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1.  A Biomechanical Model of Human Ankle Angle Changes Arising From Short Peri-Threshold Anterior Translations of Platform on Which a Subject Stands 
This study modeled ankle angle changes during small forward perturbations of a standing platform. A two-dimensional biomechanical inverted pendulum model was developed that uses sway frequencies derived from quiet standing observations on a subject's Anterior Posterior Center of Pressure (APCoP) to track ankle angle changes during a 16 mm anterior displacement perturbation of a platform on which a subject stood. This model used the total torque generated at the ankle joint as one of the inputs, and calculated it assuming a PID controller. This feedback system generated a simulated ankle torque based on the angular position of the center of mass (CoM) with respect to vertical line passing through the ankle joint. This study also assumed that the internal components of the net torque were only a controller torque and a sway-pattern-generating torque. The final inputs to the model were the platform acceleration and anthropometric terms. This model of postural sway dynamics predicted sway angle and the trajectory of the center of mass. Knowing these relationships can advance an understanding of the ankle strategy employed in balance control.
doi:10.1109/IEMBS.2007.4353289
PMCID: PMC2261377  PMID: 18002955
Sway Frequencies; Biomechanical Model; Ankle Angle; APCoP; Center of Mass
2.  A Phase-Locked Loop Model of the Response of the Postural Control System to Periodic Platform Motion 
A phase-locked loop (PLL) model of the response of the postural control system to periodic platform motion is proposed. The PLL model is based on the hypothesis that quiet standing (QS) postural sway can be characterized as a weak sinusoidal oscillation corrupted with noise. Because the signal to noise ratio is quite low, the characteristics of the QS oscillator are not measured directly from the QS sway, instead they are inferred from the response of the oscillator to periodic motion of the platform. When a sinusoidal stimulus is applied, the QS oscillator changes speed as needed until its frequency matches that of the platform, thus achieving phase lock in a manner consistent with a PLL control mechanism. The PLL model is highly effective in representing the frequency, amplitude, and phase shift of the sinusoidal component of the phase-locked response over a range of platform frequencies and amplitudes. Qualitative analysis of the PLL control mechanism indicates that there is a finite range of frequencies over which phase lock is possible, and that the size of this capture range decreases with decreasing platform amplitude. The PLL model was tested experimentally using nine healthy subjects and the results reveal good agreement with a mean phase shift error of 13.7° and a mean amplitude error of 0.8 mm.
doi:10.1109/TNSRE.2010.2047593
PMCID: PMC2913702  PMID: 20378479
Mathematical model; phase-locked loop; postural control
3.  A Quiet Standing Index for Testing the Postural Sway of Healthy and Diabetic Adults Across a Range of Ages 
A quietstanding index is developed for tracking the postural sway of healthy and diabetic adults over a range of ages. Several postural sway features are combined into a single composite feature C that increases with age a. Sway features are ranked based on the r2 -values of their linear regression models, and the composite feature is a weighted sum of selected sway features with optimal weighting coefficients determined using principal component analysis. A performance index based on both reliability and sensitivity is used to determine the optimal number of features. The features used to form C include power and distance metrics. The quiet standing index is a scalar that compares the composite feature C to a linear regression model f (a) using C′ (a) = C/f (a). For a motionless subject, C′ = 0, and when the composite feature exactly matches the healthy control (HC) model, C′ = 1. Values of C′ ≫ 1 represent excessive postural sway and may indicate impaired postural control. Diabetic neurologically intact subjects, nondiabetic peripheral neuropathy subjects (PN), and diabetic PN subjects (DPN) were evaluated. The quiet standing indexes of the PN and DPN groups showed statistically significant increases over the HC group. Changes in the quiet standing index over time may be useful in identifying people with impaired balance who may be at an increased risk of falling.
doi:10.1109/TBME.2008.2003270
PMCID: PMC2836593  PMID: 19342327
Diabetes; peripheral neuropathy (PN); postural sway metrics; quiet standing index

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