- Email: [email protected]
Reflex ankle stiffness is inversely correlated with natural body sway
Gait & Posture 44 (2016) 128–130
Contents lists available at ScienceDirect
Gait & Posture journal homepage: www.elsevier.com/locate/gaitpost
Short communication
Reflex ankle stiffness is inversely correlated with natural body sway Brianna L. Julien *, Andrew P. Bendrups Department of Physiology, Anatomy and Microbiology, College of Science, Health and Engineering, La Trobe University, Bundoora, VIC 3086, Australia
A R T I C L E I N F O
A B S T R A C T
Article history: Received 7 January 2015 Received in revised form 21 October 2015 Accepted 1 December 2015
We aimed to determine whether effective ankle stiffness (EAS), measured during slow unperceived perturbations of stance, is related to natural anterior–posterior body sway. Because the perturbations are not perceived, any neural component of the response to perturbation is assumed to be ‘‘reflex’’, in the broad sense of an involuntary response to a stimulus. Subjects stood on a force platform for three 10-min trials. EAS was obtained from the average slope (Dt/Da) of the relation between ankle torque (t) and ankle angle (a), recorded during repeated perturbations delivered at the waist by a weak spring. EAS was normalised using the subject’s ‘‘load stiffness’’ (LS), calculated from mass (m) and height (h) above the ankle joint (mgh). Sway was obtained from fluctuations in ankle angle prior to perturbation. Variation in EAS and sway between subjects provided spread of data for correlation. There were no significant changes in EAS or sway across trials. All subjects had higher EAS than LS and mean EAS (1124 N m/rad) was significantly greater (p < 0.01) than mean LS (531 N m/rad). There was a strong significant inverse correlation between mean sway and mean normalised EAS (r = 0.68, p = 0.03). We conclude that the body, in response to slow unperceived perturbations, simulates an inverted pendulum with a stiffness of about twice LS and that EAS is largely generated by neural modulation of postural muscles. The inverse correlation between EAS and body sway suggests that the reflex mechanisms responding to perturbation also influence the extent of natural sway. ß 2015 Elsevier B.V. All rights reserved.
Keywords: Effective stiffness Ankle Sway Inverted pendulum Standing Reflex
1. Introduction Ankle stiffness has been regarded as a major factor determining body sway in an inverted pendulum model of standing [1,2]. However, Loram and co-workers have argued that intrinsic mechanical ankle stiffness cannot maintain balance [3] and that normal balance is achieved by intermittent control of the calf muscles, which in itself causes sway [4]. In any case, postural stability must depend on modulation of neural output. Whereas measurement of intrinsic stiffness requires elimination of the influences of neural modulation, Fitzpatrick et al. [5] applied slow unperceived perturbations to standing subjects and measured ankle torque (t) and ankle angle (a) to obtain a measure of net ankle stiffness (Dt/Da) which includes neural components. This effective ankle stiffness (EAS) increased when subjects were asked to stand still, suggesting that subjects were modulating EAS to control their sway. Since the response to perturbation occurs
* Corresponding author at: La Trobe University, Plenty Road, Bundoora, VIC 3086, Australia. Tel.: +61 3 9479 5599. E-mail addresses: [email protected] (B.L. Julien), [email protected] (A.P. Bendrups). http://dx.doi.org/10.1016/j.gaitpost.2015.12.001 0966-6362/ß 2015 Elsevier B.V. All rights reserved.
over a long time-scale (seconds), it is assumed to include all active and passive contributions to ankle torque, other than voluntary movement, which is excluded because the perturbations are unperceived. The neurally-mediated component of the response, evident as a rise in electromyographic activity in the calf muscles [6], broadly fits the definition of ‘‘reflex’’, as an involuntary response to a stimulus. We aimed to determine whether this reflex response to perturbation is related to natural anterior–posterior body sway. We use the concept of ‘‘stiffness’’ (EAS) to indicate the strength of response–we would describe a subject who strongly resists perturbation as standing ‘‘stiffly’’, whether due to mechanical stiffness or neural modulation of calf muscle activity. 2. Methods The institution’s human ethics committee approved the project and the 10 healthy adult subjects (5 females, mean age = 46.8; SD = 8.8 years) gave informed consent prior to participation. Subjects stood on a hinged force platform incorporating a central force gauge opposite the hinge, with a horizontal position transducer attached to their left calf and a servomotor attached to their waist via a 15-cm weak spring (stiffness = 8.2 N/m). Data were recorded with a PowerLab/4SPTM and Chart v3.6TM, sampling
B.L. Julien, A.P. Bendrups / Gait & Posture 44 (2016) 128–130
approximately by mgh, where m is the mass of the subject above the ankle joint, g is the gravitational constant, and h is the height of the center of mass (COM) above the ankle joint [5]. LS was calculated using an estimated height of COM [Kozyrev, 1962, cited in 6] adjusted for the estimated weight of the feet [7] and height of the ankle joint [8]; LS calculated this way agrees with empirical measurements during slow sway [see 5]. LS was used to normalise EAS [3,9,10] to eliminate the factors of height and weight and provide a measure of relative strength of response to perturbation, above the minimum required to stand. Statistical analysis was conducted using SPSS software (v.21) at a level of significance of p < 0.05. A Pearson product-moment correlation determined statistical significance of the relation between EAS and sway, using values averaged across three trials. A paired two-tailed t test compared LS with EAS; effect size was assessed using Cohen’s d. A one-factor repeated-measures ANOVA compared EAS and sway across trials; effect sizes were assessed using h2.
EAS = 1087 Nm/rad
Torque
129
mgh = 507 Nm/rad
0.2 Nm 0.02 deg Ankle Angle Fig. 1. Typical result of averaging ankle angle (8) and torque (N m) data during the initial pull phase (3 s) of perturbation in Subject 5. The arrow shows the direction of pull. The dotted line represents the calculated load stiffness (mgh) of this subject. EAS = effective ankle stiffness.
3. Results There were no significant changes in EAS [F(2,18) = 0.34, p = 0.72,
h2 < 0.01] or sway [F(2,18) = 0.02, p = 0.98, h2 < 0.01] across the three trials (Table 1); trial data were pooled for further analysis. All subjects had higher EAS than LS, and mean EAS (1124 Nm/rad) was significantly greater than mean LS (531 N m/rad) with large effect size [t(9) = 5.7, p < 0.01, d = 2.12; Table 1]. There was a strong significant inverse correlation between mean sway and mean normalised EAS (r = 0.68, p = 0.03; Fig. 2).
unfiltered at 100 Hz. The ankle angle was calculated by simple trigonometry. Changes in torque were calculated by multiplying measured force changes by the distance between the force gauge and hinge. Perturbations delivered by the servomotor consisted of a single sinusoidal anterior–posterior pull-release cycle at 0.1 Hz and 8 cm peak to peak amplitude. The displacement was largely taken up by the spring, so that the perturbation produced a typical body displacement of <0.28 of sway. Data were collected during three 10-min trials separated by 5 min of seated rest; measurements were repeated to assess reproducibility and increase precision. Subjects were instructed to stand ‘‘at ease’’ in their normal stance, look straight ahead and avoid moving. Perturbations were delivered approximately 30 s apart. No subjects could detect the perturbations, when tested before trials began. During each trial, responses to 20 perturbations were recorded, smoothed (3-point moving average), and averaged over the first 3 s of the perturbation to isolate the response from background fluctuations in torque and sway. EAS was obtained from the slope of the average relation between ankle angle and torque (Fig. 1). The standard deviation of ankle angle data, recorded 12 s prior to each perturbation, provided a measure of body sway. Variation in EAS and sway between subjects provided spread of data for correlation. Load stiffness (LS), or gravitational torque per unit ankle angle, determines the minimal EAS required to stand [5] and is given
4. Discussion Our empirical observation, similar to Fitzpatrick et al. [5], is that the body, in response to slow unperceived perturbations, simulates an inverted pendulum with a stiffness of about twice LS, although EAS must be largely generated by neural modulation of postural muscles rather than elasticity of connective tissues, assuming that intrinsic ankle stiffness during standing is somewhat less than LS [3]: the correlation between EAS and sway may be partly due to differences in intrinsic stiffness, but it must also reflect automatic neural control [see 5]. Most subjects adopted a relatively relaxed stance (e.g., EAS/LS < 2) whereas some strongly resisted perturbation (e.g., EAS/LS > 3), despite all being asked to stand at ease (Fig. 2). These differences presumably reflect the strength of their postural ‘‘reflexes’’. What causes the torque response to slow perturbation? In measuring average change over repeated perturbations, we cannot distinguish between the contributions of passive factors, simple
Table 1 Load stiffness (LS), effective ankle stiffness (EAS) and ankle sway data across subjects and trials. There were no significant effects of trial on EAS or sway. *Mean EAS was significantly greater than LS . Subject
1 2 3 4 5 6 7 8 9 10 Mean SD
LS (N m/rad)
EAS (N m/rad)
Sway (8)
Trial 1
Trial 2
Trial 3
501 539 676 592 507 654 473 361 401 604
812 1081 1073 1803 827 1350 890 651 1405 987
1098 998 1235 1588 1087 1472 893 698 1071 991
947 1199 935 2243 781 1782 1033 634 1237 930
*531 103
1088 344
1113 263
1172 489
Significance of bold values (p < 0.01).
Mean
Ratio (EAS/LS)
Trial 1
Trial 2
Trial 3
Mean
952 1093 1081 1878 898 1535 939 661 1238 969
0.120 0.076 0.128 0.089 0.154 0.045 0.106 0.132 0.071 0.135
0.132 0.071 0.172 0.083 0.110 0.051 0.158 0.095 0.059 0.141
0.156 0.079 0.174 0.089 0.131 0.056 0.113 0.079 0.077 0.119
0.136 0.075 0.158 0.087 0.132 0.051 0.126 0.102 0.069 0.132
1.90 2.03 1.60 3.17 1.77 2.35 1.99 1.83 3.08 1.60
*1124 351
0.106 0.034
0.107 0.042
0.107 0.038
0.107 0.035
2.13 0.57
130
B.L. Julien, A.P. Bendrups / Gait & Posture 44 (2016) 128–130
Acknowledgements The project was supported by Faculty and Postgraduate Support Grants. We thank Dr. Doug Rogers and Dr. Philip Dooley for reviewing initial drafts of the manuscript and Mr. David Orr for advice on biomechanical terminology.
Conflict of interest The authors report no conflicts of interest.
References
Fig. 2. Relation between normalised effective ankle stiffness (EAS/LS) and sway (deg). EAS and sway data are the means of the three trials per subject. There was a strong inverse correlation between EAS and sway.
reflexes and more complex feed-forward mechanisms [4,11]; any discontinuous changes reflecting intermittent control [4] would be smoothed out by averaging. Only voluntary contributions are excluded, because the perturbation is not perceived. The inverse correlation between EAS and body sway suggests that the reflex mechanisms responding to perturbation also influence the extent of natural sway, and implies that the effects on body sway observed by Fitzpatrick et al. [5,12] were obtained through changes in the reflex component of EAS. In contrast, Ho and Bendrups [10] found relatively high ‘‘ankle reflex stiffness’’ in elderly subjects with histories of falls, indicating that high EAS is not necessarily associated with postural stability and could be a sign of reflex overcompensation. This could explain why Kang and Lipsitz [13] found no inverse relation between changes in anterior– posterior sway and their estimate of postural stiffness in a dualtask study in the elderly. In providing an indication of the strength of automatic postural control, EAS during unperceived perturbation could be useful in clinical assessment of postural instability.
[1] Gurfinkel VS, Osovets SM. Dynamics of equilibrium of the vertical posture in man. Biofizika 1972;17(3):478–85. [2] Winter DA, Patla AE, Rietdyk S, Istiac MC. Ankle muscle stiffness in the control of balance during quiet standing. J Neurophysiol 2001;85:2630–3. [3] Loram ID, Maganaris CN, Lakie M. The passive, human calf muscles in relation to standing: the non-linear decrease from short range to long range stiffness. J Physiol 2007;584(2):661–75. [4] Loram ID, Maganaris CN, Lakie M. Human postural sway results from frequent: ballistic bias impulses by soleus and gastrocnemius. J Physiol 2005;564(1): 295–311. [5] Fitzpatrick RC, Taylor JL, McCloskey DI. Ankle stiffness of standing humans in response to imperceptible perturbation: reflex and task-dependent components. J Physiol 1992;454:533–47. [6] Zatsiorsky VM. Kinetics of human motion. Champaign, IL: Human Kinetics; 2002. [7] Patla AE, Ishac MG, Winter DA. Anticipatory control of center of mass and joint stability during voluntary arm movement from a standing posture: interplay between active and passive control. Exp Brain Res 2002;143:318–27. [8] Isman RE, Inman VT. Anthropometric studies on the human foot and ankle. Bull Prosthet Res 1969;10–11:97–129. [9] Casadio M, Morasso PG, Sanguineti V. Direct measurement of ankle stiffness during quiet standing: implications for control modelling and clinical application. Gait Posture 2005;21(4):410–24. [10] Ho CY, Bendrups AP. Ankle reflex stiffness during unperceived perturbation of standing in elderly subjects. J Gerontol A: Biol Sci Med Sci 2002;57A(9): B344–50. [11] Fitzpatrick R, Burke D, Gandevia SC. Loop gain of reflexes controlling human standing measured with the use of postural and vestibular disturbances. J Neurophysiol 1996;76:3994–4008. [12] Fitzpatrick R, Rogers DK, McCloskey D. Stable human standing with lowerlimb muscle afferents providing the only sensory input. J Physiol 1994;480(2): 395–403. [13] Kang HG, Lipsitz LA. Stiffness control of balance during quiet standing and dual task in older adults: the MOBILIZE Boston Study. J Neurophysiol 2010;104: 3510–7.
Contents lists available at ScienceDirect
Gait & Posture journal homepage: www.elsevier.com/locate/gaitpost
Short communication
Reflex ankle stiffness is inversely correlated with natural body sway Brianna L. Julien *, Andrew P. Bendrups Department of Physiology, Anatomy and Microbiology, College of Science, Health and Engineering, La Trobe University, Bundoora, VIC 3086, Australia
A R T I C L E I N F O
A B S T R A C T
Article history: Received 7 January 2015 Received in revised form 21 October 2015 Accepted 1 December 2015
We aimed to determine whether effective ankle stiffness (EAS), measured during slow unperceived perturbations of stance, is related to natural anterior–posterior body sway. Because the perturbations are not perceived, any neural component of the response to perturbation is assumed to be ‘‘reflex’’, in the broad sense of an involuntary response to a stimulus. Subjects stood on a force platform for three 10-min trials. EAS was obtained from the average slope (Dt/Da) of the relation between ankle torque (t) and ankle angle (a), recorded during repeated perturbations delivered at the waist by a weak spring. EAS was normalised using the subject’s ‘‘load stiffness’’ (LS), calculated from mass (m) and height (h) above the ankle joint (mgh). Sway was obtained from fluctuations in ankle angle prior to perturbation. Variation in EAS and sway between subjects provided spread of data for correlation. There were no significant changes in EAS or sway across trials. All subjects had higher EAS than LS and mean EAS (1124 N m/rad) was significantly greater (p < 0.01) than mean LS (531 N m/rad). There was a strong significant inverse correlation between mean sway and mean normalised EAS (r = 0.68, p = 0.03). We conclude that the body, in response to slow unperceived perturbations, simulates an inverted pendulum with a stiffness of about twice LS and that EAS is largely generated by neural modulation of postural muscles. The inverse correlation between EAS and body sway suggests that the reflex mechanisms responding to perturbation also influence the extent of natural sway. ß 2015 Elsevier B.V. All rights reserved.
Keywords: Effective stiffness Ankle Sway Inverted pendulum Standing Reflex
1. Introduction Ankle stiffness has been regarded as a major factor determining body sway in an inverted pendulum model of standing [1,2]. However, Loram and co-workers have argued that intrinsic mechanical ankle stiffness cannot maintain balance [3] and that normal balance is achieved by intermittent control of the calf muscles, which in itself causes sway [4]. In any case, postural stability must depend on modulation of neural output. Whereas measurement of intrinsic stiffness requires elimination of the influences of neural modulation, Fitzpatrick et al. [5] applied slow unperceived perturbations to standing subjects and measured ankle torque (t) and ankle angle (a) to obtain a measure of net ankle stiffness (Dt/Da) which includes neural components. This effective ankle stiffness (EAS) increased when subjects were asked to stand still, suggesting that subjects were modulating EAS to control their sway. Since the response to perturbation occurs
* Corresponding author at: La Trobe University, Plenty Road, Bundoora, VIC 3086, Australia. Tel.: +61 3 9479 5599. E-mail addresses: [email protected] (B.L. Julien), [email protected] (A.P. Bendrups). http://dx.doi.org/10.1016/j.gaitpost.2015.12.001 0966-6362/ß 2015 Elsevier B.V. All rights reserved.
over a long time-scale (seconds), it is assumed to include all active and passive contributions to ankle torque, other than voluntary movement, which is excluded because the perturbations are unperceived. The neurally-mediated component of the response, evident as a rise in electromyographic activity in the calf muscles [6], broadly fits the definition of ‘‘reflex’’, as an involuntary response to a stimulus. We aimed to determine whether this reflex response to perturbation is related to natural anterior–posterior body sway. We use the concept of ‘‘stiffness’’ (EAS) to indicate the strength of response–we would describe a subject who strongly resists perturbation as standing ‘‘stiffly’’, whether due to mechanical stiffness or neural modulation of calf muscle activity. 2. Methods The institution’s human ethics committee approved the project and the 10 healthy adult subjects (5 females, mean age = 46.8; SD = 8.8 years) gave informed consent prior to participation. Subjects stood on a hinged force platform incorporating a central force gauge opposite the hinge, with a horizontal position transducer attached to their left calf and a servomotor attached to their waist via a 15-cm weak spring (stiffness = 8.2 N/m). Data were recorded with a PowerLab/4SPTM and Chart v3.6TM, sampling
B.L. Julien, A.P. Bendrups / Gait & Posture 44 (2016) 128–130
approximately by mgh, where m is the mass of the subject above the ankle joint, g is the gravitational constant, and h is the height of the center of mass (COM) above the ankle joint [5]. LS was calculated using an estimated height of COM [Kozyrev, 1962, cited in 6] adjusted for the estimated weight of the feet [7] and height of the ankle joint [8]; LS calculated this way agrees with empirical measurements during slow sway [see 5]. LS was used to normalise EAS [3,9,10] to eliminate the factors of height and weight and provide a measure of relative strength of response to perturbation, above the minimum required to stand. Statistical analysis was conducted using SPSS software (v.21) at a level of significance of p < 0.05. A Pearson product-moment correlation determined statistical significance of the relation between EAS and sway, using values averaged across three trials. A paired two-tailed t test compared LS with EAS; effect size was assessed using Cohen’s d. A one-factor repeated-measures ANOVA compared EAS and sway across trials; effect sizes were assessed using h2.
EAS = 1087 Nm/rad
Torque
129
mgh = 507 Nm/rad
0.2 Nm 0.02 deg Ankle Angle Fig. 1. Typical result of averaging ankle angle (8) and torque (N m) data during the initial pull phase (3 s) of perturbation in Subject 5. The arrow shows the direction of pull. The dotted line represents the calculated load stiffness (mgh) of this subject. EAS = effective ankle stiffness.
3. Results There were no significant changes in EAS [F(2,18) = 0.34, p = 0.72,
h2 < 0.01] or sway [F(2,18) = 0.02, p = 0.98, h2 < 0.01] across the three trials (Table 1); trial data were pooled for further analysis. All subjects had higher EAS than LS, and mean EAS (1124 Nm/rad) was significantly greater than mean LS (531 N m/rad) with large effect size [t(9) = 5.7, p < 0.01, d = 2.12; Table 1]. There was a strong significant inverse correlation between mean sway and mean normalised EAS (r = 0.68, p = 0.03; Fig. 2).
unfiltered at 100 Hz. The ankle angle was calculated by simple trigonometry. Changes in torque were calculated by multiplying measured force changes by the distance between the force gauge and hinge. Perturbations delivered by the servomotor consisted of a single sinusoidal anterior–posterior pull-release cycle at 0.1 Hz and 8 cm peak to peak amplitude. The displacement was largely taken up by the spring, so that the perturbation produced a typical body displacement of <0.28 of sway. Data were collected during three 10-min trials separated by 5 min of seated rest; measurements were repeated to assess reproducibility and increase precision. Subjects were instructed to stand ‘‘at ease’’ in their normal stance, look straight ahead and avoid moving. Perturbations were delivered approximately 30 s apart. No subjects could detect the perturbations, when tested before trials began. During each trial, responses to 20 perturbations were recorded, smoothed (3-point moving average), and averaged over the first 3 s of the perturbation to isolate the response from background fluctuations in torque and sway. EAS was obtained from the slope of the average relation between ankle angle and torque (Fig. 1). The standard deviation of ankle angle data, recorded 12 s prior to each perturbation, provided a measure of body sway. Variation in EAS and sway between subjects provided spread of data for correlation. Load stiffness (LS), or gravitational torque per unit ankle angle, determines the minimal EAS required to stand [5] and is given
4. Discussion Our empirical observation, similar to Fitzpatrick et al. [5], is that the body, in response to slow unperceived perturbations, simulates an inverted pendulum with a stiffness of about twice LS, although EAS must be largely generated by neural modulation of postural muscles rather than elasticity of connective tissues, assuming that intrinsic ankle stiffness during standing is somewhat less than LS [3]: the correlation between EAS and sway may be partly due to differences in intrinsic stiffness, but it must also reflect automatic neural control [see 5]. Most subjects adopted a relatively relaxed stance (e.g., EAS/LS < 2) whereas some strongly resisted perturbation (e.g., EAS/LS > 3), despite all being asked to stand at ease (Fig. 2). These differences presumably reflect the strength of their postural ‘‘reflexes’’. What causes the torque response to slow perturbation? In measuring average change over repeated perturbations, we cannot distinguish between the contributions of passive factors, simple
Table 1 Load stiffness (LS), effective ankle stiffness (EAS) and ankle sway data across subjects and trials. There were no significant effects of trial on EAS or sway. *Mean EAS was significantly greater than LS . Subject
1 2 3 4 5 6 7 8 9 10 Mean SD
LS (N m/rad)
EAS (N m/rad)
Sway (8)
Trial 1
Trial 2
Trial 3
501 539 676 592 507 654 473 361 401 604
812 1081 1073 1803 827 1350 890 651 1405 987
1098 998 1235 1588 1087 1472 893 698 1071 991
947 1199 935 2243 781 1782 1033 634 1237 930
*531 103
1088 344
1113 263
1172 489
Significance of bold values (p < 0.01).
Mean
Ratio (EAS/LS)
Trial 1
Trial 2
Trial 3
Mean
952 1093 1081 1878 898 1535 939 661 1238 969
0.120 0.076 0.128 0.089 0.154 0.045 0.106 0.132 0.071 0.135
0.132 0.071 0.172 0.083 0.110 0.051 0.158 0.095 0.059 0.141
0.156 0.079 0.174 0.089 0.131 0.056 0.113 0.079 0.077 0.119
0.136 0.075 0.158 0.087 0.132 0.051 0.126 0.102 0.069 0.132
1.90 2.03 1.60 3.17 1.77 2.35 1.99 1.83 3.08 1.60
*1124 351
0.106 0.034
0.107 0.042
0.107 0.038
0.107 0.035
2.13 0.57
130
B.L. Julien, A.P. Bendrups / Gait & Posture 44 (2016) 128–130
Acknowledgements The project was supported by Faculty and Postgraduate Support Grants. We thank Dr. Doug Rogers and Dr. Philip Dooley for reviewing initial drafts of the manuscript and Mr. David Orr for advice on biomechanical terminology.
Conflict of interest The authors report no conflicts of interest.
References
Fig. 2. Relation between normalised effective ankle stiffness (EAS/LS) and sway (deg). EAS and sway data are the means of the three trials per subject. There was a strong inverse correlation between EAS and sway.
reflexes and more complex feed-forward mechanisms [4,11]; any discontinuous changes reflecting intermittent control [4] would be smoothed out by averaging. Only voluntary contributions are excluded, because the perturbation is not perceived. The inverse correlation between EAS and body sway suggests that the reflex mechanisms responding to perturbation also influence the extent of natural sway, and implies that the effects on body sway observed by Fitzpatrick et al. [5,12] were obtained through changes in the reflex component of EAS. In contrast, Ho and Bendrups [10] found relatively high ‘‘ankle reflex stiffness’’ in elderly subjects with histories of falls, indicating that high EAS is not necessarily associated with postural stability and could be a sign of reflex overcompensation. This could explain why Kang and Lipsitz [13] found no inverse relation between changes in anterior– posterior sway and their estimate of postural stiffness in a dualtask study in the elderly. In providing an indication of the strength of automatic postural control, EAS during unperceived perturbation could be useful in clinical assessment of postural instability.
[1] Gurfinkel VS, Osovets SM. Dynamics of equilibrium of the vertical posture in man. Biofizika 1972;17(3):478–85. [2] Winter DA, Patla AE, Rietdyk S, Istiac MC. Ankle muscle stiffness in the control of balance during quiet standing. J Neurophysiol 2001;85:2630–3. [3] Loram ID, Maganaris CN, Lakie M. The passive, human calf muscles in relation to standing: the non-linear decrease from short range to long range stiffness. J Physiol 2007;584(2):661–75. [4] Loram ID, Maganaris CN, Lakie M. Human postural sway results from frequent: ballistic bias impulses by soleus and gastrocnemius. J Physiol 2005;564(1): 295–311. [5] Fitzpatrick RC, Taylor JL, McCloskey DI. Ankle stiffness of standing humans in response to imperceptible perturbation: reflex and task-dependent components. J Physiol 1992;454:533–47. [6] Zatsiorsky VM. Kinetics of human motion. Champaign, IL: Human Kinetics; 2002. [7] Patla AE, Ishac MG, Winter DA. Anticipatory control of center of mass and joint stability during voluntary arm movement from a standing posture: interplay between active and passive control. Exp Brain Res 2002;143:318–27. [8] Isman RE, Inman VT. Anthropometric studies on the human foot and ankle. Bull Prosthet Res 1969;10–11:97–129. [9] Casadio M, Morasso PG, Sanguineti V. Direct measurement of ankle stiffness during quiet standing: implications for control modelling and clinical application. Gait Posture 2005;21(4):410–24. [10] Ho CY, Bendrups AP. Ankle reflex stiffness during unperceived perturbation of standing in elderly subjects. J Gerontol A: Biol Sci Med Sci 2002;57A(9): B344–50. [11] Fitzpatrick R, Burke D, Gandevia SC. Loop gain of reflexes controlling human standing measured with the use of postural and vestibular disturbances. J Neurophysiol 1996;76:3994–4008. [12] Fitzpatrick R, Rogers DK, McCloskey D. Stable human standing with lowerlimb muscle afferents providing the only sensory input. J Physiol 1994;480(2): 395–403. [13] Kang HG, Lipsitz LA. Stiffness control of balance during quiet standing and dual task in older adults: the MOBILIZE Boston Study. J Neurophysiol 2010;104: 3510–7.