Single Inverted Pendulum Validation for Bi-Pedal Quiet Standing in Healthy Controls and Persons with Parkinson’s Disease

Abstract

The goal of this study was to validate the SIP model for bi-pedal quiet standing on healthy old adults and people with PD by comparing the linear and nonlinear measures extracted from the COP that the SIP creates (COPSIP), and the ones extracted from the experimental COP (COPexp). In addition, this study intended to determine if the accuracy of the COPSIP to replicate the COPexp was sensitive to the current practice of assuming zero as initial conditions (ICs) in the differential equation (DEQ) of the SIP. It was also investigated if the accuracy of the COPSIP was sensitive to the linearization of the DEQ that describes the motion of the SIP. Finally, this study investigated if it is appropriate to use a SIP model in unperturbed sway studies that analyze PD progression, since it is usually believed that people with PD sway like a SIP due to the increment of stiffness at the ankles. This study showed that using zero, instead of optimized, ICs in the SIP DEQ is a practice that increases the error of the COPSIP in terms of magnitude and shape of curve when compared to the COPexp. In addition, this study determined that linearizing the DEQ around the vertical position of the SIP is a safe practice, since at worst, 3% of similarity would be lost when the linear DEQ is used, instead of the nonlinear DEQ. Regarding the optimized ICs, this study proposed to select as optimized ICs the set that maximizes the Cross Correlation between the COPSIP (calculated using the linear DEQ) and the COPexp. This study also showed that the SIP is a valid model for unperturbed sway studies on healthy adults and people with PD, if an error of 30% or less is accepted in the linear and nonlinear measures extracted from the COPexp, and the COPSIP is calculated using the linear DEQ with optimized ICs. In fact, the COPSIP has a 30% or less error only for certain linear and nonlinear measures (depending on the subject group); therefore, the SIP is a 70% (or more) valid model depending on the linear and nonlinear measures that want to be replicated from the COPexp. Finally, this study also showed that as PD progresses and ankle stiffness increases, the SIP becomes a less valid model. The increment of stiffness at the ankles reduces their motion, making the hips move more to maintain balance. This proposes that a double inverted pendulum could represent better the unperturbed sway of moderate to more severe PD subjects.