Gait & Posture 39 (2014) 728–732
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Dynamic stability and steering control following a sport-induced concussion Kaley C. Powers, Jayne M. Kalmar, Michael E. Cinelli * Department of Kinesiology and Physical Education, Wilfrid Laurier University Waterloo, ON, Canada
A R T I C L E I N F O
A B S T R A C T
Article history: Received 3 May 2013 Received in revised form 3 October 2013 Accepted 8 October 2013
Loss of balance control is one of the cardinal symptoms following a concussion; however, the ability to detect the duration of these balance impairments seems to largely depend on task type and complexity. Typical balance assessment tools are simplistic and do not challenge dynamic balance control. Changing direction represents an internal perturbation that challenges the balance control system. The purpose of this study was to examine the effects of a concussion on dynamic stability and steering control. Nine male intercollegiate North American football players who experienced a concussion (CONC) were tested during the symptomatic phase (acute) and again once they had been cleared to return to play (RTP) while the controls (age- and position-matched teammates) were tested at a single time point coinciding with the acute phase testing of their matched injured player. All participants performed a steering task, requiring them to walk straight or turn in the direction of a visual cue located either 608 or 458 to the left or right of the centre line. CONC demonstrated increased swing time variability, segmental re-orientation variability, and the amount of time it took the centre of mass to reach the minimum lateral dynamic stability margin. These results suggest that CONC were more unstable and adopted a conservative gait strategy. Differences in the variability measures persisted even after the athlete was cleared to RTP. Overall, the findings reveal that intercollegiate football players with concussions have difficulty controlling temporal characteristics of gait, which cause dynamic instability to persist even at RTP. ß 2013 Elsevier B.V. All rights reserved.
Keywords: Concussion Dynamic balance control Steering Temporal variability
1. Introduction It is estimated that 1.6–3.8 million concussions occur annually in the United States alone [1], presenting with a variable range of symptoms. The variability in the signs and symptoms of concussion poses the greatest challenge to clinicians and therapists who diagnose, monitor, and manage the injury. Compared to other symptoms, poor balance control is fairly consistently observed immediately following the injury [2]; however, the ability to detect the duration of impaired balance appears to vary based on the task and the sensitivity of the measures used to assess performance. Static stability, for instance, recovers within 3–5 days using the balance error scoring system (BESS) [2], yet differences in centre of pressure (COP) velocity and displacement are still observed greater than 15 days post-injury [3–5]. If static stability tasks demonstrate balance impairments post-concussion then a dynamic task
* Corresponding author at: Department of Kinesiology and Physical Education, Wilfrid Laurier University, 75 University Ave, W. Rm. 501 Waterloo, ON, Canada. Tel.: +1 519 884 0710; fax: +1 519 747 4594. E-mail addresses:
[email protected],
[email protected] (M.E. Cinelli). 0966-6362/$ – see front matter ß 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.gaitpost.2013.10.005
should theoretically challenge the balance control system to a greater extent. Previous research assessing dynamic stability control has frequently employed a dual-task paradigm, with individuals experiencing a concussion (CONC) simultaneously performing a gait and cognitive task [6,7]. The increased attentional demands of the cognitive task results in altered or compromised gait stability [8]. Compromised gait stability causes CONC to adopt a conservative gait strategy by reducing speed to better control centre of mass (COM) movement [9,10]. Conservative gait during a dual-task paradigm has been demonstrated to persist up to 28 days following a concussion [6]. Obstacle avoidance tasks following a concussion have also elicited differences in performance as a result of changes in stability. For instance, CONC increase trailing limb toe clearance during obstacle clearance [11] and have smaller clearance distances during obstacle circumvention [12]. However, the effect of changes in stability following a concussion during an internal perturbation, such as a steering task, in the absence of an explicit secondary cognitive task still remains unknown. Therefore, the purpose of the current study was twofold: (1) to examine the effect of an internal perturbation (change-indirection) on dynamic stability in a population with symptomatic concussions; and (2) to determine if these effects persisted when
K.C. Powers et al. / Gait & Posture 39 (2014) 728–732
the athletes were asymptomatic and cleared to return to play (RTP). It was hypothesized that CONC would demonstrate conservative gait as a result of failing to adequately control the relationship between their COM and base of support (BOS) during the task. Furthermore, CONC would exhibit atypical patterns of segmental re-orientation. These changes in the acute phase were expected to still be present once the athlete was cleared to return to sport as current assessments are not sensitive enough to detect these subclinical deficits. 2. Methods 2.1. Participants Nine male intercollegiate North American football players who experienced a concussion (CONC) were evaluated using the SCAT2 and recruited for participation in the study by the team’s Certified Athletic Therapist. CONC were age- and position-matched (Table 1A) with nine healthy players from the same team who served as controls (CONT) (Table 1B). Exclusion criteria for all participants were any medications or injury that would affect normal stability or gait. A concussion in the previous 12 months was an additional exclusion criterion for controls to avoid lingering deficits from previous concussions. Ideally, all participants would have no prior history of concussions but that would not be representative of the sporting environment and difficult to achieve following a single team for one season. Participants provided written informed consent to participate in this study that was approved by the Institutional Research Ethics Board. 2.2. Experimental design Participants with concussions were tested during their symptomatic (CONCacute) phase and then again following clearance to RTP (CONCRTP) by the Certified Athletic Therapist (Table 1A). Controls were tested at a single time point within five days of the date when their concussed counterpart was tested in the symptomatic (acute) phase. All participants completed a health history questionnaire that included the SCAT2 symptom evaluation checklist on each testing day. The SCAT2 symptom evaluation checklist asked participants to rate the severity of 22-listed symptoms on a scale from 0 (none) to 6 (severe). 2.3. Experimental set-up Kinematic data was collected using the OptoTrak camera system (Northern Digital Inc., Waterloo, ON, Canada) at a sampling frequency of 60 Hz. Participants were outfitted with five rigid bodies, each containing three infrared emitting diodes (IREDs) and one additional IRED marker on each heel. Rigid bodies were placed on the following locations: back of the head, upper torso, lower
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back and one on the posterior surfaces of each lower leg. Rigid bodies were used as reference points for seventeen digitized landmarks on the body: right and left ears, glenohumeral joints, posterior superior iliac spines of the pelvis, greater trochanter of femurs, tibiofemoral joints, anterior ankles, fifth metatarsals, heels and one point on the T12 vertebra. 2.4. Experimental protocol Participants were instructed to walk from a marked starting position at a self-selected comfortable pace towards a trigger mat located on the floor 2.65 m away. The starting foot and the foot that struck the trigger mat were noted and remained consistent for all trials and between days for players with concussions. Participants were informed that upon striking the trigger mat, one of four lights (608 left, 458 left, 458 right, 608 right) would illuminate and they were to take two additional steps after the trigger before steering in the direction of the light. Additionally, if no light turned on, they were instructed to continue walking straight (Fig. 1). Participants completed a total of eighteen trials; three baseline (straightwalking) trials and fifteen experimental trials. The trials were organized into three blocks, containing one trial from each of the five possible directions in a randomized order, to ensure that if a participant needed to stop early due to symptoms each direction would be collected at least once; however, this was not an issue as all participants completed eighteen trials. 2.5. Data analysis Since each participant was free to step on the trigger consistently with either foot, turn directions were classified as: step narrow 608, step narrow 458, step wide 608, step wide 458 or straight to allow comparison between individuals. For example, if a participant stepped on the mat with their left foot and triggered a right light to turn on, upon taking two additional steps, they would initiate the right turn with a wide step. Conversely, if a left light had turned on, the turn would be initiated by taking a narrow (or cross-over) step. Additionally, for certain measures, the task was segmented into three phases: approach (from start to the trigger mat), postural adjustment (from trigger mat to onset of turn) and turn. Variables of interest during the approach phase were traditional gait parameters (step length, step width, and gait velocity), trunk roll angle and swing time variability (coefficient of variation). Centre of Mass (COM) was calculated using a modified version of Winter’s [13] weighted average of the 17 digitized points. The minimum lateral dynamic stability margin (DSMmin) and time to reach the DSMmin were calculated across all phases (approach, postural adjustment and turn). DSMmin was calculated as the minimum distance between the medial–lateral (M–L) position of the COM and the lateral border of the BOS (5th metatarsal) during
Table 1A Participants with concussions demographic and concussion history information. Participant
Age (years)
# previous concussions
Days since concussion (acute)
SCAT2 symptom score (acute)
Days since concussion (RTP)
SCAT2 symptom score (RTP)
1 2 3 4 5 6 7 8 9
19.66 20.75 19.29 20.35 22.02 19.41 21.48 20.44 18.12
0 0 0 1 1 0 2 2 0
1 8 13 11 3 3 4 4 1
37 4 67 44 5 29 21 51 56
15 34 41 34 11 10 30 48 15
0 0 5 1 1 0 0 4 0
Average
20.17
0.67
34.89
26.44
1.22
5.33
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Table 1B Control participants demographic and concussion history information. Participant
Age (years)
# previous concussions
Time since last concussion (years)
SCAT2 symptom score
1 2 3 4 5 6 7 8 9
18.77 19.28 18.93 21.63 20.21 20.7 19.76 23.41 19.84
0 1 0 4 3 0 0 0 1
– 2 – 3 1 – – – 5
0 0 0 28 0 1 0 0 6
Average
20.28
1
2.75
single support (similar to [20]). The DSMmin was chosen because it represented the point at which the centre of pressure (COP) repels the COM forward in order for the next step to occur. The time to reach DSMmin was calculated as the DSMmin distance divided by the lateral velocity of the COM at the first instant of single support. During the postural adjustment phase, segmental re-orientation along the vertical axis (yaw) was measured. Segmental reorientation was defined as the difference between trunk rotation onset and head rotation onset during the four turn conditions only. Rotation onset of both segments was defined as the time when rotation of the segment was greater than three standard deviations of the mean during straight walking. Standard deviation of segmental re-orientation across three trials was defined as segmental re-orientation variability. 2.6. Statistical analysis Statistical analyses were performed using Statistica 6.0 (StatSoft Inc., Tulsa, OK). Initial analyses compared the CONC during the acute phase to the controls and only the dependent measures that produced significant group differences were used to compare the CONC at RTP to control group. This was done to determine if the dependent measure had recovered at the time
Fig. 1. Experimental set-up of steering control task, separated into phases for data analysis. Participants walked straight during the approach phase and upon stepping on the trigger, one of four lights illuminated. In the two additional steps following the trigger mat (postural adjustment phase) participants planned to turn. In the turn phase, they steered in the direction of the light or continued walking straight if no light illuminated. Refer to methods section for more detail.
3.89
of RTP. Separate repeated measures factorial ANOVAs (5 directions 2 groups) were performed for each traditional gait parameter, as well as trunk roll angle and swing time variability. Repeated measures factorial ANOVAs were performed on the average segmental re-orientation onsets (4 directions 2 groups), segmental re-orientation variability (4 directions 2 groups), DSMmin (5 directions 2 groups) and time to DSMmin (5 directions 2 groups). Tukey’s HSD post hoc analysis was used to detect differences between means when significant (p < 0.05) main effects or interactions were identified. Effect sizes were calculated for significant group effects and expressed as Cohen’s d. Data are presented as mean standard deviation. 3. Results 3.1. Traditional gait parameters In the acute (symptomatic) phase following a concussion, no significant group, steering direction or interaction effects in step length (CONCacute: 62.35 6.71 cm, CONT: 60.15 5.97 cm), step width (CONCacute: 18.43 2.65 cm, CONT: 15.73 5.09 cm), gait velocity (CONCacute: 102.32 15.08 cm/s, CONT: 100.35 10.77 cm/ s), and trunk roll angle (CONCacute: 8.99 3.948, CONT: 7.85 2.868) were observed. However, swing-time variability was significantly greater in CONCacute compared to CONT (F(1,16) = 8.88, p = 0.009, Cohen’s d = 1.40). At return-to-play (asymptomatic), CONCRTP still demonstrated increased variability (F(1,16) = 10.41, p = 0.005, Cohen’s d = 1.52) compared to CONT (Fig. 2).
Fig. 2. Swing time variability (mean coefficient of variation) for the concussed group at two time-points: acute and return to play (RTP) and the healthy matched control group. *Denotes significantly greater than the control group (p < 0.05).
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3.2. Minimum lateral dynamic stability margin (DSMmin) The average DSMmin was not significantly different between the CONCacute and the CONT groups. Steering direction revealed a significant main effect (F(4,64) = 32.78, p < 0.0001), with the largest DSMmin occurring during the straight condition (10.34 2.32 cm). There was no interaction effect between group and steering direction. 3.3. Time to reach DSMmin Significant main effects of group (F(1,16) = 5.95, p = 0.027, Cohen’s d = 1.15) (Fig. 3) and steering direction (F(4,64) = 6.87, p < 0.001) were found with CONCacute displaying a longer time to reach the DSMmin (0.097 0.060 s) than CONT (0.071 0.022 s). Step wide 458 (0.098 0.087 s) and straight directions (0.098 0.030 s) had significantly longer times to reach DSMmin than step narrow 608 (0.070 0.022 s) and step narrow 458 (0.070 0.024 s). The CONCRTP did not have significantly different time to reach DSMmin than the CONT group (Fig. 3), implying that this variable had recovered while the same main effect of steering direction (F(4,64) = 19.28, p < 0.001) remained significant. Additionally, in both the acute and RTP phases, there were no interaction effects. 3.4. Segmental re-orientation No significant group or interaction effects in the acute phase were demonstrated for segmental re-orientation; however, a significant main effect of steering direction on segmental reorientation (F(3,48) = 3.06, p = 0.037) was found with step wide 608 having the longest segmental re-orientation latency (0.527 0.044 s) compared to all other turn directions. A significant main effect of group only (F(1,16) = 8.77, p = 0.009, Cohen’s d = 1.40) was observed in the segmental re-orientation variability with CONCacute being much more variable than CONT. This deficit remained at RTP (F(1,16) = 8.71, p = 0.009, Cohen’s d = 1.56), with CONCRTP being more variable than CONT (Fig. 4). 4. Discussion The purpose of this study was to determine the effects of a sport-induced (North American football) concussion during the symptomatic and asymptomatic phases on dynamic stability while performing a steering task. For persons with concussions who already demonstrate balance problems, it was hypothesized that
Fig. 3. Time centre of mass took to reach the lateral minimum dynamic stability margin for the concussed group at two time-points: acute and return to play (RTP) and the healthy matched control group (mean standard error). *Denotes significantly greater than control group (p < 0.05).
Fig. 4. Segmental re-orientation variability (mean standard deviation) for the concussed group at two time-points: acute and return to play (RTP) and the healthy matched control group. *Denotes significantly greater than controls (p < 0.05).
changes in direction would provide internal perturbations to the balance control system [14] and exacerbate the individuals’ balance problems. Previous research has demonstrated that individuals with concussions adopt a conservative gait strategy in order to maintain dynamic stability [7,8]. This is typically observed as a decrease in stride length and a subsequent reduction in anterior-posterior velocity. The lack of group differences in stride length and gait velocity could be explained by the homogenous sample of athletes. Parker and colleagues [9] reported that high-impact sport athletes (such as North American football) demonstrate slower gait than non-athletes, even in the absence of concussion. Therefore, outside of their sport environment, both athletes with and without concussion are likely to display similar gait characteristics during the straight-walking approach phase in which the gait parameters were measured. However, swing time variability was greater in CONCacute than CONT and this difference persisted even at RTP, suggesting a lack of recovery from the concussion. Swing time variability has been suggested as a predictor of fall risk in an older adult population [15,16] and may serve as an indicator of impaired stability. As adaptation to current gait patterns can occur within the same step cycle [17,18], swing time variability can arise from instability carried over from a previous step or the accumulation of instability over several step cycles. Nonetheless, altered gait variability arises from altered neuromotor control, such is the case with concussions, and reflects the resultant integrated output of the locomotor system [19]. The time to reach the DSMmin also represents neuromotor function as the spatiotemporal characteristics of the COM must be continually controlled with respect to the position of the foot during the single support phase of gait. In the current study, only CONCacute demonstrated a greater time to reach the DSMmin than the CONT group, suggesting a conservative control of dynamic stability immediately following concussion. The effect of this conservative control allowed the CONCacute more time (i.e., greater gain from mechanoreceptors) during the single support phase to assess their current level of stability prior to taking the next step. The DSMmin is used as a marker of dynamic stability, as a larger distance between the COM and the lateral border of the BOS is indicative of greater balance control [20,21]. In the current study, it was expected that the athletes with concussions would demonstrate a smaller DSMmin, particularly in the step narrow turn trials; however, no differences were found between groups. There are
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two possible explanations for this: (1) as previously mentioned the additional information gained by reducing the time to reach DSMmin may be sufficient to effectively control the COM during single support and maintain an adequate safety margin; and (2) it is also possible that the visual cue used to indicate a change in travel path direction served as a stable reference point in which the CNS could use to guide individuals to an end point (anchor) [22] for both groups. Strong visual transients capture attention [23] and Hollands et al. [24] demonstrated that the body uses vision as an anchor to re-establish a locomotor axis. As individuals with concussions rely heavily on vision to control balance [3], providing a visual cue may have reduced the challenge to dynamic stability (DSMmin) inherent in changing direction by facilitating proper body alignment. However, if this were the case, both groups would have demonstrated similar segmental re-orientation patterns and this was not the case in the current study. Segmental re-orientation is typically a sequential top-down process [25] beginning with rotation of the head to allow for eye gaze to be directed in the new travel path followed by the trunk, hips and lower body [14,24,26]. Athletes with concussions demonstrated increased segmental re-orientation variability at both the acute and RTP phases compared to controls. The steering strategy in the control group was to initiate head reorientation prior to trunk re-orientation, whereas the group with concussions varied greatly between: (1) head re-orientation preceding trunk re-orientation (acute: 74.07%; RTP: 80.56% of trials); (2) trunk re-orientation onset occurring first (acute: 9.26%; RTP: 10.18%); and (3) an en bloc rotation of head and trunk segments simultaneously (acute: 16.67%; RTP: 9.26%). Since participants were instructed to take two steps prior to initiating the turn, the task allowed proactive control of balance and therefore, these results are not attributed to a slowed reaction time following a concussion [27]. Rather, proactive control for steering initiates a postural adjustment [28] and may reflect a cognitive event requiring attentional resources in a population with concussions. Research that uses dual-task paradigms have demonstrated that when individuals with concussions are presented with cognitive tasks which demand attention during gait, it can result in altered dynamic stability [6]. It is possible that although not explicit in the task, the anticipation of an upcoming change-in-direction served as a dual-task, competing for attentional resources and impairing sequential segment re-orientation. Additionally, the segmental re-orientation variability could have resulted from impaired information processing and movement coordination by the CNS [29]. In a sport environment, re-orientation variability may cause vulnerability to being hit as trunk rotation could be initiated prior to the head turning to enable vision towards the oncoming player. In conclusion, our findings demonstrate that concussions experienced by intercollegiate North American football players result in increased variability in swing time and segmental reorientation. Additionally, cognitively demanding tasks compete for neural resources and may detract from dynamic stability following a concussion. To fully exploit concussion deficits, individuals should be tested using a task that better challenges dynamic stability with altered or no vision available because visual cues may help to offset the appearance of balance deficits. Conflict of interest The authors declare that they have no conflicts of interest regarding this study.
References [1] Langlois J, Rutland-Brown W, Wald M. The epidemiology and impact of traumatic brain injury. Journal of Head Trauma Rehabilitation 2006; 21:375–8. [2] McCrea M, Guskiewicz KM, Marshall SW, Barr W, Randolph C, Cantu RC, et al. Acute effects and recovery time following concussion in collegiate football players: the NCAA Concussion Study. Journal of American Medical Association 2003;290:2556–63. [3] Geurts AC, Knoop JA, Van Limbeek J. Is postural control associated with mental functioning in the persistent postconcussion syndrome? Archives of Physical Medicine and Rehabilitation 1999;80:144–9. [4] Slobounov S, Sebastianelli W, Hallett M. Residual brain dysfunction observed one year post-mild traumatic brain injury: combined EEG and balance study. Clinical Neurophysiology 2012;123:1755–61. [5] Thompson JW, Sebastianelli W, Slobounov S. EEG and postural correlates of mild traumatic brain injury in athletes. Neuroscience Letters 2005;377: 158–63. [6] Parker TM, Osternig LR, Van Donkelaar P, Chou L-S. Gait stability following concussion. Medicine and Science in Sports and Exercise 2006;38:1032–40. [7] Catena RD, Van Donkelaar P, Chou L-S. Cognitive task effects on gait stability following concussion. Experimental Brain Research 2007;176:23–31. [8] Parker TM, Osternig LR, Lee H-J, Van Donkelaar P, Chou L-S. The effect of divided attention on gait stability following concussion. Clinical Biomechanics 2005;20:389–95. [9] Parker TM, Osternig LR, Van Donkelaar P, Chou L-S. Balance control during gait in athletes and non-athletes following concussion. Medical Engineering & Physics 2008;30:959–67. [10] Basford JR, Chou L-S, Kaufman KR, Brey RH, Walker A, Malec JF, et al. An assessment of gait and balance deficits after traumatic brain injury. Archives of Physical Medicine and Rehabilitation 2003;84:343–9. [11] Catena RD, Van Donkelaar P, Chou L-S. Altered balance control following concussion is better detected with an attention test during gait. Gait & Posture 2007;25:406–11. [12] Fait P, McFayden B, Swaine B, Cantin J. Alterations to locomotor navigation in a complex environment at 7 and 30 days following a concussion in an elite athlete. Brain Injury 2009;23:362–9. [13] Winter DA. Biomechanics and Motor Control of Human Movement. fourth ed. Hoboken, NJ: John Wiley & Sons Inc.; 2004. [14] Patla AE, Adkin A, Ballard T. Online steering: coordination and control of body center of mass, head and body reorientation. Experimental Brain Research 1999;129:629–34. [15] Springer S, Giladi N, Peretz C, Yogev G, Simon ES, Hausdorff JM. Dual-tasking effects on gait variability: the role of aging, falls, and executive function. Movement Disorders 2006;21:950–7. [16] Verghese J, Holtzer R, Lipton RB, Wang C. Quantitative gait markers and incident fall risk in older adults. Journal of Gerontology 2009;64:896–901. [17] Patla AE, Prentice SD, Robinson C, Neufeld J. Visual control of locomotion: strategies for changing direction and for going over obstacles. Journal of Experimental Psychology 1991;17:603–34. [18] Rietdyk S, Patla AE. Does the step length requirement in the subsequent step influence the strategies used for step length regulation in the current step? Human Movement Science 1994;13:109–27. [19] Hausdorff JM, Rios Da, Edelberg HK. Gait variability and fall risk in communityliving older adults: a 1-year prospective study. Archives of Physical Medicine and Rehabilitation 2001;82:1050–60. [20] Maki BE, Cheng KC-C, Mansfield A, Scovil CY, Perry SD, Peters AL, et al. Preventing falls in older adults: new interventions to promote more effective change-in-support balance reactions. Journal of Electromyography and Kinesiology 2008;18:243–54. [21] Pai Y-C, Patton JL. Centre of mass velocity-position predictions for balance control. Journal of Biomechanics 1997;30:347–54. [22] Grasso R, Pre´vost P, Ivanenko YP, Berthoz A. Eye-head coordination for the steering of locomotion in humans: an anticipatory synergy. Neuroscience Letters 1998;253:115–8. [23] Franconeri SL, Hollingworth A, Simons DJ. Do new objects capture attention? Psychological Science 2005;16:275–81. [24] Hollands M, Sorensen K, Patla AE. Effects of head immobilization on the coordination and control of head and body reorientation and translation during steering. Experimental Brain Research 2001;140:223–33. [25] Grasso R, Glasauer S, Takei Y, Berthoz A. The predictive brain: anticipatory control of head direction for the steering of locomotion. NeuroReport 1996;7:1170. [26] Hollands M, Ziavra NV, Bronstein AM. A new paradigm to investigate the roles of head and eye movements in the coordination of whole-body movements. Experimental Brain Research 2004;154:261–6. [27] Parker TM, Osternig LR, Van Donkelaar P, Chou L-S. Recovery of cognitive and dynamic motor function following concussion. British Journal of Sports Medicine 2007;41:868–73. [28] Xu D, Carlton LG, Rosengren KS. Anticipatory postural adjustments for altering direction during walking. Journal of Motor Behavior 2004;36:316–26. [29] Aruin AS. The organization of anticipatory postural adjustments. Journal of Automatic Control 2002;12:31–7.