Postural control model interpretation of stabilogram diffusion analysis

Collins and De Luca [Collins JJ, De Luca CJ (1993) Exp Brain Res 95. 308-31 8] introduced a new method known as stabilogram diffusion analysis that pro vides a quantitative statistical measure of the apparently random variation s of center-of-pressure (COP) trajectories recorded during quiet upright st ance in humans. This analysis generates a stabilogram diffusion function (S DF) that summarizes the mean square COP displacement as a function of the t ime interval between COP comparisons. SDFs have a characteristic two-part f orm that suggests the presence of two different control regimes: a short-te rm open-loop control behavior and a longer-term closed-loop behavior. This paper demonstrates that a very simple closed-loop control model of upright stance can generate realistic SDFs. The model consists of an inverted pendu lum body with torque applied at the ankle joint. This torque includes a ran dom disturbance torque and a control torque. The control torque is a functi on of the deviation terror signal) between the desired upright body positio n and the actual body position, and is generated in proportion to the error signal, the derivative of the error signal, and the integral of the error signal [i.e. a proportional, integral and derivative (PID) neural controlle r]. The control torque is applied with a time delay representing conduction , processing, and muscle activation delays. Variations in the PID parameter s and the time delay generate variations in SDFs that mimic real experiment al SDFs, This model analysis allows one to interpret experimentally observe d changes in SDFs in terms of variations in neural controller and time dela y parameters rather than in terms of open-loop versus closed-loop behavior.