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Kinetic analysis of forwards and backwards stair descent
Gait & Posture 27 (2008) 564–571 www.elsevier.com/locate/gaitpost
Kinetic analysis of forwards and backwards stair descent Franc¸ois G. D.Beaulieu a, Lucie Pelland b, D. Gordon E. Robertson a,* a
School of Human Kinetics, University of Ottawa, Ottawa, Ontario, Canada b School of Rehabilitation Therapy, Queen’s University, Kingston, Canada
Received 3 June 2006; received in revised form 24 June 2007; accepted 13 July 2007
Abstract The activity of descending stairs increases loading at the joints of the lower extremities as compared to walking, which may cause discomfort and or difficulties in completing the task. This study compared and contrasted the kinematics and kinetics of both forwards and backwards stair descent to those of level walking. We compared the support moments and moment powers of the lower limb joints while descending stairs forwards at a self-selected pace, backwards at a self-selected pace and forwards at the same pace as backwards. Participants were 10 healthy young adults (6 men and 4 women) aged 20–35 years. Sagittal plane kinematics and ground reaction forces were collected and moments of force computed using inverse dynamics. The ratio of stance/swing phase changed from 59:41 for normal level walking to between 65:35 and 70:30 for forward stair descent but backwards descent was 58:42. Stair descent produced larger doublepeak support moments with reduced ankle plantar flexor and increased knee extensor moments as compared to level walking (>95thpercentile confidence interval). The hip moments during stair descent were relatively small and highly variable. We observed significantly larger distances between the centres of pressure and the stair edges for backwards stair descent versus forwards stair descent. These results demonstrate that stair descent, even at a slower pace, requires greater power from the knee extensors than level walking but that backwards stair descent significantly reduced the peak knee power during midstance and provided a potentially safer means of descending stairs than forwards stair descent. # 2007 Elsevier B.V. All rights reserved. Keywords: Gait; Mechanical power; Support moment; Inverse dynamics; Falls
1. Introduction Daily, we encounter stairs at the workplace, during leisure activities, pedestrian travel and at home. For those with muscle weakness or joint dysfunction, such as arthritis, ascending and particularly descending stairs can be a difficult, risky and painful task. One solution that occasional long-distance runners and athletes use to deal with the difficulty of descending stairs after heavy exercise is to descend them backwards. Backwards stair descent is also commonly used when stairs are very steep such as on ladders or ships where forward descent can easily result in a fall. * Corresponding author. Tel.: +1 613 562 5800x4253; fax: +1 613 562 5149. E-mail addresses: [email protected] (F.G. D.Beaulieu), [email protected] (L. Pelland), [email protected] (D.G.E. Robertson). 0966-6362/$ – see front matter # 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.gaitpost.2007.07.010
Falls on stairs are a leading cause of accidental deaths and of morbidity [1] and have therefore attracted attention concerning injury prevention [2,3]. Backwards stair descent may offer a less stressful and safer means of descending stairs under certain circumstances. Since stairs are an integral part of our societal architecture, the ability to manage stairs in a safe and independent fashion is important. For people injured [4] or physically [1,5,6] or cognitively impaired [7] and for the elderly [8,9], stair descent can be strenuous, painful and even dangerous [10]. Suitable strategies should therefore be available to permit safe and comfortable stair descent. The purpose of this study was to investigate backwards stair descent as an alternate strategy for descending stairs. We wanted to quantify the differences in the patterns of the joint kinetics of the lower extremity to better understand the energetic and loading demands of backwards compared to forwards descent and level walking. We will use the data
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compiled and reported by Winter [11] for comparisons with level walking. Furthermore, we wished to examine whether backwards stair descent was potentially safer in terms of preventing falls caused by being too close to the stair edge.
2. Methods Lower extremity mechanics during forward and backward stair descent were analyzed for 10 able-bodied subjects 20–35 years old (6 males and 4 females). Prior research on stair climbing has demonstrated the effects of leg length on lower extremity mechanics [5,7,12,13] and as such, a stratified recruitment approach was used to ensure a range of heights in our subject group from 165 to 184 cm (see Table 1 for relevant subject information). A questionnaire screened subjects to exclude people with histories of lower extremity joint and muscle impairment. Prior to data recording, subjects provided written informed consent as approved by the responsible ethics committee. Subjects completed blocks of five stair descent trials under three experimental conditions: forward stair descent at self-selected speed (NF), backward stair descent at self-selected speed (NB) and slower forward stair descent at the same speed as each subject’s backward stair descent (SF). External pacing by metronome ensured that speed of descent remained constant within conditions. Stair descent trials were completed on a three-step laboratory staircase (Fig. 1), with step dimensions: 20 cm riser and 30 cm tread [10,12–14]. Subjects started at the landing at the top of the staircase and stepped down onto a force platform (Kistler model 9281C) on the first step. The contralateral leg, which was not analyzed, stepped down to the second step, followed by the ipsilateral leg stepping down to floor level. Subjects continued walking at floor level. The contribution of the arms was eliminated by asking subjects to keep their arms folded across their chest during stair descent. Segmental motions of the lower limb were recorded on digital video at 60 Hz. The camera was placed perpendicular to the plane of motion so that the right side was filmed during forward stair descent but the left side was filmed during backwards stair descent. Reflective markers were affixed to the iliac crest, greater trochanter, lateral condyle of the tibia, lateral malleolus, lateral calcaneus, base of the 5th-metatarsal and the hallux. Segmental positions were captured offline (Ariel Performance Analysis System), low-pass filtered (6 Hz) and time normalized over the stride cycle from footstrike (FS) on the second step to the foot-strike on the floor. Ground reaction forces were acquired (at 240 Hz) with Kistler BioWare
Fig. 1. Schematic of laboratory staircase with force platform on step two.
software and low-pass filtered with a 20 Hz cutoff. Forces were then synchronized with the segmental positions using Biomech Motion Analysis Software [22]. Inverse dynamics [15,16] computed the net moments of force and then their powers at the three joints of the lower extremity were calculated. Moments of force at the three lower extremity joints were summed to determine the support moment [17]. Each subject’s trials (5) for each condition were normalized to body mass, time normalized and ensemble averaged. Then, each subject’s ensemble average data were ensemble averaged to obtain a grand ensemble for each condition for comparisons among stair descent conditions and for contrasts with published level walking data [11]. A repeated-measures ANOVA was performed to identify differences in peak knee moments and powers during the period when the knee extensors performed negative work during midstance (label K3). This event was selected because the powers during this event were largest and it occurred at a period of stair descent where failure could result in collapse. Post hoc tests were performed by dependent-groups t-tests. In addition, to quantify the risk of slipping down the stairs, time integrals of the horizontal distances between the centres of pressure and the edge of the stair were computed for the SF and NB descents. Differences between the two groups were evaluated by a dependent-groups t-test.
3. Results Fig. 2 compares the support moments and the hip, knee and ankle moments for backwards stair descent and the two speeds of forwards stair descent compared to those reported by Winter [11] for normal-speed level walking. The moments were plotted so that extensor moments were
Table 1 Subject information Subject
Mass (kg) Height (cm) Normal forwards (NF) descent time (s) a Normal backwards (NB) descent time (s)a,b Normal backwards (NB) distance–time integral (cms) c Slow forwards (SF) distance–time integral (cms)c a b c
1
2
3
4
5
6
7
8
9
10
72.0 172 1.10 1.35 10.5 5.7
81.0 181 1.18 1.45 8.5 7.1
72.0 179 1.23 1.19 8.6 5.0
81.0 184 1.01 1.47 9.9 8.7
85.0 180 1.12 1.52 7.9 3.5
54.1 163 1.17 1.41 8.6 4.0
69.0 172 1.08 1.39 9.1 5.4
57.0 164 1.39 1.13 9.1 3.9
66.0 178 1.05 1.54 Not done Not done
65.8 168 0.98 1.05 8.1 7.5
Average duration from foot-strike of the second step to the next foot-strike of same foot (i.e., two steps). Slow forwards (SF) descent times were approximately the same as normal backwards. Average time integrals of the horizontal distance from the stair edge to the centre of pressure of the ground reaction force.
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Fig. 2. Ensemble averages of the support moments and the net moments of force for normal-speed walking, slow and normal-speed forward stair descent and normal-speed backwards stair descent. Positive moments at all joints are extensor. Errors bars for the support moment of walking indicate the 95th-percentile confidence intervals.
positive to agree with how Winter reported his data [11]. Furthermore, the abscissas were normalized as a percentage of stride duration with 0% occurring at initial foot-strike. Notice that NF and SF stair descents had average support times (stance phase times) of 65% and 64% of stride cycle, respectively, versus 59% for level walking, this despite the fact the SF descent was paced the same as NB descent. In contrast, NB stair descent had a stance phase slightly shorter than normal walking, averaging 58% of stride duration. Also shown in Fig. 2 are the 95th-percentile confidence intervals (CI) for the support moment of normal-speed, level walking as derived from Winter [11]. Notice that the support moments for the SF and NF descents both exceeded the 95th-percentile CI of level walking during the latter half of their stance phases beginning at approximately 40% of the total stride duration. In contrast, the support moment for backwards descent was less than the 95th-percentile CI during midstance and well within the 95th-percentile CI of level walking during the latter half of stance. Furthermore, NB descent exceeded the 95th-percentile CI during early stance until approximately 10% of stride duration. Fig. 3 shows the moments of force and powers of the hip, knee and ankle moments for NB, SF and NF stair descents compared to data from normal walking. In this figure, the moments were plotted using the normal right-hand rule convention. Thus, positive moments at the hip are flexor, at the knee are extensor and at the ankle are dorsiflexor.
Furthermore, the abscissas were rescaled to units of seconds based on the average stride durations for the various gait conditions. This scaling yields temporally correct kinetic histories and better illustrate the angular impulses produced by the moments of force and the works done by the moment powers. Notice also that the hip powers are scaled differently than those at the ankle and knee because of their comparatively smaller magnitudes. Labels for important bursts of power were included based on the research conducted by Winter [11]. An additional burst of ankle power, labeled A1*, was added that typically does not occur during walking. This burst of power happens during stair descent because initial-contact begins with a forefoot landing and then a drop to the heel under eccentric control by the plantar flexors. In contrast, walking usually has a heel-to-toe landing. Another burst of hip power, labeled H4, was added because it was considerably larger during forward stair descent (NF) and of similar magnitude and duration during SF descent as that for level walking. This positive power by the hip extensors causes extension of the thigh during late swing to position the thigh well in front of the body before stair/ floor landing. Such work takes place during level walking, but the amount of work done is small. Presumably, this event was not considered important enough by Winter to identify it as a major aspect of level gait; however, NF stair descent produced two to three times more power and
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Fig. 3. Comparison of normal and slow forward and backwards stair descent kinetics with normal walking. Moments (left) and powers (right) are normalized to body mass. Top graphs are for the hip, the middle graphs are for the knee and the bottom graphs are for the ankle. Positive moments at the hip are flexor; positive moments at the knee are extensor; positive moments at the ankle are dorsiflexor.
work than level gait or SF descent. NB stair descent, in contrast, required that the hip extensors perform negative work, labeled H5, to restrict the amount of flexion caused by the pendulum-like swing of the lower extremity. Probably the most important difference during NB descent as compared to NF and SF was the burst of power labeled, K3, which produced significantly reduced peak knee extensor eccentric powers (P = 0.005) even though the peak moments were not significantly different (P > 0.05). The K3 powers had the largest peak powers during normal forwards (NF) stair descent but was significantly reduced by slowing descent and going backwards down the stairs; NB having the greater reduction. This event was considered significant not only because of the high powers required but because it occurred when the knee was at maximum flexion and the
knee moments were close to their maximum levels. Thus, a failure to maintain the eccentric work done could permit collapse of the knee and a fall down the stairs. Fig. 4 presents comparisons of the moments and powers of NF and NB stair descents. The abscissae of these data are normalized to percentage of stride rather than average stride duration. Also included are the 95th-percentile confidence intervals to indicate between subject variability. The time integrals of the horizontal positions of the centres of pressure from the step edge for the SF and NB conditions are reported in Table 1. Time integrals for NF were not computed because of the larger stance durations. NB descent significantly increased the amount of distance–time that the centre of pressure stayed away from the tipping edge (P < 0.001). The larger this integral becomes the longer the centre of pressure stays away from the stair edge.
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Fig. 4. Comparison of normal-speed forwards (thin lines) and backwards (thick lines) stair descent kinetics with their 95th-percentile confidence intervals. Moments (left) and powers (right) are normalized to body mass. Top graphs are for the hip, the middle graphs are for the knee and the bottom graphs are for the ankle. Positive moments at the hip are flexor; positive moments at the knee are extensor; positive moments at the ankle are dorsiflexor. Vertical bars represent start of swing phase.
4. Discussion The purpose of this study was to investigate backwards stair descent as an alternate strategy for descending stairs. We quantified the differences in the patterns of the joint kinetics of the lower extremity to better understand the energetic and loading demands of backwards compared to forwards descent and level walking. In the following discussion, we examine whether backwards stair descent is potentially safer in terms of preventing falls from slipping or tripping. The differences in the NB support moment were due to changes mainly in the hip moment of force and to a lesser extent the ankle moment. The only differences in the knee
moments of force occurred during midstance when NB descent had smaller magnitudes than both speeds of forwards descent. The knee moments for all types of stair descent, however, consistently exceeded those achieved during level walking. Presumably, the smaller knee moments during level walking are due to the body maintaining its height above the ground instead of descending the height of two steps each movement cycle. At the hip, the most obvious difference occurred in early stance when for NB descent an extensor moment occurred that was similar to but peaked slightly later (8% of gait cycle) than that of level walking. In contrast, the forward descents (SF and NF) both recruited flexor moments that worked eccentrically to control the amount of hip extension.
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The other major difference between backwards descent and the two forward descents was the elevated level of the plantar flexor moment during early stance of NB descent. During level walking, a dorsiflexor or a very low plantar flexor moment occurs in early stance whereas stair descent requires a relatively large plantar flexor moment due to the forefoot landing rather than the typical heel-to-toe motion of level gait. The larger support moments, as compared to level walking, during late stance for SF and NF stair descent were due to higher plantar flexor moments as compared to NB descent. These plantar flexors moments were still lower by about one half of those during level walking. This reduced need for a plantar flexor moment was presumably because stair descent requires less horizontal motion than does level walking. A typical stride of level walking is much longer than the forward motion required of stair descent. In this study, the forward motion of stair descent consisted of 60 cm per stride (i.e., twice the tread length of the stairs). Stride length (i.e., two steps) in walking, of course, varies with the height of the subject but is usually in excess of 1.30 m [18] for adults. The results obtained for forward stair descent agree in most details to those of previous studies despite technical differences in stair design and force plate implementation. For instance, the support moments for NF descent matched the pattern obtained by Salsich et al. [19] and McFadyen and Winter [16] despite the differences in the riser and tread lengths (20.0 and 30.0 cm vs. McFadyen and Winter’s 22.0 and 28.0 cm and Salsich et al.’s 20.5 and 27.5 cm). Each study exhibited a double-peak pattern for stair descent with both peaks approximately equal with peak powers between 1.4 and 2.0 Nm/kg. Curiously NB descent of the current study was in closer agreement with the support moments reported during stair ascent. Typically stair ascent produces a higher initial peak greater than 2.0 Nm/kg with a lower second peak of around 1.0 Nm/kg or less [16,19]. Perhaps this is because in backwards stair descent the body faces the same way with respect to the stairs as during stair ascent. When comparing the individual moments of force that combine to form the support moment, greater differences were apparent especially about the hip moment of force. The most obvious difference between NB and both SF and NF for the hip moment was that the direction of the moment was extensor rather than flexor during the first 15% of the stride cycle (foot-strike to foot-strike). There is no agreement, however, among other published studies on the pattern of the hip moments of force during stair descent. For instance, Salsich et al. [19], Wu et al. [20] and two of McFadyen and Winter’s subjects [16] showed patterns of extensor then flexor moments during the stance phase similar to our NB descent data whereas the data from Riener et al. [21] and our NF and McFadyen and Winter’s third subject exhibited flexor moments throughout the stance phase. Such discrepancies among different subjects’ hip moments have long been recognized even for level gait where differences of
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stair design and implementation were not complicating factors. Fortunately, for comparative purposes there was much more consistency across studies for the patterns of the ankle moment during forwards stair descent. In general, the moment of force was plantar flexor throughout and had a double-peaked appearance with peaks of approximately the same magnitude. Each peak typically ranged between 0.6 and 1.5 Nm/kg. Wu et al. [20] reported the least similar pattern because their second peak was less prominent than other studies. NB stair descent, in contrast, did not have a major second peak presumably because unlike forwards stair descent the foot is flexed backwards to clear the nose (corner) of the stairs whereas during forwards stair descent the plantar flexors are required to perform work (power burst A2) to propel the foot and particularly the heel over the nose of the stairs. This may give a significant safety advantage for backwards stair descent because one of the possible mechanisms for falling down stairs is having the heel of the shoes, particularly women’s higher heels, catch on the stair nose. With backwards stair descent, the heel is unlikely to ‘‘trip’’ on the stair nose because it is already higher than the step before the foot starts to cross the nose. If anything, the toes are the part of the foot that might not clear the nose since they are the last part of the foot to clear the step. Another important factor that makes backwards stair descent less risky at inducing a fall is that shoes tend to have heights that are more variable at the heel than at the toe. Heel heights obviously vary more in women’s shoes than in men’s and therefore more care must be taken descending stairs whenever a person changes from one heel height to another. If an error occurs and the heel catches the stair nose, the person in single support with the line of gravity outside the base of support, may be unable to swing the tripped leg forward quickly enough to establish a second base of support to prevent falling. With backwards stair descent there is less variability in the height of the shoe’s toe box and therefore less likely that a trip will occur. Furthermore, because the foot lifts up and backwards (forwards with respect to the stairs), the likelihood of a trip diminishes. In addition, during backwards stair ascent most people are inclined to use a railing to provide a third support and, thus, if a fall does occur the person falls towards the stairs instead of pitching down the stairs with its consequently more severe injuries. The main purpose of the current study was to identify whether backwards stair descent significantly reduces the peak moments of force and powers required of the knee moment during the stance phase. Unexpectedly, the peak knee moments during early and late stance were not significantly different (i.e., within 95th-percentile CI) among the three descent conditions but all descents were significantly higher (>95th-percentile CI) than those experienced during level walking. In fact, during late stance the moment of force for level walking was flexor while stair descent required a second burst from the extensors to enable lowering of the body by controlled flexion at the knee. Such
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a pattern is well documented in the literature having been shown previously by Kowalk et al. [22], McFadyen and Winter [16], Salsich et al. [19] and Riener et al. [21]. Nevertheless, the most obvious difference between backwards and forwards descent occurred due to reductions in the work done and the peak power (P = 0.005) required during the phase labeled K3 in Fig. 3. This phase was a briefer percentage of the stride cycle during backwards stair descent (28–55% vs. 25–65%) and had a 45% lower peak power than NF stair descent. SF descent also reduced the peak power at K3 but by only 20% but did not decrease the duration of the power phase significantly. This phase occurs just before and during the critical single-support phase of stair descent when the knee must lower the whole body to the next step. Furthermore, although there were differences in the powers produced at H2 and H3, forwards stair descent actually reduced the effort needed by the hip flexors and so should not be considered as a factor that would make stair descent more difficult for persons with hip problems as compared with the efforts required for normal level walking. The reduction in the power and consequently the work done by the hip flexors, as mentioned previously, is due to the reduced step length that typically occurs with stair descent as compared to walking. In addition, the swing limb stays at approximately the same height before and after the swing phase in walking but in stair descent the swing limb lowers with the assistance of gravity and therefore needs less positive work. Another important consideration about backwards stair descent concerns the type of fall that may occur because of a failure of the lower extremity’s moments to maintain adequate support. In the case of forwards stair descent, it is clear that the trajectory of the torso’s centre of gravity is farther forward of the step than during backwards stair descent. In backwards stair descent, the body is lowered and than moved across the step whereas in forwards descent there is a continuous oblique path forwards and downwards. Thus, a failure during backwards descent results in a fall into the steps whereas forwards descent results in falls down the steps. The added falling distance and the possible continuation of the fall down the remainder of the stairs make a fall during forwards stair descent more serious and potentially fatal.
5. Conclusions The following conclusions primarily concern the differences between backwards stair descent, forwards stair descent and level walking based on comparisons of the patterns of the ankle, knee and hip moments of force and powers. 1. Backwards stair descent significantly reduced the peak powers produced by the knee extensors during the critical single-support phase of stair descent as compared to normal-speed and slow forwards stair descent.
2. Backwards stair descent increased the distance of the centre of pressure from the stair edge making it less likely for a slip to occur that might cause a fall. Additionally, backwards stair descent increases the foot clearance (toe and heel) during the swing phase further reducing the chance of a fall. 3. Backwards stair descent required a burst of negative work by the hip extensors during the swing phase whereas forwards stair descent required positive work by the hip extensors. 4. Backwards stair decent required almost no work by the ankle plantar flexors during the push-off phase of stair descent while forwards stair descent required small amounts of work but less work than for level walking. Backwards stair descent required a larger plantar flexor moment of force during weight acceptance.
Conflict of interest statement This study has been approved by the Ethics Committee of the University of Ottawa and is free of any conflicts of interest.
References [1] Simoneau GG, Cavanagh PR, Ulbrecht JS, Leibowitz HW, Tyrrell RA. The influence of visual factors on fall-related kinematic variables during stair descent by older women. J Gerontol Med Sci 1991;46: M188–95. [2] Andriacchi TP, Andersson GBJ, Fermier RW, Stern D, Galante JO. A study of lower-limb mechanics during stair-climbing. J Bone Joint Surg 1980;62A:749–57. [3] Nahorniak MT, Gorton GE, Gannotti ME, Masso PD. Kinematic compensations as children reciprocally ascend and descend stairs with unilateral and bilateral solid AFOs. Gait Posture 1999;9:199–206. [4] Durand A, Richards CL, Malouin F, Bravo B. Motor recovery after arthroscopic partial menisectomy: analysis of gait and the ascent of and descent of stairs. J Bone Joint Surg 1993;75:202–14. [5] Hughes C, Kaufman K, Morrey B, Morrey M, An K. Gender differences in knee kinematics and kinetics during stair climbing and level walking in adults with osteoarthritis of the knee. In: Proceedings of the 24th American Society of Biomechanics conference; 2000. [6] Thambyah A, Thiagarajan P, Hong JGC. Knee joint moments during stair climbing of patients with anterior cruciate ligament deficiency. Clin Biomech 2004;19:489–96. [7] Sparrow WA, Shinkfield AJ, Summers JJ. Gait characteristics in individuals with mental retardation: unobstructed level-walking, negotiating obstacles, and stair climbing. Human Movement Sci 1998;17:167–87. [8] Startzell JK, Owens AD, Mulfinger LM, Cavanagh PR. Stair negotiation in older people: a review. J Am Geriatrics Soc 2000;48: 567–80. [9] Wyatt JP, Beard D, Busuttil A. Fatal falls, down stairs. Injury 1999;30:31–4. [10] Asher J. Toward a safer design for stairs. Job Safety Health 1977;(September):27–32. [11] Winter DA. The biomechanics and motor control for human gait: normal, elderly and pathological. Waterloo: Waterloo Biomechanics; 1991.
F.G. D.Beaulieu et al. / Gait & Posture 27 (2008) 564–571 [12] Livingston LA, Stevenson JM, Olney SJ. Stair climbing kinematics on stairs of differing dimensions. Arch Phys Med Rehab 1991;76:398– 402. [13] McCrory JL, Gilchrist LA. Ascent kinematics on stairs of different dimensions. Med Sci Sports Exerc 2000;32(Suppl. 5):192. [14] Irvine C, Snook S, Sparshatt J. Stairway risers and treads: acceptable and preferred dimensions. Appl Ergon 1990;21: 215–25. [15] Costigan PA, Wyss UP, Deluzio KJ. Force and moment at the normal knee during stair climbing. In: Proceedings of the Third North American congress on biomechanics; 1998. [16] McFayden BJ, Winter DA. An integrated biomechanical analysis of normal stair ascent and descent. J Biomech 1988;21: 733–44. [17] Winter DA. Overall principle of lower limb support during stance phase of gait. J Biomech 1980;13:923–7. [18] Kirtley C. Clinical gait analysis. Toronto: Churchill Livingstone; 2006 .
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[19] Salsich GB, Brecter JH, Powers CM. Lower extremity kinetics during stair ambulation in patients with and without patellofemoral pain. Clin Biomech 2001;16:906–12. [20] Wu W-L, Huang P-J, Lin C-J, Chen W-Y, Huang K-F, Cheng Y-M. Lower extremity kinematics and kinetics during level walking and stair climbing with triple arthrodesis or subtalar fusion. Gait Posture 2005;21:263–70. [21] Riener R, Rabuffetti M, Frigo C. Stair ascent and descent at different inclinations. Gait Posture 2002;15:32–44. [22] Kowalk DL, Duncan JA, Vaughan CL. Abduction–adduction moments at the knee during stair ascent and descent. J Biomech 1996;29:383–8.
Internet link [23] http://www.health.uottawa.ca/biomech/csb/software/biomech.htm.
Kinetic analysis of forwards and backwards stair descent Franc¸ois G. D.Beaulieu a, Lucie Pelland b, D. Gordon E. Robertson a,* a
School of Human Kinetics, University of Ottawa, Ottawa, Ontario, Canada b School of Rehabilitation Therapy, Queen’s University, Kingston, Canada
Received 3 June 2006; received in revised form 24 June 2007; accepted 13 July 2007
Abstract The activity of descending stairs increases loading at the joints of the lower extremities as compared to walking, which may cause discomfort and or difficulties in completing the task. This study compared and contrasted the kinematics and kinetics of both forwards and backwards stair descent to those of level walking. We compared the support moments and moment powers of the lower limb joints while descending stairs forwards at a self-selected pace, backwards at a self-selected pace and forwards at the same pace as backwards. Participants were 10 healthy young adults (6 men and 4 women) aged 20–35 years. Sagittal plane kinematics and ground reaction forces were collected and moments of force computed using inverse dynamics. The ratio of stance/swing phase changed from 59:41 for normal level walking to between 65:35 and 70:30 for forward stair descent but backwards descent was 58:42. Stair descent produced larger doublepeak support moments with reduced ankle plantar flexor and increased knee extensor moments as compared to level walking (>95thpercentile confidence interval). The hip moments during stair descent were relatively small and highly variable. We observed significantly larger distances between the centres of pressure and the stair edges for backwards stair descent versus forwards stair descent. These results demonstrate that stair descent, even at a slower pace, requires greater power from the knee extensors than level walking but that backwards stair descent significantly reduced the peak knee power during midstance and provided a potentially safer means of descending stairs than forwards stair descent. # 2007 Elsevier B.V. All rights reserved. Keywords: Gait; Mechanical power; Support moment; Inverse dynamics; Falls
1. Introduction Daily, we encounter stairs at the workplace, during leisure activities, pedestrian travel and at home. For those with muscle weakness or joint dysfunction, such as arthritis, ascending and particularly descending stairs can be a difficult, risky and painful task. One solution that occasional long-distance runners and athletes use to deal with the difficulty of descending stairs after heavy exercise is to descend them backwards. Backwards stair descent is also commonly used when stairs are very steep such as on ladders or ships where forward descent can easily result in a fall. * Corresponding author. Tel.: +1 613 562 5800x4253; fax: +1 613 562 5149. E-mail addresses: [email protected] (F.G. D.Beaulieu), [email protected] (L. Pelland), [email protected] (D.G.E. Robertson). 0966-6362/$ – see front matter # 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.gaitpost.2007.07.010
Falls on stairs are a leading cause of accidental deaths and of morbidity [1] and have therefore attracted attention concerning injury prevention [2,3]. Backwards stair descent may offer a less stressful and safer means of descending stairs under certain circumstances. Since stairs are an integral part of our societal architecture, the ability to manage stairs in a safe and independent fashion is important. For people injured [4] or physically [1,5,6] or cognitively impaired [7] and for the elderly [8,9], stair descent can be strenuous, painful and even dangerous [10]. Suitable strategies should therefore be available to permit safe and comfortable stair descent. The purpose of this study was to investigate backwards stair descent as an alternate strategy for descending stairs. We wanted to quantify the differences in the patterns of the joint kinetics of the lower extremity to better understand the energetic and loading demands of backwards compared to forwards descent and level walking. We will use the data
F.G. D.Beaulieu et al. / Gait & Posture 27 (2008) 564–571
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compiled and reported by Winter [11] for comparisons with level walking. Furthermore, we wished to examine whether backwards stair descent was potentially safer in terms of preventing falls caused by being too close to the stair edge.
2. Methods Lower extremity mechanics during forward and backward stair descent were analyzed for 10 able-bodied subjects 20–35 years old (6 males and 4 females). Prior research on stair climbing has demonstrated the effects of leg length on lower extremity mechanics [5,7,12,13] and as such, a stratified recruitment approach was used to ensure a range of heights in our subject group from 165 to 184 cm (see Table 1 for relevant subject information). A questionnaire screened subjects to exclude people with histories of lower extremity joint and muscle impairment. Prior to data recording, subjects provided written informed consent as approved by the responsible ethics committee. Subjects completed blocks of five stair descent trials under three experimental conditions: forward stair descent at self-selected speed (NF), backward stair descent at self-selected speed (NB) and slower forward stair descent at the same speed as each subject’s backward stair descent (SF). External pacing by metronome ensured that speed of descent remained constant within conditions. Stair descent trials were completed on a three-step laboratory staircase (Fig. 1), with step dimensions: 20 cm riser and 30 cm tread [10,12–14]. Subjects started at the landing at the top of the staircase and stepped down onto a force platform (Kistler model 9281C) on the first step. The contralateral leg, which was not analyzed, stepped down to the second step, followed by the ipsilateral leg stepping down to floor level. Subjects continued walking at floor level. The contribution of the arms was eliminated by asking subjects to keep their arms folded across their chest during stair descent. Segmental motions of the lower limb were recorded on digital video at 60 Hz. The camera was placed perpendicular to the plane of motion so that the right side was filmed during forward stair descent but the left side was filmed during backwards stair descent. Reflective markers were affixed to the iliac crest, greater trochanter, lateral condyle of the tibia, lateral malleolus, lateral calcaneus, base of the 5th-metatarsal and the hallux. Segmental positions were captured offline (Ariel Performance Analysis System), low-pass filtered (6 Hz) and time normalized over the stride cycle from footstrike (FS) on the second step to the foot-strike on the floor. Ground reaction forces were acquired (at 240 Hz) with Kistler BioWare
Fig. 1. Schematic of laboratory staircase with force platform on step two.
software and low-pass filtered with a 20 Hz cutoff. Forces were then synchronized with the segmental positions using Biomech Motion Analysis Software [22]. Inverse dynamics [15,16] computed the net moments of force and then their powers at the three joints of the lower extremity were calculated. Moments of force at the three lower extremity joints were summed to determine the support moment [17]. Each subject’s trials (5) for each condition were normalized to body mass, time normalized and ensemble averaged. Then, each subject’s ensemble average data were ensemble averaged to obtain a grand ensemble for each condition for comparisons among stair descent conditions and for contrasts with published level walking data [11]. A repeated-measures ANOVA was performed to identify differences in peak knee moments and powers during the period when the knee extensors performed negative work during midstance (label K3). This event was selected because the powers during this event were largest and it occurred at a period of stair descent where failure could result in collapse. Post hoc tests were performed by dependent-groups t-tests. In addition, to quantify the risk of slipping down the stairs, time integrals of the horizontal distances between the centres of pressure and the edge of the stair were computed for the SF and NB descents. Differences between the two groups were evaluated by a dependent-groups t-test.
3. Results Fig. 2 compares the support moments and the hip, knee and ankle moments for backwards stair descent and the two speeds of forwards stair descent compared to those reported by Winter [11] for normal-speed level walking. The moments were plotted so that extensor moments were
Table 1 Subject information Subject
Mass (kg) Height (cm) Normal forwards (NF) descent time (s) a Normal backwards (NB) descent time (s)a,b Normal backwards (NB) distance–time integral (cms) c Slow forwards (SF) distance–time integral (cms)c a b c
1
2
3
4
5
6
7
8
9
10
72.0 172 1.10 1.35 10.5 5.7
81.0 181 1.18 1.45 8.5 7.1
72.0 179 1.23 1.19 8.6 5.0
81.0 184 1.01 1.47 9.9 8.7
85.0 180 1.12 1.52 7.9 3.5
54.1 163 1.17 1.41 8.6 4.0
69.0 172 1.08 1.39 9.1 5.4
57.0 164 1.39 1.13 9.1 3.9
66.0 178 1.05 1.54 Not done Not done
65.8 168 0.98 1.05 8.1 7.5
Average duration from foot-strike of the second step to the next foot-strike of same foot (i.e., two steps). Slow forwards (SF) descent times were approximately the same as normal backwards. Average time integrals of the horizontal distance from the stair edge to the centre of pressure of the ground reaction force.
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Fig. 2. Ensemble averages of the support moments and the net moments of force for normal-speed walking, slow and normal-speed forward stair descent and normal-speed backwards stair descent. Positive moments at all joints are extensor. Errors bars for the support moment of walking indicate the 95th-percentile confidence intervals.
positive to agree with how Winter reported his data [11]. Furthermore, the abscissas were normalized as a percentage of stride duration with 0% occurring at initial foot-strike. Notice that NF and SF stair descents had average support times (stance phase times) of 65% and 64% of stride cycle, respectively, versus 59% for level walking, this despite the fact the SF descent was paced the same as NB descent. In contrast, NB stair descent had a stance phase slightly shorter than normal walking, averaging 58% of stride duration. Also shown in Fig. 2 are the 95th-percentile confidence intervals (CI) for the support moment of normal-speed, level walking as derived from Winter [11]. Notice that the support moments for the SF and NF descents both exceeded the 95th-percentile CI of level walking during the latter half of their stance phases beginning at approximately 40% of the total stride duration. In contrast, the support moment for backwards descent was less than the 95th-percentile CI during midstance and well within the 95th-percentile CI of level walking during the latter half of stance. Furthermore, NB descent exceeded the 95th-percentile CI during early stance until approximately 10% of stride duration. Fig. 3 shows the moments of force and powers of the hip, knee and ankle moments for NB, SF and NF stair descents compared to data from normal walking. In this figure, the moments were plotted using the normal right-hand rule convention. Thus, positive moments at the hip are flexor, at the knee are extensor and at the ankle are dorsiflexor.
Furthermore, the abscissas were rescaled to units of seconds based on the average stride durations for the various gait conditions. This scaling yields temporally correct kinetic histories and better illustrate the angular impulses produced by the moments of force and the works done by the moment powers. Notice also that the hip powers are scaled differently than those at the ankle and knee because of their comparatively smaller magnitudes. Labels for important bursts of power were included based on the research conducted by Winter [11]. An additional burst of ankle power, labeled A1*, was added that typically does not occur during walking. This burst of power happens during stair descent because initial-contact begins with a forefoot landing and then a drop to the heel under eccentric control by the plantar flexors. In contrast, walking usually has a heel-to-toe landing. Another burst of hip power, labeled H4, was added because it was considerably larger during forward stair descent (NF) and of similar magnitude and duration during SF descent as that for level walking. This positive power by the hip extensors causes extension of the thigh during late swing to position the thigh well in front of the body before stair/ floor landing. Such work takes place during level walking, but the amount of work done is small. Presumably, this event was not considered important enough by Winter to identify it as a major aspect of level gait; however, NF stair descent produced two to three times more power and
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Fig. 3. Comparison of normal and slow forward and backwards stair descent kinetics with normal walking. Moments (left) and powers (right) are normalized to body mass. Top graphs are for the hip, the middle graphs are for the knee and the bottom graphs are for the ankle. Positive moments at the hip are flexor; positive moments at the knee are extensor; positive moments at the ankle are dorsiflexor.
work than level gait or SF descent. NB stair descent, in contrast, required that the hip extensors perform negative work, labeled H5, to restrict the amount of flexion caused by the pendulum-like swing of the lower extremity. Probably the most important difference during NB descent as compared to NF and SF was the burst of power labeled, K3, which produced significantly reduced peak knee extensor eccentric powers (P = 0.005) even though the peak moments were not significantly different (P > 0.05). The K3 powers had the largest peak powers during normal forwards (NF) stair descent but was significantly reduced by slowing descent and going backwards down the stairs; NB having the greater reduction. This event was considered significant not only because of the high powers required but because it occurred when the knee was at maximum flexion and the
knee moments were close to their maximum levels. Thus, a failure to maintain the eccentric work done could permit collapse of the knee and a fall down the stairs. Fig. 4 presents comparisons of the moments and powers of NF and NB stair descents. The abscissae of these data are normalized to percentage of stride rather than average stride duration. Also included are the 95th-percentile confidence intervals to indicate between subject variability. The time integrals of the horizontal positions of the centres of pressure from the step edge for the SF and NB conditions are reported in Table 1. Time integrals for NF were not computed because of the larger stance durations. NB descent significantly increased the amount of distance–time that the centre of pressure stayed away from the tipping edge (P < 0.001). The larger this integral becomes the longer the centre of pressure stays away from the stair edge.
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Fig. 4. Comparison of normal-speed forwards (thin lines) and backwards (thick lines) stair descent kinetics with their 95th-percentile confidence intervals. Moments (left) and powers (right) are normalized to body mass. Top graphs are for the hip, the middle graphs are for the knee and the bottom graphs are for the ankle. Positive moments at the hip are flexor; positive moments at the knee are extensor; positive moments at the ankle are dorsiflexor. Vertical bars represent start of swing phase.
4. Discussion The purpose of this study was to investigate backwards stair descent as an alternate strategy for descending stairs. We quantified the differences in the patterns of the joint kinetics of the lower extremity to better understand the energetic and loading demands of backwards compared to forwards descent and level walking. In the following discussion, we examine whether backwards stair descent is potentially safer in terms of preventing falls from slipping or tripping. The differences in the NB support moment were due to changes mainly in the hip moment of force and to a lesser extent the ankle moment. The only differences in the knee
moments of force occurred during midstance when NB descent had smaller magnitudes than both speeds of forwards descent. The knee moments for all types of stair descent, however, consistently exceeded those achieved during level walking. Presumably, the smaller knee moments during level walking are due to the body maintaining its height above the ground instead of descending the height of two steps each movement cycle. At the hip, the most obvious difference occurred in early stance when for NB descent an extensor moment occurred that was similar to but peaked slightly later (8% of gait cycle) than that of level walking. In contrast, the forward descents (SF and NF) both recruited flexor moments that worked eccentrically to control the amount of hip extension.
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The other major difference between backwards descent and the two forward descents was the elevated level of the plantar flexor moment during early stance of NB descent. During level walking, a dorsiflexor or a very low plantar flexor moment occurs in early stance whereas stair descent requires a relatively large plantar flexor moment due to the forefoot landing rather than the typical heel-to-toe motion of level gait. The larger support moments, as compared to level walking, during late stance for SF and NF stair descent were due to higher plantar flexor moments as compared to NB descent. These plantar flexors moments were still lower by about one half of those during level walking. This reduced need for a plantar flexor moment was presumably because stair descent requires less horizontal motion than does level walking. A typical stride of level walking is much longer than the forward motion required of stair descent. In this study, the forward motion of stair descent consisted of 60 cm per stride (i.e., twice the tread length of the stairs). Stride length (i.e., two steps) in walking, of course, varies with the height of the subject but is usually in excess of 1.30 m [18] for adults. The results obtained for forward stair descent agree in most details to those of previous studies despite technical differences in stair design and force plate implementation. For instance, the support moments for NF descent matched the pattern obtained by Salsich et al. [19] and McFadyen and Winter [16] despite the differences in the riser and tread lengths (20.0 and 30.0 cm vs. McFadyen and Winter’s 22.0 and 28.0 cm and Salsich et al.’s 20.5 and 27.5 cm). Each study exhibited a double-peak pattern for stair descent with both peaks approximately equal with peak powers between 1.4 and 2.0 Nm/kg. Curiously NB descent of the current study was in closer agreement with the support moments reported during stair ascent. Typically stair ascent produces a higher initial peak greater than 2.0 Nm/kg with a lower second peak of around 1.0 Nm/kg or less [16,19]. Perhaps this is because in backwards stair descent the body faces the same way with respect to the stairs as during stair ascent. When comparing the individual moments of force that combine to form the support moment, greater differences were apparent especially about the hip moment of force. The most obvious difference between NB and both SF and NF for the hip moment was that the direction of the moment was extensor rather than flexor during the first 15% of the stride cycle (foot-strike to foot-strike). There is no agreement, however, among other published studies on the pattern of the hip moments of force during stair descent. For instance, Salsich et al. [19], Wu et al. [20] and two of McFadyen and Winter’s subjects [16] showed patterns of extensor then flexor moments during the stance phase similar to our NB descent data whereas the data from Riener et al. [21] and our NF and McFadyen and Winter’s third subject exhibited flexor moments throughout the stance phase. Such discrepancies among different subjects’ hip moments have long been recognized even for level gait where differences of
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stair design and implementation were not complicating factors. Fortunately, for comparative purposes there was much more consistency across studies for the patterns of the ankle moment during forwards stair descent. In general, the moment of force was plantar flexor throughout and had a double-peaked appearance with peaks of approximately the same magnitude. Each peak typically ranged between 0.6 and 1.5 Nm/kg. Wu et al. [20] reported the least similar pattern because their second peak was less prominent than other studies. NB stair descent, in contrast, did not have a major second peak presumably because unlike forwards stair descent the foot is flexed backwards to clear the nose (corner) of the stairs whereas during forwards stair descent the plantar flexors are required to perform work (power burst A2) to propel the foot and particularly the heel over the nose of the stairs. This may give a significant safety advantage for backwards stair descent because one of the possible mechanisms for falling down stairs is having the heel of the shoes, particularly women’s higher heels, catch on the stair nose. With backwards stair descent, the heel is unlikely to ‘‘trip’’ on the stair nose because it is already higher than the step before the foot starts to cross the nose. If anything, the toes are the part of the foot that might not clear the nose since they are the last part of the foot to clear the step. Another important factor that makes backwards stair descent less risky at inducing a fall is that shoes tend to have heights that are more variable at the heel than at the toe. Heel heights obviously vary more in women’s shoes than in men’s and therefore more care must be taken descending stairs whenever a person changes from one heel height to another. If an error occurs and the heel catches the stair nose, the person in single support with the line of gravity outside the base of support, may be unable to swing the tripped leg forward quickly enough to establish a second base of support to prevent falling. With backwards stair descent there is less variability in the height of the shoe’s toe box and therefore less likely that a trip will occur. Furthermore, because the foot lifts up and backwards (forwards with respect to the stairs), the likelihood of a trip diminishes. In addition, during backwards stair ascent most people are inclined to use a railing to provide a third support and, thus, if a fall does occur the person falls towards the stairs instead of pitching down the stairs with its consequently more severe injuries. The main purpose of the current study was to identify whether backwards stair descent significantly reduces the peak moments of force and powers required of the knee moment during the stance phase. Unexpectedly, the peak knee moments during early and late stance were not significantly different (i.e., within 95th-percentile CI) among the three descent conditions but all descents were significantly higher (>95th-percentile CI) than those experienced during level walking. In fact, during late stance the moment of force for level walking was flexor while stair descent required a second burst from the extensors to enable lowering of the body by controlled flexion at the knee. Such
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a pattern is well documented in the literature having been shown previously by Kowalk et al. [22], McFadyen and Winter [16], Salsich et al. [19] and Riener et al. [21]. Nevertheless, the most obvious difference between backwards and forwards descent occurred due to reductions in the work done and the peak power (P = 0.005) required during the phase labeled K3 in Fig. 3. This phase was a briefer percentage of the stride cycle during backwards stair descent (28–55% vs. 25–65%) and had a 45% lower peak power than NF stair descent. SF descent also reduced the peak power at K3 but by only 20% but did not decrease the duration of the power phase significantly. This phase occurs just before and during the critical single-support phase of stair descent when the knee must lower the whole body to the next step. Furthermore, although there were differences in the powers produced at H2 and H3, forwards stair descent actually reduced the effort needed by the hip flexors and so should not be considered as a factor that would make stair descent more difficult for persons with hip problems as compared with the efforts required for normal level walking. The reduction in the power and consequently the work done by the hip flexors, as mentioned previously, is due to the reduced step length that typically occurs with stair descent as compared to walking. In addition, the swing limb stays at approximately the same height before and after the swing phase in walking but in stair descent the swing limb lowers with the assistance of gravity and therefore needs less positive work. Another important consideration about backwards stair descent concerns the type of fall that may occur because of a failure of the lower extremity’s moments to maintain adequate support. In the case of forwards stair descent, it is clear that the trajectory of the torso’s centre of gravity is farther forward of the step than during backwards stair descent. In backwards stair descent, the body is lowered and than moved across the step whereas in forwards descent there is a continuous oblique path forwards and downwards. Thus, a failure during backwards descent results in a fall into the steps whereas forwards descent results in falls down the steps. The added falling distance and the possible continuation of the fall down the remainder of the stairs make a fall during forwards stair descent more serious and potentially fatal.
5. Conclusions The following conclusions primarily concern the differences between backwards stair descent, forwards stair descent and level walking based on comparisons of the patterns of the ankle, knee and hip moments of force and powers. 1. Backwards stair descent significantly reduced the peak powers produced by the knee extensors during the critical single-support phase of stair descent as compared to normal-speed and slow forwards stair descent.
2. Backwards stair descent increased the distance of the centre of pressure from the stair edge making it less likely for a slip to occur that might cause a fall. Additionally, backwards stair descent increases the foot clearance (toe and heel) during the swing phase further reducing the chance of a fall. 3. Backwards stair descent required a burst of negative work by the hip extensors during the swing phase whereas forwards stair descent required positive work by the hip extensors. 4. Backwards stair decent required almost no work by the ankle plantar flexors during the push-off phase of stair descent while forwards stair descent required small amounts of work but less work than for level walking. Backwards stair descent required a larger plantar flexor moment of force during weight acceptance.
Conflict of interest statement This study has been approved by the Ethics Committee of the University of Ottawa and is free of any conflicts of interest.
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Internet link [23] http://www.health.uottawa.ca/biomech/csb/software/biomech.htm.