Mechanisms of interpersonal sway synchrony and stability

Abstract

Here we explain the neural and mechanical mechanisms responsible for synchronizing sway and improving postural control during physical contact with another standing person. Postural control processes were modelled using an inverted pendulum under continuous feedback control. Interpersonal interactions were simulated either by coupling the sensory feedback loops or by physically coupling the pendulums with a damped spring. These simulations precisely recreated the timing and magnitude of sway interactions observed empirically. Effects of firmly grasping another person's shoulder were explained entirely by the mechanical linkage. This contrasted with light touch and/or visual contact, which were explained by a sensory weighting phenomenon; each person's estimate of upright was based on a weighted combination of veridical sensory feedback combined with a small contribution from their partner. Under these circumstances, the model predicted reductions in sway even without the need to distinguish between self and partner motion. Our findings explain the seemingly paradoxical observation that touching a swaying person can improve postural control.

Keywords: feedback model; interpersonal; posture.

Figure 1.

Experimental conditions. Each participant stood on a separate force platform. There were three touch conditions (shown in figure) and four visual conditions (EC, EO, AS1 and AS2) producing a total of 12 conditions. During the LT condition a FSR was placed between participants' fingertips to monitor contact force.

Figure 2.

Postural control model. The model consists of an inverted pendulum under PID control, based upon Peterka [19]. The parameters K_P, K_I and K_D define the PID constants, respectively. Sway was generated by adding a disturbance signal (T_d) to the control torque (T_c). This consisted of filtered Gaussian noise. Pendulum angle (θ) was processed to derive centre of mass (COM) and COP. COP was subsequently differentiated to obtain COPv for comparison with the empirical data. Pendulum moment of inertia is denoted by J, and s depicts the Laplacian operator. Parameter values are depicted in table 1. For further details, see Peterka [19].

Figure 3.

Coupling the model feedback loops. (a) A simplified version of the model, adapted from figure 2, is duplicated above to represent two people interacting. Feedback loops are coupled together. The estimate of pendulum position which feeds into the PID controller is a weighted combination of ‘self’ and ‘partner’. The weightings are determined by the gain functions G and G_c. As G_c increases and G is reduced, the estimation becomes more reliant upon partner feedback. This principle is depicted in (b). Person 1's estimate of body position (dotted figure) is a weighted combination of veridical feedback combined with a small contribution from person 2. Assuming gains of 0.9(G) and 0.1(G_c), this means that person 1's estimate of body position is (0.9 × 20) + (0.1 × 40) = 22°. An implicit assumption is that each person assumes the other to be a fixed vertical reference point.

Figure 4.

Physically coupling the pendulums. (a,b) The two model subjects are physically coupled together by a damped spring. This is depicted schematically in (b) by the torsional spring. As one pendulum moves, it will exert torque upon the other, and vice versa. The torque exerted by the spring is a function of the difference in pendulum positions. K and B represent stiffness and damping, respectively. Although omitted for clarity, when physical coupling was engaged it was always combined with the feedback loop coupling depicted in figure 3.

Figure 5.

Effects of interpersonal touch and vision upon sway. Sagital COPv is shown in (a) for all conditions. Percentage changes in sway relative to the NC condition are shown in (b). Bars show s.e.m.

Figure 6.

Sway cross-correlations. Sagittal COPv traces from each subject pair were cross-correlated. Traces depict mean r values ±95% confidence intervals. Vertical and horizontal lines depict zero-lag and zero-correlation values, respectively. ‘Asymmetric vision’ refers to the condition in which one subject's eyes were open and their partner's closed. In this condition, significant correlations at positive lag reflect the ‘blind’ subject leading the sighted.

Figure 7.

(a,b) Cross-correlation peak values and latencies. Average maxima and latencies of COPv–COPv cross-correlations.

Figure 8.

(a–c) Model sway cross-correlations. A postural feedback control model was used to generate sway cross-correlations (black) for direct comparison against empirical data (grey). Insets are parameter values derived from the model optimization procedure. G = gain; G_c = coupling gain; τ = feedback delay (s); τ_c = coupling feedback delay(s). For asymmetric conditions (a(ii),b(ii),c(ii)), separate values were ascribed to each model subject. For the shoulder contact condition (c), the physical interaction between subjects was modelled by a damped spring with the following parameters: K = stiffness (Nm deg⁻¹); B = damping (Nm deg⁻¹ s⁻¹).

Figure 9.

Effect of model parameter variation upon sway reduction. Model parameters were systematically varied to determine their effect upon sway. Sway reduction was calculated as the percentage change between coupled and uncoupled models. Positive values indicate that coupling reduced sway. (a) The effect of varying gains while delays were kept constant. (b) The effect of varying delays while gains were kept constant. (c) The effect of varying stiffness and damping when the models were coupled by a damped spring (in addition to coupling the feedback loops). Black dots depict percentage sway reduction when parameters were fixed to those values derived by the optimization procedure (figure 8). G = gain; G_c = coupling gain; τ = delay (s); τ_c = coupling delay (s); K = stiffness; B = damping.

Figure 10.

Effect of different baseline sway upon benefits of coupling. The baseline (uncoupled) sway of person 1 was systematically modulated by changing their noise gain while person 2's baseline sway was kept constant. The beneficial effect of coupling was then measured as the percentage change between coupled and uncoupled sway, for each model person. The region of mutual benefit refers to the area where both persons exhibit a reduction in sway, despite differences in baseline stability.