Abstract
A growing consensus across otherwise disparate perspectives on perception and action is that visually guided postural control emerges from within task constraints. Task constraints generate physiological fluctuations across various parts of the body. These fluctuations foster exploration of the available sensory information. For instance, standard deviation (SD) and temporal correlations of bodily sway can indicate how richly postural control samples available mechanical and visual information. Too much or too little SD entails destabilization of posture. Temporal correlations show a similar relationship, but they have also been shown to support carrying sampled information to other aspects of the postural system. The present study shows that increasing visual constraints on posture reveals an adaptive relationship between SD and temporal correlations of postural fluctuations. In short, changing the viewing distance of a fixation target shows that temporal correlations self-correct themselves across time and diminish SD across time as well. Notably, these relationships were strong for all viewing distances except the most comfortable viewing and reaching distance. This self-correcting relationship allows the visual layout itself to press the postural system into a poise for engaging with objects and events in the surrounding.
1. Introduction
1.1. Stability of suprapostural visual activities at longer scales rests on fluctuating behavior at shorter scales
Standing quietly and maintaining focus on a target in front of us is the preamble to very many coordinated behaviors—we might lean forward and reach or track the target’s progress and bat it away. However, this starting position is not merely the preamble to action but is already a rich wellspring of the action itself, exhibiting a continuous stream of intermittent fluctuations. We can see these fluctuations in our bodily center of mass (CoM) and center of pressure (CoP), where ground reaction forces meet our lower extremities. So long as they do not pitch the CoP beyond the base of support, these fluctuations are crucial to maintaining a quiet stance [1,2]. This variability offers the body a subtle and flexible command of the mechanical surface underfoot [3,4], exemplifying long-respected proposals that noise can stabilize nonlinear-dynamical systems [5,6].
Lacing our postural system into our visual field are eyes, moving to lock focus on a distal point in the world. Admittedly, maintaining focus involves “fixations” of the eyes no less than upright posture can seem “still,” but this fixation is not stasis: fixations are regularly recognized as a class of movement [7] consisting of a vibrant, fluctuating foundation of smaller movements called “microsaccades” [8]. These microsaccades serve to stabilize images that would otherwise fade on a static retina [9], thus playing a similar role to the visual system that fluctuations play for the postural system. Indeed the exploratory role of fluctuating movements extends to the extremities of the body besides and intermediating between upright posture and vision [10], suggesting a strong role for postural sway in supporting visual perception [11–13]. Thus, even when standing quietly upright while fixating at a visual target, the body is coursing with fluctuations ferrying information across the body.
The present work aims to explore how visual effort might affect how fluctuations flow within the bodywide postural system. Postural fluctuations produce translations and rotations of visible surfaces specific to the spatial relationships of the objects in the visual field. These movement-induced translations and rotations compose an optic flow that provides visual support for the subsequent movement. Thus, subtle postural sway offers the sighted organism a rich source of information about the layout of objects in the visual field. The visual layout itself then presses the postural system into a poise for engaging with objects and events in the surrounding. Visual targets appearing closer to or farther from the looking postural system impose retina-specific constraints of oculomotor convergence [14,15] and chromatic aberration [16]. Consequently, changes in a target’s size relative to other aspects of the visual field entails changes in optic flow (figure 1). These multi-scale factors affect postural stability, reflecting changes in postural configurations and hence in the flow of information needed to organize these postures.
1.2. Perceptual constraints on postural stability could reshape intrapostural interactivity
In the present study, we aim to explore how changing the viewing distance might change how the postural system exchanges fluctuations within and between CoM and CoP. We examined the relationship between bulk variability in CoP fluctuations (i.e., standard deviation, SD) and temporal structure (i.e., fractal scaling, H) in CoM and CoP fluctuations. The implication of SD is the prevailing tradition, but that of fractality rests on two until-recently parallel bodies of evidence, one specifically requiring variations in fractal geometry for modeling the bodywide organization of the movement system and the second suggesting that capacity of bodily fluctuations to ferry information inheres at least partially in its fractal structure. Movement depends on the bodywide network of connective tissues and nervous tissues, forming flexible relationships that balance tensions with compressions at multiple scales of analysis [17–23]. This organization entails a specifically multifractal geometry that embodies multiple scale-invariant patterns of behavior (e.g., microsaccades within the saccades that intersperse larger saccades by the eye and turns by the head) across time and across space. CoP fractality has repeatedly borne a consistent relationship to perceptual judgments of visual and haptic stimuli [24–29], and research into perceptual tasks (e.g., manually wielding an object to judge heaviness or length) while standing shows that a bodywide flow of fractal fluctuations precedes and shapes the verbal articulation of perceptual judgments [30,31]. Hence, a fractal flow within posture seems to support information flow and might provide a glimpse of the control policy emerging from bodily situation in task constraints.
1.3. Visual effort for fixating across different viewing distances could reveal different relationships amongst CoM fractality, CoP fractality, and CoP SD
1.3.1. The task
The present work is a reanalysis of a previous study that manipulated viewing distance while measuring CoM and CoP [32]. Healthy adults stood maintained a quiet stance under six different conditions: a control condition with eyes closed and five conditions with eyes open and fixating on a red laser point projected on surfaces at 20, 50, 135, 220, and 305 cm distance. We reanalyzed these data by carving individual trials under each viewing condition into non-overlapping sub-trial segments, estimating fractal scaling and SD within each segment, and using vector autoregression (VAR) modeling to test the interactions among these descriptors across segments within each trial.
1.3.2. The hypotheses
Hypothesis 1: Weaker intrapostural interactivity while standing quietly with eyes closed
First, respecting the evidence that maintaining fixation recruits oculomotor effort that can perturb posture [33,34], we predicted that the addition of a fixation task to quiet standing would generally accentuate intrapostural interactivity, suggesting that standing quietly with eyes closed would show weaker evidence of intrapostural interactivity.
Hypothesis 2: Resemblance between the 50-cm viewing condition and the eyes-closed condition
The 50-cm viewing distance is within the comfortable viewing distance, ideal for the human eyes’ focus of red light [16], as well as ideal for requiring the least straining oculomotor convergence [14,15]. Hence, our last and most specific prediction was that the 50-cm viewing condition would yield intrapostural interactivity most closely resembling that in the eyes-closed condition. That is, because 50-cm requires the least visual strain, the effects among CoM fractality, CoP fractality, and CoP SD would show the least differences from the eye-closed condition.
Hypothesis 3: Self-correction of fractality across 10-s segments
Postural sway is more correlated at short timescales on the order of 10 s and more anticorrelated over longer timescales [35]. For instance, posture roams freely about a fixed average CoP position but self-corrects at the margins of the base of support to maintain a quiet stance [35–37]. In this sense, we predicted that fractality itself would show similar self-corrections over time, with prior increases in fractality followed by subsequent alternating decreases and increases in fractality. This self-correcting feature would be a crucial part of any control in which temporal correlations stabilize sway.
Hypothesis 4: Inverse relationship between fractality and SD across 10-s segments
Because fractality entails long-range temporally organized responsivity to mechanical perturbations [38,39], we expected an inverse relationship between either or both of CoP and CoM fractality and CoP SD. That is, increases in CoP and CoM fractality would predict later decreases in CoP SD (Hypothesis 4a), as well as increases in CoP-SD would predict later decreases in CoP and CoM fractality (Hypothesis 4b). This feature could reflect a second key component of task-dependent emergent postural control.
2. Materials and methods
2.1. Participants
Seven adult men and nine adult women (M±1SD age = 23.8±3.9 years) without any skeletal or neuromuscular disorder voluntarily participated after providing verbal and written consent approved by the Institutional Review Board (IRB) at the University of Georgia (Athens, GA).
2.2. Experimental task and procedure
Each participant stood barefoot with one foot on each of two force plates (AMTI Inc., Watertown, MA), 25 cm apart (figure 1a). From behind the participant, a laser pen projected a static point-light on the center of a 5×5” white tripod-mounted screen in front of a white visual-field-filling background. The two force plates measured 3D moments and ground reaction forces. The full-body motion of each participant was measured using VICON Plug-in Gait full-body 39 marker set and an 8-camera VICON motion tracking system (VICON Inc., Los Angeles, CA). The kinetic and kinematic data were synchronized and sampled at 100 Hz.
Each participant was instructed to maintain a quiet stance for 120 s under six different viewing conditions: eyes closed and while fixating visually on the point-light point positioned at 25, 50, 135, 220, and 305 cm distance in front. Each participant completed 18 trials (6 conditions × 3 trials) in a single 90-min session with randomized trial order and with breaks on request and between every six trials.
2.3. Data processing
All data processing was performed in MATLAB 2019b (Matlab Inc., Natick, MA). The position of the bodily center of mass (CoM) was estimated by submitting segment lengths of the head, trunk, pelvis, and left and right hand, forearm, upper arm, thigh, shank and foot to the equations provided by Zatsiorsky and Seluyanov [40], which yielded a 3D center of pressure (CoP) series describing CoM position along the participant’s anterior-posterior (AP), medial-lateral (ML), and superior-inferior axes. 3D moments and ground reaction forces measured on each trial yielded a 2D center of pressure (CoP) series describing CoP position along the participant’s AP and ML axes. Over 120 s duration, each trial yielded a 3D CoM series and a 2D CoP series each of 120 s or 12000 samples, divided into 12 segments of 10 s or 1000 samples each. Each segment yielded two 999-sample one-dimensional series: a CoM spatial Euclidean displacement (SED) series describing the amplitude of CoM displacement (figures 2a to 2f) and a CoP planar Euclidean displacement (PED) series describing the amplitude of CoP displacement (figures 2a to 2f).
2.4. Detrended fluctuation analysis (DFA)
DFA estimates Hurst’s exponent, H, describing the growth of root mean square (RMS) fluctuations with time for first-order displacements known as fractional Gaussian noises (fGn) [41,42]. First, it integrates time series x (t) with N samples to produce y (t) :
Next, DFA computes RMS residuals from the linear trend yn(t) over nonoverlapping n-length bins of y (t) to build a fluctuation function f (N) : for n<N/4. On standard scales, f (N) is a power law: where H is the scaling exponent. H is estimated as the slope of f (N) in log-log plots:
DFA estimated HfGn for the original version (i.e., unshuffled) and a shuffled version (i.e., a version with the temporal information destroyed) of each CoM SED series (CoM-HfGn) and CoP PED series (CoP-HfGn) over the following bin sizes: 4, 8, 12,… 128; figures 2g and 2h).
2.5. Vector autoregression (VAR) analysis
VAR captures linear interdependencies amongst concurrent series and here modeled intrapostural effects of CoM-HfGn, CoP-HfGn, and CoP-SD in one segment on CoM-HfGn, CoP-HfGn, and CoP-SD in subsequent segments (figure 3). VAR describes each variable based on its own lagged value and that of each other variable. Lag is ideally increased until the residuals appear independently and are distributed identically [43].
VAR allows forecasting unique effects of endogenous variables on later values of each other through impulse-response functions (IRFs). IRFs evaluate the relationship between f (t) and g(t + τ), or between g(t) and f (t + τ), where τ is a whole number corresponding to a segment within a trial. Provided VAR residuals are independent and identically distributed (i.i.d.), orthongonalizing these residuals allows simulating an “impulse” to the system by adding 1SEM to any single variable, and using VAR coefficients to describe propagation of later “responses” across all endogenous variables. The IRF describes how an impulse in one series changes later predicted values in a different time series [44,45]. All VAR models converged with lag 1, with residuals passing all tests for i.i.d. status. We performed VAR analysis using the vars package in RStudio [46].
2.6. Statistical analysis of pairwise IRFs
A regression model [47] treated IRFs between each pair of postural descriptors as the dependent measure and tested the effect of predictors including the full-factorial set Trial × Segment × Impulse × Response using the nlme package for RStudio [48]. Impulse and Response served as class variables encoding the different descriptors (CoP-HfGn and CoM-HfGn, and CoP-SD) serving as impulse and as response variables, respectively. Orthogonal linear, quadratic, and cubic polynomials of Segment modeled how impulse-response relationships changed over 999-sample segments within a trial. We used the cubic polynomial to capture the general nonlinear decay of IRFs across later segments. The interactions of HfGn or SD with Segment indicated changes in these effects with different third-order polynomial responses over subsequent trials. The Impulse × Response terms highlighted significant differences of specific impulse-response pairs from the global patterns.
3. Results
3.1 CoM and CoP showed fractal fluctuations
HfGn for all original series fell in the fractal range (0.5 < HfGn < 1; figures 2g and 2h) and significantly exceeded for all corresponding shuffled series (ps < 0.0001; table S1), indicating fractal fluctuation in both CoM and CoP. Crossovers between shorter-(bin sizes: 4, 8, 12,…64) and longer-scale (bin sizes: 4, 8, 12,… 128) behavior exhibited no reliable differences, as HfGn estimates from only shorter-scale behavior correlated strongly with HfGn estimates from the entire DFA fluctuation function (CoM: Spearman’s ρs = 0.96, 0.91, 0.94, 0.94, 0.93, and 0.94 for the eyes-closed and the 25-, 50-, 135-, 220-, and 305-cm eyes-open conditions, respectively, ps < 0.0001); CoP: ρs = 0.96, 0.89, 0.93, 0.92, 0.91, and 0.94, ps < 0.0001).
3.2. Maintaining a quiet stance with eyes closed weakened intrapostural interactivity with trials (Hypothesis 1)
When maintaining a quiet stance with eyes closed, prior increases in CoM-HfGn showed no significant later CoP-SD responses and only subtle later CoP-HfGn and CoM-HfGn responses (figures 4a and 4b). Regression modeling of IRFs (table S2) showed that increases in CoM-HfGn preceded a short-term subsequent decrease and slow, nonlinear rebound (Segment(Quad): b = −6.19×10−1, p = 0.017; and Segment(Cubic): b = 5.36×10−1, p = 0.040) in all variables except CoP-SD (Segment(Quad) × Response(CoP-SD): b = 6.21×10−1, p = 0.092). This decrease-and-nonlinear-rebound was canceled out with Trial for later CoM-HfGn responses (Trial × Segment(Quad): b = 4.29×10−1, p < 0.001; Trial × Segment(Cubic): b = −3.27×10−1, p = 0.007) but showed no such change for later CoP-HfGn responses (Trial × Segment(Quad) × Response(CoP-HfGn): b = −4.04×10−1, p = 0.018; and Trial × Segment(Cubic) × Response(CoP-HfGn): b = 3.45×10−1, p = 0.042) and CoP-SD responses (Trial × Segment(Quad) × Response(CoP-SD): b = −4.27×10−1, p = 0.012; and Trial × Segment(Cubic) × Response(CoP-SD): b = 3.28×10−1, p = 0.054).
Closing eyes weakened the responsivity of all measures to prior increases in each other and in CoM-HfGn, amounting to no later effects of SD and vanishing effects of CoP-HfGn with Trial (figure 4c and 4d). Specifically, regression terms canceled out and reversed effects of prior increases of CoP-SD (Segment(Quad) × Impulse(CoP-SD): b = 7.95×10−1, p = 0.031) and CoP-HfGn (Segment(Quad) × Impulse(CoP-HfGn): b = 1.35×100, p < 0.001). The eyes-closed condition did show positive effects of prior increases in CoP-HfGn on later effects decaying slowly with Segment (Segment(Linear) × Impulse(CoP-HfGn): b = −7.05×10−1, p = 0.056; and Segment(Quad) × Impulse(CoP-HfGn): b = 1.35×100, p < 0.0001), but this effect disappeared with Trial (Trial × Segment(Linear) × Impulse(CoP-HfGn): b = 4.86×10−1, p = 0.004; Trial × Segment(Quad) × Impulse(CoP-HfGn): b = −1.04×100, p < 0.0001).
Critically, the eyes-closed condition diminished intrapostural interactions between CoP-HfGn and CoP-SD, leaving CoP-SD to predict much of the later behavior elsewhere. All significant interactions involving Impulse(CoP-HfGn) and Response(CoP-SD) significantly canceled out the corresponding lower-order interactions of Impulse(CoP-HfGn), effectively muting the effects of a prior CoP-HfGn impulse on later CoP-SD responses [e.g., Segment(Quad) × Impulse(CoP-HfGn) × Response(CoP-SD): b = −1.36×100, p = 0.009; Trial × Segment(Linear) × Impulse(CoP-HfGn) × Response(CoP-SD): b = −4.81×10−1, p = 0.046; Trial × Segment(Quad) × Impulse(CoP-HfGn) × Response(CoP-SD): b = 1.04×100, p < 0.0001]. Effects promoting greater CoP-HfGn at first generally vanished with Trial (Trial × Segment(Linear) × Impulse(CoP-HfGn) × Response(CoP-HfGn): b = −5.54×10−1, p = 0.021; Trial × Segment(Quad) × Impulse(CoP-HfGn) × Response(CoP-HfGn): b = −1.55×100, p = 0.003). Across trials, prior increases in CoP-SD exerted a weaker decrease-and-nonlinear-rebound form on later CoM-HfGn responses (Trial × Segment(Quad) × Impulse(CoP-SD): b = −5.50×10−1, p = 0.001; and Trial × Segment(Cubic) × Impulse(CoP-SD): b = 3.02×100, p = 0.077) but retained this later effect on CoM-HfGn (Trial × Segment(Quad) × Impulse(CoP-SD) × Response(CoP-CoM-HfGn): b = 5.37×10−1, p = 0.023) and on itself (Trial × Segment(Quad) × Impulse(CoP-SD) × Response(CoP-SD): b = 5.48×10−1, p = 0.023).
Though not pictured here, this latter effect held robustly across all viewing conditions: prior increases in CoP-SD predicted later increases in CoP-SD, with the size of this later increase dwindling quadratically at a decreasing rate with Segment (table S2).
3.3. Intrapostural interactivity in the 50-cm viewing condition resembled that in the eyes-closed condition than that in other viewing conditions (Hypothesis 3)
Visually fixating at 50 cm elicited the least amount of intrapostural interactivity, closely resembling the eyes-closed condition. This point is evident first in terms of the number of significant effects. For instance, the regression model yielded 72 coefficients for each condition (tables S2–S6). Compared to effects for all other eyes-open conditions, the 50-cm condition showed significant but opposite effects of Segment(Linear), Trial × Segment(Linear), and Trial × Segment(Linear) × Response(CoP-SD) from the 135-cm condition (table S3), and a significant but opposite effect of Trial × Segment(Linear) × Response(CoP-HfGn) from all other eyes-open conditions (table S4). Of the remaining nine significant effects, Impulse(CoP-HfGn), Segment(Linear) × Impulse(CoP-SD) and Trial × Impulse(CoP-HfGn) did not show significance in any other eyes-open condition, and one other followed the same sign but was little more than half as large as the same significant effect for all other eyes-open conditions (table S4).
In short, these distinctions entailed that, with Trial, the 50-cm condition showed greater but shorter-term reductions in SD following increases in CoP-HfGn, for instance, more negative change in CoP-SD with Trial (Trial × Impulse(CoP-HfGn) × Response(CoP-SD): b = −4.98×10−3, p = 0.023; table S6) and stronger subsequent positive linear growth in CoP-SD (Trial × Segment(Linear) × Impulse(CoP-HfGn): b = 4.87×10−1, p = 0.043; table S4) than in other eyes-open conditions. The other eyes-open conditions typically showed a decrease in CoP-SD following an increase in CoP-HfGn, but the subsequent rebound of CoP-HfGn to zero change was slower and more nonlinear with Trial (Trial × Segment(Quad) × Impulse(CoP-HfGn) × Response(CoP-SD): bs = −1.19×100, −9.22×10−1, −1.17×100, and −1.12×100 for the 20-, 135-, 220-, and 305-cm conditions, respectively, ps < 0.01; table S4). Critically, the 50-cm condition was the only condition that did not show this change in the nonlinearity of later responses in CoP-SD.
3.4. CoM-HfGn and CoP-HfGn self-corrected from segment to segment within a trial but showed sparse effects on each other (Hypothesis 3)
In the eyes-open conditions, increases in CoM-HfGn and CoP-HfGn (CoM-HfGn and CoP-HfGn, respectively) predicted later increases and decreases in alternation over subsequent segments (tables S2 and S5; figures 4a and 4d), suggesting that the eyes-open conditions prompted a sort of self-correcting maintenance of fractality within CoM and CoP. Thus, the act of visually fixating prompted fractality to fall in and out of zero change or to cycle around zero change with negative and positive changes following each other. The model did not yield significant IRF relationships between CoM-HfGn and CoP-HfGn (table S2; figures 4b, c): only the 220-cm viewing condition was accompanied by a CoM-HfGn impulse that predicted later CoP-HfGn responses (figure 4d).
3.5. Increases in CoP-HfGn and CoP-SD predicted subsequent decreases in each other with trials (Hypothesis 4)
In the eyes-open conditions, prior impulses in CoP-HfGn and CoP-SD both predicted later decreases in CoP-SD and CoP-HfGn, respectively (figure 5; table S5). These IRF relationships remained robust with Trial, more so for the effects of a prior CoP-SD impulse on later CoP-HfGn responses (figure 5a) than for the effects of a prior CoP-HfGn impulse on later CoP-SD responses (figure 5b). The 305-cm viewing condition failed to show a significant relationship between a prior CoP-SD impulse and later CoP-HfGn responses on only one trial. The 25-, 135-, and 220-cm conditions each exhibited one, one, and two trials, respectively, that failed to show a relationship between a prior CoP-HfGn impulse and later CoP-SD responses.
4. Discussion
We tested four specific hypothesis concerning how visual effort might moderate intrapostural interactivity. First, we predicted that standing quietly with eyes closed would exhibit weaker intrapostural interactivity (Hypothesis 1). Second, we predicted that CoM-HfGn and CoP-HfGn would self-correct over time (Hypothesis 2). Third, we predicted an inverse relationship between SD and fractality over time, that is, that increases in CoM-HfGn and CoP-HfGn would prompt later decreases in CoP-SD (Hypothesis 3a) and that increases in CoP-SD would prompt later decreases in CoM-HfGn and CoP-HfGn (Hypothesis 3b). Fourth, we predicted that these intrapostural interactions in the 50-cm viewing condition would most closely resemble intrapostural interactions in the eyes-closed condition (Hypothesis 4). Results supported all four hypotheses with the only exception being the failure of CoM-HfGn to participate in the relationships predicted in Hypothesis 3.
The regression modeling of IRFs revealed that in the eyes-closed condition, most effects of CoM-HfGn, CoP-HfGn, and CoP-SD on themselves and on each other were brief and canceled out with Segment and Trial (Hypothesis 1). Figures 4 and 5 show that IRF modeling did yield some significant later responses, but the non-significant coefficients yielded by the model reflect the fact that these significant responses were sparse and unstable.
CoM-HfGn and CoP-HfGn did indeed self-correct (Hypothesis 2), with zig-zag IRF plots indicating alternation between temporal correlations (i.e., persistence) and anticorrelations (i.e., antipersistence) or at least between varying degrees of temporally correlated persistence. These switches occurred as quickly as from one 10-s segment to the next, but this lag-1-segment relationship was not uniform across time or conditions (figures 4 a and 4c). This finding resonates with the canonical idea that sway shows short-term persistence followed by long-term antipersistence [35,36]. The variation from greater or lesser temporal correlations from segment to segment is fleeting. These zig-zag IRF plots may reflect, first, greater persistence of sway within the base of support’s canter and, second, braking or reversing by the postural control system as it approaches the margins of the base of support [1,2]. However, testing this spatial interpretation would benefit from “rambling-trembling” frameworks that recognize a slow-moving reference point anchoring CoP within the base of support [49,50]. These findings thus warrant further investigations into how visual information moderates the rambling-trembling aspects of posture (e.g., [50,51]).
The 50-cm viewing condition yielded intrapostural interactivity that most closely resembled that in the eyes-closed condition (Hypothesis 3). The effects between CoP-SD and CoP-HfGn in the 50-cm condition gradually decayed across trials (figure 5). These effects did not show up in every trial for all other viewing conditions, but the regression coefficient found significant nonzero effects between fractality and SD for all other viewing conditions and only predicted the canceling out of these effects for 50-cm condition. Hence, the viewing distances known to strain oculomotor convergence [14,15] prompted less of the intrapostural relationships that supported posture at other viewing distances. Additionally, the predicted effects of SD on later fractality were robust for all trials across all condition, and those of fractality on later SD were less robust for the 135- and 220-cm conditions. This latter difference indicates that, to some extent, targets at medium distances beyond the comfortable viewing distance might also stabilize posture [52].
Prior increases in CoP-SD and CoP-HfGn predicted later decreases in CoP-SD and CoP-HfGn, respectively (Hypothesis 4). As noted in Results for Hypothesis 1, prior increases in CoP-SD predicted later increases in itself with Segment, thus showing none of the self-corrective aspects shown by CoP-HfGn. Hence, increase in CoP-SD predicted both later increases in CoP-SD and later decreases in CoP-HfGn, and increases in CoP-HfGn predicted later decreases in both CoP-SD and CoP-HfGn.
4.2. Glimpses of a possible control policy for visually guided quiet stance
The present results offer insights into a possible control policy for postural stability that balances CoP-HfGn with an excess of CoP-SD. If left to SD alone, posture would lean towards higher variability without clear bound: any increase in SD would predict later increases, and those later increases would predict even later increases, and so on. The predicted later decreases in fractality would then only serve to promote greater SD. It is only the corrective aspect of fractality that might allow posture to rein in the apparently self-promoting and unbounded SD. For instance, any decreases in fractality following increases in SD might trigger subsequent increases in fractality that would induce a negative check on SD. This causal interpretation aims only to offer a possible control policy that these results could reflect. Such causal interpretation warrants manipulations of SD and fractality of CoP fluctuations (if only indirectly) through a balance board or vibrotactile stimulation.
The present results from VAR analysis examining relationships between earlier impulses and later responses raise new questions for future work. For instance, past work involving explicit feedback to participants completing a motor task found that performance feedback weakened temporal correlations in movement variability in the task [53–55]. In the task of counting seconds by tapping a finger [53], the feedback provided with each tap allowed participants to offset deviations in a way that prevented errors from propagating from one tap to the next. At first glance, this finding seems at odds with the present finding that better performance—standing more quietly with less SD—would follow from and contribute to stronger and not weaker temporal correlations. However, it is possible that, in postural tasks, greater sway is endogenous, implicit feedback that signals the postural control system that corrections are appropriately implemented. In this way, if some proportion of SD reflects sway that triggers postural corrections (e.g., [56]), then the present findings would align with past findings of feedback decorrelating movement variability.
This proposed control policy may resolve long-standing questions about how fluctuations support movement stability—explicitly speaking to the “loss of complexity” hypothesis that fractal sway might be the signature of stability, suggestive of young, healthy, and typically developing physiology. This hypothesis has proven provocative but controversial. Indeed, exploratory clinical research found that temporal correlations might wander within but also beyond the fractal range. But the clinical implications were mixed, with some results indicating stronger temporal correlations in sway for younger, healthier and more typically developing participants [38,57] and other results indicating the opposite [57–59]. Meanwhile, experimental work applying “white-noise”—that is, temporally uncorrelated—mechanical vibration to the feet found that this, by definition, non-fractal and so non-complex signal stabilized sway [60,61]. In finding that greater temporal correlations were associated with later decreases in SD of sway, the present results align well with only half of the exploratory evidence and poorly with the finding that uncorrelated stimulation reduced sway.
Making matters seem even more paradoxical, results have curiously diverged within the same research paradigms in this vein. A reanalysis of Priplata et al.’s [61] data yielded two details [62]. Firstly, white-noise stimulation reduced temporal correlations in sway. So, in the case of unhealthy level of complexity, decorrelating overly correlated fluctuations may be an effective clinical strategy. However, secondly and less straightforwardly, the reanalysis showed that white-noise stimulation elicited stronger reduction of sway for participants exhibiting stronger temporal correlations. In a sense, white-noise stimulation seems to wipe out its efficacy by counteracting the very conditions of endogenous postural fluctuations that give it a stabilizing effect. This self-nullifying aspect of the stimulation seemed quite puzzling.
The present work solves some of this puzzle. All past work sought to find predictive effects of fluctuation patterns by associating concurrent variables: temporal correlations and sway variability for the same postural measurement series. The major contributions of examining prior effects and later responses are twofold: first, fractal temporal correlations self-correct, and second, stronger temporal correlations reduce CoP-SD. Together, these two points provide a framework in which the present findings align neatly with research on white-noise stimulation stabilizing posture [60,61] and to explain how fractal temporal correlations could be sometimes stabilizing and sometimes destabilizing.
Self-correction of fractal temporal correlations has been the key feature missing from the portrayal of postural stability until now. If fractal temporal correlations did not self-correct, then SD would increase or decrease unchecked, subverting postural stability [3,4]. Lack of self-correction in temporal correlations would mean that temporal correlations and SD might push each other to opposite extremes. Posture lacking sufficient variability would be unstable and overly temporally correlated; posture having too much variability would be unstable and have too little temporal correlations. Understanding self-correction in temporal correlations might then be one of the key directions for future work. Differences is temporal correlations are well-known [35,36] and often replicated [37]. The novelty lies in recognizing that weaker temporal correlations in longer timescales may hold only on average, consisting of shorter-timescale ebbing and flowing of temporal correlations. Across 10-s segments within a single trial, the VAR found a sequence of fleeting (e.g., 10-s) bouts of postural sway predicting later alternations between more or less temporal correlations.
The exact basis of this alternation of temporal correlations warrants further investigation. The question of whether these spatial constraints govern temporal correlations’ self-correction would benefit from rigorous test in the “rambling-trembling” framework. This framework recognizes that the fixed reference point anchoring CoP within the base of support drifts slowly. Thus, it is important to model the rise and fall of temporal correlations as a function of the distance between the fixed reference point and the edges of the base of support. The space that “rambling” leaves open for stable, “trembling” may govern how quickly temporal correlations alternate. Such modeling could add to the ongoing elaborations of the rambling-trembling framework to include visual constraints [50,51].
We do mean this proposal to only serve as a glimpse of what needs further validation. Naturally, the correlational analysis results are prone to mischaracterizing the measured variables as actual causal variables. SD and fractal scaling are measurements commonly thought to be essential state variables in postural control. They may reflect contributions from a limited subset of actual control parameters. Certainly, SD and fractal exponents are not inherently physiological features but emergent properties of the postural task. However, actual control parameters may be no less emergent from task constraints—one of the rare agreements between current cognitivist theorizing about visual attention [63] and long-standing views in ecological psychology [64]. So, although the emergent control may not have the same labels for its control parameters, similar observed relationships could explain a host of previous results, as discussed above.
Visually fixating brings a prestressed quiet stance into one with informational coupling with the visual stimulus. Past work has repeatedly implicated fractal fluctuations in the head and upper torso for using visual information to organize action [28,29,65–68]. Visual inspection of IRF plots indicated rare instances of effects from or responses from CoM fractality on or to SD (1 trial in the 50-, 135-, and 305-cm conditions), but the regression modeling indicated no stable relationship. So, the absence of significant IRF relationships for CoM-HfGn on CoP-SD is puzzling. However, past evidence suggests that fluctuations in the upper body moderate the use of visual information beyond and possibly in collaboration with the retina’s microsaccades. CoP and movements of the upper extremities exhibit a close mutual predictive relationship in fractal and multifractal fluctuations even without involving a significant role of torso fluctuations [30,31]. Indeed, should tensegrity-themed metaphors for the movement system be apt [18], then we can expect relatively less local relationships, and CoM may be one of the multiple intermediary links in the anatomical change that need not always participate in controlling posture. Fuller-body set of measurements may allow clearer portrayal of causal relationships knitting retinal fluctuations with CoP fluctuations.
Supplementary materials
Dataset 1. DFA exponents used for VAR analysis.
Table S1. Mean±s.e.m. values of HfGn yielded by DFA for the original (unshuffled) and a shuffled version of each CoM SED and CoP PED time series, and coefficients of paired samples t-tests comparing the two.
Table S2. Regression coefficients for all effects for the eyes-closed condition.
Table S3. Regression coefficients by the eyes-open conditions for the effects and interactions of Segment, Trial, Response(CoP-HfGn), and Response(CoP-SD) without specific pairwise interactions.
Table S4. Regression coefficients by the eyes-open conditions for interactions of Segment, Trial, Impulse(CoP-HfGn), and Impulse(CoP-SD) without specific pairwise interactions.
Table S5. Regression coefficients by the eyes-open conditions for interactions of Segment and Trial with specific pairwise self-interactions (i.e., of prior impulses of CoP-HfGn on itself, and of prior impulses of CoP-SD on itself).
Table S6. Regression coefficients by the eyes-open conditions for interactions of Segment and Trial with specific pairwise other-interactions (i.e., of prior impulses of CoP-HfGn on later values of CoP-SD, and of prior impulses of CoP-SD on later values of CoP-HfGn).
Footnotes
Ethics statement. The present study was approved by the Institutional Review Board (IRB) at the University of Georgia (Athens, GA). All participants provided verbal and written informed consent before participation.
Data accessibility. All data analyzed in the present study are available upon request.
Competing interests. Data available as part of the electronic supplementary material.