Margins of postural stability in Parkinson’s disease: an application of control theory

Introduction: Postural instability is a restrictive feature in Parkinson’s disease (PD), usually assessed by clinical or laboratory tests. However, the exact quantification of postural stability, using stability theorems that take into account human dynamics, is still lacking. We investigated the feasibility of control theory and the Nyquist stability criterion—gain margin (GM) and phase margin (PM)—in discriminating postural instability in PD, as well as the effects of a balance-training program. Methods: Center-of-pressure (COP) data of 40 PD patients before and after a 4-week balance-training program, and 20 healthy control subjects (HCs) (Study1) as well as COP data of 20 other PD patients at four time points during a 6-week balance-training program (Study2), collected in two earlier studies, were used. COP was recorded in four tasks, two on a rigid surface and two on foam, both with eyes open and eyes closed. A postural control model (an inverted pendulum with a Proportional-integral-derivative (PID) controller and time delay) was fitted to the COP data to subject-specifically identify the model parameters thereby calculating |GM| and PM for each subject in each task. Results: PD patients had a smaller margin of stability (|GM| and PM) compared with HCs. Particularly, patients, unlike HCs, showed a drastic drop in PM on foam. Clinical outcomes and margins of stability improved in patients after balance training. |GM| improved early in week 4, followed by a plateau during the rest of the training. In contrast, PM improved late (week 6) in a relatively continuous-progression form. Conclusion: Using fundamental stability theorems is a promising technique for the standardized quantification of postural stability in various tasks.