Two-dimensional Langevin approach to the human stabilogram

Two-dimensional Langevin equation is considered as a model of the center of pressure (COP) random walk at quiet standing condition. The matrix of the mean square displacement describes quantitatively the COP random walk. Twenty-six young subjects were included in the study. Elements of the matrix of the mean square displacement derived from experimental data are well approximated by theoretical expressions derived from the Langevin equation, in the short-term regime. We have studied statistical properties of the COP displacements. Non-Gaussian behaviour of the displacements is indicated by the characteristic functions. New coordinate system constituted and utilised by the postural control system (PCS) was found for every subject. This new coordinate system is turned with respect to the system defined by the anatomy of the body. In this new coordinate system the matrix of the mean square displacement takes the form close to diagonal. The status of PCS in this new coordinate system can be quantified by the elements of the diffusion matrix, which are the measure of the stochastic activity of that system, rotation angle of new coordinate system and the friction coefficient. We have applied this analysis to examine how the visual inputs affect the PCS. We have found that the stochastic activity of the PCS increases after exclusion of the visual inputs. We have also shown that the visual system does not affect the friction coefficient. Furthermore, we have found that orientation of the new coordinate system chosen by PCS at included visual inputs differs from the orientation at excluded visual inputs.