Gait & Posture 44 (2016) 1–6
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The use of force-plate posturography in the assessment of postural instability Janusz W. Błaszczyk a,b,* a b
Department of Biomechanics, Jerzy Kukuczka Academy of Physical Education, Katowice, Poland Department of Neurophysiology, Nencki Institute of Experimental Biology, 02-093 Warsaw, Poland
A R T I C L E I N F O
A B S T R A C T
Article history: Received 26 March 2015 Received in revised form 21 August 2015 Accepted 7 October 2015
Force-plate posturography is a simple method that is commonly used in the contemporary laboratory and clinic to assess postural control. Despite the obvious advantages and popularity of the method, universal standards for posturographic tests have not been developed thus far: most postural assessments are based on the standard spatiotemporal metrics of the center-of-foot pressure (COP) recorded during quiet stance. Unfortunately, the standard COP characteristics are strongly dependent on individual experimental design and are susceptible to distortions such as the noise of signal digitalization, which often makes the results from different laboratories incomparable and unreliable. The COP trajectories were recorded in subjects standing still, with eyes open (EO) and then, with eyes closed (EC). The 168 subjects were divided into 3 experimental groups: young adults, older adults, and patients with Parkinson’s disease. Three novel output measures: the sway directional index (DI), the sway ratio (SR), and the sway vector (SV) were applied to assess the postural stability in the experimental groups. The controlled variables: age, pathology, and visual conditions, uniquely affected the output measures. The basic attributes of the SV: its reference position, magnitude, and azimuth, provided a unique set of descriptors for postural control that allowed me unambiguously to differentiate the decline in postural stability caused by natural ageing and Parkinson’s disease. As shown in previous investigations, the SV attributes, when optimally filtered with a low-pass filter, were highly independent of the trial length and the sampling frequency, and were unaffected by the sampling noise. In conclusion, the SV may be recommended as the useful standard in static posturography. ß 2015 Elsevier B.V. All rights reserved.
Keywords: Postural stability Sway vector Parkinson’s disease Elderly
1. Introduction The use of postural sway in the clinical context is not new but so far no widespread consensus has emerged about the methods, techniques and interpretation of the data [1–4]. There are extensive attempts to resolve these inconsistences by searching for adequate and reliable methods of posturographic signal parametrization that would reveal an unambiguous relationship between sway and postural stability [5–11]. During quiet stance, postural control is commonly viewed as a continuous process of the stabilization of a multilink inverted pendulum [12,13]. In static posturography, this process corresponds with maintaining the body’s center of mass (COM) at the reference position (RP) within the predefined area of stability
* Correspondence address: Department of Biomechanics Jerzy Kukuczka Academy of Physical Education, Katowice, Poland. E-mail address:
[email protected] http://dx.doi.org/10.1016/j.gaitpost.2015.10.014 0966-6362/ß 2015 Elsevier B.V. All rights reserved.
within the base of support [14]. It is believed that the control generally works in the feedback mode and automatically executes the pre-programmed corrective actions in response to internal or external perturbations. Due to numerous nonlinearities and delays within the neuromuscular system, the COM performs tiny spontaneous oscillations around the RP known as postural sway. The robustness of postural control allows, however, a stable standing posture to be maintained despite various uncertainties and disturbances including postural sway. There is a consensus that the highest level of robustness in postural control is observed in young, healthy subjects. Natural ageing and most neurodegenerative diseases, including Parkinson’s disease (PD), significantly augment uncertainty and noise in postural control. These, in turn, increase the probability of an uncontrolled crossing of stability limits and balance loss [9,14]. This can happen when the RP placement, or the sway amplitude and direction, exceed the permissible limits [10,11]. The clinical manifestation of balance deficiency is the increased susceptibility to falls with their often irreversible or even potentially fatal consequences. It is important,
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therefore, that clinicians identify balance problems reliably and as early as possible. Thus far, force-plate posturography remains the safeest and most attractive method to assess balance [1,3,4]. In this method, the postural control assessment is based on the characteristics of the center-of-foot pressure (COP) oscillations which are equivalent to spontaneous COM motions on the level of the base of support [3]. Unfortunately, there are several methodological limitations which restrict its widespread clinical application [2,3,10]. Firstly, it is commonly believed that the COP signals are free from measurement distortions that may affect the results. However, there is a growing body of evidence indicating that poor design of the posturographic hardware and software may substantially impact the COP signal assessment [2,3,10]. Secondly, most of the commonly analyzed COP output measures are neither sensitive enough and nor do they exhibit the specific effects for postural balance deficit [1,3]. Thus, the standard spatiotemporal analysis of the COP may provide only descriptive information of rather limited value and without any direct insight into underlying control deficits. Several factors, such as individual experimental design and even the hardware characteristics, should also be considered as potential sources of discrepancy. Consequently, the COP sampling frequency, the trial length, and number of trials must be considered as factors that may impact on the results [2,10,15,16]. To date, there is a consensus in force-plate posturography that the average COP velocity, assessed in several (3–5) 60-second trials, may provide some inferences on postural stability [2,15–17]. Recognizing these problems, researchers were compelled to implement more advanced analytical methods in postural sway analysis [2–4,18–22]. Continuing with this line of research, I focused on the application of the COP directional metrics in balance assessment. To date, these metrics proved to be almost independent of the test duration and the individual experimental settings, making them very attractive in the assessment of postural stability [3,4]. This study aimed to verify whether my novel COP directional measures and in particular the sway vector (SV) would exhibit a sufficient specificity to ageing and Parkinson’s disease (PD). Hence, the COP directional characteristics and their sensitivity to visual conditions were tested in 3 experimental groups, each with well-documented differences in balance control. The verification of these objectives represents a preliminary step in establishing the feasibility of using static posturography in the clinical assessment of postural stability.
digitalization they were filtered off-line with the Chebyshev II 10th order low-pass filters (Matlab v. 6.0, The MathWorks, Inc, USA). In order to establish an optimal cut-off frequency, I tested filtering within the range 5–12 Hz. Next, the low-pass filtering at 0.4 Hz allowed me to retrieve the COM trajectory from the COP data [3]. The COP path length (STotal) and its directional components (SAP and SML) were used to compute: 1. The sway vector (SV) in polar coordinates where the vector length was equal to the mean COP (or COM) velocity, and its angle was wCOP(COM) = arctangent (SAP/SML). The concept of the SV is shown in Fig. 1. The algorithms used for its calculation and the necessary data processing procedures are provided in detail in the Appendix. 2. The AP and the ML directional indices defined as DIAP = SAP/ STotal; DIML = SML/STotal [4]. 3. The sway ratio (SR): COP/COM path lengths [3]. All statistical analyses in this study were performed using the Statistica version 6.0 software (StatSoft, Inc. USA). The two-way analysis of variance with one dependent factor (vision) was used to examine differences in the analyzed parameter between the three experimental groups. The ANOVAs were followed by post hoc Fisher’s Least Significant Difference test. A p value smaller than 0.05 was considered significant. 3. Results Statistical analysis showed highly significant differences in the outcome variables between the groups. In the analysis, the impact
2. Materials and methods The research was accepted by the Senate Ethics Committee of the Jerzy Kukuczka Academy of Physical Education. All participants gave their written informed consent. Three groups of participants were tested: (Y) the young adults, N = 60 (30 males and 30 females, mean age 21 2 years); (E) older adults, N = 54, mean age 64 8 years; and (PD) patients with a diagnosis of idiopathic Parkinson’s disease without dyskinesia and motor fluctuations above grade 3, N = 54, mean age 65 9 years. The E and PD group consisted of 20 female and 34 male subjects. According to Hoehn/Yahr scale, 12 patients scored at stage I, 33 at stage II and 10 at stage III [10]. The young and older adults reported having no neurological or movement disorders. During the standard tests, the subject was required to maintain a quiet, comfortable stance whilst standing barefoot on the force platform, with heels aligned at a reference line and arms kept comfortably at the side. The COP oscillations were recorded by a force-plate (QFP Medicapteurs, France) in six 26.5-second trials: 3 with eyes open (EO) and 3 with eyes closed (EC). The trials were randomized and there was a short rest break between them. The signals were sampled at 40 Hz and to remove the noise of signal
Fig. 1. The concept of the sway vector (SV) in postural control. The SV is characterized by its length L (i.e. the average COP velocity) and its polar angle w. The length of the vector corresponds with the uncertainty in postural control which affects the stability of standing posture. The application point of the localized SV is the COP reference position (RP). In older adults and PD patients, the RP is shifted forward to compensate for postural instability. The stability area (SA) is a set of points that satisfies the postural stability conditions. The dashed area represents a safety margin (SM) where the width can also be adjusted depending on the overall postural stability, and to compensate for the control deficit. The area outside of stability limits (SL) represents the set of instability points.
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of each group and the visual conditions (EO vs. EC) and the filtering frequency on the aforementioned postural sway indices were tested. The impact of the low-pass filtering on the sway vector parameters in young subjects is depicted in Fig. 2. 3.1. COP sway vector (SVCOP) ANOVA showed significant effects of both group (F2,165 = 29.5, p 0.001) and vision (F1,165 = 146, p 0.001) on the SVCOP length. In the E and PD groups, the mean length of the vector was significantly higher compared with the Y group (Table 1 and Fig. 2). Eye closure resulted in the lengthening of the SVCOP in all groups (p 0.002). The lowest effect was observed in the Y group, whilst the highest was noticed in the PD group. As a consequence, the group-by-vision interaction reached the level of significance (F2,165 = 16.2, p 0.001). ANOVA revealed significant effects of group type (F2,165 = 28.0, p 0.001) and vision (F1,165 = 80.1, p 0.001) on the SVCOP angle (wCOP) (Fig. 3 lower panel). In the Y group, the mean angle in EO test was 0.92 0.08 radian. It was significantly lower (p 0.001) in comparison with the E group (1.0 0.1 rad), but did not differ from that in the PD group (0.94 0.17, p < 0.16). In all groups, EC resulted in a significant increase in the wCOP: 0.02 rad (p 0.05) in the young; 0.12 rad (p 0.001) in the elderly, and 0.05 rad (p 0.001) in the PD group (Table 1). The group-by-vision interaction reached the level of significance (F2,165 = 12.1, p 0.001). 3.2. COM sway vector (SVCOM) Changes in postural control, due to standard experimental manipulations with visual input, resulted in changes of the SVCOM characteristics (Fig. 4). ANOVA revealed significant effects of both group (p 0.001) and vision (p 0.001) on the SVCOM length. In the young group, the mean SVCOM length in the EO tests was 2.56 0.62 mm/s, i.e. significantly lower (p 0.001) when compared
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Table 1 Descriptive statistics of the selected center-of-foot pressure (COP) measures (mean SD) in three experimental groups: Young (Y), older adults (E) and Parkinson’s disease (PD). EO – ‘‘eyes open’’, EC – ‘‘eyes closed’’. * – significant difference at p 0.0001. Posturographic measure
F2,165 (p)
Group
EO
EC
COP SV length VCOP [mm/s]
29.5 (0.0001)
PD*
18.5 11.2
26.4 16.1
E* Y*
12.2 4.7 9.8 1.6
17.4 7.2 12.2 2.7
PD*
0.94 0.17
0.99 0.16
E* Y**
1.0 0.1 0.92 0.1
1.1 0.1 0.94 0.1
PD*
3.8 1.7
4.6 2.2
*
E Y*
2.9 0.8 2.6 0.6
3.8 1.4 3.1 0.9
PD**
0.94 0.2
0.98 0.2
E Y
1.0 0.2 0.94 0.1
1.1 0.2 0.93 0.1
PD*
0.73 0.10
0.76 0.09
*
E Y
0.78 0.06 0.77 0.01
0.84 0.05 0.77 0.01
PD*
0.53 0.12
0.50 0.11
*
E Y
0.47 0.08 0.49 0.01
0.40 0.08 0.49 0.01
PD**
0.73 0.1
0.76 0.1
E Y
0.76 0.1 0.73 0.1
0.81 0.1 0.72 0.1
PD
0.53 0.15
0.50 0.15
E* Y
0.49 0.15 0.53 0.1
0.43 0.15 0.55 0.1
PD*
5.6 4.4
6.7 5.4
E Y
4.6 1.9 4.1 0.9
5.1 2.3 4.2 1.0
PD*
5.7 4.3
7.0 5.2
E Y
4.5 2.1 4.3 1.5
4.9 2.6 4.1 1.2
COP SV angle wCOP [radians]
COM SV length VCOM [mm/s]
COM SV angle wCOM [radians]
28.0 (0.0001)
15.9 (0.0001)
6.95 (0,002)
*
COP DIAP
COP DIML
COM DIAP
18.6 (0.0001)
20.0 (0.0001)
7.8 (0.001)
*
COM DIML
SRAP
SRML
* **
8.8 (0.001)
7.3 (0.001)
9.2 (0.001)
Test
p 0.0001. p 0.05.
with both the E group (2.93 0.84 mm/s) and the PD group (3.76 1.75). Eye closure resulted in a significant increase in the SVCOM length to: 3.1 0.9 mm/s (p 0.001) in Y, 3.8 1.36 mm/s (p 0.001) in E, and 4.61 2.25 mm/s (p 0.001) in the PD patients. ANOVA showed highly significant effects of group (F2,165 = 6.95, p 0.002) and vision (F1,165 = 10.72, p 0.002) on the wCOM angle (Fig. 4 lower panel). Its mean value with EO was 0.94 0.12 rad in group Y, 1.0 0.2 rad in group E, and 0.94 0.22 rad in PD patients. The angle in the EC trials increased to 1.08 0.18 rad (0.0001) in group E and to 0.98 0.22 radian (p 0.05) in the PD group (Table 1). There was also significant group-by-vision interaction (F2,165 = 4.57, p 0.02). 3.3. COP and COM Directional Indices (DI) Fig. 2. Impact of the COP signal low-pass filtering on sway vector parameters: vector length and it angle in young, healthy subjects.
In the young group, both the COP DIAP and the DIML stayed at the constant level of 0.77 0.01 and 0.49 0.01 for AP and ML
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4
***
50
*** ***
***
0,8
40 35
**
30
DIAP
COP SV Length [mm/s]
45
***
0,6
EO EC
0,4
EO
25
0,2
EC
20
***
1
**
*** 0
15
Y
E
PD
10
1 5
E
***
PD
DIML
Y
1,5
COP SV Angle [rad]
***
***
**
EO EC
0,4
0
1
Y
E
PD
Fig. 5. Directional indices of the COP (DIAP and DIML) in: young (Y), elderly (E), and patients with Parkinson’s disease (PD), while standing still with their eyes open (EO), and eyes closed (EC). The error bars represent standard deviations.
EO EC
0,5
Y
(p 0.001). Closed eyes in the E and PD resulted in a significant (p 0.01) increase in the DIAP while their DIML decreased significantly. Details of these analyses and results of COM DIs are shown in Table 1.
E
PD
Fig. 3. Polar coordinates (mean and standard deviation) of the COP SV in: young (Y), elderly (E), and patients with Parkinson’s disease (PD), while standing still with their eyes open (EO), and eyes closed (EC).
respectively, regardless of visual conditions (Fig. 5). Statistical analysis confirmed, however, a significant (p .001) dependence of both DIs on vision in both E and PD groups. In the elderly, the mean COP DIAP was higher compared with those in the PD group 10
COM SV Length [mm/s]
***
0,6
0,2
0
***
9
***
8
***
7
***
6
***
5
EO
***
EC
4 3 2 1 0
Y
E ***
1,5
PD
***
Results of this analysis are summarized in Table 1. In the young group, the mean values of the AP sway ratio (4.1 0.9) were significantly lower compared with the other groups and independent on vision (4.2 1.0 in EC testing, p < 0.66). The mean SRAP reached the highest magnitude in patients with PD (5.6 4.4 (EO) and 6.7 5.4 (EC) (p 0.001). A less pronounced and insignificant increase in the AP SR from 4.58 1.9 (EO) to 5.1 2.2 (EC) (p 0.07) was noticed in the E group. The mean SRAP in both E and PD groups differed from the Y group (F2,165 = 7.28, p 0.001) and significant differences were found between the PD group and the E group in both the EO and EC trials (Table 1). The results of the ANOVA showed significant effects of both group (F2,165 = 9.2, p 0.001) and vision (F1,165 = 7.45, p 0.01), and group by vision interaction (F2,165 = 5.75, p 0.005) on SRML. In young subjects, the exclusion of vision resulted in an insignificant decrease in the mean SRML (from 4.3 1.5 (EO) to 4.05 1.3 (EC), p 0.46). In contrast, both the elderly and PD groups exhibited an increase in this parameter but it was significant only in the PD group (5.7 4.3 to 7.03 5.2, p 0.001). 4. Discussion
*** 1 EO EC
0,5
0
Y
3.4. Sway ratio (SR)
*** ***
COM SV Angle [rad]
***
***
0,8
0
E
PD
Fig. 4. Polar coordinates of the SV COM in: young (Y), elderly (E), and patients with Parkinson’s disease (PD), while standing quietly with eyes open (EO), and eyes closed (EC). The error bars represent standard deviations.
This study aimed to quantify the directional characteristics of spontaneous postural sway in order to establish the novel prognostic metrics related to postural instability. For this purpose, the COP trajectories were assessed in subjects from 3 experimental groups with well documented differences in postural stability. Their sway characteristics were analyzed using 3 novel measures: SV, DI and SR. All the measures showed several advantages, making them unique in the assessment of postural control. They are virtually independent of such critical factors as the length of a trial and as well as the COP sampling frequency [3,4]. The most comprehensive measure proved to be the sway vector.
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The SV concept is an extension of the stability radius applied in the control theory [23], which in basic terms describes the largest magnitude of perturbation that might be tolerated by postural control without loss of balance. The stability radius of postural control is, therefore, determined by the dimensions of the stability area, which could be modeled by an ellipse centered around the COP reference position [14,24]. Two separate mechanisms must be considered for postural control in the AP and ML directions [12] therefore each axis would correspond to a different stability radius [4,25]. These mechanisms are, however, mutually interrelated by the object of the control since they act on the same inverted pendulum of human body [3,4,12]. This interaction is represented here by the SV angle. Therefore, to obtain a better insight into postural control and its changes due to ageing and pathology, all components of the localized SV (its point of application, length, and angle) should be analyzed. During quiet stance, the SV point of application is the COP reference position (RP) i.e., the average of the COP coordinates within the stability area [24]. In young individuals during quiet stance the RP is positioned almost in the middle of the stability area [14,24]. At the same time, their range of sway is negligible compared with the size of the stability area. Both ageing and PD move the RP towards the anterior boundary of stability [10,14] which could be considered as a compensatory strategy. Such a strategy results in a flexed posture of the PD patient [28]. This posture further increases the SV magnitude while the area of stability is reduced at the expense of margin of safety. As a result, the postural stability declines rapidly [10,11,14,26]. Anisotropy of postural sway implies the asymmetry of both the postural control and the stability area [4,14]. My present results of the DI in young healthy subjects are consistent with previous findings and show that these metrics are very stable [4]. It could be seen here in a very low standard deviation of both DIAP and DIML in a group of 60 control subjects. These measures, however, are sensitive to stability decline due to ageing and PD. The most stable posture as seen in young healthy subjects is characterized by almost invariant DIs (DIAP = 0.77, DIML = 0.49). Consequently, the ratio that is used to determine the SV angle is also constant. This fixed angle and the SV of 0.92 rad set the optimal level of interaction between the AP and ML controls and may be considered as a valid determinant of postural stability. The decline of postural stability in the E and PD groups has a varied impact on the DI and SV indices. In contrast to young healthy subjects, a significantly increased length of the SV and an altered mean polar angle characterized stability in older adults. In this population, both attributes of the SV exhibited a higher sensitivity to visual control, documenting a decline in the postural control. As could be expected, more pronounced changes in SV attributes were observed in patients with Parkinson’s diseases, apparent from their less stable posture [3,7–11,26,28]. Compared with the elderly, an additional forward shift of the RP was noticed in the PD group [10,11,28] which was accompanied by an increase in sway velocity (the SV length in the present study). In contrast to the age-related decline in postural stability, which was additionally characterized by the increased sway angle, the mean value of this metrics in PD remained at the level characteristic for the Y group. This result documents the effectiveness of the flexed posture strategy in maintaining AP-ML interaction at the optimal level. Thus, the SV angle maps specific changes in the control system making it irreplaceable in the assessment of postural compensatory mechanisms. The action of these mechanisms is seen also in the increase of both the DIML and SRML magnitudes, particularly in the ‘‘eyes closed’’ tests. The directional sway measures represent uncertainty in postural control and allow the stability deficits to be pinpointed. Recent studies revealed that the AP COP trajectory and the activity
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of the ankle plantar flexors are closely related [13,27]. Therefore, the SR values assessed in this study may be used to estimate the efforts in postural control that allow the maintenance of a spontaneously swaying COP position at RP [3]. As could be expected, the exclusion of vision did not affect SR in young healthy subjects but did result in an increase of the AP and ML SR in both the elderly and PD groups. The SR increase suggests poorer postural control in the older adults and PD patients [7,9,10]. A higher SR value in PD, as observed in the current study, may correspond with increased tremor-type oscillations, as seen in the patients who are more prone to falls [7–11]. The latter inference seems reasonable because despite the higher SR value, an increase in the magnitude of the COP and the COM SV was observed in the PD group compared with more stable elderly subjects. In conclusion, the directional measures (SV, DI and SR) have proven their salient features as well as their specificity and sensitivity to detect postural stability impairments due to ageing and pathology. It appears that these sway measures can provide a better assessment of postural control (particularly in terms of biomechanical and physiological characteristics) and that the directional output measures can be readily interpreted. When tested, the measures provided a reliable standard for the assessment of postural stability, and hence, can be used as predictors of balance impairments. These results confirm sensitivity and specificity of the SV components to postural stability decline, and allow me to recommend the sway vector as a useful measure in both the laboratory and clinical assessment of postural control. Acknowledgments This research was supported by the statutory funds from the Jerzy Kukuczka Academy of Physical Education in Katowice. I thank Diana Chwiejczak for her valuable comments and edits on the manuscript. Conflict of interest I declare no conflict of interest.
Appendix A. Supplementary data Supplementary data associated with this article can be found, in the online version, at http://dx.doi.org/10.1016/j.gaitpost.2015.10. 014. References [1] Raymakers JA, Samson MM, Verhaar HJJ. The assessment of body sway and the choice of the stability parameter(s). Gait Posture 2005;21:48–58. [2] Scoppa F, Capra R, Gallamini M, Shiffer R. Clinical stabilometry standardization. Basic definitions – acquisition interval – sampling frequency. Gait Posture 2013;37:290–2. [3] Błaszczyk JW. Sway ratio – a new measure for quantifying postural stability. Acta Neurobiol Exp (Warsaw) 2008;68:51–7. [4] Błaszczyk JW, Beck M, Sadowska D. Assessment of postural stability in young healthy subjects based on directional features of posturographic data: vision and gender effects. Acta Neurobiol Exp (Warsaw) 2014;74:433–42. [5] Maki BE, Holliday PJ, Topper AK. A prospective study of postural balance and risk of falling in an ambulatory and independent elderly population. J Gerontol Med Sci 1994;49:M72–84. [6] Piirtola M, Era P. Force platform measurements as predictors of falls among older people—a review. Gerontology 2006;52:1–16. [7] Schoneburg B, Mancini M, Horak F, Nutt JG. Framework for understanding balance dysfunction in Parkinson’s disease. Mov Disord 2013;28:1474–82. http://dx.doi.org/10.1002/mds.25613. [8] Kerr G, Morrison S, Silburn P. Coupling between limb tremor and postural sway in Parkinson’s disease. Mov Disord 2008;23:386–94. [9] Frenklach A, Louie S, Koop M, Bronte-Stewart H. Excessive postural sway and the risk of falls at different stages of Parkinson’s disease. Motor Control 2009; 24:377–85.
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J.W. Błaszczyk / Gait & Posture 44 (2016) 1–6
[10] Błaszczyk JW, Orawiec R. Assessment of postural control in patients with Parkinson’s disease: sway ratio analysis. Hum Mov Sci 2011;30:396–404. [11] Menant JC, Latt MD, Mentz HB, Fung VS, Lord SR. Postural sway approaches center of mass stability limits in Parkinson’s disease. Mov Disord 2011;26: 637–43. [12] Winter DA, Prince F, Frank JS, Powell C, Zabjek KF. Unified theory of A/P and M/ L balance in quiet stance. J Neurophysiol 1996;75:2334–43. [13] Maurer C, Peterka RJ. A new interpretation of spontaneous sway measures based on simple model of human postural control. J Neurophysiol 2005;93: 189–200. [14] Błaszczyk JW, Lowe DL, Hansen PD. Ranges of postural stability and their changes in the elderly. Gait Posture 1994;2:11–7. [15] Corriveau H, Hebert R, Prince F, Raiche M. Intrasession reliability of the center of pressure minus center of mass variable of postural control in healthy elderly. Arch Phys Med Reh 2000;81:45–8. [16] Pinsault N, Vuillerme N. Test-retest reliability of centre of foot pressure measures to assess postural control during unperturbed stance. Med Eng Phys 2009;31:276–86. [17] Swanenburg J, deBruin ED, Favero K, Uebelhart D, Mulder T. The reliability of postural measures in single and dual tasking in elderly fallers and non-fallers. BMC Musculoskeletal Disorders 2008;9:162. http://www.biomedcentral.com/ 1471-2474/9/162S. [18] Collins JJ, De Luca CJ. Open-loop and closed-loop control of posture: a random walk analysis of center of pressure trajectories. Exp Brain Res 1993;95: 308–18.
[19] Błaszczyk JW, Klonowski W. Postural stability and fractal dynamics. Acta Neurobiol Exp (Warsaw) 2001;61:105–12. [20] Sabatini AM. Analysis of postural sway using entropy measures of signal complexity. Med Biol Eng Comput 2000;38:617–24. [21] Rocchi L, Chiari L, Cappello A. Feature selection of stabilometric parameters based on principal component analysis. Med Biol Eng Comput 2004;42:71–9. [22] Bottaro A, Yasutake Y, Nomura T, Casadio M, Morasso P. Bounded stability of the quiet standing posture: an intermittent control model. Hum Mov Sci 2008;27:473–95. [23] Hindrichsen D, Pritchard AJ. Stability radii of linear systems. Sys Contr Lett 1986;7:1–10. [24] Błaszczyk JW. The method of spatial distribution histograms and contour plots applied to postural stability evaluation in young and elderly subjects. In: Gantchev N, Gantchev GN, editors. From basic motor control to function recovery. Sofia: Academic Publishing House; 1999. p. 197–202. [25] Saripalle SK, Paiva GC, Cliett 3rd TC, Derakhshani RR, King GW, Lovelace CT. Classification of body movements based on posturographic data. Hum Mov Sci 2014;33:238–50. [26] Horak FB, Dimitrova D, Nutt JG. Direction-specific postural instability in subjects with Parkinson’s disease. Exp Neurol 2005;193:504–21. [27] Borg F, Finell M, Herrala M, Hakala I. Analyzing gastrocnemius EMG-activity and sway data from quiet and perturbed standing. J Electromyogr Kinesiol 2007;17:622–34. [28] Błaszczyk JW, Orawiec R, Duda-Kłodowska D, Opala G. Assessment of postural instability in patients with Parkinson’s disease. Exp Brain Res 2007;183:107–14.