Scaling of plantarflexor muscle activity and postural time-to-contact in response to upper-body perturbations in young and older adults

Abstract

In this study, we describe and compare the compensatory responses of healthy young and older adults to sequentially increasing upper-body perturbations. The scaling of plantarflexor muscular activity and minimum time-to-contact (TtC_MIN) was examined, and we determined whether TtC_MIN predictions of instability (stepping transitions) for the older subjects were similar to those we previously reported for younger subjects (Hasson et al. in J Biomech 41:2121–2129, 2008). We found that the older subjects stepped at a lower perturbation level than the younger subjects; however, this response was appropriate based on their greater center of mass (CoM) accelerations, which may have been caused by differences in pre-perturbation states between the age groups. Although the CoM acceleration increased linearly with perturbation magnitude, the amount of gastrocnemius and soleus muscular activity increased nonlinearly in both age groups. There were no differences in the maximum plantarflexor torque responses, suggesting that the maximum torque capabilities of the older subjects were not limiting factors. As previously demonstrated in the younger subjects, the older subjects showed a quadratic decrease in TtC_MIN with increasing perturbation magnitude. The vertices of the quadratics gave accurate predictions of stepping transitions in both age groups, even though the older subjects stepped at lower perturbation magnitudes. By probing the postural system’s behavior through sequentially increasing upper-body perturbations, we observed a complementary nonlinear scaling of muscle activity and TtC_MIN, which suggests that subjects could use TtC or a correlate as an informational variable to help determine whether a step is necessary.

Appendix

The perturbation force, anterior–posterior center of mass (CoM) kinematics, and the corresponding time-to-contact (TtC) for a young subject in response to a postural perturbation are illustrated in Fig. 8a. The TtC was first calculated at each time-step as

$$ {\text{TtC}} = {\frac{{ - v \pm \sqrt {v^{2} - 2a(p - p_{\text{toe}} )} }}{a}} $$

(1)

where p, v, and a are the instantaneous anterior–posterior positions, velocities, and accelerations of the CoM, respectively, and p _toe is the anterior–posterior location of the toe boundary marker. In the present study, we only considered one-dimensional (anterior–posterior) motion in the TtC calculation. However, the TtC can also be calculated in two dimensions (e.g. to anterior–posterior and medial–lateral base of support boundaries); see Slobounov et al. 1997 for details.

Fig. 8

a Perturbation force, anterior–posterior center of mass kinematics, and the time-to-contact (TtC) in response to a postural perturbation (causing forward sway) for a young subject. The open circles denote the instantaneous center of mass kinematics associated with the minimum TtC (TtC_MIN, solid circle). Note that the center of mass position is given with respect to the ankle joint (ankle = 0 m). b Schematic representing the TtC calculation for one instant in time, corresponding with TtC_MIN indicated by the solid circle in the TtC time series. See text for details

Let us consider an example of the TtC calculation for a single point in time (0.085 s after the start of the perturbation, solid circle in Fig. 8). The instantaneous CoM kinematics (denoted by open circles in Fig. 8) are as follows:

$$ p = 0.026\;{\text{m}},\quad v = 0.120\;{\text{m/s}},\quad a = 2.59\;{\text{m/s}}^{2} $$

(2)

Solving Eq. 1 using a toe boundary position of p _toe = 0.20 m [the CoM and toe positions are referenced to the ankle in these calculations (ankle = 0 m)] gives a positive and negative solution:

$$ {\text{TtC}} = [ - 0.416\;{\text{s}},\;0.323\;{\text{s}}] $$

(3)

These solutions are depicted graphically in Fig. 8b. The instantaneous CoM state (defined by the given kinematics) is shown as an open circle, and these kinematic conditions are extrapolated in the past (negative time) and future (positive time) directions (the zero crossings indicate the solutions). The negative solution is discarded; the positive solution represents the time it would take the center of mass to contact the toe base of support boundary if it accelerated at a constant rate. This positive solution, denoted by a solid circle, is the predicted TtC for that one instant in time.

Although this example is for a single time point, the TtC calculation is performed at each time point, generating a TtC time series (Fig. 8a). In the present study, the TtC time series was then searched and the minimum selected (TtC_MIN) for further analysis. For convenience, in this example, the chosen data point corresponds with TtC_MIN, occurring 0.085 s after the perturbation initiation.

Note that it is necessary to calculate the TtC to both the anterior (toe) and posterior (heel) base of support boundaries to have a “complete” TtC time series (as shown in Fig. 8a). In this case, whichever TtC is shorter (to the toe or heel) is chosen at each time point. For the present study, only TtC to the anterior boundary was of interest.