Stochastic Dynamics of Postural Sway Modeled by Double Ornstein Uhlenbeck Process

Abstract The Center-of-Pressure in anteroposterior direction (CoPx) exhibits two regime dynamics during quiet stance. First regime is slowly changing equilibrium points determined by higher nervous system. Second includes the fast postural corrections around it. We proposed a novel system of stochastic differential equations, double Ornstein Uhlenbeck process (dOU), where the long-term mean of first OU is controlled by the second OU. We derived the closed forms of the correlation and the power spectral density (PSD) functions. Four parameters were optimized in frequency domain over experimental data. We found that the mean reversion rate of second OU governs the dominant sway frequency while its volatility scales the associated variation. Fast reflexive postural adjustments around the equilibrium are modeled by first OU. The phenomenological dOU model exploits two independent Wiener processes as the driving forces in random dynamics of CoPx while mean reversion rates serve for bounded variability of balance considering biomechanical constraints.