Stochastic dynamics of postural sway modeled by double Ornstein Uhlenbeck process

Area of Science:

• Biomechanics
• Human postural control
• Dynamical systems theory

Background:

• Quiet stance involves complex postural adjustments.
• Center-of-pressure (CoPx) dynamics reflect these adjustments.
• Existing models may not fully capture multi-level control.

Purpose of the Study:

• To investigate two-level dynamics in anteroposterior CoPx (CoPx).
• To propose and validate a novel double Ornstein-Uhlenbeck (dOU) process model.
• To analyze postural control under varying sensory and surface conditions.

Main Methods:

• Developed a coupled stochastic differential equation model (dOU).
• Derived analytical correlation and power spectral density (PSD) functions.
• Experimentally tested eight healthy subjects across four sensory conditions on rigid and compliant surfaces.
• Optimized model parameters by comparing experimental PSD estimates with analytical functions.

Main Results:

• The mean reversion rate (λ) of the fast postural correction process was higher on rigid surfaces.
• On rigid surfaces, CoPx dynamics were primarily described by a single Ornstein-Uhlenbeck (OU) process.
• On compliant surfaces, λ approached the slow process's rate (κ), with increased volatility, suggesting pronounced two-level dynamics.
• The dOU model effectively captured bounded diffusive characteristics of CoPx.

Conclusions:

• Two-level CoPx dynamics are more evident on compliant surfaces.
• The dOU model provides a robust framework for analyzing complex postural sway.
• Findings highlight the influence of surface compliance on postural control strategies.