Rambling and trembling trajectories in the analysis of postural sway prior to the self-paced and reaction time tasks

Abstract

Objective: Previous studies suggested that center of pressure (COP) shifts occur before an expected perturbation in the form of early and anticipatory postural adjustments which operate in a short time scale. However, the effect of such perturbations on pre-existing postural set on a longer time scale remained uncovered. The purpose of this study was to investigate whether rambling and trembling components of the COP trajectories depend on postural task or phase of trial before a self-initiated perturbation.

Materials and Methods: Twenty-four young healthy participants took part in the study. Subjects performed three postural tasks, namely, (i) quiet stance task: 60 seconds quiet stance, (ii) self-paced task: maximal vertical jump from quiet stance under the self-paced time condition, and (iii) reaction-time task: maximal vertical jump from quiet stance under the reaction-time condition. Postural sway features were examined in two phases, the first and last 20 seconds of the trials.

Results: The features of rambling and trembling components of the COP trajectories were affected by postural task or phase of trial. The ellipse area of the COP and rambling trajectories were significantly different among postural tasks. The median frequency was significantly different between the phases of trials for the COP and rambling trajectories.

Conclusion: This study indicated task-specific changes in postural sway features. Rambling and trembling trajectories, which would reflect two underlying human postural control mechanisms as maintaining the body's equilibrium with respect to a moving reference point and oscillating around the moving reference point respectively, were affected differently before a whole-body maximum-effort self-initiated perturbation.

Introduction

Even in static conditions, human postural control is an actively controlled process by the neurophysiological mechanisms which is also the basis for dynamic postural adjustments preceding, during, and subsequent voluntary movements. It has been stated that postural adjustments are not elicited by only postural reflexes in response to perturbations but also emanated from supraspinal commands to the musculoskeletal system (1). In postural motor tasks, the reaction forces originating from the contact of limb(s) and the environment change as a function of active forces (e.g., forces generated by muscle contraction) developed by the musculoskeletal system and passive forces thereof (e.g., forces due to inertia of body parts). The ground reaction forces and moments of forces arising from the contact of the feet and the ground, especially in the form of the application point of the equivalent force system, i.e., center of pressure (COP) (2), is of particular interest to study postural adjustments in relation to postural sway.

It has been demonstrated that prior to the initiation of a voluntary movement from quiet stance, COP shifts occur before the expected perturbation (3). That phenomenon has been explained by the notion of feed-forward postural adjustments (i.e., early and anticipatory postural adjustments, EPAs and APAs, respectively).  APAs are defined as the activation of postural muscles in a feedforward manner before initiation of a voluntary movement, in anticipation movement would cause destabilizing forces (4). For instance, in vertical jump movements, the existence of APA has been evidenced by a backward COP shift caused by modulation of antagonistic lower leg muscles (5). On the other hand, pre-existing postural set of the forthcoming perturbation have been shown to modulate postural adjustments (6). It is a general observation that several factors such as readiness, attention, and expectations can greatly affect motor responses to stimuli (7). As a potential mediator of pre-existing postural set, time constraint has been linked to influence postural adjustments. Such that, under a simple reaction time instruction, time constraint has been shown to modify spatio-temporal features of APAs (8). That study, however, only focused on the APAs which operate in a short-term interval of time (<1 s) of perturbation onset.

Human upright posture exhibits an everlasting oscillatory behavior, and it has long been recognized that postural sway during standing has two underlying components or processes: a slow non-oscillatory and a faster oscillatory one (9). Indeed, several researchers have presented models and analyses to investigate those components or processes, and named them as, for instance, open-loop (for short-term interval of time (<1 s)) and closed-loop (for long-term interval of time (>1 s)) (10,11), or conservative and operative (12). Zatsiorsky and Duarte (13,14) proposed a method to decompose those two processes from COP trajectories and termed them as rambling and trembling. The authors postulated that human postural control mechanisms instantly maintain the body's equilibrium in upright posture with respect to a moving reference point. Then, the rambling component describes the non-oscillatory motion of that moving reference point, migration of reference point, and the trembling component describes fast oscillatory motion around the moving reference point. The amplitude of the former component is about three times larger than the latter one, on the other hand, the trembling frequency is about four-fold larger than the rambling frequency in young healthy adults (14). It has been suggested that the rambling reflects supraspinal control mechanisms of human upright posture, while the trembling reflects spinal reflexes and biomechanical properties of the elements of the postural system in the periphery (15).

Several sway features have been used to reflect the effects of perturbations and interventions, and influence of biomechanical factors as well as other factors such as age, sex, and illness on postural sway (16-19). Those sway features or measures as root mean square (RMS) distance, mean distance, range, fitted circle and ellipse areas have been used to quantify excursions of COP over the base of support, i.e., amplitude of postural sway (17). Those sway features were found to be reliable (19) and able to identify differences between perturbations (17). Particularly, fitted ellipse areas, for instance, have been used to measure drug effects (20), to estimate afferent inputs for postural stability with alcohol intervention (16), to test the hypothesis whether a person can voluntarily reduce postural sway (15).

Self-initiated perturbations such as voluntary leg (21) or arm movements (22) from normal upright standing have received extensive attention in relation to investigation of postural adjustments just prior to (<1 s) perturbations. However, the effect of such perturbations on pre-existing postural set on a longer time scale and the supraspinal and spinal mechanisms associated with the observed COP excursions in the preceding long-term (>1 s) postural control before a whole-body maximum-effort self-initiated perturbation such as maximal vertical jump remained uncovered. In this study, we hypothesized that such a self-initiated perturbation would influence pre-existing postural set which would reflect measures of postural sway during quiet stance preceding the perturbation. We aimed to test that hypothesis by studying features of rambling and trembling components of the COP trajectories while standing quietly in upright erect posture in preparation of a maximal motor task with and without a time constraint.

Material and Methods

Participants

Twenty-four healthy young subjects (12 male and 12 female, age:21.1±2.2 years, height:173.2±4.9 cm, weight:71.8±3.8 kg) voluntarily participated in the study. The participants were healthy and had no known musculoskeletal or neurological disorders. All participants gave informed consent as required by the Declaration of Helsinki. The study was approved by the local ethics committee.

A priori statistical power analysis was performed for sample size estimation using the G*Power 3.1 software (23) with the option of effect size specification (24). With an alpha=0.05, power=0.80, and effect size f(V)=0.8, the projected sample size needed was 17 subjects for repeated measures ANOVA within-factors design.

Apparatus

A strain gauge-based force plate (AMTI-OR6-7-OP-2000), a personal computer, and a LCD monitor was used in data collection procedures. The force plate registered six analog signals of the ground reaction forces (Fx,Fy,Fz) and moments (Mx,My,Mz) during stance. The analog signals were conditioned and pre-amplified with the signal conditioner, then digitized at 100 Hz with a 16-bit A/D data acquisition (DAQ) module (NI-USB-6225) and fed to the computer. DAQ process management and user feedback were controlled by a custom program running in a MATLAB DAQ session. The digital signals were further manipulated and analyzed in the MATLAB software environment.

Procedures

The participants performed five trials of each three different postural tasks: (i) QS task: 60 seconds quiet stance (QS), (ii) SP task: maximal vertical jump (MVJ) from QS under the self-paced (SP) time condition, (iii) RT task: MVJ from QS under the reaction-time (RT) time condition. For the QS, the participants were asked to stand quietly on the force plate with open eyes, and self-position their feet parallelly on the center of the plate with arms hanging at their sides and head looking forward to the center of the monitor screen that was positioned at the eye level and about 1.5 m away from the force plate (Figure 1). For the MVJ, the participants were asked to jump with maximal effort without using arms and land onto the center of the plate. In all trials of three different postural tasks, the screen displayed text indicating the then-current postural task and a raising bar that becomes full at 60 seconds. In all postural tasks, the participants were asked to stand quietly for 60 seconds, however, in the SS and RT, after 60 seconds, the subjects also performed an MVJ from QS either at a self-paced time in the following 30 seconds or whenever they heard a beep sound presented between the following 5 to 15 seconds respectively. Each participant performed 15 trials in a different random order. Before the experimental trials, subjects performed practice trials for familiarization to the experimental procedures.

Figure 1. The schematic presentation of the experimental setup

If an activity requires attention, then some of the limited capacity of attention must be allocated to its performance (25). As the amount of attentional capacity is considered to be limited, some other activity that also requires a certain amount of this capacity will compete with the other activities for these limited attentional resources, in this way, performance could deteriorate if this capacity was approached by the task requirements (25). It was claimed that attentional requirements for postural control and cognitive activity are not constant yet variable depending on the processing demands of the task (26). In the QS task, the subject only needs to keep quiet stance while following the raising bar on the screen that becomes full at 60 seconds. On the SP task, the subject is not just in quiet stance but in a state of readiness to make a movement (7) as MVJ in a self-paced manner after the raising bar on the screen becomes full. On the RT task, the subject is also in a state of readiness to make a movement as MVJ after the raising bar on the screen becomes full, yet this time, in a reaction time manner, thus the subject additionally has to give attention to a beep sound that would be presented randomly in time. It is therefore possible to consider the RT task as more attentionally challenging than the SP task, and both RT and SP tasks more attentionally challenging than the QS task.

Signal Processing

The digitized ground reaction forces and moments signals from all subjects and trials were filtered with a zero-lag, low-pass, and bi-directional second order Butterworth filter at 10 Hz. From the filtered signals, the coordinates of the point of the application of the ground reaction forces (i.e., center of pressure or COP) were calculated by using the following equations in the anterior-posterior (AP) and medial-lateral (ML) directions respectively. The trajectories of COP_AP and COP_ML displacements were used to describe the human postural sway.

COP_AP = (–M_y–h*F_x)/F_z

COP_ML = (+M_x–h*F_y)/F_z

where x-axes of the force plate register the forces in the AP direction of the participant, y-axes of the force plate register the forces in the ML direction of the participant, Fz is the vertical ground reaction force on the force plate, and h (a positive value) is the vertical distance between the center of the top of the plate and the measurement origin of the force plate. The mean values subtracted from each corresponding COP_AP and COP_ML time series before further analysis.

The COP_AP and COP_ML trajectories were then decomposed into Rambling (RM) and Trembling (TR) trajectories separately (14). Briefly, to obtain the RM trajectory in the AP direction (RM_AP), first, every instance when the horizontal force (F_x) is zero (instant equilibrium point or IEP) in the AP direction were identified by using linear interpolation on the horizontal force time series. Then, the COP_AP positions at those IEPs were determined and interpolated by cubic spline functions to estimate the RM_AP trajectory. Next, the TR trajectory in the AP direction (i.e., TR_AP) was estimated as the deviation of the COP_AP trajectory from the RM_AP trajectory (Figure 2, 3, and 4). The same procedure was then repeated separately on the ML counterparts of the COP and horizontal force (for COP_ML, that is F_y) trajectories to obtain RM_ML and TR_ML.

Figure 2. For the QS task, the center of pressure (COP), rambling (RM), and trembling (TR) trajectories in the anterior-posterior (AP) and medial-lateral (ML) directions for a representative subject. The blue line shows the fitted ellipse

Figure 3. For the SP task, the center of pressure (COP), rambling (RM), and trembling (TR) trajectories in the anterior-posterior (AP) and medial-lateral (ML) directions for a representative subject. The blue line shows the fitted ellipse

Figure 4. For the RT task, the center of pressure (COP), rambling (RM), and trembling (TR) trajectories in the anterior-posterior (AP) and medial-lateral (ML) directions for a representative subject. The blue line shows the fitted ellipse

To quantify human postural sway in quiet stance, the sway areas covered by COP, RM, and TR trajectories on the x-y or AP-ML planes were estimated. The area estimation based on elliptic area approximation to the sway data. A method based on the principal component analysis was used to compute the exact 95% prediction ellipse area (E-area) in which 95% of the discrete data points of the future observations would lie within the perimeter of the ellipse (27,28). E-area was calculated for each COP and its decompositions, i.e., RM and TR, trajectories for the initial 20 seconds of the trials (early phase) and also for the last 20 seconds of the stance in the QS task or 20 seconds before the MVJ in the SP and RT tasks (late phase). The initiation of MVJ was identified by analyzing the changes in the vertical force trajectory. To do that, first, the mean value of the vertical force in the first 60 seconds of stance (mean60) and the absolute value of the peak difference between the vertical force trajectory and the mean value of the vertical force (max-residual) were computed. Then, the start of MVJ was detected as the first instant when the absolute value of the deviation of the vertical force trajectory from the mean60 is greater than the 1.5 times max-residual (29). Along with E-area, mean velocity (VEL), RMS distance (RMS), and median frequency (MEDFREQ) (17) of COP, RM, and TR trajectories were calculated not on separate AP or ML trajectories but on the resultant distance time series which is the vector distance of each pair of points in the AP and ML plane (i.e., [AP[n]² + ML[n]²]^½ for n=1,...,N, where N is the number of data points (17).

Statistical analysis

Statistical analysis was performed using SPSS v23 on the mean values of postural sway measures calculated from five trials of three postural tasks. The data was subjected to two-way (postural task (3 levels: QS, SP, RT) and phase of trial (2 levels: early, late) conditions) repeated measure analysis of variance (ANOVA) with Huynh-Feldt correction. For post hoc analysis, Fisher's least-significant difference (LSD) test was applied to determine statistical significance. Significance level was set at p<0.05.

Results

Ellipse area

The mean value and standard deviation of the E-area of postural sway during quiet stance were presented in Table 1.

Table 1. The mean and standard deviation (SD) of the ellipse area of the COP (center of pressure), RM (rambling), and TR (trembling) trajectories for the early and late phases of the trials for the quiet stance (QS), QS with self-paced (SP) and reaction-time (RT) conditions before the perturbation

Center of pressure trajectory

For the COP trajectory, the ANOVA yielded a main effect of the postural task condition for the ellipse area (p=0.038, η²=0.275). Post-hoc analyses revealed that the subjects in the QS task produced a significantly smaller area (mean=83.44 mm²) compared to the RT task (mean=105.52 mm²). The ANOVA also revealed that there was no significant main effect of the phase of trial (p=0.233, η²=0.126).

Rambling trajectory

For the RM trajectory, the ANOVA yielded a main effect of the postural task condition for the ellipse area (p=0.035, η²=0.272). Post-hoc analyses revealed that the subjects in the QS task produced a significantly smaller area (mean=64.60 mm²) compared to the RT task (mean=83.84 mm²). The ANOVA also revealed that there was no significant main effect of the phase of trial (p=0.052, η²=0.302).

Trembling trajectory

For the TR trajectory, the ANOVA did not yield a main effect of the postural task condition for the ellipse area (p=0.601, η²=0.045). The ANOVA also revealed that there was no significant main effect of the phase of trial (p=0.063, η²=0.279).

Median frequency

The mean value and standard deviation of the MEDFREQ of postural sway during quiet stance were presented in Table 2.

Table 2. The mean and standard deviation (SD) of the median frequency of the COP (center of pressure), RM (rambling), and TR (trembling) trajectories for the early and late phases of the trials for the quiet stance (QS), QS with self-paced (SP) and reaction-time (RT) conditions before the perturbation

Center of pressure trajectory

For the COP trajectory, the ANOVA did not yield a main effect of the postural task condition for the MEDFREQ (p=0.277, η²=0.109). The ANOVA also revealed that there was a significant main effect of the phase of trial (p=0.008, η²=0.492). Post-hoc analyses revealed that the MEDFREQ in the early phase was significantly smaller (mean=0.264, SD = 0.054 Hz) compared to the late phase (mean=0.290, SD = 0.065 Hz).

Rambling trajectory

For the RM trajectory, the ANOVA did not yield a main effect of the postural task condition for the MEDFREQ (p=0.321, η²=0.098). The ANOVA also revealed that there was a significant main effect of the phase of trial (p=0.020, η²=0.400). Post-hoc analyses revealed that the MEDFREQ in the early phase was significantly smaller (mean=0.207, SD = 0.030 Hz) compared to the late phase (mean=0.220, SD = 0.036 Hz).

Trembling trajectory

For the TR trajectory, the ANOVA did not yield a main effect of the postural task condition for the ellipse area (p=0.425, η²=0.075). The ANOVA also revealed that there was no significant main effect of the phase of trial (p=0.063, η²=0.281).

Mean velocity

The mean value and standard deviation of the VEL of postural sway during quiet stance were presented in Table 3.

Table 3. The mean and standard deviation (SD) of the mean velocity of the COP (center of pressure), RM (rambling), and TR (trembling) trajectories for the early and late phases of the trials for the quiet stance (QS), QS with self-paced (SP) and reaction-time (RT) conditions before the perturbation

Center of pressure trajectory

For the COP trajectory, the ANOVA did not yield a main effect of the postural task condition for the VEL (p=0.368, η²=0.087). The ANOVA also revealed that there was no significant main effect of the phase of trial (p=0.504, η²=0.042).

Rambling trajectory

For the RM trajectory, the ANOVA did not yield a main effect of the postural task condition for the VEL (p=0.630, η²=0.088). The ANOVA also revealed that there was no significant main effect of the phase of trial (p=0.063, η²=0.280).

Trembling trajectory

For the TR trajectory, the ANOVA did not yield a main effect of the postural task condition for the ellipse area (p=0.326, η²=0.097). The ANOVA also revealed that there was no significant main effect of the phase of trial (p=0.314, η²=0.092).

RMS distance

The mean value and standard deviation of the RMS of postural sway during quiet stance were presented in Table 4.

Table 4. The mean and standard deviation (SD) of the RMS distance of the COP (center of pressure), RM (rambling), and TR (trembling) trajectories for the early and late phases of the trials for the quiet stance (QS), QS with self-paced (SP) and reaction-time (RT) conditions before the perturbation

Center of pressure trajectory

For the COP trajectory, the ANOVA did not yield a main effect of the postural task condition for the RMS (p=0.204, η²=0.134). The ANOVA also revealed that there was a significant main effect of the phase of trial (p=0.006, η²=0.510). Post-hoc analyses revealed that the RMS in the early phase was significantly greater (mean=2.209, SD = 0.718 mm) compared to the late phase (mean=1.936, SD = 0.534 mm).

Rambling trajectory

For the RM trajectory, the ANOVA did not yield a main effect of the postural task condition for the RMS (p=0.086, η²=0.388). The ANOVA also revealed that there was a significant main effect of the phase of trial (p=0.005, η²=0.533). Post-hoc analyses revealed that the RMS in the early phase was significantly greater (mean=2.019, SD = 0.686 mm) compared to the late phase (mean=1.733, SD = 0.491 mm).

Trembling trajectory

For the TR trajectory, the ANOVA did not yield a main effect of the postural task condition for the ellipse area (p=0.677, η²=0.075). The ANOVA also revealed that there was a significant main effect of the phase of trial (p=0.007, η²=0.493).  Post-hoc analyses revealed that the RMS in the early phase was significantly greater (mean=0.672, SD = 0.213 mm) compared to the late phase (mean=0.591, SD = 0.152 mm).

Discussion

This study was conducted to examine the features of rambling and trembling components of the COP trajectories while standing quietly in upright erect posture in preparation of a MVJ with and without a time constraint. To do so, the postural sway signals captured during the postural tasks as QS, SP, and RT were decomposed into RM and TR components which would reflect two underlying human postural control mechanisms as maintaining the body's equilibrium with respect to a moving reference point and oscillating around the moving reference point respectively. Four measures were used to quantify postural sway as E-area, MEDFREQ, VEL, and RMS. The findings of the study partly supported our hypothesis that changes over the features of the postural sway during quiet stance would be postural task dependent. There were significant differences between the QS and RT postural tasks on the E-area of the COP and RM trajectories but not of the TR trajectory. Another significant finding of this study was that the MEDFREQ was significantly different between the early and late phases of the postural tasks for the COP and its RM component but not for the TR component.  

The sway area during quiet stance increased on average in state of readiness to make a movement as MVJ. This increase, however, reflected into the COP and RM trajectories but not into the TR trajectory. The E-area (27) is a traditional and widely used postural sway measure and considered as an index of overall postural performance, the smaller the sway area, the better the performance (30). That would indicate that postural performance decreases by increasing the challenge of postural task. According to the rambling-trembling hypothesis, postural sway arises from both the deviation from the reference position (TR) and the reference point migration (RM). The COP and RM trajectories are highly correlated (14), hence it would be expected that changes in the E-area of the COP and RM trajectories were similar. On the other hand, the E-area of the TR component did not change among postural tasks.

The MEDFREQ of postural sway between the early and late phases of quiet stance among postural tasks were different significantly. Such frequency measures as mean, median, 80% power frequency provide a general view of the frequency content of the postural sway (31). The trembling median frequency is larger than the rambling median frequency in young healthy adults (0.74 vs 0.21 Hz) (14). Our results agreed with that finding since we estimated TR MEDFREQ as 0.631 Hz and RM MEDFREQ as 0.220 Hz in the late phase (0.588 vs. 0.207 Hz in the early phase). The mean or median frequencies of sway are considered as indexes of ankle stiffness, the higher frequency of sway, the more apparent stiffness around the ankle joint (31,32). As the MEDFREQ of sway increased in the late phase of trials, it could be inferred from that finding that ankle joint apparent stiffness was modulated by the subjects in state of readiness to make a movement as MVJ.

The sway velocity across postural tasks and phases of the trials did not change. In our analysis, we estimated resultant velocity which reflects the efficiency of the postural control system with regard to the neuromuscular activity required to maintain postural task, the smaller the velocity, the better the postural control (31). As the VEL of sway was similar among postural tasks and between the phases of trials, it could be inferred from that finding that the neuromuscular activity required to maintain postural tasks through the trials were similar. The average VEL of TR across tasks was greater than VEL of RM (5.822 vs. 3.707 m/s). Body sway along the RM trajectory does not induce substantial restoring forces, but the TR trajectory does since it is highly negatively correlated with the horizontal force and the deviation from gravity line (14). Taken altogether, the TR component might demand more neuromuscular activity than the RM component.

Lastly, RMS distance postural sway between the early and late phases of quiet stance among postural tasks differed significantly. Also, RMS increased by increasing the challenge of postural task (1.969, 2.118, and 2.130 mm for the COP trajectory of QS, SP, and RT tasks respectively). As the COP signals were demeaned before further processing, RMS and standard deviation measures, which are variability indexes of sway, gave the same result (31). The findings of the study indicated that variability of sway is phase dependent, as sway variability decreased from 2.209 mm (early phase) to 1.934 mm (late phase) on average for the COP trajectory (2.019 vs. 1.733 mm for RM and 0.672 vs. 0.591 mm for TR). The reason for the decrease in variability might be a change in postural set in the late phase of the trials which could decrease small exploratory movements of the feet (33,34).

Certain limitations affected our study. It is common that postural adjustments have been studied with not only force records but also with electromyographic (EMG) records (8). Muscle activation patterns of postural muscles could have enabled us to study the observed changes in a more detailed manner. Additional studies may be designed in which ground reactions force and EMG signals are recorded synchronously.

Conclusion

This study investigated the features of rambling and trembling components of the COP trajectories and its RM and components while standing quietly in upright erect posture in preparation of a MVJ with and without a time constraint. The findings of the study indicated that several features of the postural sway during quiet stance would be postural task or phase of the trial dependent. The E-area of the COP and RM trajectories were significantly different among postural tasks. The MEDFREQ was significantly different between the phases of the trials for the COP and RM trajectories.

Cite this article as: Celik H, Yilmaz U, Arpinar Avsar P. Rambling and trembling trajectories in the analysis of postural sway prior to the self-paced and reaction time tasks. Turk J Sports Med. 2023; 58(4):146-54; https://doi.org/10.47447/tjsm.0750

The approval for this study was obtained from Hacettepe University, Non-Invasive Clinical Research Ethics Committee, Ankara, Türkiye (Decision no: 2019/13-17 Date: 14.05.2019).

Concept – HC, PAA; Design – HC, PAA; Supervision – HC; Materials – HC; Data Collection and/or Processing – HC, UY, PAA; Analysis and Interpretation – HC, UY, PAA; Literature Review – HC; Writing Manuscript - HC, UY, PAA; Critical Reviews - HC

The authors declared no conflicts of interest with respect to authorship and/or publication of the article.

This research was partially supported by The Scientific and Technological Research Council of Turkey under Grant 115S535.

References

1. Shumway-Cook A, Woollacott MH. Motor control: translating research into clinical practice. 5th ed. Wolters Kluwer; 2017.
2. Winter DA. Biomechanics and Motor Control of Human Movement. John Wiley & Sons; 2009.
3. Aruin AS, Latash ML. The role of motor action in anticipatory postural adjustments studied with self-induced and externally triggered perturbations. Exp Brain Res. 1995;106(2):291–300.
4. Woollacott M. Anticipatory Postural Responses. In: Binder MD, Hirokawa N, Windhorst U, editors. Encyclopedia of Neuroscience. Heidelberg: Springer; 2009. p. 134–5.
5. Pellec AL, Maton B. Anticipatory postural adjustments are associated with single vertical jump and their timing is predictive of jump amplitude. Exp Brain Res. 1999;129(4):551–8.
6. Crenna P, Frigo C. A motor programme for the initiation of forward-oriented movements in humans. J Physiol. 1991;437:635-53.
7. Prochazka A. Sensorimotor gain control: A basic strategy of motor systems? Prog Neurobiol. 1989;33(4):281–307.
8. De Wolf S, Slijper H, Latash ML. Anticipatory postural adjustments during self-paced and reaction-time movements. Exp Brain Res. 1998;121(1):7–19.
9. Kiemel T, Oie KS, Jeka JJ. The slow dynamics of postural sway are in the feedback loop. J Neurophysiol.2006;95(3):1410–8.
10. 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(2):308–18.
11. Collins JJ, De Luca CJ. Random walking during quiet standing. Phys Rev Lett. 1994;73(5):764.
12. Lestienne FG, Gurfinkel VS. Posture as an organizational structure based on a dual process: a formal basis to interpret changes of posture in weightlessness. In: Allum OP and JHJ, editor. Progress in Brain Research. Elsevier; 1988. p. 307–13.
13. Zatsiorsky VM, Duarte M. Instant equilibrium point and its migration in standing tasks: rambling and trembling components of the stabilogram. Motor Control. 1999;3(1):28–38.
14. Zatsiorsky VM, Duarte M. Rambling and trembling in quiet standing. Motor Control. 2000;4(2):185–200.
15. Danna-Dos-Santos A, Degani AM, Zatsiorsky VM, Latash ML. Is voluntary control of natural postural sway possible? J Mot Behav. 2008;40(3):179–85.
16. Bhattacharya A, Morgan R, Shukla R, Ramakrishanan HK, Wang L. Non-invasive estimation of afferent inputs for postural stability under low levels of alcohol. Ann Biomed Eng. 1987;15(6):533–50.
17. Prieto TE, Myklebust JB, Hoffmann RG, Lovett EG, Myklebust BM. Measures of postural steadiness: differences between healthy young and elderly adults. IEEE Trans Biomed Eng. 1996;43(9):956–66.
18. Chiari L, Rocchi L, Cappello A. Stabilometric parameters are affected by anthropometry and foot placement. Clin Biomech. 2002;17(9–10):666–77.
19. Lin D, Seol H, Nussbaum MA, Madigan ML. Reliability of COP-based postural sway measures and age-related differences. Gait Posture. 2008;28(2):337–42.
20. Hasan SS, Robin DW, Shiavi RG. Drugs and postural sway: quantifying balance as a tool to measure drug effects. IEEE Eng Med Biol Mag. 1992;11(4):35–41.
21. Nardone A, Schieppati M. Postural adjustments associated with voluntary contraction of leg muscles in standing man. Exp Brain Res. 1988;69(3):469–80.
22. Bouisset S, Zattara M. A sequence of postural movements precedes voluntary movement. Neurosci Lett.1981;22(3):263–70.
23. Faul F, Erdfelder E, Lang AG, Buchner A. G*Power 3: A flexible statistical power analysis program for the social, behavioral, and biomedical sciences. Behav Res Methods. 2007;39(2):175–91.
24. Cohen J. Statistical power analysis for the behavioral sciences. 2nd ed. Routledge; 1988.
25. Schmidt RA, Lee TD, Winstein CJ, Wulf G, Zelaznik HN. Motor control and learning: a behavioral emphasis. 6th ed. Champaign: Human Kinetics; 2019.
26. Posner MI. Components of Skilled Performance: Human limitations of attention and memory are basic to the analysis of skilled performance. Science. 1966;152(3730):1712–8.
27. Schubert P, Kirchner M. Ellipse area calculations and their applicability in posturography. Gait Posture. 2014;39(1):518–22.
28. Duarte M. Comments on “Ellipse area calculations and their applicability in posturography”(Schubert and Kirchner, vol. 39, pages 518-522, 2014). Gait Posture. 2015;41(1):44–5.
29. Moir GL. Three different methods of calculating vertical jump height from force platform data in men and women. Meas Phys Educ Exerc Sci. 2008;12(4):207–18.
30. Asseman F, Caron O, Crémieux J. Is there a transfer of postural ability from specific to unspecific postures in elite gymnasts? Neurosci Lett. 2004;358(2):83–6.
31. Paillard T, Noé F. Techniques and methods for testing the postural function in healthy and pathological subjects. Biomed Res Int. 2015;2015:e891390.
32. Warnica MJ, Weaver TB, Prentice SD, Laing AC. The influence of ankle muscle activation on postural sway during quiet stance. Gait Posture. 2014;39(4):1115–21.
33. Riley MA, Mitra S, Stoffregen TA, Turvey MT. Influences of body lean and vision on unperturbed postural sway. Motor Control. 1997;1(3):229–46.
34. Vuillerme N, Vincent H. How performing a mental arithmetic task modify the regulation of centre of foot pressure displacements during bipedal quiet standing. Exp Brain Res. 2006;169(1):130–4.