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Gait stability, variability and complexity on inclined surfaces
Accepted Manuscript Gait Stability, Variability and Complexity on Inclined Surfaces Marcus Fraga Vieira, Fábio Barbosa Rodrigues, Gustavo Souto de Sá e Souza, Rina Márcia Magnani, Georgia Cristina Lehnen, Natalia Guimarães Campos, Adriano O. Andrade PII: DOI: Reference:
S0021-9290(17)30078-7 http://dx.doi.org/10.1016/j.jbiomech.2017.01.045 BM 8117
To appear in:
Journal of Biomechanics
Accepted Date:
27 January 2017
Please cite this article as: M.F. Vieira, F.B. Rodrigues, G.S.d. Souza, R.M. Magnani, G.C. Lehnen, N.G. Campos, A.O. Andrade, Gait Stability, Variability and Complexity on Inclined Surfaces, Journal of Biomechanics (2017), doi: http://dx.doi.org/10.1016/j.jbiomech.2017.01.045
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Gait Stability, Variability and Complexity on Inclined Surfaces
Marcus Fraga Vieira1,2,*, Fábio Barbosa Rodrigues1, Gustavo Souto de Sá e Souza1, Rina Márcia Magnani1, Georgia Cristina Lehnen1, Natalia Guimarães Campos1, Adriano O. Andrade2
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Bioengineering and Biomechanics Laboratory, Federal University of Goiás, Goiânia, Brazil Faculty of Electrical Engineering, Postgraduate Program in Electrical and Biomedical
Engineering, Centre for Innovation and Technology Assessment in Health, Federal University of Uberlândia, Brazil
* Corresponding author Bioengineering and Biomechanics Laboratory Universidade Federal de Goiás Avenida Esperança s/n, Campus Samambaia Zip Code: 74690-900 – Goiania, Goias, Brazil E-mail address: [email protected] [email protected]
Word count: 3484 words
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Abstract This study evaluated the gait stability, variability, and complexity of healthy young adults on inclined surfaces. A total of 49 individuals walked on a treadmill at their preferred speed for 4 minutes at inclinations of 6, 8, and 10% in upward (UP) and downward (DOWN) conditions, and in horizontal (0%) condition. Gait variability was assessed using average standard deviation trunk acceleration between strides (VAR), gait stability was assessed using margin of stability (MoS) and maximum Lyapunov exponent (λs), and gait complexity was assessed using sample entropy (SEn). Trunk variability (VAR) increased in the medial-lateral (ML), anterior-posterior, and vertical directions for all inclined conditions. The SEn values indicated that movement complexity decreased almost linearly from DOWN to UP conditions, reflecting changes in gait pattern with longer and slower steps as inclination increased. The DOWN conditions were associated with the highest variability and lowest stability in the MoS ML, but not in λs. Stability was lower in UP conditions, which exhibited the largest λs values. The overall results support the hypothesis that inclined surfaces decrease gait stability and alter gait variability, particularly in UP conditions.
Keywords: gait variability; inclined walking; margin of stability; maximum Lyapunov exponent; nonlinear analysis
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1. Introduction The maintenance of balance during human gait is a challenge for the postural control system (Winter, 1995), since balance and posture control are essential mechanisms in locomotion (Dimitrijevic and Larsson, 1981). Outdoor walking surfaces are generally not flat; surface topography varies in terms of its unevenness and inclination. With regard to the latter, footpath inclination may be manmade, as is the case for ramps that facilitate inclusive access to buildings, or it may a consequence of the environment at hand, as is the case for pavement laid on hills. Whatever the origin, sloped surfaces, as compared to level surfaces, impose a particularly different demand to maintain walking balance. Thus, gait kinematic changes have been studied on multi-surfaces to determine the effects of aging on the variability of gait (Marigold and Patla, 2008), acceleration patterns of the head and pelvis have been studied when walking on irregular surface levels (Menz et al., 2003), and some studies have reported data that were collected for walking on a variety of inclined surfaces (Ferraro et al., 2013; McIntosh et al., 2006; Scaglioni-Solano and Aragón-Vargas, 2014; Tulchin et al., 2010). However, to date no study have reported gait stability, complexity, and variability of trunk acceleration when walking on inclined surfaces, to develop an understanding of how the motor system of young individuals responds to such conditions. Due to the lack of a comprehensive description of these gait aspects on inclines in healthy subjects and the need for this as a pre-requisite for future research concerned with pathological gait, the present study was conducted. Young adults exhibit different kinematic characteristics when walking on inclines, compared to level ground, to properly advance the center of mass (COM) forward and upward (or downward) against increased gravitational demands (McIntosh et al., 2006; ScaglioniSolano and Aragón-Vargas, 2014; Tulchin et al., 2010). Compared to level ground walking, the ability to walk on inclines requires a different lower extremity motor pattern, which
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includes increased range of motion in the ankle (Prentice et al., 2004; Tulchin et al., 2010), increased/decreased hip and knee flexion at initial foot contact when walking up/walking down (Lay et al., 2006; Leroux et al., 2002), and increased force and joint moment production (Lay et al., 2006; McIntosh et al., 2006). Therefore, kinematic changes, including increased/decreased step length when walking up/down and decreased/increased gait cadence when walking up/down are observed (McIntosh et al., 2006). Moreover, young adults seek to optimize forward progression, mobility, and efficiency while walking (Rogers et al., 2008). The gait patterns of young adults, characterized by phases of instability that lead to forward progression and lateral shifting of the body COM at each step, are detrimental in terms of stability. Since it is possible that forward progression changes when walking on an inclined surface, it is expected that COM shifting, and, consequently, stability is also affected. Therefore, results obtained from previous studies on level walking may not be generalized to inclined surfaces, particularly with regard to stability and variability, and, to the best of our knowledge, no previous studies have assessed stability, complexity, and variability of trunk acceleration when walking on inclined surfaces. Gait variability and stability are influenced by the ability to optimally control gait from one stride to the next (Hausdorff et al., 2001). However, as postulated by Stergiou and Decker (2011), “variability does not equate with stability”. Variability refers to the ability of the motor system to perform in a wide variety of task and environmental constraints, while stability refers to the dynamic ability to recover from an external perturbation. Variability is quantified using measures derived from linear statistics, such as the standard deviation of a time series, whereas stability can be quantified not only using linear methods, but also using measures derived from nonlinear dynamics, such as the maximum Lyapunov exponent (λs). The variations in human movement are distinguishable from noise; they have a deterministic
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origin, being neither random nor independent. The variations from one task display a temporal structure, captured by nonlinear tools. In this approach, the manner in which gait evolves over time becomes important (Stergiou and Decker, 2011). Therefore, variability and stability cover different aspects of a time series: the magnitude and the structure/organization of the variations existing in a time series, respectively. Thus, linear and nonlinear variables were computed in the present study. For optimal operation of the motor system, a moderate amount of variability is expected as a necessary condition for adaptability, since a system with a total absence of variability will lack the repertoire to negotiate even subtle perturbations (Hamill et al., 1999; van Emmerik et al., 2016). In contrast, a large amount of variability may be detrimental to the motor control system; greater variability can mean that it is incapable of accurately achieving the desired target. Therefore, the average standard deviation between strides (VAR) of medial-lateral (ML), anterior-posterior (AP), and vertical (V) trunk acceleration, a common linear measure of variability in gait studies (Dingwell et al., 2001), was computed in the present study, as maintaining stability of the upper body is critical for human locomotion (MacKinnon and Winter, 1993). Higher levels of trunk variability have shown to be indicative of poor task performance (van Emmerik et al., 2016). System adaptability and complexity, which refers to the presence of nonrandom fluctuation on time in the apparently irregular dynamics of a system (Manor et al., 2010), was evaluated by a nonlinear variable, the sample entropy (SEn) of trunk velocity. Entropy has been used in a variety of studies in biomechanics, to quantify the dynamical structure of human postural sway (Ko and Newell, 2016; Ramdani et al., 2009), the time and frequency structure of force output in adult humans (Vaillancourt et al., 2004), and the stride-to-stride fluctuations in gait (Georgoulis et al., 2006). Loss of complexity has been related to poorer
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performance. However, recent results suggest that changes in complexity can instead be task dependent (Ko and Newell, 2016; van Emmerik et al., 2016). Gait stability was assessed by local dynamic stability (LDS), and an inverted pendulum-model-based variable, margin of stability (MoS), which is a purely biomechanical concept. The estimation of LDS, which is derived from dynamic system theory, is a nonlinear concept of assessing gait stability (Bruijn et al., 2013). This concept assumes that the motor control system ensures a dynamically more stable gait if the divergence exponent, λs over a period of 0.5 strides, remains lower between trajectories in a reconstructed state space that reflects gait dynamics. Thus, an increase in λs implies a decrease of LDS. Unlike traditional measures of gait variability that treat each gait cycle as independent, the LDS evaluates the evolution of stability over the course of several strides. LDS was lower in older fall-prone adults when compared to young and older healthy adults (Lockhart and Liu, 2008), was lower in patients with neurological disorders when compared to healthy individuals (Reynard et al., 2014), decreases from 40-50 years old (Terrier and Reynard, 2015), was lower after general fatigue (Vieira et al., 2016), and was lower in cerebellar patients (Hoogkamer et al., 2015). The MoS is calculated as the distance between the extrapolated center of mass (XCOM) and the border of the base of support, in which XCOM accounts for not only the position of the COM, but also its velocity (Hof et al., 2005). The closer the XCOM to the border of the base of support, the more likely it is that a loss of balance may occur. Thus, a decrease in MoS is detrimental to stability. Therefore, the present study evaluated gait variability, stability, and complexity on inclined surfaces from a fundamental point of view, to expand the understanding of gait adaptations under these conditions and provide some direction for future studies (data are available as supplementary file). We investigated the gait of young adults on surfaces inclined by -10, -8, -6, 0, 6, 8, and 10% (± 25% of 8%, a standard for inclines in Civil Engineering and
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Architecture (“Americans with Disabilities Act homepage,” 2016, “Secretaria Nacional de Promoção dos Direitos da Pessoa com Deficiência,” 2016)). We hypothesized that inclines decrease gait stability and alter gait variability and complexity, and that this is more pronounced in walking down, since some previous studies have shown that this is biomechanically more challenging than walking up, imposing greater demands on the musculoskeletal system related to an increased risk of slipping, altered mechanism of power absorption, and decreased gait pattern smoothness (Leroux et al., 2002; McIntosh et al., 2006; Scaglioni-Solano and Aragón-Vargas, 2014).
2. Methods 2.1 Participants A total of 49 healthy young individuals (25 males and 24 females, 24.5±5.5 years old, 68.1±10.8 kg, 1.70±0.08 m) participated in this study. They voluntarily signed an informed consent form. Next, they were submitted to protocols previously approved by the Local Research Ethics Committee.
2.2 Equipment Reflective markers were attached to the lateral malleoli, the heels, the heads of the second and fifth metatarsals, and the T1 vertebrae of all participants. A cluster of four reflective markers was attached between the left and right posterior superior iliac spines (PSIS) for MoS calculations. These markers were used for movement registration with a 3D motion capture system that used 10 infrared cameras operating at 100 Hz (Vicon Nexus, Oxford Metrics, Oxford, UK).
2.3 Protocol
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The participants walked on a level and inclined treadmill at their preferred walking speed (PWS). First, the level PWS was evaluated following a previously reported protocol (Kang and Dingwell, 2008a), and this was adopted for all trials, since no significant difference in PWS across inclinations was found in a pilot test. The participants then performed seven trials of 4 min at treadmill inclinations of -10, -8, and -6% (DOWN-walking down), 0 (HORhorizontal), 10, 8, and 6% (UP-walking up), adjusted in a randomized order. The participants rested for 2 min between trials.
2.4 Data Analysis Prior to data analysis, with the exception of the calculation of λs and SEn, kinematic data were low-pass filtered with a fourth-order, zero-lag, Butterworth filter with a cut-off frequency of 6 Hz. For each trial, all parameters were calculated for 150 strides. First, the initial and final 15 seconds of each trial were discarded (Hak et al., 2013), after which all steps were detected as the zero-cross of the heel-marker velocity (Zeni et al., 2008). The intermediate 150 strides were then selected, discarding the initial and final strides exceeding 150. A customized Matlab code was used for data analysis.
2.4.1 Gait Variability Gait variability was assessed using the average standard deviation (SD) of ML, AP, and V trunk acceleration along normalized strides (VAR) (Toebes et al., 2015). In order to compute VAR, each stride was time normalized (0–100%). At each of the 101 normalized time points, the SD of the ML, AP, and V trunk acceleration over the 150 strides was calculated, after which the average of these 101 standard deviations was determined (Dingwell et al., 2001).
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2.4.2 Gait Stability Gait stability was assessed using two descriptors: MoS and LDS. The MoS was calculated using the adapted method proposed by Hak et al. (2013). The COM was estimated as the average of the four cluster markers attached between the left and right PSIS, and the length of the inverted pendulum (l) as the maximum height of the estimated COM. The XCOM was calculated as COM plus its velocity multiplied by the factor / (Hof et al., 2005), where g is the gravity acceleration. The MoS was calculated as the distance between XCOM and the fifth metatarsal head marker of the leading foot for ML MoS, and the heel marker of the leading foot for backward (BW) MoS. The minimum value of the MoS within each step was averaged over the 150 strides. The LDS evaluation was based on the λs, which was computed using Rosenstein’s algorithm (Rosenstein et al., 1993). In brief, the ML, AP, and V trunk velocity was calculated using the three points method from the T1 marker raw data (Kang and Dingwell, 2008b). Next, the velocity signal was time-normalized to 15,000 samples, preserving differences in stride time between strides (Bruijn et al., 2009). A high-dimension attractor was constructed using the normalized T1 marker velocity and its delayed copies. A delay of 10 samples was used, based on the mean value of the minimum of the mutual information function across all data, and a dimensionality of five was found to be sufficient, based on global false nearest neighbor analysis. For each point in state-space, a nearest neighbor was found and the Euclidean distance between these points was tracked for 10 strides, resulting in as many time distance curves as time points in state-space. The divergence curve was calculated as the mean of the natural log of the time-distance curves. The short-term λs was calculated as the slope of a linear fit to the first 50 samples (time needed for one step) of the divergence curve. Thus, λs indicates the relative rate of divergence over one step, resulting from a small difference in initial conditions.
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2.4.3 Gait Complexity SEn was calculated in order to quantify the degree of complexity and predictability of variations of ML, AP, and V trunk velocity. SEn is the negative natural logarithm of the conditional probability that a time series of length N, having repeated itself for m samples within a tolerance r, will also repeat itself for m+1 points, eliminating self-matching (Ramdani et al., 2009). Parameter values of m=2 and r=0.2 were selected. SEn reflects the likelihood that similar patterns of observations will not be followed by additional, similar observations. A time series containing numerous repetitive patterns, that is, one that is more predictable, has a relatively small SEn and lacks complexity, whereas a less predictable process has a higher SEn and greater complexity.
2.5 Statistical Analysis Repeated measures analysis of variance (ANOVA) was used to assess the effects of different inclinations, followed by Bonferroni post-hoc tests, for the variables with a normal distribution (Shapiro-Wilk test, p>0.05), with the exception of VAR. The latter variable was tested using the nonparametric Friedman test, followed by a post hoc analysis using the Wilcoxon signed-rank test, with the application of a Bonferroni correction. The statistical analysis was performed using SPSS software, version 17 (SPSS Inc., Chicago, IL), and the significance level was set at p<0.05.
3. Results
3.1 Gait Variability
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There were significant differences in VAR (Fig. 1, Table 1) among treadmill inclinations in all directions (Friedman test, χ2=92.012, p<0.001; χ2=107.055, p<0.001; χ2=147.516, p<0.001 for ML, AP, and V, respectively). VAR also significantly increased in both UP and DOWN conditions in all directions.
Figure 1.
Table 1.
3.2 Gait Stability There were significant differences in λs (Fig. 2, Table 2) among treadmill inclinations in all directions (repeated measures ANOVA, F=6.928, p<0.001; F=8.490, p<0.001; F=32.549, p<0.001 for ML, AP, and V, respectively). There was also a significant increase in λs in inclined conditions compared to the HOR condition (except for the ML direction in the DOWN condition), with UP conditions exhibiting the greatest λs values.
Figure 2.
There were significant differences in MoS (Fig. 3, Table 2) among treadmill inclinations (repeated measures ANOVA, F=7.046, p<0.001; F=107.003, p<0.001 for MoS ML and BW, respectively). MoS ML was lower in the DOWN and greater in the UP conditions compared to the HOR condition. The opposite was observed for MoS BW: greater values were found for the DOWN conditions than the HOR conditions, whereas lower values
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were observed for the UP conditions compared to the HOR conditions, with no differences among the different UP conditions.
Figure 3.
Table 2.
3.3 Gait Complexity There were significant differences in SEn (Fig. 4, Table 3) among treadmill inclinations in all directions (repeated measures ANOVA, F=27.379, p<0.001; F=28.734, p<0.001; F=8.576, p<0.001 for ML, AP, and V, respectively). A decreasing SEn trend from DOWN to UP conditions was observed in all directions, with the highest values being found for AP SEn.
Figure 4.
Table 3.
4. Discussion In the present study, we investigated the gait stability, variability, and complexity of healthy young individuals when walking on an inclined treadmill at PWS. We hypothesized that inclined surfaces decrease gait stability and alter gait variability, and complexity, and that this result would be more pronounced in DOWN conditions. Therefore, we used different
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spatiotemporal and nonlinear variables to investigate gait stability, variability, and complexity with regard to -10, -8, -6, 0, 6, 8 and 10% inclined surfaces. The results showed that spatiotemporal variables (see Supplement A) changed with inclination, as did trunk variability (VAR), stability (λs, MoS), and complexity (SEn), which partially supports the initial hypothesis: DOWN conditions presented the greatest variability and the lowest stability in relation to MoS ML, but not in relation to λs, which was lower in DOWN conditions, indicating greater LDS. The greatest λs values were observed for UP conditions, indicating lower LDS, as were the lowest SEn values, indicating reduced complexity.
4.1 Gait Variability The increased gait variability under inclined conditions, assessed by the behavior of trunk acceleration variability (VAR), is an indicator of poorer task performance. However, it may be compensation for the demands imposed on the motor system in healthy young individuals. A common assumption in many studies on locomotion has been that increased variability is detrimental to system performance, and it has been associated with instability and increased risk of falls. Nevertheless, in multiple degree of freedom systems, variability is an inevitable and necessary condition for optimality and adaptability (Lipsitz, 2002; Manor et al., 2010; Najafi et al., 2010; van Emmerik et al., 2016). Variability patterns in spatiotemporal gait variables may not reflect variability patterns in segmental coordination of upper-body and lower segments (van Emmerik et al., 1999). Indeed, some studies have shown that a certain amount of variability appears to be evidence of healthy and stable movement (Hamill et al., 1999; Miller et al., 2010). Therefore, variability may indicate the range of coordination patterns used to complete a motor task, that is, there is a functional role for variability that
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expresses the range of possible patterns that a movement system can accomplish (van Emmerik et al., 2016).
4.2 Gait Stability ML MoS decreased under DOWN conditions, indicating poorer dynamic stability. However, this decrease, with a corresponding increase in SF (see Supplement A), contrasts with the results obtained by Hak et al. (2013) on level walking, even if we compare results from a constant speed (the largest imaginary diagonal on the top left of the graph in Figure 4 in Hak et al., 2013), as these authors found a direct relationship between MoS ML and SF. A possible explanation for this may be the increased movement of the pelvis in DOWN conditions, due to the differences of foot contact heights. Such pelvic movement leads to greater and faster oscillation of the COM in the ML direction. This influences the calculation of the XCOM, bringing it closer to the base of support border, which, in turn, decreases MoS ML. This issue should be the subject of further studies. With regard to MoS BW, our results are in accordance with those of Hak et al. (2013): the increase of MoS BW in DOWN conditions is likely due to a corresponding decrease in stride length (see Supplement A). Our results support previous observations that the decrease in SL is a strategy to increase MoS BW, and thus to increase stability (Hak et al., 2013). The effects of inclination on LDS, evaluated by λs, revealed a decrease in gait stability for both UP and DOWN conditions; several authors have previously highlighted the use of λs to assess dynamic balance (Bruijn et al., 2012; Dingwell and Marin, 2006; Hak et al., 2013; Hoogkamer et al., 2015; Reynard and Terrier, 2015, 2014; Terrier and Reynard, 2015). Theoretical and experimental studies have highlighted the importance of the frontal plane in the regulation of dynamic stability, since it is considered that gait is stable in the AP and V
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directions, and active control is required to stabilize the body in the ML direction (Bauby and Kuo, 2000). LDS decreased in the ML direction for the UP condition, but not for the DOWN condition. The decreased pelvic lateral drop toward the swing leg (Leroux et al., 2002), associated with increased hip flexion, and increased SL and decreased SF in the UP conditions (see Supplement A) may explain this finding. Such a gait pattern leads to an increased single-stance phase, decreasing ML LDS. However, we found a more significant increase of λs in the AP and V directions. These results indicate that inclines substantially decrease gait stability in these directions, a circumstance that would equally require an active control to stabilize the body in those directions. Inclines impose several factors that must be negotiated by the motor control system, including requirements to raise or lower the body’s COM and the associated mechanical effort, the vertical displacement during each stride, and the altered friction demands and foot clearance (McIntosh et al., 2006). There are short phases in the early- and late-stance phase when friction demands are high, due to high horizontal forces. The pelvic tilt increases, influencing hip flexion and trunk motion, which, in turn, change forward momentum, more anteriorly positioning the body’s COM (Lay et al., 2006; Leroux et al., 2002; McIntosh et al., 2006). All these aspects of walking on inclines occur in the sagittal plane and may explain the changes observed in AP and V stability, as well as the significant increase/decrease of MoS BW in DOWN/UP conditions, respectively.
4.3 Gait Complexity The SEn values indicate that the movement complexity decreased almost linearly from DOWN to UP. The lower movement complexity observed under UP conditions may be explained by the gait pattern adopted, specifically by the larger SL and smaller SF (see
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Supplement A). Furthermore, although the variability also increased in the UP condition, this increase was lower than in the DOWN condition. Together, these results may have contributed to the decreased ML LDS observed in UP conditions: reduced SEn (complexity) and variability in UP, compared to DOWN, conditions can be interpreted as a reduced system capacity to recover from perturbations. In conclusion, although walking on inclines affects gait stability, variability, and complexity, the motor system is robust in healthy young individuals, in consonance with previously reported locomotor adaptations to overcome the demands imposed by inclines.
4.4 Study Limitations This study has some limitations that should be noted. Although there were no statistically significant differences among PWS calculated in the different inclinations, they were different. Therefore, it would be of interest to collect data using the corresponding PWS of each condition in future gait stability studies on inclined surfaces, particularly with regard to other populations.
Conflict of interest None declared.
Acknowledgments The authors are thankful to governmental agencies CAPES, CNPq, FAPEG, and FAPEMIG for supporting this study.
References
17
Americans with Disabilities Act homepage. Retrieved at 07/05/2016, from
18
variability in the anterior cruciate ligament deficient knee during walking: The use of the approximate entropy in orthopaedics. J. Clin. Monit. Comput. 20, 11–18. doi:10.1007/s10877-006-1032-7 Hak, L., Houdijk, H., Beek, P.J., Van Dieë, J.H., 2013. Steps to take to enhance gait stability: The effect of stride frequency, stride length, and walking speed on local dynamic stability and margins of stability. PLoS One 8. doi:10.1371/journal.pone.0082842 Hamill, J., Van Emmerik, R.E. a, Heiderscheit, B.C., Li, L., 1999. A dynamical systems approach to lower extremity running injuries. Clin. Biomech. 14, 297–308. doi:10.1016/S0268-0033(98)90092-4 Hausdorff, J.M., Rios, D.A., Edelberg, H.K., 2001. Gait variability and fall risk in community-living older adults: a 1-year prospective study. Arch. Phys. Med. Rehabil. 82, 1050–6. doi:10.1053/apmr.2001.24893 Hof, A.L., Gazendam, M.G.J., Sinke, W.E., 2005. The condition for dynamic stability. J. Biomech. 38, 1–8. doi:10.1016/j.jbiomech.2004.03.025 Hoogkamer, W., Bruijn, S.M., Sunaert, S., Swinnen, S.P., Van Calenbergh, F., Duysens, J., 2015. Toward new sensitive measures to evaluate gait stability in focal cerebellar lesion patients. Gait Posture 41, 592–6. doi:10.1016/j.gaitpost.2015.01.004 Kang, H.G., Dingwell, J.B., 2008a. Separating the effects of age and walking speed on gait variability. Gait Posture 27, 572–577. doi:10.1016/j.gaitpost.2007.07.009 Kang, H.G., Dingwell, J.B., 2008b. Effects of walking speed, strength and range of motion on gait stability in healthy older adults. J. Biomech. 41, 2899–2905. doi:10.1016/j.jbiomech.2008.08.002 Ko, J.H., Newell, K.M., 2016. Aging and the complexity of center of pressure in static and dynamic postural tasks. Neurosci. Lett. 610, 104–109. doi:10.1016/j.neulet.2015.10.069 Lay, A.N., Hass, C.J., Gregor, R.J., 2006. The effects of sloped surfaces on locomotion: a
19
kinematic and kinetic analysis. J. Biomech. 39, 1621–8. doi:10.1016/j.jbiomech.2005.05.005 Leroux, A., Fung, J., Barbeau, H., 2002. Postural adaptation to walking on inclined surfaces: I. Normal strategies. Gait Posture 15, 64–74. doi:10.1016/S0966-6362(01)00181-3 Lipsitz, L. a, 2002. Dynamics of stability: the physiologic basis of functional health and frailty. J. Gerontol. A. Biol. Sci. Med. Sci. 57, B115–B125. doi:10.1093/gerona/57.3.B115 Lockhart, T., Liu, J., 2008. Differentiating fall-prone and healthy adults using local dynamic stability. Ergonomics 51, 1860–1872. doi:10.1080/00140130802567079.Differentiating MacKinnon, C.D., Winter, D. a., 1993. Control of whole body balance in the frontal plane during human walking. J. Biomech. 26, 633–644. doi:10.1016/0021-9290(93)90027-C Manor, B., Costa, M.D., Hu, K., Newton, E., Starobinets, O., Kang, H.G., Peng, C.K., Novak, V., Lipsitz, L. a, 2010. Physiological complexity and system adaptability: evidence from postural control dynamics of older adults. J. Appl. Physiol. 109, 1786–1791. doi:10.1152/japplphysiol.00390.2010 Marigold, D.S., Patla, A.E., 2008. Age-related changes in gait for multi-surface terrain. Gait Posture 27, 689–696. doi:10.1016/j.gaitpost.2007.09.005 McIntosh, A.S., Beatty, K.T., Dwan, L.N., Vickers, D.R., Ã, A.S.M., Beatty, K.T., Dwan, L.N., Vickers, D.R., 2006. Gait dynamics on an inclined walkway. J. Biomech. 39, 2491–2502. doi:10.1016/j.jbiomech.2005.07.025 Menz, H.B., Lord, S.R., Fitzpatrick, R.C., 2003. Acceleration patterns of the head and pel v is when walking on le v el and irregular surfaces. Gait Posture 18, 35–46. doi:10.1093/gerona/58.5.M446 Miller, R.H., Chang, R., Baird, J.L., Van Emmerik, R.E.A., Hamill, J., 2010. Variability in kinematic coupling assessed by vector coding and continuous relative phase. J. Biomech.
20
43, 2554–2560. doi:10.1016/j.jbiomech.2010.05.014 Najafi, B., Miller, D., Jarrett, B.D., Wrobel, J.S., 2010. Does footwear type impact the number of steps required to reach gait steady state?: An innovative look at the impact of foot orthoses on gait initiation. Gait Posture 32, 29–33. doi:10.1016/j.gaitpost.2010.02.016 Prentice, S.D., Hasler, E.N., Groves, J.J., Frank, J.S., 2004. Locomotor adaptations for changes in the slope of the walking surface. Gait Posture 20, 255–265. doi:10.1016/j.gaitpost.2003.09.006 Ramdani, S., Seigle, B., Lagarde, J., Bouchara, F., Bernard, P.L., 2009. On the use of sample entropy to analyze human postural sway data. Med. Eng. Phys. 31, 1023–1031. doi:10.1016/j.medengphy.2009.06.004 Reynard, F., Terrier, P., 2015. Role of visual input in the control of dynamic balance: variability and instability of gait in treadmill walking while blindfolded. Exp. Brain Res. 233, 1031–1040. doi:10.1007/s00221-014-4177-5 Reynard, F., Terrier, P., 2014. Local dynamic stability of treadmill walking: Intrasession and week-to-week repeatability. J. Biomech. 47, 74–80. doi:10.1016/j.jbiomech.2013.10.011 Reynard, F., Vuadens, P., Deriaz, O., Terrier, P., 2014. Could local dynamic stability serve as an early predictor of falls in patients with moderate neurological gait disorders? A reliability and comparison study in healthy individuals and in patients with paresis of the lower extremities. PLoS One 9, e100550. doi:10.1371/journal.pone.0100550 Rogers, H.L., Cromwell, R.L., Grady, J.L., 2008. Adaptive changes in gait of older and younger adults as responses to challenges to dynamic balance. J. Aging Phys. Act. 16, 85–96. Rosenstein, M.T., Collins, J.J., De Luca, C.J., 1993. A practical method for calculating largest Lyapunov exponents from small data sets. Phys. D Nonlinear Phenom. 65, 117–134.
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doi:10.1016/0167-2789(93)90009-P Scaglioni-Solano, P., Aragón-Vargas, L.F., 2014. Age-related differences when walking downhill on different sloped terrains. Gait Posture 41, 153–158. doi:10.1016/j.gaitpost.2014.09.022 Secretaria Nacional de Promoção dos Direitos da Pessoa com Deficiência. Retrieved at 07/05/2016, from
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of axial rigidity during locomotion in parkinson disease. Arch. Phys. Med. Rehabil. 80, 186–191. doi:10.1016/S0003-9993(99)90119-3 Vieira, M.F., de Sá e Souza, G.S., Lehnen, G.C., Rodrigues, F.B., Andrade, A.O., 2016. Effects of general fatigue induced by incremental maximal exercise test on gait stability and variability of healthy young subjects. J. Electromyogr. Kinesiol. 30, 161–167. doi:10.1016/j.jelekin.2016.07.007 Winter, D., 1995. Human balance and posture control during standing and walking. Gait Posture 3, 193–214. doi:10.1016/0966-6362(96)82849-9 Zeni, J. a., Richards, J.G., Higginson, J.S., 2008. Two simple methods for determining gait events during treadmill and overground walking using kinematic data. Gait Posture 27, 710–714. doi:10.1016/j.gaitpost.2007.07.007
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Fig. 1. A: ML, B: AP, and C: V average standard deviation (VAR) behavior for the different treadmill inclinations (DOWN-negative values, UP-positive values). Upward/downward arrows: significant pairwise comparisons (p<0.05).
Fig. 2. Maximum Lyapunov exponent behavior (λs) for ML (A), AP (B) and V (C) directions for the different treadmill inclinations (DOWN-negative values, UP-positive values). Upward/downward arrows: significant pairwise comparisons (p<0.05).
Fig. 3. A: ML and B: BW Margin of Stability (MoS) behavior for the different treadmill inclinations (DOWN-negative values, UP-positive values). Upward/downward arrows: significant pairwise comparisons (p<0.05).
Fig. 4. A: ML, B: AP, and C: V sample entropy (Sen) behavior for the different treadmill inclinations (DOWN-negative values, UP-positive values). Upward/downward arrows: significant pairwise comparisons (p<0.05).
Fig. A1. A: Step length (SL), B: Step frequency (SF) behavior for the different treadmill inclinations (DOWN-negative values, UP-positive values). Upward/downward arrows: significant pairwise comparisons (p<0.05).
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Table 1. Gait variability variable VAR for the inclined conditions Inclined Conditions Variables
-10%
-8%
-6%
0%
6%
8%
10%
p value
VAR ML (m/s2)
0.24(0.06)
0.22(0.05)
0.21(0.06)
0.19(0.04)
0.20(0.06)
0.21(0.05)
0.22(0.05)
<0.001*
VAR AP (m/s2)
0.25(0.05)
0.24(0.05)
0.22(0.05)
0.19(0.03)
0.22(0.05)
0.24(0.05)
0.26(0.06)
<0.001*
VAR V (m/s2)
0.39(0.09)
0.35(0.08)
0.30(0.07)
0.24(0.06)
0.28(0.07)
0.30(0.08)
0.34(0.08)
<0.001*
Values expressed as mean (standard deviation). p value: Friedman test. Inclined conditions - negative values: downward walking, positive values: upward walking. ML: medial-lateral; AP: anterior-posterior; V: vertical.
Table 2. Gait stability variables for the inclined conditions Inclined Conditions Variables
-10%
-8%
-6%
0%
6%
8%
10%
p value
λs ML
1.88(0.20)
1.87(0.22)
1.88(0.22)
1.88(0.25)
1.92(0.27)
1.98(0.27)
2.04(0.26)
<0.001
λs AP
2.08(0.24)
2.05(0.22)
1.98(0.27)
1.98(0.27)
2.06(0.29)
2.12(0.32)
2,19(0.31)
<0.001
λs V
1.71(0.25)
1.64(0.26)
1.51(0.26)
1.36(0.24)
1.51(0.28)
1.72(0.29)
1.88(0.28)
<0.001
MoS ML (cm)
4.92(1.58)
4.89(1.94)
4.77(2.09)
5.37(2.13)
5.72(2.17)
5.63(2.28)
5.85(2.21)
<0.001
MoS BW (cm)
16.49(4.78)
14.73(4.96)
12.76(5.26)
6.92(4.81)
4.39(4.85)
4.03(5.38)
4.25(5.29)
<0.001
Values expressed as mean (standard deviation). p value: repeated measures ANOVA. Inclined conditions - negative values: downward walking, positive values: upward walking. ML: medial-lateral; AP: anterior-posterior; V: vertical; BW: backward.
Table 3. Gait complexity variable for the inclined conditions Inclined Conditions Variables
-10%
-8%
-6%
0%
6%
8%
10%
p value
SEn ML
0.36(0.04)
0.35(0.04)
0.34(0.05)
0.31(0.05)
0.30(0.06)
0.29(0.05)
0.29(0.05)
<0.001
SEn AP
0.60(0.12)
0.61(0.12)
0.61(0.14)
0.58(0.12)
0.51(0.12)
0.51(0.09)
0.49(0.09)
<0.001
SEn V
0.35(0.06)
0.36(0.06)
0.35(0.06)
0.36(0.05)
0.34(0.05)
0.33(0.04)
0.32(0.04)
<0.001
Values expressed as mean (standard deviation). p value: repeated measures ANOVA. Inclined conditions - negative values: downward walking, positive values: upward walking. ML: medial-lateral; AP: anterior-posterior; V: vertical.
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Table A1. Spatiotemporal variables for the inclined conditions Inclined Conditions Variables SL (cm) SF (Hz)
-10%
-8%
-6%
0%
6%
8%
10%
p value
54.7(8.1) 1.89(0.11)
56.5(8.1) 1.85(0.11)
57.4(8.2) 1.82(0.11)
60.4(7.2) 1.74(0.13)
61.9(6.8) 1.72(0.15)
62.1(7.6) 1.69(0.15)
62.5(7.2) 1.71(0.15)
<0.001
Values expressed as mean (standard deviation). p value: repeated measures ANOVA. Inclined conditions - negative values: downward walking, positive values: upward walking.
<0.001
S0021-9290(17)30078-7 http://dx.doi.org/10.1016/j.jbiomech.2017.01.045 BM 8117
To appear in:
Journal of Biomechanics
Accepted Date:
27 January 2017
Please cite this article as: M.F. Vieira, F.B. Rodrigues, G.S.d. Souza, R.M. Magnani, G.C. Lehnen, N.G. Campos, A.O. Andrade, Gait Stability, Variability and Complexity on Inclined Surfaces, Journal of Biomechanics (2017), doi: http://dx.doi.org/10.1016/j.jbiomech.2017.01.045
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Gait Stability, Variability and Complexity on Inclined Surfaces
Marcus Fraga Vieira1,2,*, Fábio Barbosa Rodrigues1, Gustavo Souto de Sá e Souza1, Rina Márcia Magnani1, Georgia Cristina Lehnen1, Natalia Guimarães Campos1, Adriano O. Andrade2
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Bioengineering and Biomechanics Laboratory, Federal University of Goiás, Goiânia, Brazil Faculty of Electrical Engineering, Postgraduate Program in Electrical and Biomedical
Engineering, Centre for Innovation and Technology Assessment in Health, Federal University of Uberlândia, Brazil
* Corresponding author Bioengineering and Biomechanics Laboratory Universidade Federal de Goiás Avenida Esperança s/n, Campus Samambaia Zip Code: 74690-900 – Goiania, Goias, Brazil E-mail address: [email protected] [email protected]
Word count: 3484 words
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Abstract This study evaluated the gait stability, variability, and complexity of healthy young adults on inclined surfaces. A total of 49 individuals walked on a treadmill at their preferred speed for 4 minutes at inclinations of 6, 8, and 10% in upward (UP) and downward (DOWN) conditions, and in horizontal (0%) condition. Gait variability was assessed using average standard deviation trunk acceleration between strides (VAR), gait stability was assessed using margin of stability (MoS) and maximum Lyapunov exponent (λs), and gait complexity was assessed using sample entropy (SEn). Trunk variability (VAR) increased in the medial-lateral (ML), anterior-posterior, and vertical directions for all inclined conditions. The SEn values indicated that movement complexity decreased almost linearly from DOWN to UP conditions, reflecting changes in gait pattern with longer and slower steps as inclination increased. The DOWN conditions were associated with the highest variability and lowest stability in the MoS ML, but not in λs. Stability was lower in UP conditions, which exhibited the largest λs values. The overall results support the hypothesis that inclined surfaces decrease gait stability and alter gait variability, particularly in UP conditions.
Keywords: gait variability; inclined walking; margin of stability; maximum Lyapunov exponent; nonlinear analysis
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1. Introduction The maintenance of balance during human gait is a challenge for the postural control system (Winter, 1995), since balance and posture control are essential mechanisms in locomotion (Dimitrijevic and Larsson, 1981). Outdoor walking surfaces are generally not flat; surface topography varies in terms of its unevenness and inclination. With regard to the latter, footpath inclination may be manmade, as is the case for ramps that facilitate inclusive access to buildings, or it may a consequence of the environment at hand, as is the case for pavement laid on hills. Whatever the origin, sloped surfaces, as compared to level surfaces, impose a particularly different demand to maintain walking balance. Thus, gait kinematic changes have been studied on multi-surfaces to determine the effects of aging on the variability of gait (Marigold and Patla, 2008), acceleration patterns of the head and pelvis have been studied when walking on irregular surface levels (Menz et al., 2003), and some studies have reported data that were collected for walking on a variety of inclined surfaces (Ferraro et al., 2013; McIntosh et al., 2006; Scaglioni-Solano and Aragón-Vargas, 2014; Tulchin et al., 2010). However, to date no study have reported gait stability, complexity, and variability of trunk acceleration when walking on inclined surfaces, to develop an understanding of how the motor system of young individuals responds to such conditions. Due to the lack of a comprehensive description of these gait aspects on inclines in healthy subjects and the need for this as a pre-requisite for future research concerned with pathological gait, the present study was conducted. Young adults exhibit different kinematic characteristics when walking on inclines, compared to level ground, to properly advance the center of mass (COM) forward and upward (or downward) against increased gravitational demands (McIntosh et al., 2006; ScaglioniSolano and Aragón-Vargas, 2014; Tulchin et al., 2010). Compared to level ground walking, the ability to walk on inclines requires a different lower extremity motor pattern, which
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includes increased range of motion in the ankle (Prentice et al., 2004; Tulchin et al., 2010), increased/decreased hip and knee flexion at initial foot contact when walking up/walking down (Lay et al., 2006; Leroux et al., 2002), and increased force and joint moment production (Lay et al., 2006; McIntosh et al., 2006). Therefore, kinematic changes, including increased/decreased step length when walking up/down and decreased/increased gait cadence when walking up/down are observed (McIntosh et al., 2006). Moreover, young adults seek to optimize forward progression, mobility, and efficiency while walking (Rogers et al., 2008). The gait patterns of young adults, characterized by phases of instability that lead to forward progression and lateral shifting of the body COM at each step, are detrimental in terms of stability. Since it is possible that forward progression changes when walking on an inclined surface, it is expected that COM shifting, and, consequently, stability is also affected. Therefore, results obtained from previous studies on level walking may not be generalized to inclined surfaces, particularly with regard to stability and variability, and, to the best of our knowledge, no previous studies have assessed stability, complexity, and variability of trunk acceleration when walking on inclined surfaces. Gait variability and stability are influenced by the ability to optimally control gait from one stride to the next (Hausdorff et al., 2001). However, as postulated by Stergiou and Decker (2011), “variability does not equate with stability”. Variability refers to the ability of the motor system to perform in a wide variety of task and environmental constraints, while stability refers to the dynamic ability to recover from an external perturbation. Variability is quantified using measures derived from linear statistics, such as the standard deviation of a time series, whereas stability can be quantified not only using linear methods, but also using measures derived from nonlinear dynamics, such as the maximum Lyapunov exponent (λs). The variations in human movement are distinguishable from noise; they have a deterministic
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origin, being neither random nor independent. The variations from one task display a temporal structure, captured by nonlinear tools. In this approach, the manner in which gait evolves over time becomes important (Stergiou and Decker, 2011). Therefore, variability and stability cover different aspects of a time series: the magnitude and the structure/organization of the variations existing in a time series, respectively. Thus, linear and nonlinear variables were computed in the present study. For optimal operation of the motor system, a moderate amount of variability is expected as a necessary condition for adaptability, since a system with a total absence of variability will lack the repertoire to negotiate even subtle perturbations (Hamill et al., 1999; van Emmerik et al., 2016). In contrast, a large amount of variability may be detrimental to the motor control system; greater variability can mean that it is incapable of accurately achieving the desired target. Therefore, the average standard deviation between strides (VAR) of medial-lateral (ML), anterior-posterior (AP), and vertical (V) trunk acceleration, a common linear measure of variability in gait studies (Dingwell et al., 2001), was computed in the present study, as maintaining stability of the upper body is critical for human locomotion (MacKinnon and Winter, 1993). Higher levels of trunk variability have shown to be indicative of poor task performance (van Emmerik et al., 2016). System adaptability and complexity, which refers to the presence of nonrandom fluctuation on time in the apparently irregular dynamics of a system (Manor et al., 2010), was evaluated by a nonlinear variable, the sample entropy (SEn) of trunk velocity. Entropy has been used in a variety of studies in biomechanics, to quantify the dynamical structure of human postural sway (Ko and Newell, 2016; Ramdani et al., 2009), the time and frequency structure of force output in adult humans (Vaillancourt et al., 2004), and the stride-to-stride fluctuations in gait (Georgoulis et al., 2006). Loss of complexity has been related to poorer
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performance. However, recent results suggest that changes in complexity can instead be task dependent (Ko and Newell, 2016; van Emmerik et al., 2016). Gait stability was assessed by local dynamic stability (LDS), and an inverted pendulum-model-based variable, margin of stability (MoS), which is a purely biomechanical concept. The estimation of LDS, which is derived from dynamic system theory, is a nonlinear concept of assessing gait stability (Bruijn et al., 2013). This concept assumes that the motor control system ensures a dynamically more stable gait if the divergence exponent, λs over a period of 0.5 strides, remains lower between trajectories in a reconstructed state space that reflects gait dynamics. Thus, an increase in λs implies a decrease of LDS. Unlike traditional measures of gait variability that treat each gait cycle as independent, the LDS evaluates the evolution of stability over the course of several strides. LDS was lower in older fall-prone adults when compared to young and older healthy adults (Lockhart and Liu, 2008), was lower in patients with neurological disorders when compared to healthy individuals (Reynard et al., 2014), decreases from 40-50 years old (Terrier and Reynard, 2015), was lower after general fatigue (Vieira et al., 2016), and was lower in cerebellar patients (Hoogkamer et al., 2015). The MoS is calculated as the distance between the extrapolated center of mass (XCOM) and the border of the base of support, in which XCOM accounts for not only the position of the COM, but also its velocity (Hof et al., 2005). The closer the XCOM to the border of the base of support, the more likely it is that a loss of balance may occur. Thus, a decrease in MoS is detrimental to stability. Therefore, the present study evaluated gait variability, stability, and complexity on inclined surfaces from a fundamental point of view, to expand the understanding of gait adaptations under these conditions and provide some direction for future studies (data are available as supplementary file). We investigated the gait of young adults on surfaces inclined by -10, -8, -6, 0, 6, 8, and 10% (± 25% of 8%, a standard for inclines in Civil Engineering and
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Architecture (“Americans with Disabilities Act homepage,” 2016, “Secretaria Nacional de Promoção dos Direitos da Pessoa com Deficiência,” 2016)). We hypothesized that inclines decrease gait stability and alter gait variability and complexity, and that this is more pronounced in walking down, since some previous studies have shown that this is biomechanically more challenging than walking up, imposing greater demands on the musculoskeletal system related to an increased risk of slipping, altered mechanism of power absorption, and decreased gait pattern smoothness (Leroux et al., 2002; McIntosh et al., 2006; Scaglioni-Solano and Aragón-Vargas, 2014).
2. Methods 2.1 Participants A total of 49 healthy young individuals (25 males and 24 females, 24.5±5.5 years old, 68.1±10.8 kg, 1.70±0.08 m) participated in this study. They voluntarily signed an informed consent form. Next, they were submitted to protocols previously approved by the Local Research Ethics Committee.
2.2 Equipment Reflective markers were attached to the lateral malleoli, the heels, the heads of the second and fifth metatarsals, and the T1 vertebrae of all participants. A cluster of four reflective markers was attached between the left and right posterior superior iliac spines (PSIS) for MoS calculations. These markers were used for movement registration with a 3D motion capture system that used 10 infrared cameras operating at 100 Hz (Vicon Nexus, Oxford Metrics, Oxford, UK).
2.3 Protocol
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The participants walked on a level and inclined treadmill at their preferred walking speed (PWS). First, the level PWS was evaluated following a previously reported protocol (Kang and Dingwell, 2008a), and this was adopted for all trials, since no significant difference in PWS across inclinations was found in a pilot test. The participants then performed seven trials of 4 min at treadmill inclinations of -10, -8, and -6% (DOWN-walking down), 0 (HORhorizontal), 10, 8, and 6% (UP-walking up), adjusted in a randomized order. The participants rested for 2 min between trials.
2.4 Data Analysis Prior to data analysis, with the exception of the calculation of λs and SEn, kinematic data were low-pass filtered with a fourth-order, zero-lag, Butterworth filter with a cut-off frequency of 6 Hz. For each trial, all parameters were calculated for 150 strides. First, the initial and final 15 seconds of each trial were discarded (Hak et al., 2013), after which all steps were detected as the zero-cross of the heel-marker velocity (Zeni et al., 2008). The intermediate 150 strides were then selected, discarding the initial and final strides exceeding 150. A customized Matlab code was used for data analysis.
2.4.1 Gait Variability Gait variability was assessed using the average standard deviation (SD) of ML, AP, and V trunk acceleration along normalized strides (VAR) (Toebes et al., 2015). In order to compute VAR, each stride was time normalized (0–100%). At each of the 101 normalized time points, the SD of the ML, AP, and V trunk acceleration over the 150 strides was calculated, after which the average of these 101 standard deviations was determined (Dingwell et al., 2001).
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2.4.2 Gait Stability Gait stability was assessed using two descriptors: MoS and LDS. The MoS was calculated using the adapted method proposed by Hak et al. (2013). The COM was estimated as the average of the four cluster markers attached between the left and right PSIS, and the length of the inverted pendulum (l) as the maximum height of the estimated COM. The XCOM was calculated as COM plus its velocity multiplied by the factor / (Hof et al., 2005), where g is the gravity acceleration. The MoS was calculated as the distance between XCOM and the fifth metatarsal head marker of the leading foot for ML MoS, and the heel marker of the leading foot for backward (BW) MoS. The minimum value of the MoS within each step was averaged over the 150 strides. The LDS evaluation was based on the λs, which was computed using Rosenstein’s algorithm (Rosenstein et al., 1993). In brief, the ML, AP, and V trunk velocity was calculated using the three points method from the T1 marker raw data (Kang and Dingwell, 2008b). Next, the velocity signal was time-normalized to 15,000 samples, preserving differences in stride time between strides (Bruijn et al., 2009). A high-dimension attractor was constructed using the normalized T1 marker velocity and its delayed copies. A delay of 10 samples was used, based on the mean value of the minimum of the mutual information function across all data, and a dimensionality of five was found to be sufficient, based on global false nearest neighbor analysis. For each point in state-space, a nearest neighbor was found and the Euclidean distance between these points was tracked for 10 strides, resulting in as many time distance curves as time points in state-space. The divergence curve was calculated as the mean of the natural log of the time-distance curves. The short-term λs was calculated as the slope of a linear fit to the first 50 samples (time needed for one step) of the divergence curve. Thus, λs indicates the relative rate of divergence over one step, resulting from a small difference in initial conditions.
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2.4.3 Gait Complexity SEn was calculated in order to quantify the degree of complexity and predictability of variations of ML, AP, and V trunk velocity. SEn is the negative natural logarithm of the conditional probability that a time series of length N, having repeated itself for m samples within a tolerance r, will also repeat itself for m+1 points, eliminating self-matching (Ramdani et al., 2009). Parameter values of m=2 and r=0.2 were selected. SEn reflects the likelihood that similar patterns of observations will not be followed by additional, similar observations. A time series containing numerous repetitive patterns, that is, one that is more predictable, has a relatively small SEn and lacks complexity, whereas a less predictable process has a higher SEn and greater complexity.
2.5 Statistical Analysis Repeated measures analysis of variance (ANOVA) was used to assess the effects of different inclinations, followed by Bonferroni post-hoc tests, for the variables with a normal distribution (Shapiro-Wilk test, p>0.05), with the exception of VAR. The latter variable was tested using the nonparametric Friedman test, followed by a post hoc analysis using the Wilcoxon signed-rank test, with the application of a Bonferroni correction. The statistical analysis was performed using SPSS software, version 17 (SPSS Inc., Chicago, IL), and the significance level was set at p<0.05.
3. Results
3.1 Gait Variability
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There were significant differences in VAR (Fig. 1, Table 1) among treadmill inclinations in all directions (Friedman test, χ2=92.012, p<0.001; χ2=107.055, p<0.001; χ2=147.516, p<0.001 for ML, AP, and V, respectively). VAR also significantly increased in both UP and DOWN conditions in all directions.
Figure 1.
Table 1.
3.2 Gait Stability There were significant differences in λs (Fig. 2, Table 2) among treadmill inclinations in all directions (repeated measures ANOVA, F=6.928, p<0.001; F=8.490, p<0.001; F=32.549, p<0.001 for ML, AP, and V, respectively). There was also a significant increase in λs in inclined conditions compared to the HOR condition (except for the ML direction in the DOWN condition), with UP conditions exhibiting the greatest λs values.
Figure 2.
There were significant differences in MoS (Fig. 3, Table 2) among treadmill inclinations (repeated measures ANOVA, F=7.046, p<0.001; F=107.003, p<0.001 for MoS ML and BW, respectively). MoS ML was lower in the DOWN and greater in the UP conditions compared to the HOR condition. The opposite was observed for MoS BW: greater values were found for the DOWN conditions than the HOR conditions, whereas lower values
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were observed for the UP conditions compared to the HOR conditions, with no differences among the different UP conditions.
Figure 3.
Table 2.
3.3 Gait Complexity There were significant differences in SEn (Fig. 4, Table 3) among treadmill inclinations in all directions (repeated measures ANOVA, F=27.379, p<0.001; F=28.734, p<0.001; F=8.576, p<0.001 for ML, AP, and V, respectively). A decreasing SEn trend from DOWN to UP conditions was observed in all directions, with the highest values being found for AP SEn.
Figure 4.
Table 3.
4. Discussion In the present study, we investigated the gait stability, variability, and complexity of healthy young individuals when walking on an inclined treadmill at PWS. We hypothesized that inclined surfaces decrease gait stability and alter gait variability, and complexity, and that this result would be more pronounced in DOWN conditions. Therefore, we used different
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spatiotemporal and nonlinear variables to investigate gait stability, variability, and complexity with regard to -10, -8, -6, 0, 6, 8 and 10% inclined surfaces. The results showed that spatiotemporal variables (see Supplement A) changed with inclination, as did trunk variability (VAR), stability (λs, MoS), and complexity (SEn), which partially supports the initial hypothesis: DOWN conditions presented the greatest variability and the lowest stability in relation to MoS ML, but not in relation to λs, which was lower in DOWN conditions, indicating greater LDS. The greatest λs values were observed for UP conditions, indicating lower LDS, as were the lowest SEn values, indicating reduced complexity.
4.1 Gait Variability The increased gait variability under inclined conditions, assessed by the behavior of trunk acceleration variability (VAR), is an indicator of poorer task performance. However, it may be compensation for the demands imposed on the motor system in healthy young individuals. A common assumption in many studies on locomotion has been that increased variability is detrimental to system performance, and it has been associated with instability and increased risk of falls. Nevertheless, in multiple degree of freedom systems, variability is an inevitable and necessary condition for optimality and adaptability (Lipsitz, 2002; Manor et al., 2010; Najafi et al., 2010; van Emmerik et al., 2016). Variability patterns in spatiotemporal gait variables may not reflect variability patterns in segmental coordination of upper-body and lower segments (van Emmerik et al., 1999). Indeed, some studies have shown that a certain amount of variability appears to be evidence of healthy and stable movement (Hamill et al., 1999; Miller et al., 2010). Therefore, variability may indicate the range of coordination patterns used to complete a motor task, that is, there is a functional role for variability that
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expresses the range of possible patterns that a movement system can accomplish (van Emmerik et al., 2016).
4.2 Gait Stability ML MoS decreased under DOWN conditions, indicating poorer dynamic stability. However, this decrease, with a corresponding increase in SF (see Supplement A), contrasts with the results obtained by Hak et al. (2013) on level walking, even if we compare results from a constant speed (the largest imaginary diagonal on the top left of the graph in Figure 4 in Hak et al., 2013), as these authors found a direct relationship between MoS ML and SF. A possible explanation for this may be the increased movement of the pelvis in DOWN conditions, due to the differences of foot contact heights. Such pelvic movement leads to greater and faster oscillation of the COM in the ML direction. This influences the calculation of the XCOM, bringing it closer to the base of support border, which, in turn, decreases MoS ML. This issue should be the subject of further studies. With regard to MoS BW, our results are in accordance with those of Hak et al. (2013): the increase of MoS BW in DOWN conditions is likely due to a corresponding decrease in stride length (see Supplement A). Our results support previous observations that the decrease in SL is a strategy to increase MoS BW, and thus to increase stability (Hak et al., 2013). The effects of inclination on LDS, evaluated by λs, revealed a decrease in gait stability for both UP and DOWN conditions; several authors have previously highlighted the use of λs to assess dynamic balance (Bruijn et al., 2012; Dingwell and Marin, 2006; Hak et al., 2013; Hoogkamer et al., 2015; Reynard and Terrier, 2015, 2014; Terrier and Reynard, 2015). Theoretical and experimental studies have highlighted the importance of the frontal plane in the regulation of dynamic stability, since it is considered that gait is stable in the AP and V
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directions, and active control is required to stabilize the body in the ML direction (Bauby and Kuo, 2000). LDS decreased in the ML direction for the UP condition, but not for the DOWN condition. The decreased pelvic lateral drop toward the swing leg (Leroux et al., 2002), associated with increased hip flexion, and increased SL and decreased SF in the UP conditions (see Supplement A) may explain this finding. Such a gait pattern leads to an increased single-stance phase, decreasing ML LDS. However, we found a more significant increase of λs in the AP and V directions. These results indicate that inclines substantially decrease gait stability in these directions, a circumstance that would equally require an active control to stabilize the body in those directions. Inclines impose several factors that must be negotiated by the motor control system, including requirements to raise or lower the body’s COM and the associated mechanical effort, the vertical displacement during each stride, and the altered friction demands and foot clearance (McIntosh et al., 2006). There are short phases in the early- and late-stance phase when friction demands are high, due to high horizontal forces. The pelvic tilt increases, influencing hip flexion and trunk motion, which, in turn, change forward momentum, more anteriorly positioning the body’s COM (Lay et al., 2006; Leroux et al., 2002; McIntosh et al., 2006). All these aspects of walking on inclines occur in the sagittal plane and may explain the changes observed in AP and V stability, as well as the significant increase/decrease of MoS BW in DOWN/UP conditions, respectively.
4.3 Gait Complexity The SEn values indicate that the movement complexity decreased almost linearly from DOWN to UP. The lower movement complexity observed under UP conditions may be explained by the gait pattern adopted, specifically by the larger SL and smaller SF (see
16
Supplement A). Furthermore, although the variability also increased in the UP condition, this increase was lower than in the DOWN condition. Together, these results may have contributed to the decreased ML LDS observed in UP conditions: reduced SEn (complexity) and variability in UP, compared to DOWN, conditions can be interpreted as a reduced system capacity to recover from perturbations. In conclusion, although walking on inclines affects gait stability, variability, and complexity, the motor system is robust in healthy young individuals, in consonance with previously reported locomotor adaptations to overcome the demands imposed by inclines.
4.4 Study Limitations This study has some limitations that should be noted. Although there were no statistically significant differences among PWS calculated in the different inclinations, they were different. Therefore, it would be of interest to collect data using the corresponding PWS of each condition in future gait stability studies on inclined surfaces, particularly with regard to other populations.
Conflict of interest None declared.
Acknowledgments The authors are thankful to governmental agencies CAPES, CNPq, FAPEG, and FAPEMIG for supporting this study.
References
17
Americans with Disabilities Act homepage. Retrieved at 07/05/2016, from
18
variability in the anterior cruciate ligament deficient knee during walking: The use of the approximate entropy in orthopaedics. J. Clin. Monit. Comput. 20, 11–18. doi:10.1007/s10877-006-1032-7 Hak, L., Houdijk, H., Beek, P.J., Van Dieë, J.H., 2013. Steps to take to enhance gait stability: The effect of stride frequency, stride length, and walking speed on local dynamic stability and margins of stability. PLoS One 8. doi:10.1371/journal.pone.0082842 Hamill, J., Van Emmerik, R.E. a, Heiderscheit, B.C., Li, L., 1999. A dynamical systems approach to lower extremity running injuries. Clin. Biomech. 14, 297–308. doi:10.1016/S0268-0033(98)90092-4 Hausdorff, J.M., Rios, D.A., Edelberg, H.K., 2001. Gait variability and fall risk in community-living older adults: a 1-year prospective study. Arch. Phys. Med. Rehabil. 82, 1050–6. doi:10.1053/apmr.2001.24893 Hof, A.L., Gazendam, M.G.J., Sinke, W.E., 2005. The condition for dynamic stability. J. Biomech. 38, 1–8. doi:10.1016/j.jbiomech.2004.03.025 Hoogkamer, W., Bruijn, S.M., Sunaert, S., Swinnen, S.P., Van Calenbergh, F., Duysens, J., 2015. Toward new sensitive measures to evaluate gait stability in focal cerebellar lesion patients. Gait Posture 41, 592–6. doi:10.1016/j.gaitpost.2015.01.004 Kang, H.G., Dingwell, J.B., 2008a. Separating the effects of age and walking speed on gait variability. Gait Posture 27, 572–577. doi:10.1016/j.gaitpost.2007.07.009 Kang, H.G., Dingwell, J.B., 2008b. Effects of walking speed, strength and range of motion on gait stability in healthy older adults. J. Biomech. 41, 2899–2905. doi:10.1016/j.jbiomech.2008.08.002 Ko, J.H., Newell, K.M., 2016. Aging and the complexity of center of pressure in static and dynamic postural tasks. Neurosci. Lett. 610, 104–109. doi:10.1016/j.neulet.2015.10.069 Lay, A.N., Hass, C.J., Gregor, R.J., 2006. The effects of sloped surfaces on locomotion: a
19
kinematic and kinetic analysis. J. Biomech. 39, 1621–8. doi:10.1016/j.jbiomech.2005.05.005 Leroux, A., Fung, J., Barbeau, H., 2002. Postural adaptation to walking on inclined surfaces: I. Normal strategies. Gait Posture 15, 64–74. doi:10.1016/S0966-6362(01)00181-3 Lipsitz, L. a, 2002. Dynamics of stability: the physiologic basis of functional health and frailty. J. Gerontol. A. Biol. Sci. Med. Sci. 57, B115–B125. doi:10.1093/gerona/57.3.B115 Lockhart, T., Liu, J., 2008. Differentiating fall-prone and healthy adults using local dynamic stability. Ergonomics 51, 1860–1872. doi:10.1080/00140130802567079.Differentiating MacKinnon, C.D., Winter, D. a., 1993. Control of whole body balance in the frontal plane during human walking. J. Biomech. 26, 633–644. doi:10.1016/0021-9290(93)90027-C Manor, B., Costa, M.D., Hu, K., Newton, E., Starobinets, O., Kang, H.G., Peng, C.K., Novak, V., Lipsitz, L. a, 2010. Physiological complexity and system adaptability: evidence from postural control dynamics of older adults. J. Appl. Physiol. 109, 1786–1791. doi:10.1152/japplphysiol.00390.2010 Marigold, D.S., Patla, A.E., 2008. Age-related changes in gait for multi-surface terrain. Gait Posture 27, 689–696. doi:10.1016/j.gaitpost.2007.09.005 McIntosh, A.S., Beatty, K.T., Dwan, L.N., Vickers, D.R., Ã, A.S.M., Beatty, K.T., Dwan, L.N., Vickers, D.R., 2006. Gait dynamics on an inclined walkway. J. Biomech. 39, 2491–2502. doi:10.1016/j.jbiomech.2005.07.025 Menz, H.B., Lord, S.R., Fitzpatrick, R.C., 2003. Acceleration patterns of the head and pel v is when walking on le v el and irregular surfaces. Gait Posture 18, 35–46. doi:10.1093/gerona/58.5.M446 Miller, R.H., Chang, R., Baird, J.L., Van Emmerik, R.E.A., Hamill, J., 2010. Variability in kinematic coupling assessed by vector coding and continuous relative phase. J. Biomech.
20
43, 2554–2560. doi:10.1016/j.jbiomech.2010.05.014 Najafi, B., Miller, D., Jarrett, B.D., Wrobel, J.S., 2010. Does footwear type impact the number of steps required to reach gait steady state?: An innovative look at the impact of foot orthoses on gait initiation. Gait Posture 32, 29–33. doi:10.1016/j.gaitpost.2010.02.016 Prentice, S.D., Hasler, E.N., Groves, J.J., Frank, J.S., 2004. Locomotor adaptations for changes in the slope of the walking surface. Gait Posture 20, 255–265. doi:10.1016/j.gaitpost.2003.09.006 Ramdani, S., Seigle, B., Lagarde, J., Bouchara, F., Bernard, P.L., 2009. On the use of sample entropy to analyze human postural sway data. Med. Eng. Phys. 31, 1023–1031. doi:10.1016/j.medengphy.2009.06.004 Reynard, F., Terrier, P., 2015. Role of visual input in the control of dynamic balance: variability and instability of gait in treadmill walking while blindfolded. Exp. Brain Res. 233, 1031–1040. doi:10.1007/s00221-014-4177-5 Reynard, F., Terrier, P., 2014. Local dynamic stability of treadmill walking: Intrasession and week-to-week repeatability. J. Biomech. 47, 74–80. doi:10.1016/j.jbiomech.2013.10.011 Reynard, F., Vuadens, P., Deriaz, O., Terrier, P., 2014. Could local dynamic stability serve as an early predictor of falls in patients with moderate neurological gait disorders? A reliability and comparison study in healthy individuals and in patients with paresis of the lower extremities. PLoS One 9, e100550. doi:10.1371/journal.pone.0100550 Rogers, H.L., Cromwell, R.L., Grady, J.L., 2008. Adaptive changes in gait of older and younger adults as responses to challenges to dynamic balance. J. Aging Phys. Act. 16, 85–96. Rosenstein, M.T., Collins, J.J., De Luca, C.J., 1993. A practical method for calculating largest Lyapunov exponents from small data sets. Phys. D Nonlinear Phenom. 65, 117–134.
21
doi:10.1016/0167-2789(93)90009-P Scaglioni-Solano, P., Aragón-Vargas, L.F., 2014. Age-related differences when walking downhill on different sloped terrains. Gait Posture 41, 153–158. doi:10.1016/j.gaitpost.2014.09.022 Secretaria Nacional de Promoção dos Direitos da Pessoa com Deficiência. Retrieved at 07/05/2016, from
22
of axial rigidity during locomotion in parkinson disease. Arch. Phys. Med. Rehabil. 80, 186–191. doi:10.1016/S0003-9993(99)90119-3 Vieira, M.F., de Sá e Souza, G.S., Lehnen, G.C., Rodrigues, F.B., Andrade, A.O., 2016. Effects of general fatigue induced by incremental maximal exercise test on gait stability and variability of healthy young subjects. J. Electromyogr. Kinesiol. 30, 161–167. doi:10.1016/j.jelekin.2016.07.007 Winter, D., 1995. Human balance and posture control during standing and walking. Gait Posture 3, 193–214. doi:10.1016/0966-6362(96)82849-9 Zeni, J. a., Richards, J.G., Higginson, J.S., 2008. Two simple methods for determining gait events during treadmill and overground walking using kinematic data. Gait Posture 27, 710–714. doi:10.1016/j.gaitpost.2007.07.007
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Fig. 1. A: ML, B: AP, and C: V average standard deviation (VAR) behavior for the different treadmill inclinations (DOWN-negative values, UP-positive values). Upward/downward arrows: significant pairwise comparisons (p<0.05).
Fig. 2. Maximum Lyapunov exponent behavior (λs) for ML (A), AP (B) and V (C) directions for the different treadmill inclinations (DOWN-negative values, UP-positive values). Upward/downward arrows: significant pairwise comparisons (p<0.05).
Fig. 3. A: ML and B: BW Margin of Stability (MoS) behavior for the different treadmill inclinations (DOWN-negative values, UP-positive values). Upward/downward arrows: significant pairwise comparisons (p<0.05).
Fig. 4. A: ML, B: AP, and C: V sample entropy (Sen) behavior for the different treadmill inclinations (DOWN-negative values, UP-positive values). Upward/downward arrows: significant pairwise comparisons (p<0.05).
Fig. A1. A: Step length (SL), B: Step frequency (SF) behavior for the different treadmill inclinations (DOWN-negative values, UP-positive values). Upward/downward arrows: significant pairwise comparisons (p<0.05).
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Table 1. Gait variability variable VAR for the inclined conditions Inclined Conditions Variables
-10%
-8%
-6%
0%
6%
8%
10%
p value
VAR ML (m/s2)
0.24(0.06)
0.22(0.05)
0.21(0.06)
0.19(0.04)
0.20(0.06)
0.21(0.05)
0.22(0.05)
<0.001*
VAR AP (m/s2)
0.25(0.05)
0.24(0.05)
0.22(0.05)
0.19(0.03)
0.22(0.05)
0.24(0.05)
0.26(0.06)
<0.001*
VAR V (m/s2)
0.39(0.09)
0.35(0.08)
0.30(0.07)
0.24(0.06)
0.28(0.07)
0.30(0.08)
0.34(0.08)
<0.001*
Values expressed as mean (standard deviation). p value: Friedman test. Inclined conditions - negative values: downward walking, positive values: upward walking. ML: medial-lateral; AP: anterior-posterior; V: vertical.
Table 2. Gait stability variables for the inclined conditions Inclined Conditions Variables
-10%
-8%
-6%
0%
6%
8%
10%
p value
λs ML
1.88(0.20)
1.87(0.22)
1.88(0.22)
1.88(0.25)
1.92(0.27)
1.98(0.27)
2.04(0.26)
<0.001
λs AP
2.08(0.24)
2.05(0.22)
1.98(0.27)
1.98(0.27)
2.06(0.29)
2.12(0.32)
2,19(0.31)
<0.001
λs V
1.71(0.25)
1.64(0.26)
1.51(0.26)
1.36(0.24)
1.51(0.28)
1.72(0.29)
1.88(0.28)
<0.001
MoS ML (cm)
4.92(1.58)
4.89(1.94)
4.77(2.09)
5.37(2.13)
5.72(2.17)
5.63(2.28)
5.85(2.21)
<0.001
MoS BW (cm)
16.49(4.78)
14.73(4.96)
12.76(5.26)
6.92(4.81)
4.39(4.85)
4.03(5.38)
4.25(5.29)
<0.001
Values expressed as mean (standard deviation). p value: repeated measures ANOVA. Inclined conditions - negative values: downward walking, positive values: upward walking. ML: medial-lateral; AP: anterior-posterior; V: vertical; BW: backward.
Table 3. Gait complexity variable for the inclined conditions Inclined Conditions Variables
-10%
-8%
-6%
0%
6%
8%
10%
p value
SEn ML
0.36(0.04)
0.35(0.04)
0.34(0.05)
0.31(0.05)
0.30(0.06)
0.29(0.05)
0.29(0.05)
<0.001
SEn AP
0.60(0.12)
0.61(0.12)
0.61(0.14)
0.58(0.12)
0.51(0.12)
0.51(0.09)
0.49(0.09)
<0.001
SEn V
0.35(0.06)
0.36(0.06)
0.35(0.06)
0.36(0.05)
0.34(0.05)
0.33(0.04)
0.32(0.04)
<0.001
Values expressed as mean (standard deviation). p value: repeated measures ANOVA. Inclined conditions - negative values: downward walking, positive values: upward walking. ML: medial-lateral; AP: anterior-posterior; V: vertical.
25
Table A1. Spatiotemporal variables for the inclined conditions Inclined Conditions Variables SL (cm) SF (Hz)
-10%
-8%
-6%
0%
6%
8%
10%
p value
54.7(8.1) 1.89(0.11)
56.5(8.1) 1.85(0.11)
57.4(8.2) 1.82(0.11)
60.4(7.2) 1.74(0.13)
61.9(6.8) 1.72(0.15)
62.1(7.6) 1.69(0.15)
62.5(7.2) 1.71(0.15)
<0.001
Values expressed as mean (standard deviation). p value: repeated measures ANOVA. Inclined conditions - negative values: downward walking, positive values: upward walking.
<0.001