Statistical analysis of quiet stance sway in 2-D

Subjects exposed to a rotating environment that perturbs their postural sway show adaptive changes in their voluntary spatially directed postural motion to restore accurate movement paths but do not exhibit any obvious learning during passive stance. We have found, however, that a variable known to characterize the degree of stochasticity in quiet stance can also reveal subtle learning phenomena in passive stance. We extended Chow and Collins (Phys Rev E 52(1):909-912, 1995) one-dimensional pinned-polymer model (PPM) to two dimensions (2-D) and then evaluated the model's ability to make analytical predictions for 2-D quiet stance. To test the model, we tracked center of mass and centers of foot pressures, and compared and contrasted stance sway for the anterior-posterior versus medio-lateral directions before, during, and after exposure to rotation at 10 rpm. Sway of the body during rotation generated Coriolis forces that acted perpendicular to the direction of sway. We found significant adaptive changes for three characteristic features of the mean square displacement (MSD) function: the exponent of the power law defined at short time scales, the proportionality constant of the power law, and the saturation plateau value defined at longer time scales. The exponent of the power law of MSD at a short time scale lies within the bounds predicted by the 2-D PPM. The change in MSD during exposure to rotation also had a power-law exponent in the range predicted by the theoretical model. We discuss the Coriolis force paradigm for studying postural and movement control and the applicability of the PPM model in 2-D for studying postural adaptation.