While much attention has been paid to understanding slip-related falls in humans, little has been focused on curvilinear paths despite their prevalence, distinct biomechanical demands and increased slipping threat. We determined the mechanics, compensatory stepping reactions and fall risk associated with slips during fixed-speed walking across ranges of path curvature, slipped foot and slip onset phase contexts possible in the community, which builds upon previous work by examining speed-independent effects of curvilinear walking. Twenty-one participants experienced 15 unconstrained slips induced by a wearable friction-reducing device as motion capture and harness load cell data were recorded. Falls were most likely after early stance slips to the inside foot and increased at tighter curvatures. Slip distance and peak velocity decreased as slips began later in stance phase, did not differ between feet, and accelerated on tighter paths. Slipping foot directions relative to heading transitioned from anterior (forward) to posterior (backward) as slips began later in stance, were ipsilateral (toward the slipping foot side) and contralateral (toward the opposite side) for the outside and inside foot, respectively, and became increasingly ipsilateral/contralateral on tighter curvatures. Compensatory steps were placed anteriorly and ipsilaterally after outside and inside foot slips, respectively, and lengthened at later onset phases for outside foot slips only. Our findings illustrate slip magnitude and fall risk relationships that suggest slip direction may influence the balance threat posed by a slip, imply that walking speed may modify slip likelihood, and indicate the most destabilizing curved walking contexts to target in future perturbation-based balance training approaches.

Concurrent stability and maneuverability are essential features of locomotion to evade predators and negotiate complex environments without loss of traction (Alexander, 2002; Full et al., 2002; Jindrich and Qiao, 2009). Fundamental principles for attaining stable yet maneuverable locomotion apply remarkably well across species of vastly different postures and morphologies. For example, the gait dynamics of sprawled hexapods, quadrupeds and upright bipeds can all be modeled as an inverted pendulum (Blickhan and Full, 1993), leg contact angles are an important slip-and-fall risk factor in both guinea fowl and humans (Brady et al., 2000; Clark and Higham, 2011), and the steering functions of inside and outside legs relative to a turn are analogous between cockroaches, ostriches and humans (Jindrich and Full, 1999; Jindrich et al., 2007; Orendurff et al., 2006). Inside and outside leg asymmetries, propulsion limitations and friction demands associated with turning also cause many animals, including humans, to slow their gait (Brown et al., 2021; Chang and Kram, 2007; Courtine and Schieppati, 2003; Orendurff et al., 2006; Tan and Wilson, 2011; Turcato et al., 2015; Wheatley et al., 2018; Wynn et al., 2015). Humans also increase braking ground reaction forces during turns to prevent over-rotation about their longitudinal axis, which is due to unique weight distributions and moments of inertia compared with other oft-studied bipeds such as ostriches or guinea fowl (Jindrich et al., 2006, 2007).

Despite the exceptional ability of animals to maneuver and maintain balance, situations often arise where these abilities are insufficient and a fall occurs. Falls are a frequent cause of morbidity and mortality in humans specifically (Bergen et al., 2016; Moreland et al., 2020), incurring billions of dollars in medical costs on the US healthcare system (Florence et al., 2018) and negative physical and psychological effects that compound to cause poorer health outcomes (Delbaere et al., 2004; Grisso et al., 1991; Harvey and Close, 2012; Zijlstra et al., 2007). Of the multitude of possible causes, walking is the most common activity during which falls occur in all settings (Berg et al., 1997; Robinovitch et al., 2013), with environmental factors such as slips contributing the largest portion of falling incidents in the community (Berg et al., 1997; Crenshaw et al., 2017). Consequently, slipping during walking has been a prominent focus for a wealth of perturbation-based balance training studies and fall prevention protocols (McCrum et al., 2022; Pai and Bhatt, 2007). However, the complexity of the environments that humans navigate and how these environments influence slip-and-fall risk have yet to be adequately integrated into balance and fall prevention training approaches.

While both recovery from and training on lab-based slips in humans have been examined in depth, most of this work was restricted to walking along straight trajectories. Obstacles in our daily environments necessitate the use of non-linear gait patterns; indeed, up to 45% of steps taken act to change our heading (Glaister et al., 2007). Curvilinear walking and turning differ biomechanically from straight walking in many ways, some of which may directly pertain to the risk of experiencing a slip (Beschorner et al., 2016). For example, mediolateral ground reaction forces double under the outside foot and reverse direction under the inside foot relative to a 1.0 m radius curved path compared with straight walking at the same speed (Orendurff et al., 2006). Similar increases in mediolateral forces are present during 90 deg angular turns alongside anteroposterior force modulation to decelerate and accelerate when entering and exiting the turn, respectively (Glaister et al., 2008). At the same time, vertical ground reaction force peaks compared with straight walking are reduced, if different at all (Dixon et al., 2014; Turcato et al., 2015). Increases in shear ground reaction forces coupled with unchanged or concomitant reductions in vertical forces lead to static friction demands reaching coefficients of μ=0.45 to avoid a slip (Burnfield et al., 2005; Fino and Lockhart, 2014; Yamaguchi et al., 2013), more than twice what is required during straight walking (Cham and Redfern, 2002; Hanson et al., 1999; Redfern et al., 2001). Unsurprisingly considering the above-described kinetic adjustments, significant adaptations in muscle activation and coordination at the individual and whole-limb level have also been observed (Courtine and Schieppati, 2004; Courtine et al., 2006; Ventura et al., 2015). Finally, curvilinear walking increases the angular momentum acting on the body (Nolasco et al., 2019), reduces stability margins (Tillman et al., 2022), and precedes a large portion of community-based falls that are more likely to cause hip fracture (Crenshaw et al., 2017; Cumming and Klineberg, 1994). The degree to which many of these biomechanical characteristics differ from straight walking is dependent on curvilinear walking characteristics such as path curvature, stance limb relative to the curved walking path, and walking speed (Courtine et al., 2006; Orendurff et al., 2006). Given the general asymmetry, unique biomechanics and inherent threat to stability posed by changing heading, our understanding of slip recovery and balance adaptation from straight walking slips cannot be directly applied to the curvilinear case. As a consequence, slip-specific balance training and fall prevention protocols are only designed for a limited subset of possible slipping conditions.

A small number of published studies have delivered slips to humans during angular turns or on curved walking paths, forming a base of knowledge from which to build. It is clear from this work that turn angle positively correlates with both slip-and-fall rates and mediolateral slip magnitudes (i.e. slip distance and peak velocity) (Yamaguchi et al., 2012), with the latter also being independently predictive of falling (Yamaguchi et al., 2016). Our own group previously determined the slip mechanics elicited by a variety of curved path contexts known to shape gait adaptations to curvilinear paths (i.e. path curvature, slipped foot relative to the path, slip onset timing within stance phase) (Rasmussen et al., 2022). Somewhat counter to other reports (Yamaguchi et al., 2012), slip magnitudes on curvilinear paths were not significantly influenced by path curvature; however, the slipping foot did travel in a more mediolateral direction relative to heading on tighter curvatures. Furthermore, later slip onset phases (i.e. later slip onset times within stance phase) led to significantly shorter slips in the mediolateral direction but faster slips in the anteroposterior direction, as well as modified slip directions from anteriorly to posteriorly directed. Lastly, inside foot slips were generally of lesser magnitude than outside foot slips and led to a contralateral rather than ipsilateral slip direction (Rasmussen et al., 2022). The scarcity of curvilinear slip research may stem from the necessity of these slips to be mechanically unconstrained, or free to move in any direction, distance and velocity after slip onset, to accurately simulate the task. Unconstrained slips are difficult to deliver in an unpredictable fashion using traditional lab-based methods (i.e. treadmills, sliding platforms, lubricated floors) (McCrum et al., 2017; Troy and Grabiner, 2006), particularly during non-straight walking.

The aim of the present study was to examine slip mechanics after slips delivered during fixed-speed walking across a range of path curvature, slipped foot and slip onset phase conditions, as well as the compensatory stepping reactions and fall rates evoked by these contexts in humans. In our previous study, participants were allowed to self-select a comfortable walking speed on each path curvature to elicit unconstrained slips that closely mimic those experienced in the community under similar conditions (Rasmussen et al., 2022); however, this likely modulated the influence of path curvature as walking speed naturally slows when executing a turn (Courtine et al., 2006; Turcato et al., 2015). Because the centripetal force acting on an individual during curved walking is proportional to their walking speed squared, holding walking speed constant across path curvatures allows us to isolate the independent effects of curvature on our outcomes of interest, which was not possible in our previous study (Rasmussen et al., 2022). Furthermore, we did not quantify fall rates under each condition in our previous study, which prevented strong conclusions about the relative danger posed by slips under those conditions. This experimental design is best applied to human walking given the societal problem of falls and the ease of controlling overground gait speed through feedback; however, the results will likely be generalizable to other species exhibiting inverted pendulum dynamics (Blickhan and Full, 1993). Here, we hypothesized that during fixed-speed walking, fall rates would increase with tightening path curvature, decrease with advancing slip onset phase, and be higher after outside foot slips compared with inside foot slips. In terms of slip mechanics, we hypothesized that an interaction between slipped foot and slip onset phase would influence slip directions and that slip magnitudes would decrease with advancing slip onset phase, increase with path curvature, and be greater for outside compared with inside foot slips. Finally, we hypothesized that compensatory step directions would depend on an interaction between slipped foot and slip onset phase while step distances would increase with progressing slip onset phase.

Participant recruitment

Twenty-one healthy young adults (11 males, 10 females; mean±s.d. age: 24.57±4.74 years, height: 1.72±0.12 m, mass: 71.72± 18.17 kg) provided written informed consent for participation in this study, which was approved by the University of Nebraska Medical Center Institutional Review Board (IRB# 861-18-EP) and took place during a single laboratory visit. All participants self-reported being free of any conditions that may influence gait; use of an assistive device such as a cane, walker, prosthetic or orthotic; joint or muscle pain; uncontrolled hypertension; pregnancy; and past injury due to falls beyond contusions, lacerations and abrasions. Height, mass and limb dominance were measured and recorded for each person.

Experimental design

All participants wore a form-fitting compression suit, standardized athletic shoes, fall-arresting safety harness and full-body marker set of 81 retroreflective markers. Eight medial markers (first metatarsal head, medial malleolus, and medial epicondyles of the femur and humerus, bilaterally) were removed after a static T-pose calibration to minimize marker trajectory switching, occlusion or detachment during slipping trials. In addition, participants were fitted with a Wearable Apparatus for Slip Perturbations (WASP) device on both shod feet (Fig. 1). The design and function of this device have been reported in detail elsewhere (Rasmussen and Hunt, 2019). Briefly, WASP provides adequate friction with the support surface in its attached state to facilitate normal walking (µ≈0.5), and its wearable nature enables the wearer to traverse any terrain or complete any gait task. However, friction underfoot can be suddenly reduced (µ≈0.1) to levels below what is required by curvilinear walking (µ≈0.45) (Fino and Lockhart, 2014) via a wireless trigger, which detaches the rubber outsole and exposes the wearer to lubricated polyethylene sheets laminated to the dorsal side of the outsole and plantar side of their shoe. Because slips are instigated via friction reduction when using WASP rather than a mechanical ground translation, the slipped foot is unconstrained by the device to move in any direction, distance and velocity as is the case in the environment.

Fig. 1.

Independent variables and experimental set-up employed in the present study. Each participant was exposed to combinations of slip onset phase [early (ES), mid (MS) or late stance (LS)], slipped foot (inside or outside) and path curvature, calculated as the reciprocal of the path radius (κ=1/radius). The color schemes employed in this figure are consistent with the Results figures to follow. Timing gates were placed at the ends of the paths to record the time taken to traverse the path, which was used to derive and monitor walking speed. The inset (top right) illustrates the coordinate system definition used in this study (*reference frames fixed at slip onset). The coordinate system within which the outcome measures for a particular trial were calculated was defined at slip onset based on the instantaneous orientation of the pelvis segment.

Fig. 1.

Independent variables and experimental set-up employed in the present study. Each participant was exposed to combinations of slip onset phase [early (ES), mid (MS) or late stance (LS)], slipped foot (inside or outside) and path curvature, calculated as the reciprocal of the path radius (κ=1/radius). The color schemes employed in this figure are consistent with the Results figures to follow. Timing gates were placed at the ends of the paths to record the time taken to traverse the path, which was used to derive and monitor walking speed. The inset (top right) illustrates the coordinate system definition used in this study (*reference frames fixed at slip onset). The coordinate system within which the outcome measures for a particular trial were calculated was defined at slip onset based on the instantaneous orientation of the pelvis segment.

All data collections took place within a large motion capture laboratory over a vinyl tile false floor with embedded force plates in the center of the capture volume; force plate data were not recorded. Two internally tangent semicircular paths, one with a radius of 1.0 m and the other 2.0 m, were taped on the lab floor next to a clearly defined straight walkway. Straight segments were added to both ends of the 1.0 m radius path to allow participants room to accelerate before entering the curved section of the path and to equalize the lengths of the two paths. Hereafter, the different paths will be represented by their respective curvatures κ, calculated as the reciprocal of the path radius to provide a linear interval between curved path conditions. Specifically, the 1.0 m radius path has a curvature of 1.0, the 2.0 m radius path has a curvature of 0.5, and the straight path has a curvature of 0.0 (Fig. 1). A 17-camera motion capture system (Motion Analysis Corp., Santa Rosa, CA, USA) sampled retroreflective marker positions at 100 Hz. Laser timing gates (Dashr Motion Performance Systems, Omaha, NE, USA) were placed at both ends of the paths to measure the time taken to traverse the path, which was used to derive the mean gait speed of each pass (Fig. 1). A ceiling-mounted trolley system was connected to the participants' worn safety harness during all trials to prevent ground contact during a fall. A load cell rated for 500 kg (HT Sensor Technology Co. Ltd, Xi'an, China) and sampling at 80 Hz in synchrony with the kinematic data was connected in-line with the harness system to record any body weight support provided to the participant by the harness.

Experimental protocol

All participants completed 15 slipping trials, which exposed participants to every unique combination of slip onset phase [early (ES), mid (MS) or late stance (LS)], slipped foot (inside or outside foot relative to the center of curvature), and path curvature conditions (κ=1.0, κ=0.5, κ=0.0) (Fig. 1). Prior to completing any slip trials, participants were instructed to do their best to regain balance without falling into the harness. All participants were also instructed to step on both semicircular paths with their inside foot relative to the center of curvature at all times in order to minimize unnatural step width alterations due to participants either straddling or targeting the marked path with every step taken. During the unperturbed walking portions of every trial, participants always began at the same end of the semicircular path, followed it to the other end, and turned around to follow it back to the start. This process was repeated until a slip was delivered. All participants were held to a typical healthy adult walking speed of 1.3±0.1 m s−1 (mean±s.d.; Bohannon and Andrews, 2011); attending researchers told participants to ‘walk a little faster/slower’ if the time taken to complete each pass measured by the laser timing gates placed at both ends of the semicircular paths fell outside the range corresponding with a mean walking speed of 1.3±0.1 m s−1 (i.e. 4.29–5.00 s). Each trial lasted between 1 and 3 min, with trial orders and durations randomized prior to each session using a custom MATLAB function (The MathWorks, Inc., Natick, MA, USA). After the prescribed duration for each trial, an attending researcher delivered a slip manually via wireless WASP triggering by visually targeting the predetermined foot and anticipating the predetermined stance phase for that trial. Slip perturbations were deliberately triggered to obtain a uniform distribution of slip onsets across ES, MS and LS. Only one WASP device was triggered and one foot slipped in each trial, while the opposite WASP device remained attached to supply adequate friction for a compensatory step. After each trial, participants were allowed a seated rest period during which the activated WASP outsole was reattached and the lab floor cleaned of lubricant left from the previous trial.

Data analysis

All the following analyses were completed using Visual3D software (C-Motion, Inc., Germantown, MD, USA). Marker data were low-pass filtered at 6 Hz using a fourth-order, zero-lag Butterworth filter. A marker coordinate-based method was employed to determine gait events (Zeni et al., 2008) throughout the entire pass across the semicircular path within which the slip was delivered. Slip onset times were derived from the resultant horizontal velocity of the slipped foot segment's center of mass (CoM), specifically when the horizontal velocity following heel-strike exceeded zero. Slip cessation times were defined as the moments when the slipped foot's horizontal velocity returned to zero following slip onset or, for 35 of the trials where this never occurred before toe-off, concurrent with toe-off. Heel-strike and toe-off events were also used to define stance phase durations, which in turn were used to calculate actual slip onset phases in post-processing by dividing the time between heel-strike and the instance of slip onset by the average stance duration of the same foot relative to the path. Each slip onset phase was then binned into one of the three phases of interest: ES (0–33.3% of stance), MS (33.4–66.7%) or LS (66.8–100%).

The outcome of each slip perturbation (i.e. a fall versus a recovery) was determined from load cell data measuring body weight support provided by the harness as measure of slip severity. Load cell kinetic data were low-pass filtered with a fourth-order, zero-lag Butterworth filter at 8 Hz (Brady et al., 2000; Yang and Pai, 2011). If the harness supported 30% or more of a participant's body weight at any time after slip onset in each trial, then that trial was determined to end with a fall (Yang and Pai, 2011). All other trials that did not achieve this standard were determined to end with a successful recovery.

To examine the mechanics of slips administered under the slip onset phase, slipped foot and path radius conditions controlled in this study, relative slip directions, distances and peak velocities were obtained for each successfully delivered slip from kinematic data. Because participants were not walking along a principal axis of the laboratory coordinate system, an egocentric coordinate system was defined at the moment of slip onset: the x-axis aligned with the mediolateral plane of the participant's pelvis segment (positive x: rightward), the y-axis aligned with the anteroposterior plane of the pelvis segment (positive y: anterior), and the z-axis aligned with the vertical (positive z: upward) (Fig. 1). This coordinate system aligns closest with an anatomically based frame as defined by Ho and colleagues (2023) for curved walking. All the following outcome measures are in reference to this egocentric coordinate system. Slip directions were defined as the angle between the slipping foot's linear CoM trajectory from slip onset to cessation and the participant's instantaneous heading at slip onset (i.e. the y-axis of the egocentric coordinate system). Slip directions were calculated in a range of 0 to 360 deg with 0 deg/360 deg corresponding to anterior slips (i.e. forward), 90 deg to ipsilateral slips (i.e. toward the same side of the body as the slipping foot), 180 deg to posterior slips (i.e. backward), and 270 deg to contralateral slips (i.e. toward the opposite side of the body to the slipping foot). Slip distances were taken as the resultant displacement of the slipping foot's CoM between slip onset and cessation in the horizontal plane. The greatest horizontal velocity attained by the slipping foot within the same events was taken as the peak slip velocity.

To understand the compensatory stepping reactions used by participants to regain upright balance, we also derived the first compensatory step directions relative to heading and distances from the CoM projection on the horizontal plane. While multiple compensatory steps may have been taken in some trials, we only examined the first compensatory step because the second step would be taken with the slipped foot, which has reduced friction and may result in another slip. Therefore, any compensatory steps following the first would likely be confounded by this lack of friction. First, compensatory step touchdown was defined as the moment that the non-slipped foot contacted the ground following slip onset. Compensatory step directions were considered as the angle between the vector connecting the whole-body CoM and the stepping foot segment's CoM at step touchdown and the participant's heading (i.e. the y-axis of the egocentric coordinate system), both projected on the horizontal plane. As in our slip direction calculations, the angles were computed in a range of 0 to 360 deg with 0 deg/360 deg corresponding to anterior steps (i.e. forward), 90 deg to ipsilateral steps (i.e. toward the same side of the body as the stepping foot), 180 deg to posterior steps (i.e. backward), and 270 deg to contralateral steps (i.e. toward the opposite side of the body to the stepping foot). The displacement between the stepping foot segment's CoM and whole-body CoM in the horizontal plane at compensatory step touchdown was considered as the compensatory step distance.

Statistical analysis

All the following statistical testing was completed using custom analysis scripts in the R Statistical Computing Language (http://www.R-project.org/). For all tests, the critical alpha was set to α=0.05. A variety of mixed-effects models were used in the assessment of slip and compensatory stepping mechanics because of their robustness to unbalanced datasets, which were obtained as a result of trials ending without a successfully delivered slip, inaccurate manual targeting of the prescribed slip onset phase for a given trial, or exclusion of trials because of missing kinematic data that prevented the calculation of our outcome measures. In all mixed-effects models here, slip onset phase, slipped foot relative to the path, and path curvature were entered as fixed effects, while participant was treated as a random factor to account for dependencies in the fixed effects introduced by the repeated measures design. Inside or outside foot conditions were not defined for the straight path curvature trials, resulting in a partially nested study design and rank deficiency when attempting to fit a mixed-effects model for the entire dataset. To resolve this issue, two separate models were used: one that incorporated all fixed effects while ignoring straight walking trials (Eqn 1) and another including all path curvature and onset phase fixed factors for the outside foot slip trials only (Eqn 2), both of which utilize fully crossed subsets of the entire dataset. The reason for only including outside foot trials in the second model is that much of the rotation in CoM heading to approximately follow a curved path occurs during outside foot stance (Orendurff et al., 2006); therefore, the greatest effect of curvature was expected during this time.
(1)
(2)

To assess the effect of each fixed effect on the observed fall rates, mixed-effects logistic regression was employed. For the non-directional outcome measures of slip distance, peak slip velocity and compensatory step distance, linear mixed-effects models were used. Because the slip and compensatory step direction outcome measures were periodic, linear models could not be applied to these data. For example, a linear model will consider directions of 1 deg and 359 deg in our range to be 358 deg apart when, in reality, they are only separated by 2 deg. This interpretation could generate misleading results about the statistical differences in slip or compensatory step directions between conditions. To alleviate this problem, Bayesian circular mixed-effects models were applied to the directional data (https://CRAN.R-project.org/package=bpnreg;Cremers and Klugkist, 2018; Cremers et al., 2018a,b). Input parameters for the circular mixed-effects models (i.e. burn-in period, number of iterations, lag) were tuned by assessing the convergence of fixed-effect coefficient estimates from five parallel models using Gelman plots and multivariate potential scale reduction factors (Brooks and Gelman, 1998; Gelman and Rubin, 1992; Gelman et al., 2013). Convergence was confirmed within the final analysis model's fixed-effect coefficient estimates through visual examination of trace plots (Cremers and Klugkist, 2018). Bivariate fixed-effect coefficient estimates analogous to x- and y-coordinates on the unit circle were obtained from the model, which were then transformed into univariate estimates interpretable as directions (https://CRAN.R-project.org/package=bpnreg). Significance was determined from 95% highest posterior density (HPD) intervals for each coefficient estimate: if a given 95% HPD interval did not contain zero, then we concluded that the fixed effect in question had a statistically significant effect on the outcome measure being evaluated (Cremers and Klugkist, 2018). For slip onset phases where there were three levels, the 95% HPD intervals were compared and statistical significance inferred if they did not overlap (Cremers and Klugkist, 2018).

Slip distributions across conditions

In total, 315 slip trials were attempted across the 21 participants. Slips did not occur following WASP triggering in 41 trials (13.0% of total attempted trials), leaving 274 trials for analysis. Of these, 21 slips resulted in a fall. Analog data used to determine the moment of WASP triggering were absent in eight of the remaining trials; therefore, they were not included in the distributions that follow but were included in the calculations of the other outcome measures. The study design implemented here attempted to deliver a uniform distribution of slips across all condition levels; however, a bias toward ES in friction reduction and therefore the number of slips occurring is apparent (Table 1). Slip probabilities show that MS slips were the least likely to occur while walking κ=0.0 and κ=0.5 paths, while LS was the least likely onset phase on tighter κ=1.0 paths. Outside foot slips were more likely to occur than inside foot slips within all slip onset phases (Table 1).

Table 1.

Distribution of WASP trigger phases, friction reduction phases and slips across the different combinations of curved path conditions

Distribution of WASP trigger phases, friction reduction phases and slips across the different combinations of curved path conditions
Distribution of WASP trigger phases, friction reduction phases and slips across the different combinations of curved path conditions

Fall rates on curved paths

No falls were observed on path curvatures of κ=0.0 or after a LS slip; therefore, the statistical outputs of the mixed-effects logistic regression models only compare curved path and ES or MS slip onset phases. While there was an obvious increasing trend in fall rates with increasing path curvature (Fig. 2), the main effect of path curvature was not statistically significant (z170=−1.89, P=0.059). The effect of path curvature may have been influenced by the biased distribution of successfully delivered slips toward the outside foot (118 outside foot slips versus 97 inside foot slips), which would result in marginal fall rates for each path curvature closer to the rates for the outside foot. In terms of slipped foot, we observed the opposite trend to what was expected: significantly fewer outside foot slips resulted in a fall compared with inside foot slips (z170=−3.50, P<0.001; Fig. 2). Finally, slip onset phase also had a significant effect on fall rates as predicted. MS slips led to significantly fewer falls than those during ES (z170=−2.21, P=0.027). Interestingly, falls after MS slips only occurred within the κ=1.0 path curvature condition (Fig. 2).

Fig. 2.

Fall rates across the curvilinear walking conditions tested in this study. Individual bars represent inside (red shades), outside (orange shades) or straight walking conditions (gray shades) where there is no foot condition. Bars are grouped by path curvature: κ=0.0 (white background), κ=0.5 (green background) and κ=1.0 (blue background). Values atop each bar indicate the exact fall rate for that combination of conditions. Inside foot slips caused significantly more falls than outside foot slips across path curvatures (P<0.001), and those beginning in ES were the most dangerous (P=0.027). However, the increasing trend in falls with tightening path curvature was not significant (P=0.059).

Fig. 2.

Fall rates across the curvilinear walking conditions tested in this study. Individual bars represent inside (red shades), outside (orange shades) or straight walking conditions (gray shades) where there is no foot condition. Bars are grouped by path curvature: κ=0.0 (white background), κ=0.5 (green background) and κ=1.0 (blue background). Values atop each bar indicate the exact fall rate for that combination of conditions. Inside foot slips caused significantly more falls than outside foot slips across path curvatures (P<0.001), and those beginning in ES were the most dangerous (P=0.027). However, the increasing trend in falls with tightening path curvature was not significant (P=0.059).

Slip magnitudes

As hypothesized, slip magnitudes in general decreased with progressing slip onset phase. MS and LS slips were significantly shorter (MS: t199.48=−4.98, P<0.001; LS: t200.25=−5.64, P<0.001; Fig. 3A) and slower (MS: t198.00=−2.46, P=0.015; LS: t198.60=−4.21, P<0.001; Fig. 3B) than those beginning at ES. In contrast, the expected influence of slipped foot was not found, as outside foot slips were not significantly different from inside foot slips in terms of slip distance (t195.29=1.72, P=0.087; Fig. 3A) or peak velocity (t194.90=1.90, P=0.058; Fig. 3B) though there was a trend toward greater overall magnitude. No significant influence of path curvature on slip distance was observed (κ=0.5: t149.63=−0.21, P=0.834; κ=1.0: t148.27=1.00, P=0.318; Fig. 3A), but κ=1.0 paths did elicit significantly faster slips than κ=0.0 paths (t148.15=2.82, P=0.005; Fig. 3B) while κ=0.5 paths did not (t149.06=1.34, P=0.181; Fig. 3B). While several of the most severe slips in terms of magnitude caused a fall, many fall-inducing slips were of similar magnitude to others that ended with successful recoveries (Fig. 3).

Fig. 3.

Slip magnitudes across the curvilinear walking conditions tested in this study. In both panels, boxes represent the median and interquartile range (IQR) while error bars extend to the most extreme recorded value still within 1.5×IQR of the first and third quartiles for each combination of conditions. Overlaid violin plots provide illustrations of the data distribution within each combination of conditions but are not scaled to the number of observations in each. Jitter plots provide the number of observations in each condition combination and disaggregate falls (triangles, n=21) from recoveries (circles, n=253). (A) Slip distances observed across curved walking conditions. Slips shortened as onset phase progressed (MS and LS: P<0.001), but no significant differences were attributable to foot (P=0.087) or path curvature (κ=0.5: P=0.834 and κ=1.0: P=0.318). (B) Peak slip velocities measured across curved walking conditions. Slips slowed with advancing onset phase (MS: P=0.015 and LS: P<0.001) and were faster on κ=1.0 paths than on straight (κ=0.0) paths (P=0.005). No significant difference between feet in peak slip velocity was found (P=0.058), although outside foot slips trended faster.

Fig. 3.

Slip magnitudes across the curvilinear walking conditions tested in this study. In both panels, boxes represent the median and interquartile range (IQR) while error bars extend to the most extreme recorded value still within 1.5×IQR of the first and third quartiles for each combination of conditions. Overlaid violin plots provide illustrations of the data distribution within each combination of conditions but are not scaled to the number of observations in each. Jitter plots provide the number of observations in each condition combination and disaggregate falls (triangles, n=21) from recoveries (circles, n=253). (A) Slip distances observed across curved walking conditions. Slips shortened as onset phase progressed (MS and LS: P<0.001), but no significant differences were attributable to foot (P=0.087) or path curvature (κ=0.5: P=0.834 and κ=1.0: P=0.318). (B) Peak slip velocities measured across curved walking conditions. Slips slowed with advancing onset phase (MS: P=0.015 and LS: P<0.001) and were faster on κ=1.0 paths than on straight (κ=0.0) paths (P=0.005). No significant difference between feet in peak slip velocity was found (P=0.058), although outside foot slips trended faster.

Slip directions

Slip directions relative to heading at slip onset consistently progressed from predominantly anterior to predominantly posterior as slip onset phase moved later into stance (MS 95% HPD: 116.28–133.28 deg; LS 95% HPD: 129.56–151.45 deg; Fig. 4), although these onset phases were not significantly different from each other (i.e. the 95% HPD intervals for MS and LS overlap). In terms of slipped foot, inside foot slips moved in a significantly more contralateral direction (95% HPD: 319.70–332.09 deg; Fig. 4) while outside foot slips were generally ipsilateral. Surprisingly, only the interaction between LS slip onset phase and the slipped foot was significant (95% HPD: 53.79–85.07 deg; Fig. 4) as the 95% HPD interval for the MS/slipped foot interaction overlapped with the model intercept's interval. Although we did not have a priori hypotheses regarding path curvature, we also found significant main effects indicating increasingly ipsilateral/contralateral directions with tightening path curvature (κ=0.5 95% HPD: 40.59–51.64 deg; κ=1.0: 95% HPD: 54.73–63.77 deg; Fig. 4).

Fig. 4.

Slip directions disaggregated by path curvature or slipped foot. ES, MS and LS slip onset phases within each path or foot condition are represented by light-to-dark gradients. Arrows and points represent the circular median of each condition, with error bars illustrating the interquartile range. Histogram bars include a 10 deg bin and represent the probability that a slip under the corresponding condition set traveled within that direction bin. Histogram distributions within each path curvature plot contain inside and outside foot slip conditions, leading to the broad distribution of slip directions shown in each path curvature plot. Slips transitioned from anteriorly to posteriorly directed with progressing onset phase, which moved through ipsilateral/contralateral directions for outside/inside foot slips, respectively. Tightening path curvature led to significantly greater ipsilateral or contralateral direction components.

Fig. 4.

Slip directions disaggregated by path curvature or slipped foot. ES, MS and LS slip onset phases within each path or foot condition are represented by light-to-dark gradients. Arrows and points represent the circular median of each condition, with error bars illustrating the interquartile range. Histogram bars include a 10 deg bin and represent the probability that a slip under the corresponding condition set traveled within that direction bin. Histogram distributions within each path curvature plot contain inside and outside foot slip conditions, leading to the broad distribution of slip directions shown in each path curvature plot. Slips transitioned from anteriorly to posteriorly directed with progressing onset phase, which moved through ipsilateral/contralateral directions for outside/inside foot slips, respectively. Tightening path curvature led to significantly greater ipsilateral or contralateral direction components.

Compensatory step distances

As hypothesized, we found that compensatory step distances from the CoM increased as slips began later in stance (MS: t198.54=10.28, P<0.001; LS: t199.24=9.21, P<0.001; Fig. 5). A significant effect of slipped foot also indicated that compensatory steps following outside foot slips were shorter on average than those following inside foot slips (t195.33=−12.84, P<0.001; Fig. 5). The slip onset phase/slipped foot interactions were also significant (MS/foot: t199.42=5.02, P<0.001; LS/foot: t199.63=5.25, P<0.001; Fig. 5), showing that compensatory step distances from the CoM increased with progressing slip onset phase after outside foot slips, but did not appreciably change with onset phase after inside foot slips. Again, while we did not have a priori hypotheses about path curvature effects on compensatory step distances, they shortened significantly with increasing path curvature (κ=0.5: t150.69=−4.01, P<0.001; κ=1.0: t149.43=−6.70, P<0.001; Fig. 5). In the 21 slipping trials where compensatory stepping responses were insufficient and a fall occurred, step distances were not notably different from successful recoveries (Fig. 5).

Fig. 5.

Compensatory step distances from the body center of mass (CoM) across the curvilinear walking conditions examined. Boxes represent the median and IQR while error bars extend to the most extreme recorded value still within 1.5×IQR of the first and third quartiles for each combination of conditions. Overlaid violin plots provide illustrations of the data distribution within each combination of conditions but are not scaled to the number of observations in each. Jitter plots provide the number of observations in each condition combination and disaggregate falls (n=21) from recoveries (n=253). Compensatory steps lengthened with advancing onset phase (MS and LS: P<0.001) and shortened with tightening curvature (κ=0.5 and κ=1.0: P<0.001). A significant interaction between onset phase and foot was also found, indicating that the lengthening trend with onset phase was exclusive to the outside foot (MS/foot and LS/foot: P<0.001).

Fig. 5.

Compensatory step distances from the body center of mass (CoM) across the curvilinear walking conditions examined. Boxes represent the median and IQR while error bars extend to the most extreme recorded value still within 1.5×IQR of the first and third quartiles for each combination of conditions. Overlaid violin plots provide illustrations of the data distribution within each combination of conditions but are not scaled to the number of observations in each. Jitter plots provide the number of observations in each condition combination and disaggregate falls (n=21) from recoveries (n=253). Compensatory steps lengthened with advancing onset phase (MS and LS: P<0.001) and shortened with tightening curvature (κ=0.5 and κ=1.0: P<0.001). A significant interaction between onset phase and foot was also found, indicating that the lengthening trend with onset phase was exclusive to the outside foot (MS/foot and LS/foot: P<0.001).

Compensatory step directions

For compensatory step directions, we found a significant interaction between slip onset phase and slipped foot relative to the curved path. After outside foot slips, compensatory steps were placed in a significantly more anterior direction as slip onset phase progressed beyond ES (MS 95% HPD: 3.10–9.06 deg; LS 95% HPD: 2.50–6.89 deg; Fig. 6), but in a significantly more ipsilateral direction after inside foot slips (MS/foot 95% HPD: 93.69–150.68 deg; LS/foot 95% HPD: 134.93–166.31 deg; Fig. 6). In both cases, compensatory steps after MS and LS slips were not significantly different in terms of direction.

Fig. 6.

Compensatory step directions disaggregated by path curvature or slipped foot. ES, MS and LS slip onset phases within each path or foot condition are represented by light-to-dark gradients. Arrows and points represent the circular median of each condition, with error bars illustrating the interquartile range. Histogram bars include a 10 deg bin and represent the probability that a slip under the corresponding condition set traveled within that direction bin. Note that the total height of a histogram bar containing multiple conditions is meaningless, as the probabilities only apply to individual conditions. Probabilities exceeding 100% are only needed to show the entire dataset. Histogram distributions within each path curvature plot contain inside and outside foot slip conditions, leading to the bimodal distributions seen in the compensatory step directions shown in each path curvature plot. With advancing slip onset phase, compensatory steps were placed in an increasingly anterior direction after outside foot slips but a more ipsilateral direction after inside foot slips.

Fig. 6.

Compensatory step directions disaggregated by path curvature or slipped foot. ES, MS and LS slip onset phases within each path or foot condition are represented by light-to-dark gradients. Arrows and points represent the circular median of each condition, with error bars illustrating the interquartile range. Histogram bars include a 10 deg bin and represent the probability that a slip under the corresponding condition set traveled within that direction bin. Note that the total height of a histogram bar containing multiple conditions is meaningless, as the probabilities only apply to individual conditions. Probabilities exceeding 100% are only needed to show the entire dataset. Histogram distributions within each path curvature plot contain inside and outside foot slip conditions, leading to the bimodal distributions seen in the compensatory step directions shown in each path curvature plot. With advancing slip onset phase, compensatory steps were placed in an increasingly anterior direction after outside foot slips but a more ipsilateral direction after inside foot slips.

Here, we examined the influence exerted by slip onset phase, slipped foot and path curvature on the resulting fall rates, slip mechanics and compensatory stepping reactions experienced by a cohort of healthy young adult humans during fixed-speed curvilinear walking. First, we hypothesized that later slip onset phases would reduce fall rates, shorten and slow slip perturbations, and induce larger compensatory steps. Consistent with these hypotheses, we observed decreasing fall rates and slip magnitudes, and compensatory step adaptations in terms of direction and distance from the CoM as slips began later in stance phase. In addition, and similar to our past results (Rasmussen and Hunt, 2021; Rasmussen et al., 2022), a significant anterior-to-posterior trend was found in slip direction with advancing onset phase. Second, we hypothesized that outside foot slips would cause more falls and greater slip magnitudes, while an interaction between slipped foot and slip onset phase would exist for slip and compensatory step directions. Slipped foot relative to the curved path did not have many of the effects that we expected: inside foot slips rather than outside foot slips exhibited the highest fall rates while also not being statistically different in slip magnitude. Yet, slipped foot did modify the slip direction, compensatory step direction and compensatory step distance trends seen with advancing onset phase. Specifically, slip directions possessed ipsilateral and contralateral components while compensatory step directions became less and more ipsilateral after outside and inside foot slips, respectively. Compensatory steps were generally shorter after outside foot slips but lengthened with later onset times, while those after inside foot slips were not notably different across onset phases. Finally, we hypothesized that tighter path curvature would lead to more falls and greater slip magnitudes. Increasing path curvature had no statistically significant effect on fall rates, counter to our hypothesis, but did lead to faster, more laterally directed slips and shorter compensatory steps. When compared with the results of our previous study using slower self-selected walking speeds (Rasmussen et al., 2022), this study shows that faster curved walking speeds lead to faster lateral slips but no other clear mechanical differences. This study also illustrates the disproportionate threat that ES slips pose to balance and the compensatory stepping reactions elicited by each context, which were not examined in our previous study.

Contrary to our hypotheses regarding the effects of slipped foot, inside foot slips instigated far more falls than outside foot and straight walking slips (Fig. 2) despite trending toward lesser magnitudes in terms of slip distance and peak velocity (Fig. 3). This result is somewhat counterintuitive, as greater slip magnitudes have traditionally been considered more dangerous in terms of fall risk (Brady et al., 2000; Lee et al., 2016; Lockhart et al., 2002, 2003; Strandberg and Lanshammar, 1981). Slip directions were starkly different between inside and outside foot slips, however (Fig. 4), which may suggest the reason why equally or even less severe slips led to more falls: the required compensatory step effort to recover. Contralateral inside foot slips cause the body to fall toward the path's center of curvature and away from the non-slipped outside leg, requiring the outside leg to perform a challenging cross-over step to recapture and counteract the destabilized CoM motion. This type of slip is particularly challenging when the CoM is positioned inside the inside foot as it is during human curvilinear walking at faster-than-normal speeds (Orendurff et al., 2006), which is what we observed in our data. In contrast, ipsilateral outside foot and straight walking slips destabilize the body toward the non-slipped inside leg, which is naturally better positioned to execute a quicker, safer lateral compensatory step. Cross-over steps are more likely to cause inter-limb collisions during swing, take more time to place, and ultimately result in a smaller margin of stability compared with lateral steps (Batcir et al., 2020; Hurt and Grabiner, 2015; Mille et al., 2013). These slip dynamics and associated stepping strategies likely translate to other biped species. For example, ostriches turn using crossover and sidesteps with similar frequencies (Jindrich et al., 2007), which are mechanically akin to inside and outside foot steps on a curved path, respectively. While examinations of slip recovery in biped animals have shown human-like kinematic slip prevention strategies on straight paths (i.e. anterior CoM shift, larger limb contact angles) (Bhatt et al., 2006; Brady et al., 2000; Clark and Higham, 2011), no published research to our knowledge has extended this analysis to curved paths to investigate mechanistic, side-specific recovery strategies. Cockroaches also narrow some inside and widen some outside steps when navigating a curved path as humans do (Jindrich and Full, 1999; Orendurff et al., 2006; Taylor et al., 2005). However, extrapolation of side-specific balance demands beyond bipedal morphologies may be limited as a result of the stability benefits conferred by additional legs. For example, tripod gaits in hexapods are statically stable (i.e. the vertical projection of the CoM is contained within the base of support) throughout the gait cycle except at the fastest running speeds (Full et al., 2002; Ting et al., 1994). The disparate human recovery demands of inside and outside foot slips relative to a curved path brought on by their relative slip directions point to a limitation of using slip distance or peak velocity alone to represent the threat to balance they pose. New models of slip severity that also account for relative slip direction may better represent balance threats, thereby providing a more accurate picture of destabilization in observational or experimental balance training studies where such models are employed (Brady et al., 2000; Lee et al., 2016; Lockhart et al., 2000; Yamaguchi et al., 2012).

We observed a strong dependence of slip mechanics and compensatory step attributes on slip onset phase within stance as hypothesized. Given the elevated mediolateral ground reaction forces typically acting outward from the center of curvature during curvilinear walking coupled with braking and propulsive forces in the anteroposterior direction (Glaister et al., 2008; Orendurff et al., 2006), the anterior-to-posterior transition in slip directions with advancing onset phase and larger ipsilateral/contralateral components on curved paths were expected (Fig. 4). While ground reaction forces may also play a role in determining how slip magnitudes and compensatory step responses change with slip onset phase, the body configurations present at slip onset likely are of greater influence. For example, the next placement of the non-slipped/compensatory stepping foot is nearly determined by MS (Wang and Srinivasan, 2014), meaning that notable adjustments to step placement are only possible in the first half of stance. Because the compensatory step is nearly or even already placed at later slip onsets, body weight can be or is already shifted from the slipped leg, leading to shorter slip distances and slower peak velocities. Body configuration may also explain the large, bimodal distributions seen in slip distance, peak velocity and compensatory step distance from the CoM during ES (Figs 3 and 5). Two unique recovery strategies have been described for ES slips: a walkover strategy where the slip is truncated by the CoM swinging over the slipped foot, and a skate-over strategy where the CoM balances over the slipping foot as it slides (Bhatt et al., 2006). In both cases, the compensatory step is placed in a generally forward direction. Of course, a third possibility is a backward loss of balance, where the foot slides uncontrolled and a compensatory step is placed below or behind the CoM (Bhatt et al., 2006).

Fixing walking speed at 1.3 m s−1 on all path curvature conditions allowed us to compare slip magnitude and direction results with previously published findings on curvilinear, comfortable-speed walking (Rasmussen et al., 2022) to infer the function of slowing when turning. The most noticeable differences between these studies were in the probabilities of experiencing a slip under certain contexts (Table 1). Slips across nearly all contexts were more likely to occur in the present study than in our previous study, especially when slip onset was during MS (Rasmussen et al., 2022). In both studies, inside foot slips were less likely than outside foot slips; however, the difference was seemingly less pronounced when walking speed was fixed here. Increased inside foot slip prevalence in this study is likely a direct result of a CoM positioned outside the base of support toward the center of curvature, larger mediolateral ground reaction forces (Orendurff et al., 2006) and elevated friction demands (Fino and Lockhart, 2014) that come with faster curvilinear walking speeds. Surprisingly, faster walking speeds only led to one difference in slip magnitude attributable to path curvature: slips were significantly faster on κ=1.0 paths (Fig. 3). Our previous study (Rasmussen et al., 2022) did not record load cell data and therefore did not report fall rates, which prevents the strongest conclusions regarding the influence of walking speed. Nevertheless, the comparisons that can be made indicate that faster curved walking speeds increase slipping risk, which aligns with studies on stability–maneuverability trade-offs in other species such as horses, northern quolls and buff-footed antechinuses (Tan and Wilson, 2011; Wheatley et al., 2018; Wynn et al., 2015). Published research on humans specifically has presented evidence for two objectives of slowing gait speed during curved walking: metabolic cost minimization where slower self-selected walking speeds align closely with the most efficient pace for a given curved path (Brown et al., 2021) and stability maximization where slower speeds reduce centripetal force that would otherwise increase on tighter path curvatures (Courtine and Schieppati, 2003; Orendurff et al., 2006; Yamaguchi et al., 2017). Our findings in aggregate support the latter, although this does not necessarily disprove the former as these two objectives are not mutually exclusive.

The results of this study in their totality suggest the curvilinear walking scenarios that pose the greatest threat to upright stability in the event of an unexpected slip, which could be leveraged by future perturbation-based balance training paradigms to deliver a comprehensive yet efficient intervention. For example, slips that began in ES consistently caused the most falls across all other contexts (Fig. 2). Most experimental, slip-specific balance training programs have administered slips exclusively at heel-strike or within ES if controlled (Ferreira et al., 2022), and our results here and elsewhere have repeatedly shown that that focus is well placed (Ouattas et al., 2022; Rasmussen and Hunt, 2021; Rasmussen et al., 2022). Our results also strongly suggest that inside foot slips relative to a curved path are far more destabilizing and require a different compensatory stepping strategy than outside foot or straight walking slips (Figs 2, 5 and 6). Lastly, curved path conditions led to significantly greater mediolateral slip direction components than seen during straight walking (Fig. 4), which are generally more challenging to upright stability than perturbations in the anteroposterior direction, particularly for older adults (Mille et al., 2013). This added challenge may be evidenced by the observed trend toward shorter (and, perhaps, faster) compensatory steps taken by our cohort as path curvature increased (Fig. 5). In sum, the biomechanical differences and asymmetries of curvilinear walking compared with the straight case elicit unique challenges to maintaining balance after a slip. It is unclear whether training solely on straight walking slips evokes sufficient transfer to non-straight walking contexts or even reinforces applicable recovery skills; therefore, future slip-specific balance training approaches should incorporate curvilinear walking slips to investigate these open questions. It is not feasible to expose trainees to every possible combination of curvilinear walking contexts; therefore, in the interest of efficiency, future protocols could initially focus on ES slips delivered to the inside foot while traversing a path of κ=1.0 to test whether adding curved path scenarios extract any added benefits.

We acknowledge that this study may suffer from a few potential limitations. First, a small amount of slack in the overhead harness strap was necessary to allow study participants to follow the curvilinear paths, which may have influenced the load cell data obtained from the harness that was used to determine whether each trial ended with a fall or successful recovery. However, we would expect any bias arising from this slack to be in the direction of fewer recorded falls than actually occurred; therefore, our results may actually underestimate the true fall rates due to the curvilinear paths. Second, repeated slip exposure without non-slip trials or blocks intermixed likely evoked feedforward adaptations from the participants, which may have influenced our outcome measures as a consequence (Horak et al., 1989; Pater et al., 2015; Siegmund et al., 2006). We attempted to minimize anticipatory effects across and within trials through randomization of condition orders and trial durations, respectively. Lastly, we required study participants to maintain a walking speed of 1.3 m s−1 on all path curvature conditions, which is likely faster than they otherwise would have self-selected on the κ=0.5 and κ=1.0 paths (Courtine and Schieppati, 2003; Courtine et al., 2006; Rasmussen et al., 2022). The reason for fixing walking speed across all participants and conditions was to probe the independent impacts of path curvature on slip mechanics, compensatory stepping reactions and fall rates. Because individuals naturally slow their gait speed when turning, however, the mechanics seen here may not perfectly represent those that would occur under the same conditions in the community.

In summary, we demonstrated that aspects of curvilinear walking influence slip-and-fall risk as well as the mechanics of and stepping reactions to slip perturbations. Future work building on these results should assess whether recovery skills reinforced by perturbation-based balance training using straight walking slips alone are transferable to non-straight scenarios, and whether the addition of curved walking slips imparts added stability improvements. Moreover, new slip severity models that incorporate slip direction (and its effect on overall body motion by extension) may provide more accurate depictions of balance threat, in turn being more useful tools to quantify performance or progress within a balance training program.

The authors are grateful to Drs Kota Takahashi, Brian Knarr and Dawn Venema for their helpful critiques and suggestions to improve the study and manuscript.

Author contributions

Conceptualization: C.M.R., N.H.H.; Methodology: C.M.R., C.C., N.H.H.; Validation: C.M.R., C.C., N.H.H.; Formal analysis: C.M.R.; Investigation: C.M.R., S.M., A.O., A.W.; Data curation: C.M.R., S.M., A.O., A.W.; Writing - original draft: C.M.R.; Writing - review & editing: C.M.R., S.M., A.O., A.W., C.C., N.H.H.; Visualization: C.M.R., N.H.H.; Supervision: C.C., N.H.H.; Funding acquisition: N.H.H.

Funding

This study was supported by grants from the National Institutes of Health (R15AG063106 and P20GM109090). Deposited in PMC for release after 12 months.

Data availability

The dataset collected and analysis codes used during this study are available from the corresponding author upon reasonable request.

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Competing interests

The authors declare no competing or financial interests.