Multisensory fusion and the stochastic structure of postural sway

Abstract

We analyze the stochastic structure of postural sway and demonstrate that this structure imposes important constraints on models of postural control. Linear stochastic models of various orders were fit to the center-of-mass trajectories of subjects during quiet stance in four sensory conditions: (i) light touch and vision, (ii) light touch, (iii) vision, and (iv) neither touch nor vision. For each subject and condition, the model of appropriate order was determined, and this model was characterized by the eigenvalues and coefficients of its autocovariance function. In most cases, postural-sway trajectories were similar to those produced by a third-order model with eigenvalues corresponding to a slow first-order decay plus a faster-decaying damped oscillation. The slow-decay fraction, which we define as the slow-decay autocovariance coefficient divided by the total variance, was usually near 1. We compare the stochastic structure of our data to two linear control-theory models: (i) a proportional-integral-derivative control model in which the postural system's state is assumed to be known, and (ii) an optimal-control model in which the system's state is estimated based on noisy multisensory information using a Kalman filter. Under certain assumptions, both models have eigenvalues consistent with our results. However, the slow-decay fraction predicted by both models is less than we observe. We show that our results are more consistent with a modification of the optimal-control model in which noise is added to the computations performed by the state estimator. This modified model has a slow-decay fraction near 1 in a parameter regime in which sensory information related to the body's velocity is more accurate than sensory information related to position and acceleration. These findings suggest that: (i) computation noise is responsible for much of the variance observed in postural sway, and (ii) the postural control system under the conditions tested resides in the regime of accurate velocity information.

Fast Computational Analysis of Sway Area Using Center of Pressure Data in Normal Children and Children with Cerebral Palsy

“…The duration of 20 to 25 seconds was selected to ensure the stationarity of CoP signals. Recent studies have shown that the CoP may be non-stationary when recorded for longer durations, typically exceeding 30 seconds [16,17,18,19]. Data were collected in two consecutive trials where the subjects were asked either to open or close their eyes throughout the stance period.…”

Dynamical structure of center-of-pressure trajectories in patients recovering from stroke

“…The 'smoothness' of the COP trajectories hints at strong deterministic components in the stochastic postural sway dynamics and comparatively weak influences of noise (see also Collins andDe Luca 1993, 1995;Riley et al 1999;Riley and Turvey 2002). Using linear systems theory and corresponding identification techniques, Kiemel et al (2002) similarly concluded that COP trajectories reflect a mixture of deterministic and stochastic components. However, this more traditional approach tends to downplay the importance of the repeatedly demonstrated non-linear character of the COP dynamics.…”

Stochastic two-delay differential model of delayed visual feedback effects on postural dynamics

“…Their model accounted for the characteristic mean-squared displacement and correlation functions typically seen in postural sway; however, it lacked an explicit control mechanism, which is our primary interest here. Kiemel et al (2002) used high-order linear and optimal control theory models to estimate postural states. Higher order models require many parameters and thus are very complex.…”