for determining the stability-normalised walking speed, as well as the theoretical background and data regarding the effectiveness of this approach are described in detail elsewhere50. Briefly, single two-to-three-minute-long measurements were conducted at 0.4 m s−1 up to 1.8 m s−1 in 0.2 m s−1 intervals. During a second rest period for the participants, the stability-normalised walking speed was calculated. In order to determine the stability-normalised walking speed, the mean anteroposterior MoS (see below) at foot touchdown of the final 10 steps of each walking trial (0.4 m s−1 to 1.8 m s−1) were taken and were fitted with a second-order polynomial function. For each participant, the walking speed that would result in MoS of 0.05 m was calculated from the function.

### Data processing and MoS calculation

The three-dimensional coordinates of the markers were filtered using a low pass second-order Butterworth filter (zero-phase) with a 12 Hz cut-off frequency. For all steps, the foot marker anteroposterior velocity data were used to determine foot touchdown and toe-off (the frame in which the marker velocity direction switched)75. This was then corrected based on the average discrepancy between a force plate-determined touchdown and toe-off (with a force threshold of 50 N) and the marker-determined touchdown and toe-off for all steps that contacted only one force plate. This combined method was used to be able to accurately account for foot touchdowns and toe-offs occurring in the centre of the treadmill triggering both force plates simultaneously. The anteroposterior MoS were calculated for the moment of foot touchdown as the anteroposterior difference between the base of support (anteroposterior distance between the hallux markers) and the extrapolated centre of mass (XCoM) as defined by Hof et al.52, adapted for the reduced kinematic model based on Süptitz et al.55:

$${{X}}_{{\mathrm{CoM}}} = \frac{{{{P}}_{{\mathrm{TroL}}} + {{P}}_{{\mathrm{TroR}}}}}{2} - {{P}}_{{\mathrm{HalluxP}}} + \frac{{0.5\left( {\frac{{{{V}}_{{\mathrm{TroL}}} + {{V}}_{{\mathrm{TroR}}}}}{2} + {{V}}_{{\mathrm{C}}7}} \right) + \left| {{{V}}_{{\mathrm{Belt}}}} \right|}}{{\sqrt {\frac{{{g}}}{{{{L}}_{{\mathrm{Ref}}}}}} }}$$

where PTrol, PTrol and PHalluxP represent the trochanter and the rearmost hallux marker anteroposterior positions respectively; VTrol, VTroR and VC7 are the anteroposterior velocities of the trochanter and C7 markers respectively; VBelt is the treadmill belt velocity; g is gravitational acceleration (9.81 m s−2); and LRef is the reference leg length. The MoS concept is one of the few well-defined and well-accepted biomechanical measures of mechanical stability of the body configuration during dynamic movement54, with one study demonstrating that, during a forward loss of balance, participants who required multiple recovery steps had a negative MoS value at touchdown of the first recovery step in all cases, whereas participants who only required this one recovery step all had a positive MoS53. The MoS was calculated for the following steps: baseline for each perturbation was the mean MoS of the eleventh to second last step before each perturbation (Base); the final step before each perturbation (Pre); and the first eight recovery steps following each perturbation (Post1-8).

### Statistics

Two-way repeated-measures ANOVAs with perturbation number (Pert1R, Pert2L, Pert9L and Pert10R, representing the first and final perturbations to each limb on each day) and step (Base, Pre, Post1-Post8) as factors with post-hoc Tukey’s tests for multiple comparisons were used for each day to determine the following: predictive adaptation across the perturbation protocol (Perturbation number difference in Base and Pre); acute adaptation to the perturbation on each day (Pert2L vs. Pert9L); acute interlimb transfer of adaptations on each day (Pert1R vs. Pert10R); savings in the acute recovery response to a perturbation (quicker return to baseline MoS in Day 2 Pert2L than Day 1 Pert2L). Retention of adaptations over 1 month was investigated with a separate two-way repeated-measures ANOVA with Bonferroni’s multiple comparisons test (Day 1 Pert9L vs. Day 2 Pert2L). Normality of the data was checked using the Shapiro–Wilk test and Q-Q plots. In addition to these pre-planned analyses, post-hoc explorative statistical tests were conducted (see Results). Significance was set at α = 0.05. Analyses were performed using GraphPad Prism version 7.03 for Windows (GraphPad Software Inc., La Jolla, California, USA).

### Code availability

The code used to process the motion capture data in the current study are available from the corresponding author on reasonable request.