Long term correlation and inhomogeneity of the inverted pendulum sway time-series under the intermittent control paradigm

In this study the extended detrended fluctuation analysis (EDFA) was applied to the sway data generated from an inverted pendulum (IP) model, intermittently controlled at the ankle. The time series taken into account was the center of pressure (COP), since it represents the widest used time series in posturography, and it constitutes a natural link between model and data-based analysis approaches for studying the dynamics of the human balance maintenance. COP time-series were obtained by varying the intermittent control parameters (ICP) in a uniform distribution range that ensures IP stability to quantify changes in the long-term correlation and inhomogeneity of the time-series. Globally, EDFA coefficients (α and β) showed to be sensitive to the variations of derivative control gain (D), whereas for proportional gain (P) and ρ parameters no significant trends were observed. However, relations between EDFA coefficients and ρ arose whether derivative gain is examined within a low and high regions of value. For low D gains, both α and β showed a significant correlation with ρ, which disappears when higher D values were considered. Thus EDFA coefficients can provide useful insights about the long-term correlation and local characteristics of COP timeseries, which are strictly related to the control policy adopted for maintaining balance. This supports the validity of the intermittent motor control paradigm for the human upright stance and suggests the use of EDFA in real posturography applications, in order to extract meaningful information regarding the properties of COP timeseries for different groups of patients.