Effects of lower-limb muscular fatigue on stair gait

Effects of lower-limb muscular fatigue on stair gait

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Effects of lower-limb muscular fatigue on stair gait Xingda Qu Institute of Human Factors and Ergonomics, College of Mechatronics and Control Engineering, Shenzhen University, 3688 Nanhai Avenue, Shenzhen, Guangdong Province 518060, China

art ic l e i nf o

a b s t r a c t

Article history: Accepted 1 October 2015

The objective of the present study was to determine the effects of lower-limb muscular fatigue on stair gait. Twelve healthy young male adults between 20 and 30 years old participated in the experiment. There were two experimental sessions corresponding to a no fatigue condition and a lower-limb muscular fatigue condition, respectively. Lower-limb muscular fatigue was induced using repetitive lowerlimb pushing exertions. Both ascent and descent were studied. Stair gait was assessed by lower-limb joints and trunk kinematics, and postural stability measures. It was found that lower-limb muscular fatigue compromised stair gait during descent, but did not make any difference during ascent. These findings highlighted the importance of minimizing exposures to lower-limb muscular fatigue during descent in stair accident prevention. & 2015 Elsevier Ltd. All rights reserved.

Keywords: Stair gait Kinematics Postural stability Lower-limbs Muscular fatigue

1. Introduction Stair negotiation, which is one of the most demanding locomotor tasks, is very common in daily life. Stairs are considered as one of the most hazardous locations in the workplace and at home (Cayless, 2001), as a large proportion of accidents and injuries happen when people ascend or descend stairs. The most common accidents during stair negotiation are fall accidents. Around one out of ten fall accidents take place on staircases (Startzell et al., 2000; Svänstörm, 1974). Gait abnormality is a key risk factor for falls (Rubenstein, 2006). Therefore in order to prevent stair falls, there is a need to better understand stair gait. Some researchers reported the kinematic and kinetic differences between stair negotiation and level walking (Costigan et al., 2002; Nadeau et al., 2003). It was generally found that stair gait was associated with larger lower-limb joint range of motion and larger joint moments compared to level walking. Some researchers studied age-related differences in stair gait and attempted to use their findings to explain the higher risk of falls in older adults during stair negotiation (Bosse et al., 2012; Mian et al., 2007; Novak and Brouwer, 2011). For instance, Bosse et al. (2012) found that older adults showed a lower ankle and knee joint angular impulse before the initiation of the single support phase. Based on this finding, they further suggested that decreased leg-extensor muscular output with aging is the cause of higher risk of falls in older adults during descent. E-mail address: [email protected]

Many studies presented that safe stair negotiation was dependent on adequate lower-limb muscle strength (Karamanidis and Arampatzis, 2011; Reeves et al., 2008). Muscular fatigue leads to decreased muscle strength (Vøllestad, 1997), which could be a risk factor compromising stair gait. The effects of lower-limb muscular fatigue on gait have been investigated in previous work (Longpré et al., 2013). In general, lower-limb muscular fatigue was found to have adverse effects on gait. However, in previous studies, gait was mainly assessed during level walking. The effects of lower-limb muscular fatigue on stair gait are seldom studied. A recent study has evaluated the effects of muscular fatigue of the triceps surae and quadriceps muscles in stepping down in ongoing gait (Barbieri et al., 2014). However, in this study, only localized muscular fatigue at the ankle and knee was examined. Multi-joint movements are more common than single-joint movements in both daily activities and occupational settings, and mobility of one joint is typically dependent on the position of an adjacent joint (aka. two-joint muscle effect) (Chaffin et al., 1996). Thus, applying localized muscular fatigue protocols to a single lower-limb joint is limited in replicating the muscular fatigue in real life. The objective of the present study was to determine the effects of lower-limb muscular fatigue on stair gait during both ascent and descent. Gait analysis is typically conducted from kinematic and kinetic perspectives (Prince et al., 1997). In the present study, lower limb joints and trunk kinematics were used to characterize stair gait. Kinetic analysis was not undertaken here due to the lack of necessary measuring device in the experiment. Besides, stair gait was also assessed by postural stability measures as understanding how humans maintain postural stability is essential for

http://dx.doi.org/10.1016/j.jbiomech.2015.10.004 0021-9290/& 2015 Elsevier Ltd. All rights reserved.

Please cite this article as: Qu, X., Effects of lower-limb muscular fatigue on stair gait. Journal of Biomechanics (2015), http://dx.doi.org/ 10.1016/j.jbiomech.2015.10.004i

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predicting the likelihood of falls (Hsiao and Simeonov, 2001; Rubenstein, 2006). In order to replicate the fatigue in real life, the examined lower-limb muscular fatigue was multi-joint muscular fatigue. It was hypothesized that lower-limb muscular fatigue would compromise lower limb joints and trunk kinematics, and lead to decreased postural stability, during both ascent and descent.

2. Methods 2.1. Participants Twelve healthy young male adults between 20 and 30 years old participated in the experiment. The mean 7SD of the age, height and body weight of the participants are 24.071.4 years, 174.7 76.2 cm, and 68.3 77.9 kg, respectively. All the participants self-reported to have no musculoskeletal injuries in the past 12 months. They all also self-reported to prefer using their right foot to kick a soccer ball, and such information was used to determine their foot dominance. Informed consent which was approved by the local ethical committee was obtained from each participant. 2.2. Apparatus An eight-camera motion capture system (Motion Analysis Eagle System, CA, USA) was used to collect the body kinematic data. The sampling rate was set at 100 Hz, and the raw data from the motion capture system were filtered using a second order Butterworth filter with the cut-off frequency at 6 Hz. Stair negotiation was conducted on a five-step staircase without handrail (tread 30 cm, width 80 cm, riser 15 cm). This staircase was customized based on the Singapore BCA Building Code 2007. A commercial isokinetic dynamometer (Biodex Medical Systems, Shirley, NY) was used to measure strengths and to induce lower-limb muscular fatigue. 2.3. Experimental protocol A within-subject design was adopted. There were two experimental sessions corresponding to a no fatigue condition and a lower-limb muscular fatigue condition, respectively. The participants were randomly assigned to two even groups. One group started with the no fatigue session followed by the lower-limb muscular fatigue session. The other group started with the lowerlimb muscular fatigue session followed by the no fatigue session. The interval between these two sessions was at least three days in order to minimize carry-over effects. At the beginning of each session, the participants were asked to wear tight-fitting suit. A total of 26 reflective markers were placed bilaterally over selected anatomical landmarks of the body (Fig. 1). This marker placement scheme can help model the body as a 12segment rigid body model including the head, trunk, upper arms, lower arms, thighs, shanks, and feet. After that, the stair negotiation protocol which is similar as that in Qu and Hu (2014) was introduced to the participants. Subsequently, each participant was given around two minutes to practice stair negotiation. During practice, the appropriate start points for ascent and descent for each participant were determined so that the participants could clear the first stair edge with their non-dominant foot at a selfselected comfortable speed. In the no fatigue session, stair negotiation data collection was conducted right after practice. In the lower-limb muscular fatigue session, the participants were instructed to perform fatiguing exercises after practice. The details of fatiguing exercises have been presented elsewhere (Lew and Qu, 2014). Briefly, lower-limb muscular fatigue was induced using repetitive lower-limb pushing

Fig. 1. Marker placement on the human body.

exertions on a lift simulation attachment for the commercial isokinetic dynamometer when the participants were told to lie on the floor and not to move their torso and upper limbs during the exertions. The pushing exertions involved the movements of the ankle, knee, and hip with minimal movements of the torso and upper limbs, and were performed at the rate of 10 times/min against the resistance of 60% of the corresponding maximum voluntary contraction which was determined at the beginning of the fatiguing exercises. Fatigue was considered induced when the participants were unable to perform the exertion for three consecutive attempts, and then stair negotiation data collection was started immediately. In the stair ascent trials, the participants walked from a start point about two meters away from the staircase on the ground level, and then ascended to the top of the staircase in a step-over manner. Similarly in the stair descent trials, the participants started walking on the top platform of the staircase about two meters away from the first step, and then descended to the ground by placing one foot on each step. In both the ascent and descent trials, the participants were instructed to walk at their self-selected comfortable speed, and to clear the first stair edge with their nondominant foot. An experimenter stood by the staircase to protect the participants from any unexpected incidents occurring during the experimental trials. Each participant underwent 30 trials in each session. Five ascent and five descent trials were grouped and carried out consecutively. Each ascent trial and descent trial in each group were performed in sequence. Upon completion of the 10 trials in each group, a 3 min break was provided to minimize confounding fatigue effect that did not result from the fatigue protocol used in the study. In the lower-limb muscular fatigue session, the fatiguing exercise was reinitiated after completing the first and second groups of stair negotiation trials to ensure the consistency of fatigue level between trials. 2.4. Dependent variables Dependent variables accounted for lower-limb joints and trunk kinematics and postural stability, respectively. They were measured during a complete stair gait cycle. The selected stair gait cycle during ascent was defined as that starting from the dominant foot contact on the second step (i.e. 0% of gait cycle) and ending at the dominant foot contact on the fourth step (i.e. 100% of gait cycle). During descent, the stair gait cycle was defined by the moments of dominant foot contact on the second step down

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(i.e. 0% of gait cycle) and dominant foot contact on the fourth step down (i.e. 100% of gait cycle).

descent was when the derivative of the corresponding toe marker movement in the forward direction reached a local minimum.

2.4.1. Lower-limb joints and trunk kinematics Dependent variables of lower-limb joint kinematics were measured on the dominant side (i.e., the right side for each participant). Lower-limb joint angles were defined in the sagittal plane using a two-dimensional rigid linkage model (Fig. 2). In this linkage model, the joint centers were defined as the midpoints of the corresponding bilateral joint markers (Table 1). The reference angle (0°) for each joint was defined at the standard anatomical position. Positive angles indicate ankle dorsiflexion, knee flexion, and hip flexion. Trunk orientation was determined by the midpoints of the hip joint centers and the midpoints of the shoulder markers. These dependent variables were determined at four important gait events, including dominant foot contact, non-dominant foot release, non-dominant foot contact, and dominant foot release (Fig. 3). These four gait events correspond to the boundaries of the key stair gait phases defined by McFadyen and Winter (1988) (Please see Section 4 for details). Foot contact and foot release were determined using an approach similar to Grenholm et al. (2009). In particular, foot release of both ascent and descent was defined as the moment when the corresponding toe marker raised 1 cm above the previous stationary position in the vertical direction. The foot contact of ascent was defined as the time when the derivative of the corresponding heel marker movement in the forward direction reached a local minimum, and foot contact of

2.4.2. Postural stability Postural stability was assessed in the anterior-posterior (AP) direction and medial-lateral direction, respectively, using the margin of stability (MOS) that is defined by the distance from the vertical projection of the extrapolated center of mass (XCOM) to the base of support (BOS) boundary (Hof et al., 2005). The XCOM is determined as follows: qffiffiffi 8 > < XCOM_AP ¼ COM_AP þ VEL_COM_AP  lGs qffiffiffi ð1Þ > : XCOM_ML ¼ COM_ML þ VEL_COM_ML  lF G

Shoulder

Hip θ3 θ2 Knee θ1

θ1: Ankle joint angle θ2: Knee joint angle θ3: Hip joint angle

Ankle Fig. 2. Definitions of lower-limb joint angles.

Table 1 Definitions of lower-limb joint centers. Joint centers (right side)

Definitions

Hip

24% of the distance between two ASISs (13 and 14) posteriorly, 30% of the same distance inferiorly relative to right ASIS (13) Midpoint of the right lateral (15) and medial (16) epicondyles of femur Midpoint of the right lateral (19) and medial (20) malleoli

Knee Ankle

Note: The numbers in the parentheses are the serial numbers for the reflective markers in Fig. 1. The definition of the hip joint center was given by Seidel et al. (1995).

where COM_AP and COM_ML represent the whole-body center-ofmass (COM) displacements in the AP direction and ML direction, respectively; VEL_COM_AP and VEL_COM_ML are the COM velocities in the AP direction and ML direction, respectively, and are determined as the derivatives of COM_AP and COM_ML using the finite difference method.; ls and lF are the equivalent pendulum lengths in the sagittal plane and frontal plane, respectively, and are calculated as the distance between the COM and the ankle joint center in the corresponding plane; G ¼9.81 m/s2 is the acceleration due to gravity. The COM displacement is computed as the weighted sum of each body segment's center-of-mass from the 12-segement model (Fig. 1). The parameters for estimating body segments' center-of-mass locations were provided by der Leva (1996). Because stair gait is limited by the geometry of the staircase in the AP direction, the posterior boundary of the BOS during ascent and the anterior boundary of the BOS during descent were, respectively, defined by the edge of the corresponding stair (Bosse et al., 2012). This was verified for each ascent trial by the horizontal location of the heel marker relative to the stair edge, and for each descent trail by the horizontal location of the toe marker relative to the stair edge. ML MOS was defined as lateral distance between the XCOM and the heel markers of the feet (Young et al., 2012). Postural stability was measured at the moments of nondominant foot release and non-dominant foot contact. These two gait events correspond to initiation of a single support phase and initiation of a double support phase, respectively. Note that postural stability was not assessed at dominant foot release and dominant foot contact. This is because stair gait is considered to be bilaterally symmetric, and dominant foot release and dominant foot contact also correspond to initiation of a single support phase and initiation of a double support phase, respectively. 2.5. Analysis In order to minimize inter-individual differences, ‘participants’ was considered as a random factor and ‘fatigue condition’ as a fixed factor in analysis. Analysis of variance was performed to determine the effects of lower-limb muscular fatigue on dependent variables. Level of significance was set at 0.05. Note that since ‘participants’ was a random factor, the data used in ANOVA was the dependent variable calculated from each ascent or descent trial.

3. Results Lower-limb muscular fatigue did not affect lower-limb joints kinematics during ascent (Table 2). However, lower-limb joints kinematics during descent became significantly different between the no fatigue and fatigue conditions (Table 3). Specifically, smaller ankle plantarflexion, smaller knee flexion, and smaller hip flexion were observed at the moment of dominant foot contact of descent

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Fig. 3. Illustration of the four gait events during ascent (a) and descent (b). ‘1’¼Dominant foot contact; ‘2’¼non-dominant foot release; ‘3’¼non-dominant foot contact; ‘4’¼dominant foot release. Solid line ¼ dominant (right) side; dotted line ¼ non-dominant side.

Table 2 Mean (SE) of joint kinematic measures during stair ascent. ‘*’ indicates statistical significance. ‘þ ’ suggests dorsiflexion, knee flexion, hip flexion, and trunk flexion; ‘ ’ suggests plantarflexion, and hip extension. Dependent measures Ankle joint angle (deg)

Knee joint angle (deg)

Hip joint angle (deg)

Trunk flexion angle (deg)

AP MOS (mm) ML MOS (mm)

Dominant foot Non-dominant Non-dominant Dominant foot Dominant foot Non-dominant Non-dominant Dominant foot Dominant foot Non-dominant Non-dominant Dominant foot Dominant foot Non-dominant Non-dominant Dominant foot Non-dominant Non-dominant Non-dominant Non-dominant

contact foot release foot contact release contact foot release foot contact release contact foot release foot contact release contact foot release foot contact release foot release foot contact foot release foot contact

in the fatigue condition versus no fatigue condition. At the moment of non-dominant foot release of descent, fatigue was associated with smaller knee flexion. Smaller knee flexion was also found at the moment of non-dominant foot contact of descent. There was no significant difference in lower-limb joints kinematics between the no fatigue and fatigue conditions at the moment of dominant foot release of descent. Trunk flexion was not significantly different between the two testing conditions at the selected gait events. Fatigue did not significantly affect AP MOS during ascent (Table 2). But, significant differences between the no fatigue and fatigue conditions were found in AP MOS at the events of nondominant foot release and non-dominant foot contact of descent (Table 3). In particular, fatigue resulted in smaller AP MOS in both

No fatigue

Fatigue

4.46 5.94  10.91  18.83 35.39 33.23 4.20 8.74 5.83 1.16  25.77  24.73 10.53 11.32 9.46 10.10 78.98 106.30 13.37 38.13

5.10 6.61  10.55  17.92 35.37 33.11 3.69 8.46 6.65 2.22  25.12  24.32 9.51 10.23 8.66 9.30 77.14 98.81 18.80 41.77

(0.29) (0.27) (0.43) (0.41) (0.35) (0.35) (0.23) (0.38) (0.43) (0.44) (0.37) (0.35) (0.34) (0.36) (0.33) (0.31) (1.78) (1.94) (1.68) (1.31)

p-Value (0.32) (0.29) (0.54) (0.46) (0.43) (0.43) (0.34) (0.34) (0.52) (0.48) (0.45) (0.42) (0.36) (0.35) (0.30) (0.34) (1.31) (1.85) (1.69) (1.54)

0.582 0.590 0.964 0.582 0.688 0.837 0.086 0.819 0.272 0.165 0.233 0.397 0.068 0.068 0.154 0.111 0.727 0.217 0.262 0.271

events. ML MOS was not found to be significantly different between the no fatigue and fatigue conditions during both ascent and descent.

4. Discussion Previous research has reported that lower-limb muscular fatigue affected gait during level walking (Barbieri et al., 2013) and obstacle negotiation (Hatton et al., 2013). Stair ascent raises the body to a higher level. Thus, stair ascent is a more challenging locomotor task and involves larger energy consumption compared to level walking and obstacle negotiation. Meanwhile, muscular fatigue is associated with reduced energy generation capacity.

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Table 3 Mean (SE) of joint kinematic measures during stair descent. ‘*’ indicates statistical significance. ‘þ’ suggests dorsiflexion, knee flexion, hip flexion, and trunk flexion; ‘  ’ suggests plantarflexion, and hip extension. Dependent measures Ankle joint angle (deg)

Knee joint angle (deg)

Hip joint angle (deg)

Trunk flexion angle (deg)

AP MOS (mm) ML MOS (mm)

Dominant foot Non-dominant Non-dominant Dominant foot Dominant foot Non-dominant Non-dominant Dominant foot Dominant foot Non-dominant Non-dominant Dominant foot Dominant foot Non-dominant Non-dominant Dominant foot Non-dominant Non-dominant Non-dominant Non-dominant

contact foot release foot contact release contact foot release foot contact release contact foot release foot contact release contact foot release foot contact release foot release foot contact foot release foot contact

Based on these arguments, lower-limb muscular fatigue should have compromised stair gait during ascent. Surprisingly, no differences in lower-limb joints kinematics and postural stability were found between the no fatigue and lower-limb muscular fatigue conditions during ascent, indicating that lower-limb muscular fatigue did not compromise stair ascent gait. This finding suggests that people are still able to properly control their body postures during ascent under the induced fatigue level (i.e. 30% reduction in MVC). To further reveal the relationship between lower-limb muscular fatigue and stair ascent gait, there is a need to investigate how stair ascent gait is affected at different fatigue levels in future work. Gait of stair descent is more challenging than that of ascent (Zachazewski et al., 1993). Given this fact, the fatigued participants may not be capable of controlling their movement during stair descent as well as during stair ascent. This helps explain why lower-limb joints kinematic differences were found between the no fatigue and lower-limb muscular fatigue conditions during stair descent. At the moment of dominant foot contact of descent, smaller plantarflexion, smaller knee flexion and smaller hip flexion were observed in the fatigue condition. This suggests that fatigue increased leg stiffness at this moment (Hortobagyi and DeVita, 1999). Dominant foot contact of descent defines the boundary of weight acceptance which is the phase dominated by the absorption of energy at the ankle and knee (McFadyen and Winter, 1988). McFadyen and Winter (1988) further emphasized that plantar flexors absorbed most of the energy in the phase of weight acceptance. Thus, smaller plantarflexion due to fatigue indicates that fatigue compromised energy absorption during weight acceptance of descent. Both stiffer leg and compromised energy absorption could limit the postural control capability during descent. At the initiation of both single support (i.e., non-dominant foot release) and double support (i.e., non-dominant foot contact) phases, fatigued people adopted smaller knee flexion of the dominant leg. This result suggested that fatigued people become less capable of controlling the movement of the body by flexing the knee joint of the leading leg (Bosse et al., 2012). In addition, the moment of non-dominant foot contact of descent occurs in the phase of ‘controlled lowering’, during which the knee plays an important role in energy absorption (McFadyen and Winter, 1988).

No fatigue

Fatigue

 22.20  4.98 17.52  1.07 14.37 18.16 59.90 76.62 5.15 4.83 4.18 13.06 5.09 4.82 4.63 4.14 11.02 71.78 36.34 31.6

 20.27  4.57 16.10  0.55 13.58 13.58 57.04 76.34 3.34 4.26 4.69 11.84 4.57 3.95 3.79 3.40  10.03 32.43 36.91 35.2

(0.38) (0.39) (0.71) (0.55) (0.39) (0.39) (0.53) (0.54) (0.32) (0.38) (0.37) (0.44) (0.24) (0.21) (0.21) (0.18) (2.39) (3.39) (1.65) (1.8)

p-Value (0.46) (0.50) (0.71) (0.57) (0.34) (0.49) (0.49) (0.47) (0.34) (0.39) (0.38) (0.44) (0.23) (0.22) (0.20) (0.17) (2.12) (2.74) (1.61) (1.4)

0.029* 0.626 0.223 0.465 0.042* o 0.001* o 0.001* 0.657 0.045* 0.541 0.515 0.480 0.186 0.114 0.169 0.191 0.023* 0.001* 0.672 0.526

Smaller knee flexion at this gait event in the fatigue condition suggested that energy absorption was compromised by fatigue in the phase of ‘controlled lowering’. Besides knee kinematics, it was found that postural stability at the initiation of both single support and double support phases became poorer in the fatigue condition. At the same time, it was also noted that trunk flexion was not affected by fatigue during descent. Therefore, it may be concluded that fatigue compromised postural stability at the initiation of both single support and double support phases primarily due to its effects on knee postural control. The most common accidents during stair negotiation are fall accidents, resulting from loss of postural stability. Stair descent falls generally take place in the anterior direction (Bosse et al., 2012). I found that lower-limb muscular fatigue had adverse effects on postural stability in the AP direction during descent. In addition, it was also noted that fatigued people showed a negative AP MOS at the initiation of the single support phase of descent. Similar finding was also reported by Bosse et al. (2012) who explained that though leading to a dynamically unstable posture, a negative MOS during descent might be energetically efficient for transitioning to the next step. Young et al. (2012) pointed out that a negative MOS does not necessarily mean an immediate fall, but demands immediate corrective actions to avoid a fall. Therefore, people showing negative MOS need to exert greater corrective effort. Muscular fatigue was associated with decreased muscular strength. It is reasonable to expect that fall risks are higher under the condition demanding greater corrective effort with decreased muscular strength. Based on these arguments, it may be expected that lower-limb muscular fatigue could increase the likelihood of accidental stair falls. Postural stability in the ML direction was not affected by fatigue. A possible explanation for this is that the fatiguing exercises adopted in the present study mainly involve lower-limb joints flexion and extension, and thus only fatigue muscles controlling movements in the sagittal plane. Some statistically significant differences observed in the present study were small (Table 3). A possible explanation for this is that the induced fatigue level was not high enough, so the fatigued participants did not have to alter their gait to a great degree to meet the demands of stair descent. Some measures were taken to make sure that such small differences were caused by fatigue. In particular, participants were considered as a random factor in analysis which helps minimize inter-individual differences among

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the data. Further, under each fatigue condition, 15 stair trials from each individual were included in analysis. This enhanced the reliability of the analyzed data. Some limitations exist in the present study. According to epidemiological observations, stair accidents are more serious and prevalent among older adults (Hemenway et al., 1994). However, only younger male adults were recruited in the experiment due to safety reasons. Appropriate experimental protocol should be designed in future research to study the effects of fatigue on older adults' stair gait. It is also worth studying the gender differences in such effects in future research. In addition, kinetic measures, such as joint moments, may provide a deeper understanding of the stair gait mechanisms under the fatigue condition. However, lowerlimb kinetics was not investigated in the present study because of a lack of relevant equipment. Stairs are one of the most hazardous locations in the workplace and at home (Cayless, 2001). Safe stair negotiation was dependent on adequate lower-limb muscle strength (Karamanidis and Arampatzis, 2011; Reeves et al., 2008), and muscular fatigue leads to decreased muscle strength (Vøllestad, 1997). To my best knowledge, the present study is the first attempt to investigate how lower-limb muscular fatigue affects stair gait. I found that lowerlimb muscular fatigue compromised stair gait and decreased postural stability during descent, but did not make any difference during ascent. These findings partially supported the initial hypothesis, and also highlighted the importance of minimizing exposures to lower-limb muscular fatigue during descent in stair accident prevention.

Conflict of interest The author does not have financial or personal relationship with other persons or organizations that might inappropriately influence the work presented therein.

Acknowledgements This work is supported in part by the Natural Science Foundation of Guangdong Province of China (Project # 2015A030313553).

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Please cite this article as: Qu, X., Effects of lower-limb muscular fatigue on stair gait. Journal of Biomechanics (2015), http://dx.doi.org/ 10.1016/j.jbiomech.2015.10.004i