To sustain standing posture, the muscles of the postural control system must support the body against gravity, stabilize the supporting elements of the body when other elements are moved, and ensure that the body is balanced through the vertical projection of the center of gravity lying within the base of support [18]. Instability is realized qualitatively when the projection of the center of gravity moves outside of the boundary that defines the stable base of support. However, instability can also be defined quantitatively in a dynamical framework with various measures (such as Lyapounov exponent) that capture the degree of departure of the trajectory dynamics from the attractor and hence the relative stability and instability [19].
The determination of the stability of standing posture is most usually calculated from force platform data in the form of the dynamics of the center of pressure and the evolving location of the vertical ground reaction force at the surface of support in standing. In laboratory standing-still tasks, the motion of the center of pressure provides an index of the motion of the center of gravity of the body but it is not itself a measure of the center of gravity. The stability of standing in this framework is typically determined by measures of the amount of variability of the center of pressure or more particularly the position of the center of pressure relative to the stability boundary of standing.
There have been several ways proposed to determine the stability boundary for the motion of the center of pressure. The most common approach is geometric in that it is determined relative to the spatial area that is formed from the position of the feet on the surface of support. Barin [20], for example, used this geometric approach as shown in Fig. 1. Thus, instability is realized when the location of the ground reaction force on the horizontal surface of support moves outside the geometric boundary as formed by the area of the position of the feet.
This traditional approach to determining the instability of standing posture holds several limitations. First, the geometric boundary as defined by the feet is only an approximation of the functional stability boundary for an individual, which is more appropriately determined by the functional capacities of the individual. The geometric boundary is not the same as the limits of the functional boundary so that individuals with the same foot boundary (and hence stability area) would likely have different functional boundaries due to individual differences, such as height, strength, and so on. Second, this method in using the location of the center of pressure relative to the boundary does not consider the temporal constraints of the motion of the center of pressure in the determination of stability. The center of pressure could be close in a position frame of reference to the boundary but not actually be moving toward the boundary, leaving it a poor estimate of the instantaneous functional stability of the standing posture.
Slobounov et al. [21] developed a method to determine the virtual time-to-contact (VTC) to the stability boundary in a three or even n dimensional space and applied this method to the estimate of postural stability in human standing posture. This method was applied to the motion of the center of pressure but it can also be used to assess the motion and stability of the center of gravity or other human movement properties. The motivation for such a method came from the theoretical principles of the ecological approach to perception and action [22].
The ecological approach to action places the emphasis on information for control not on departures from a stability point within the equilibrium region of the potential base of support, as in inverted pendulum models of posture, but rather on the temporal safety margin, as specified by the virtual time to collision with the stability boundary [22, 23]. A significant consequence of this approach is that the control variable for posture is defined over the organism–environment task interaction rather than simply a product of the organism [24, 25]. Initially, Carello et al. [26] postulated that the time to contact with the stability boundary may be the low-dimensional information control variable in postural regulation, and this hypothesis was initially taken up experimentally by Martin [27] and Riccio [25].
Slobounov et al. [21] calculated VTC as the instantaneous time to the functional stability boundary defined on the dynamics of each point in the time series (see the appendix in [21] for full details on the calculation of VTC). The word virtual was used because the individual does not want to actually make contact with the stability boundary, and so VTC is an estimate of the time to the boundary should it occur. This contact with the boundary would only happen in the case of a loss of stability as in a fall or change of postural mode. In this approach, a time series of the VTC can be determined that is based on the dynamics of the time to contact relative to the boundary rather the relative position of the center of pressure to the stability boundary. Figure 2 provides a schematic of the calculation of the VTC measure against the geometric boundary. The same strategy to calculate VTC can also be used against the functional boundary. In the initial Slobounov et al. study [21] with students, it was shown that the coefficients of variation of the VTC were lower than those of the velocity and acceleration of the center of pressure. The robustness of the VTC in human single-leg quiet standing has been demonstrated [28].
Slobounov et al. [29] subsequently built on this theoretical and empirical background and investigated the VTC in standing-still posture as a function of cohort group (60–69, 70–79, 80–89, and 90–96 years of age). The functional stability boundary for each participant was initially determined through having the individuals lean as far outward as they could in all directions without falling. Then the VTC from the center of pressure was calculated in standing-still trials against this individually specified functional stability boundary under different conditions.
One indication of the more highly constrained stability boundary conditions as a function of aging can be found in Fig. 3 which shows the ratio of the area of the center of pressure from standing still/area of the stability region (with between-subject standard deviations) as a function of age group and vision condition. The findings show that with increasing age, the motion of the center of pressure fills a higher proportion of the potential stability region. In other words, the spatial margin of the available center-of-pressure motion is reduced with advancing age. This aging effect occurs because of the combined effects of a great variability of motion of the center of pressure with age (e.g., [30]) and the declining area of the stability region (see also [31]). These effects are magnified in the eyes closed as opposed to the eyes open condition.
Figure 4 shows the VTC as a function of age group and vision condition. The data clearly support the conclusion that VTC declines with advancing age. This means that the older adult has less of a temporal safety margin with respect to crossing the stability boundary, a factor that could lead to a step to try to recover stability or in the worst case scenario a fall. This effect of reduced VTC should also be considered against the well-established finding of a longer reaction time in advanced age [1, 3].
It is instructive to note that while withdrawing vision reduced the functional area within the stability boundary across the age groups, there was no vision effect on the VTC within an age group. The contrast of the age effects for the spatial area and time measures provides another indication that the VTC may be the more fundamental measure in the control of postural stability. Van Wegen et al. [32, 33] using a variation of this VTC measure have shown similar age-related properties of time to contact in the control of postural stability.
Newell et al. [34] modeled the stability of standing posture as a function of age, including older adults (60–80 years of age). The stochastic processes of postural center-of-pressure profiles were examined in 3- and 5-year-old children, young adult students (mean 20 years), and an elderly age group (mean 67 years). Subjects stood still in an upright bipedal stance on a force platform under vision and nonvision conditions. The amount of motion of the center of pressure decreased with increments of age from 3 to 5 years to young adult but increased again in the elderly age group. The availability of vision decreased the amount of motion of the center of pressure in all groups except the 3-year-old group, where there was less motion of the center of pressure with no vision.
The stochastic properties of the center-of-pressure dynamics were assessed using both a two-process, random-walk model of Collins and De Luca [35, 36] and an Ornstein–Uhlenbeck model that is linear and has displacement governed only by a single stiffness term in the random walk. The two-process, open- and closed-loop model accounted for about 96% and the Ornstein–Uhlenbeck model 92% of the variance of the diffusion term. Diffusion parameters in both models showed that the data were correlated and that they varied with age in a fashion consistent with developmental accounts of the changing regulation of the degrees of freedom in action [30]. The findings suggest that it is premature to consider the trajectory of the center of pressure as a two-process, open- and closed-loop random-walk model given that: (a) the linear Ornstein–Uhlenbeck dynamic equation with only two parameters accommodates almost as much of the variance of the random walk, and (b) the linkage of a discontinuity in the diffusion process with the transition of open- to closed-loop processes is poorly founded.
These studies provide an indication of not only the temporal constraints on the stability of standing posture but also that advancing age in adulthood provides narrower temporal safety margins in the regulation of standing. These effects have been demonstrated in what is typically considered the most stable standing mode, namely, standing still with the feet side by side at a width of self-choice in a predictable environment. It seems reasonable to postulate that these age effects on the temporal margins of postural control will be magnified further in the regulation of less stable postures, such as the Rhomberg or one leg stance. Similarly, a changing and less predictable environment would also probably magnify the age-related effects of VTC. These effects, if realized, would support the general idea of the confluence of constraints interacting to determine the boundary conditions of physical activity [24], as expressed here in upright standing.
In closing this section, it should be recognized that the VTC measure seems to be a good candidate for a low-dimensional variable that is used to regulate standing posture [26]. A standard criticism of this hypothesis, however, is that the results to date, such as those reported above for VTC, are correlational and not causal about the dynamics of postural control. This criticism, although equally applicable, is rarely applied to pendulum models of posture, which dominate the literature [e.g., 37]. In this regard, it is noteworthy that Patton et al. [38] have outlined a model for human postural control that is driven by the use of safety margin information to the stability boundary in the regulation of standing posture.
Furthermore, postural stability has also been investigated in the limb postures such as the clinical protocol of finger, hand, or arm tremor [5, 39]. The VTC and the time to reacquire stability measures have not been measured in these clinical postural tasks as a function of age but the changes in postural dynamics with aging appear similar across tasks [13]. This may be because there is clearly a different clinical and personal consequence to losing the postural stability of finger control in a clinical test in contrast to the consequences of a fall in standing posture.