- Email: [email protected]
Postural control: toe-standing versus heel–toe standing
Gait and Posture 19 (2004) 11–15
Postural control: toe-standing versus heel–toe standing Lee Nolan a,∗ , D. Casey Kerrigan b b
a Department of Biomedical Engineering, Centre for Biodynamics, Boston University, Boston, MA, USA Department of Physical Medicine and Rehabilitation, Spaulding Rehabilitation Hospital’s Centre for Rehabilitation Science, Harvard Medical School, Boston, MA, USA
Accepted 13 January 2003
Abstract Toe-standing is observed in a number of populations who are able to stand without loss of balance and also those who have balance problems. Intuitively, individuals who stand on their toes are able to successfully regulate their whole body movement in order to keep themselves stable. Force platform data were collected for ten able-bodied subjects during three quiet standing postures, (a) heel–toe standing; (b) half-toe standing and (c) standing en demi pointe (full toe-standing). Differences in control mechanisms with each posture were compared using stabilogram diffusion analysis. During open-loop control (short-term), toe-standing is less stable than heel–toe standing (P<0.05). There is greater stochastic activity when toe-standing (P < 0.05), suggesting that any short-term instability is being compensated for by an increase in muscle activity across the lower joints. During closed-loop control (long-term), there is no difference in mediolateral (ML) stochastic activity (increased activity has been linked to falls) between toe-standing and heel–toe standing. In addition, toe-standing is more stable than heel–toe standing (P < s0.05). Toe-standing, in and of itself, may not be responsible for balance problems in populations who compulsorily toe-stand. © 2003 Elsevier B.V. All rights reserved. Keywords: Biomechanics; Postural control; Toe-standing
1. Introduction Toe-standing (defined as standing on the forefeet) has been observed in a number of different populations. Ballet dancers stand on their toes with well-controlled balance and tennis players and baseball players are also observed to stand on their toes in anticipation of movement. Idiopathic toe-walkers (defined as walking on the forefeet in the absence of any known cause [1]) have been observed to stand on their toes without loss of balance [2]. Intuitively, individuals who stand on their toes are able to successfully regulate their whole body movement in order to keep themselves stable. Patients with an upper motor neuron (UMN) pathology, such as cerebral palsy, stroke, traumatic brain injury and multiple sclerosis, also commonly exhibit toe-standing. ∗ Corresponding author. Present address: Laboratory for Biomechanics and Motor control, Department of Neuroscience, Karolinska Institute and Department of Sport and Health Sciences, University College of Physical Education and Sports, Box 5626, SE-114 86 Stockholm, Sweden. Tel.: +1-46-8-402-2257; fax: +1-46-8-402-2287. E-mail address: [email protected] (L. Nolan).
0966-6362/$ – see front matter © 2003 Elsevier B.V. All rights reserved. doi:10.1016/S0966-6362(03)00007-9
Toe-standing in this population is often associated with spastic paretic weakness, more pronounced distally than proximally [3]. These patients typically have balance problems [4,5], but it is unclear whether these balance problems are due to the underlying pathology of their condition or due to toe-standing in and of itself. As toe-standing is common in different populations, both in those who exhibit well-controlled balance and those who have balance problems, understanding the biomechanics of toe-standing in healthy individuals may be particularly useful in order to examine how one regulates whole body dynamics when standing on toes. Traditional methods of investigating standing balance have previously reported summary measures of the centre of pressure (COP) during quiet standing (e.g. total area of sway, mean speed of sway), but it is difficult to interpret these results in any physiologically meaningful way [6], as changes in COP are a result of changes of whole body dynamics. By investigating the dynamic character of the COP, the stabilogram (time varying coordinates of the COP) can be interpreted in terms of control systems such as open-loop and closed-loop control [7]. This analysis suggests that there are two separate control mechanisms
12
L. Nolan, D.C. Kerrigan / Gait and Posture 19 (2004) 11–15
present in quiet standing [6,7]. There is a short-term region which utilises open-loop control where there is no feedback to control balance, and a long-term region which utilises closed-loop control where the individual can then rely on feedback to maintain balance [6–12]. The short-term and long-term regions are separated by a transition point or period termed the critical point (or period) [10]. This method has previously been used in studies investigating balance problems in patients with Parkinson’s disease [12] and in the elderly [6]. It has been shown that certain populations with balance problems exhibit increased long-term stochastic activity in the mediolateral (ML) direction [6,12] when heel–toe standing. If toe-standing does not cause instability in healthy individuals, there should not be increased long-term stochastic activity in the ML direction compared with heel–toe standing. Investigating balance during toe-standing should provide insight into how open-loop and closed-loop control is utilised in order to keep stable when standing on toes. We studied the balance of able-bodied subjects, who are capable of both heel–toe standing and toe-standing, as investigating balance during toe-standing in subjects without pathologies should help distinguish the mechanisms used to balance in this way. We hypothesise that (a) there is no difference in ML stochastic activity in the long-term region between heel–toe and toe-standing, (b) standing on toes, is not more unstable in the long-term than when heel–toe standing.
2. Methods The population studied consisted of ten healthy young adults, none of whom had any known musculoskeletal, neurologic, cardiac or pulmonary pathology. The procedures for this study were approved by the Boston University Institutional Review Board, and informed consent was obtained from each subject prior to his/her participation. The subjects included five men and five women and had a mean ± S.D. age of 25 ± 3 years, height 1.73 ± 0.06 m and mass 65.6 ± 14.6 kg. Data were collected while each subject stood quietly on a force platform (Kistler Instrument Corporation, Amherst, NY, USA) in each of three different postures (Fig. 1), (a) heel–toe standing (heel–toe); (b) standing on the ball of the foot with the heel slightly raised (half-toes) and (c) standing en demi pointe (full-toes). For the two toe-standing conditions, subjects were allowed to practice standing until they felt they had become aclimmatised to the standing position. During the test, subjects were instructed to stand barefoot and place their feet a ‘comfortable width apart’. This corresponded to approximately shoulder width for all subjects. Foot placement was marked to ensure accurate replacement so that distance between the feet was the same in each postural condition for each subject. The subjects stood with their hands behind their back and eyes open, looking straight ahead. Ground reaction force data were collected (sampled
Fig. 1. The three posture conditions, (a) heel–toe standing (heel–toe); (b) standing on the ball of the foot with the heel slightly raised (half-toes) and (c) standing en demi pointe (full-toes).
at 100 Hz) for 30 s while the subjects stood on the platform. Ten trials for each subject in each condition were performed in random order. A break was given after every third trial. The COP trajectories were studied as Brownian motion one- and two-dimensional random walks [6,7,11,12]. A one-dimensional random walk is the random movement of a single particle (such as the COP) along a straight line, and the simplest case of Brownian motion. Einstein [13] showed that the mean square displacement x2 of a one-dimensional random walk was related to the time interval t by the equation: x2 = 2Dt
(1)
where D is the diffusion coefficient or the average measure of stochastic activity (the random movement) of the particle. The above equation can be applied to a two- or three-dimensional system and thus x2 and t are linearly related in any plane. An extension of this theory, termed fractional Brownian motion [14], has led Eq. (1) to be generalised as: x2 ∼ t 2H
(2)
where the scaling exponent H can be any real number in the range 0 1/2 the stochastic process is positively correlated i.e. a fractional Brownian particle moving in a particular direction will continue to move in that direction. For H<1/2 the stochastic process is negatively correlated and the particle will not continue moving in that direction. The above parameters were calculated from the collected force data using a specifically written matlab program1 . For each subject and each posture, the program generated a stabilogram-diffusion plot from the mean of ten trials by plotting the mean square COP displacement (x2 ) for increasing time intervals (t) (Fig. 2). The diffusion 1 The stabilogram-diffusion analysis program is available from URL: http://isb.ri.ccf.org/software/stamp/.
L. Nolan, D.C. Kerrigan / Gait and Posture 19 (2004) 11–15
Fig. 2. A schematic representation of the stabilogram-diffusion plot illustrating the short-term region (open-loop control), long-term region (closed-loop control), the critical point co-ordinates (t, x2 ) and the slope of the plot (diffusion coefficient).
coefficient D (the level of stochastic activity during quiet standing) was calculated from the slopes (the short-term region and the long-term region) of the resultant linear–linear plots (Fig. 2). The scaling exponent H (the correlation between step increments of the COP trajectory) was calculated from the slopes (in the short-term region and the long-term region) of the resultant log–log plots of mean square COP displacement (x2 ) versus increasing time intervals (t). These calculations were performed for each of the planar, ML and anteroposterior (AP) directions. Differences in control mechanism parameters (Diffusion coefficient D in (a) the short-term region and (b) the long term region and scaling exponent H in (a) the short-term region and (b) the long term region) with each posture were compared using analysis of variance with post-hoc Tukey test. The level of significance was set to 5% with Bonferroni adjustments to the alpha level for multiple statistical tests.
3. Results During open-loop control (short-term region), there was greater stochastic activity (diffusion coefficient D), in the planar, ML and AP directions (Table 1) in both toe-standing
13
conditions compared with heel–toe standing (P<0.05). The scaling exponent H, (the correlation between step increments of the COP movement) was more positively correlated (P<0.05) during open-loop control in the planar, ML and AP directions when toe-standing compared with heel–toe standing (Table 1), showing that the COP is more likely to move or drift away from a relative equilibrium point. During closed-loop control (long-term region), there was no significant difference in ML or AP stochastic activity (diffusion coefficient D) between toe-standing and heel–toe standing (P > 0.05) (Table 1). However, there was greater planar stochastic activity (P<0.05) when standing on full toes compared with heel–toe standing. When standing on toes, the H scaling exponent was less positively correlated (P<0.05) during closed-loop control in the planar direction compared with heel–toe standing, and for standing on full toes in the AP direction compared with heel–toe standing (Table 1). A less positive correlation suggests that the COP is less likely to move or drift away from a relative equilibrium point. No differences were found between the two toe-standing postures for any of the parameters. 4. Discussion Stabilogram diffusion analysis suggests that the movement of the COP represents the combined outcomes of both deterministic and stochastic mechanisms. This has been interpreted as an indication that during quiet standing, open-loop and closed-loop postural control mechanisms are being utilised [6]. In the short-term region (open-loop control), there is greater stochastic activity during toe-standing compared with heel–toe standing. It is suggested that the control strategy being used here results in a greater net stiffness brought about by an increase in muscle activity across the lower joints [15]. Although there is greater stochastic activity, stiffer systems are better at resisting and correcting for transient perturbations [15]. Thus, this stiffness may be the mechanism used to enable balance during the short-term
Table 1 Stabilogram diffusion analysis results Parameter
Balance condition Heel–toe
Half toes
Short-term
Full toes
Long-term
Short-term
Long-term
Short-term
Long-term
Diffusion coefficient D Planar 11.811 (4.842) ML 4.649 (2.920) AP 6.472 (3.288)
1.739 (0.906) 0.502 (0.412) 1.080 (0.773)
50.130∗ (14.581) 18.079∗ (7.584) 32.418∗ (7.785)
3.545 (1.967) 0.997 (0.563) 2.380 (1.643)
64.855∗ (20.433) 24.366∗ (8.848) 40.827∗ (12.533)
2.508∗ (0.353) 0.981 (0.371) 1.463 (0.356)
Scaling exponent H Planar 0.583 (0.078) ML 0.618 (0.091) AP 0.564 (0.072)
0.207 (0.047) 0.173 (0.073) 0.219 (0.052)
0.735∗ (0.043) 0.747∗ (0.043) 0.731∗ (0.047)
0.146∗ (0.037) 0.113 (0.052) 0.160 (0.047)
0.753∗ (0.049) 0.772∗ (0.044) 0.743∗ (0.054)
0.110∗ (0.030) 0.101 (0.027) 0.112∗ (0.036)
(mm2
s−1 )
Mean ( ± S.D.) for the diffusion coefficient D and scaling exponent H for each of the three balance conditions in the short-term and long-term region. Results are given for the planar, ML and AP directions. ∗ Significantly differs (P<0.05) from heel–toe standing.
14
L. Nolan, D.C. Kerrigan / Gait and Posture 19 (2004) 11–15
region of stance where there is no feedback. This net stiffness appears to be increased when toe-standing to ensure balance in the absence of feedback during open-loop control, possibly resulting in a system well suited to resist and correct for transient perturbations. In the short-term region (open-loop control), heel–toe standing is more stable than toe-standing (smaller scaling exponent H). The reduced stability when toe-standing may be due to both the smaller area of the foot in contact with the ground, and that an individual is likely to sway more without feedback. This lower stability may be compensated for, in part, by the increased levels of stochastic activity compared with heel–toe standing, which are better at resisting and correcting for transient perturbations. As hypothesised, there was no difference in ML stochastic activity in the long-term region between toe-standing and heel–toe standing. Increased long-term stochastic activity in the ML plane has been linked to problems with balance [16] and associated with a history of falls [12]. Lateral instability may be an indication of functional balance impairment [12]. A predominance of ML activity has been attributed to a compensatory mechanism in which the patient has limited AP sway and must utilise ML sway to introduce slight shifts and adjustments, as some amount of movement is needed to maintain balance during quiet stance [17]. Toe-standing in the long-term region, as seen from these results, exhibits sufficient movement in the AP direction to maintain balance. As hypothesised, in the long-term region (closed-loop control), toe-standing is not more unstable than heel–toe standing, infact it becomes more stable (smaller scaling exponent H). The smaller the scaling exponent H, the more negatively correlated the stochastic process i.e. a reduced trend in the future movement of the COP and thus a lower tendency for the COP to move or drift away from a relative equilibrium point [10]. Therefore, when standing on toes, an individual is less likely to drift or move away from a relative equilibrium point compared with heel–toe standing. Thus, standing on toes is not more unstable than heel–toe standing, and in the long-term it may in fact be more stable. Under closed-loop control, feedback is present and in order to balance on toes for a longer period, an individual needs to utilise the feedback and limit his/her sway area to within the borders of the part of the feet in contact with the ground. This ability to balance is seen in ballet dancers, who appear to sway very little while standing on their toes (en demi pointe). It is seen from these results that in healthy able-bodied subjects, toe-standing utilises different postural control mechanisms than heel–toe standing which do not appear to be detrimental to balance. These include, when closed-loop feedback is not available, greater short-term stochastic activity resulting in a stiffer system which is better at resisting and correcting for transient perturbations, and, when feedback is available, a more negatively correlated long-term stochastic process indicating that the COP is less likely to
drift away from a relative equilibrium point. These findings may have relevance to patients with balance problems who stand on their toes as toe-standing, in and of itself, may not be the cause of instability and falls in these patients. More research is needed to assess the effect of toe-standing on postural control mechanisms in patients with an UMN pathology or in populations who are currently being treated for balance problems. Whilst standing balance has not been investigated in patients with an UMN pathology, it is expected that these patients would naturally exhibit increased levels of stochastic activity when standing due to spastic muscle activity associated with their condition [4]. Thus, the typical pattern of spastic muscle activity could actually be advantageous for patients with an UMN pathology when standing, as it may help them correct for, or resist transient perturbations. Unfortunately, however, these patients are typically unable to also heel–toe stand precluding a direct comparison of heel–toe versus toe-standing. Thus, the present study might serve as a basis for future studies in these patients. It may be that patients with an UMN pathology or balance problems exhibit different postural control strategies than those of healthy able-bodied subjects, and that toe-standing may or may not be detrimental for them.
5. Conclusion We demonstrated, in healthy adults, different postural control mechanisms when standing on toes compared with heel–toe standing are not detrimental to balance. When standing on toes, there is greater stochastic activity in the short-term which allows greater resistance and correction for transient perturbations in the absence of feedback. There is no increased long-term stochastic activity in the ML direction, which has been linked with balance problems and falls, and an individual is not more unstable under closed-loop control compared with heel–toe standing. These findings may serve as a basis for future studies investigating balance problems in individuals, who compulsorily stand on their toes.
Acknowledgements We appreciate Jim Collins, Ph.D. for his advice and help with this study.
References [1] Hall J, Salter R, Bhalla S. Congenital short tendo-calcaneus. J Bone Jt Surg Br 1967;49:695–7. [2] Caselli M, Rzonca E, Lue B. Habitual toe-walking: evaluation and approach to treatment. Clin Podiatr Med Surg1988;5:547– 59.
L. Nolan, D.C. Kerrigan / Gait and Posture 19 (2004) 11–15 [3] Swaiman K, Russman B. Cerebral palsy. In: Swaiman K, Ashwal S, editors. Pediatric neurology. Principles and practise, vol. 1, 3rd ed. St. Louis, MI: Mosby, 1999:312–23. [4] Bleck E. Orthopaedic management. In: Cerebral palsy. Oxford: Blackwell Scientific Publications, 1987. [5] Adams J, Perry J. Gait analysis: clinical application. In: Rose J, Gamble J, editors. Human walking 2nd ed. Baltimore: Williams and Wilkins, 1994:139–64. [6] Collins J, De Luca C, Burrows A, Lipsitz L. Age-related changes in open-loop and closed-loop postural control mechanisms. Exp Brain Res 1995;104:480–92. [7] Collins J, De Luca C. Open-loop and closed-loop control of posture: a random-walk analysis of center-of-pressure trajectories. Exp Brain Res 1993;95:308–18. [8] Collins J, De Luca LC. Random walking during quiet standing. Phys Rev Lett 1994;73:764–7. [9] Collins J, De Luca C, Pavlik A, Roy S, Emley M. The effects of spaceflight on open-loop and closed-loop postural control mechanisms: human neurovestibular studies on SLS-2. Exp Brain Res 1995;107:145–50. [10] Collins J, De Luca C. The effects of visual input on open-loop and closed-loop postural control mechanisms. Exp Brain Res 1995;103: 151–63.
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[11] Collins J, De Luca C. Open-loop and closed-loop control of posture: a random walk analysis of center-of-pressure trajectories. Exp Brain Res 1995;95:308–18. [12] Mitchell S, Collins J, De Luca C, Burrows A, Lipsitz L. Open-loop and closed-loop postural control mechanisms in Parkinson’s disease: increased mediolateral activity during quiet standing. Neurosci Lett 1995;197:133–6. [13] Einstein A. Über die von der molekularkinetischen Theorie der Wärme geforderte Bewegung von in ruhenden Flüssigkeiten suspendirten Teilchen. Ann Phys 1905;322:549–60. [14] Mandelbrot B, van Ness J. Fractional Brownian motions, fractional noises and applications. SIAM Rev 1968;10:422–37. [15] Winter D, Patla A, Prince F, Ishac M, Gielo-Perczak K. Stiffness control of balance in quiet standing. J Neurophysiol 1998;80:1211– 21. [16] Maki B, Holliday P, Topper A. A prospective study of postural balance and risk of falling in an ambulatory and independent elderley population. J Gerontol 1994;49:M72–84. [17] Schieppati M, Hugon M, Grasso M, Nardone A, Galante M. The limits of equilibrium in young and elderly normal subjects and in parkinsonians. EEG Clin Neurophysiol 1994;93:286– 98.
Postural control: toe-standing versus heel–toe standing Lee Nolan a,∗ , D. Casey Kerrigan b b
a Department of Biomedical Engineering, Centre for Biodynamics, Boston University, Boston, MA, USA Department of Physical Medicine and Rehabilitation, Spaulding Rehabilitation Hospital’s Centre for Rehabilitation Science, Harvard Medical School, Boston, MA, USA
Accepted 13 January 2003
Abstract Toe-standing is observed in a number of populations who are able to stand without loss of balance and also those who have balance problems. Intuitively, individuals who stand on their toes are able to successfully regulate their whole body movement in order to keep themselves stable. Force platform data were collected for ten able-bodied subjects during three quiet standing postures, (a) heel–toe standing; (b) half-toe standing and (c) standing en demi pointe (full toe-standing). Differences in control mechanisms with each posture were compared using stabilogram diffusion analysis. During open-loop control (short-term), toe-standing is less stable than heel–toe standing (P<0.05). There is greater stochastic activity when toe-standing (P < 0.05), suggesting that any short-term instability is being compensated for by an increase in muscle activity across the lower joints. During closed-loop control (long-term), there is no difference in mediolateral (ML) stochastic activity (increased activity has been linked to falls) between toe-standing and heel–toe standing. In addition, toe-standing is more stable than heel–toe standing (P < s0.05). Toe-standing, in and of itself, may not be responsible for balance problems in populations who compulsorily toe-stand. © 2003 Elsevier B.V. All rights reserved. Keywords: Biomechanics; Postural control; Toe-standing
1. Introduction Toe-standing (defined as standing on the forefeet) has been observed in a number of different populations. Ballet dancers stand on their toes with well-controlled balance and tennis players and baseball players are also observed to stand on their toes in anticipation of movement. Idiopathic toe-walkers (defined as walking on the forefeet in the absence of any known cause [1]) have been observed to stand on their toes without loss of balance [2]. Intuitively, individuals who stand on their toes are able to successfully regulate their whole body movement in order to keep themselves stable. Patients with an upper motor neuron (UMN) pathology, such as cerebral palsy, stroke, traumatic brain injury and multiple sclerosis, also commonly exhibit toe-standing. ∗ Corresponding author. Present address: Laboratory for Biomechanics and Motor control, Department of Neuroscience, Karolinska Institute and Department of Sport and Health Sciences, University College of Physical Education and Sports, Box 5626, SE-114 86 Stockholm, Sweden. Tel.: +1-46-8-402-2257; fax: +1-46-8-402-2287. E-mail address: [email protected] (L. Nolan).
0966-6362/$ – see front matter © 2003 Elsevier B.V. All rights reserved. doi:10.1016/S0966-6362(03)00007-9
Toe-standing in this population is often associated with spastic paretic weakness, more pronounced distally than proximally [3]. These patients typically have balance problems [4,5], but it is unclear whether these balance problems are due to the underlying pathology of their condition or due to toe-standing in and of itself. As toe-standing is common in different populations, both in those who exhibit well-controlled balance and those who have balance problems, understanding the biomechanics of toe-standing in healthy individuals may be particularly useful in order to examine how one regulates whole body dynamics when standing on toes. Traditional methods of investigating standing balance have previously reported summary measures of the centre of pressure (COP) during quiet standing (e.g. total area of sway, mean speed of sway), but it is difficult to interpret these results in any physiologically meaningful way [6], as changes in COP are a result of changes of whole body dynamics. By investigating the dynamic character of the COP, the stabilogram (time varying coordinates of the COP) can be interpreted in terms of control systems such as open-loop and closed-loop control [7]. This analysis suggests that there are two separate control mechanisms
12
L. Nolan, D.C. Kerrigan / Gait and Posture 19 (2004) 11–15
present in quiet standing [6,7]. There is a short-term region which utilises open-loop control where there is no feedback to control balance, and a long-term region which utilises closed-loop control where the individual can then rely on feedback to maintain balance [6–12]. The short-term and long-term regions are separated by a transition point or period termed the critical point (or period) [10]. This method has previously been used in studies investigating balance problems in patients with Parkinson’s disease [12] and in the elderly [6]. It has been shown that certain populations with balance problems exhibit increased long-term stochastic activity in the mediolateral (ML) direction [6,12] when heel–toe standing. If toe-standing does not cause instability in healthy individuals, there should not be increased long-term stochastic activity in the ML direction compared with heel–toe standing. Investigating balance during toe-standing should provide insight into how open-loop and closed-loop control is utilised in order to keep stable when standing on toes. We studied the balance of able-bodied subjects, who are capable of both heel–toe standing and toe-standing, as investigating balance during toe-standing in subjects without pathologies should help distinguish the mechanisms used to balance in this way. We hypothesise that (a) there is no difference in ML stochastic activity in the long-term region between heel–toe and toe-standing, (b) standing on toes, is not more unstable in the long-term than when heel–toe standing.
2. Methods The population studied consisted of ten healthy young adults, none of whom had any known musculoskeletal, neurologic, cardiac or pulmonary pathology. The procedures for this study were approved by the Boston University Institutional Review Board, and informed consent was obtained from each subject prior to his/her participation. The subjects included five men and five women and had a mean ± S.D. age of 25 ± 3 years, height 1.73 ± 0.06 m and mass 65.6 ± 14.6 kg. Data were collected while each subject stood quietly on a force platform (Kistler Instrument Corporation, Amherst, NY, USA) in each of three different postures (Fig. 1), (a) heel–toe standing (heel–toe); (b) standing on the ball of the foot with the heel slightly raised (half-toes) and (c) standing en demi pointe (full-toes). For the two toe-standing conditions, subjects were allowed to practice standing until they felt they had become aclimmatised to the standing position. During the test, subjects were instructed to stand barefoot and place their feet a ‘comfortable width apart’. This corresponded to approximately shoulder width for all subjects. Foot placement was marked to ensure accurate replacement so that distance between the feet was the same in each postural condition for each subject. The subjects stood with their hands behind their back and eyes open, looking straight ahead. Ground reaction force data were collected (sampled
Fig. 1. The three posture conditions, (a) heel–toe standing (heel–toe); (b) standing on the ball of the foot with the heel slightly raised (half-toes) and (c) standing en demi pointe (full-toes).
at 100 Hz) for 30 s while the subjects stood on the platform. Ten trials for each subject in each condition were performed in random order. A break was given after every third trial. The COP trajectories were studied as Brownian motion one- and two-dimensional random walks [6,7,11,12]. A one-dimensional random walk is the random movement of a single particle (such as the COP) along a straight line, and the simplest case of Brownian motion. Einstein [13] showed that the mean square displacement x2 of a one-dimensional random walk was related to the time interval t by the equation: x2 = 2Dt
(1)
where D is the diffusion coefficient or the average measure of stochastic activity (the random movement) of the particle. The above equation can be applied to a two- or three-dimensional system and thus x2 and t are linearly related in any plane. An extension of this theory, termed fractional Brownian motion [14], has led Eq. (1) to be generalised as: x2 ∼ t 2H
(2)
where the scaling exponent H can be any real number in the range 0
L. Nolan, D.C. Kerrigan / Gait and Posture 19 (2004) 11–15
Fig. 2. A schematic representation of the stabilogram-diffusion plot illustrating the short-term region (open-loop control), long-term region (closed-loop control), the critical point co-ordinates (t, x2 ) and the slope of the plot (diffusion coefficient).
coefficient D (the level of stochastic activity during quiet standing) was calculated from the slopes (the short-term region and the long-term region) of the resultant linear–linear plots (Fig. 2). The scaling exponent H (the correlation between step increments of the COP trajectory) was calculated from the slopes (in the short-term region and the long-term region) of the resultant log–log plots of mean square COP displacement (x2 ) versus increasing time intervals (t). These calculations were performed for each of the planar, ML and anteroposterior (AP) directions. Differences in control mechanism parameters (Diffusion coefficient D in (a) the short-term region and (b) the long term region and scaling exponent H in (a) the short-term region and (b) the long term region) with each posture were compared using analysis of variance with post-hoc Tukey test. The level of significance was set to 5% with Bonferroni adjustments to the alpha level for multiple statistical tests.
3. Results During open-loop control (short-term region), there was greater stochastic activity (diffusion coefficient D), in the planar, ML and AP directions (Table 1) in both toe-standing
13
conditions compared with heel–toe standing (P<0.05). The scaling exponent H, (the correlation between step increments of the COP movement) was more positively correlated (P<0.05) during open-loop control in the planar, ML and AP directions when toe-standing compared with heel–toe standing (Table 1), showing that the COP is more likely to move or drift away from a relative equilibrium point. During closed-loop control (long-term region), there was no significant difference in ML or AP stochastic activity (diffusion coefficient D) between toe-standing and heel–toe standing (P > 0.05) (Table 1). However, there was greater planar stochastic activity (P<0.05) when standing on full toes compared with heel–toe standing. When standing on toes, the H scaling exponent was less positively correlated (P<0.05) during closed-loop control in the planar direction compared with heel–toe standing, and for standing on full toes in the AP direction compared with heel–toe standing (Table 1). A less positive correlation suggests that the COP is less likely to move or drift away from a relative equilibrium point. No differences were found between the two toe-standing postures for any of the parameters. 4. Discussion Stabilogram diffusion analysis suggests that the movement of the COP represents the combined outcomes of both deterministic and stochastic mechanisms. This has been interpreted as an indication that during quiet standing, open-loop and closed-loop postural control mechanisms are being utilised [6]. In the short-term region (open-loop control), there is greater stochastic activity during toe-standing compared with heel–toe standing. It is suggested that the control strategy being used here results in a greater net stiffness brought about by an increase in muscle activity across the lower joints [15]. Although there is greater stochastic activity, stiffer systems are better at resisting and correcting for transient perturbations [15]. Thus, this stiffness may be the mechanism used to enable balance during the short-term
Table 1 Stabilogram diffusion analysis results Parameter
Balance condition Heel–toe
Half toes
Short-term
Full toes
Long-term
Short-term
Long-term
Short-term
Long-term
Diffusion coefficient D Planar 11.811 (4.842) ML 4.649 (2.920) AP 6.472 (3.288)
1.739 (0.906) 0.502 (0.412) 1.080 (0.773)
50.130∗ (14.581) 18.079∗ (7.584) 32.418∗ (7.785)
3.545 (1.967) 0.997 (0.563) 2.380 (1.643)
64.855∗ (20.433) 24.366∗ (8.848) 40.827∗ (12.533)
2.508∗ (0.353) 0.981 (0.371) 1.463 (0.356)
Scaling exponent H Planar 0.583 (0.078) ML 0.618 (0.091) AP 0.564 (0.072)
0.207 (0.047) 0.173 (0.073) 0.219 (0.052)
0.735∗ (0.043) 0.747∗ (0.043) 0.731∗ (0.047)
0.146∗ (0.037) 0.113 (0.052) 0.160 (0.047)
0.753∗ (0.049) 0.772∗ (0.044) 0.743∗ (0.054)
0.110∗ (0.030) 0.101 (0.027) 0.112∗ (0.036)
(mm2
s−1 )
Mean ( ± S.D.) for the diffusion coefficient D and scaling exponent H for each of the three balance conditions in the short-term and long-term region. Results are given for the planar, ML and AP directions. ∗ Significantly differs (P<0.05) from heel–toe standing.
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L. Nolan, D.C. Kerrigan / Gait and Posture 19 (2004) 11–15
region of stance where there is no feedback. This net stiffness appears to be increased when toe-standing to ensure balance in the absence of feedback during open-loop control, possibly resulting in a system well suited to resist and correct for transient perturbations. In the short-term region (open-loop control), heel–toe standing is more stable than toe-standing (smaller scaling exponent H). The reduced stability when toe-standing may be due to both the smaller area of the foot in contact with the ground, and that an individual is likely to sway more without feedback. This lower stability may be compensated for, in part, by the increased levels of stochastic activity compared with heel–toe standing, which are better at resisting and correcting for transient perturbations. As hypothesised, there was no difference in ML stochastic activity in the long-term region between toe-standing and heel–toe standing. Increased long-term stochastic activity in the ML plane has been linked to problems with balance [16] and associated with a history of falls [12]. Lateral instability may be an indication of functional balance impairment [12]. A predominance of ML activity has been attributed to a compensatory mechanism in which the patient has limited AP sway and must utilise ML sway to introduce slight shifts and adjustments, as some amount of movement is needed to maintain balance during quiet stance [17]. Toe-standing in the long-term region, as seen from these results, exhibits sufficient movement in the AP direction to maintain balance. As hypothesised, in the long-term region (closed-loop control), toe-standing is not more unstable than heel–toe standing, infact it becomes more stable (smaller scaling exponent H). The smaller the scaling exponent H, the more negatively correlated the stochastic process i.e. a reduced trend in the future movement of the COP and thus a lower tendency for the COP to move or drift away from a relative equilibrium point [10]. Therefore, when standing on toes, an individual is less likely to drift or move away from a relative equilibrium point compared with heel–toe standing. Thus, standing on toes is not more unstable than heel–toe standing, and in the long-term it may in fact be more stable. Under closed-loop control, feedback is present and in order to balance on toes for a longer period, an individual needs to utilise the feedback and limit his/her sway area to within the borders of the part of the feet in contact with the ground. This ability to balance is seen in ballet dancers, who appear to sway very little while standing on their toes (en demi pointe). It is seen from these results that in healthy able-bodied subjects, toe-standing utilises different postural control mechanisms than heel–toe standing which do not appear to be detrimental to balance. These include, when closed-loop feedback is not available, greater short-term stochastic activity resulting in a stiffer system which is better at resisting and correcting for transient perturbations, and, when feedback is available, a more negatively correlated long-term stochastic process indicating that the COP is less likely to
drift away from a relative equilibrium point. These findings may have relevance to patients with balance problems who stand on their toes as toe-standing, in and of itself, may not be the cause of instability and falls in these patients. More research is needed to assess the effect of toe-standing on postural control mechanisms in patients with an UMN pathology or in populations who are currently being treated for balance problems. Whilst standing balance has not been investigated in patients with an UMN pathology, it is expected that these patients would naturally exhibit increased levels of stochastic activity when standing due to spastic muscle activity associated with their condition [4]. Thus, the typical pattern of spastic muscle activity could actually be advantageous for patients with an UMN pathology when standing, as it may help them correct for, or resist transient perturbations. Unfortunately, however, these patients are typically unable to also heel–toe stand precluding a direct comparison of heel–toe versus toe-standing. Thus, the present study might serve as a basis for future studies in these patients. It may be that patients with an UMN pathology or balance problems exhibit different postural control strategies than those of healthy able-bodied subjects, and that toe-standing may or may not be detrimental for them.
5. Conclusion We demonstrated, in healthy adults, different postural control mechanisms when standing on toes compared with heel–toe standing are not detrimental to balance. When standing on toes, there is greater stochastic activity in the short-term which allows greater resistance and correction for transient perturbations in the absence of feedback. There is no increased long-term stochastic activity in the ML direction, which has been linked with balance problems and falls, and an individual is not more unstable under closed-loop control compared with heel–toe standing. These findings may serve as a basis for future studies investigating balance problems in individuals, who compulsorily stand on their toes.
Acknowledgements We appreciate Jim Collins, Ph.D. for his advice and help with this study.
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