Validation of an ankle-hip model of balance on a balance board via kinematic frequency-content

The ankle-strategy model, where the human body is modeled as a single inverted pendulum hinged at the ankle, has been used for decades to study the dynamics and the stability of the human upright posture (UP). However, the contribution of the hip joints is critical whenever postural disturbances are considered. To account for hip contribution, a double inverted pendulum (DIP) model rotating about the ankle and hip joints has been recently proposed in our previous work but experimental validation efforts are scarce.

In the present study, it is investigated whether the DIP model is able to reproduce the experimentally observed frequency spectrum of the ankle and hip joint kinematic for young and elderly subjects balancing on a compliant surface. The DIP model based and experimental kinematics are compared via Fourier analysis to obtain their corresponding amplitude spectrum density (ASD) functions. Quantitative comparisons of the ASD functions are accomplished through Bland-Altman (B&A) analysis, and Pearson correlation coefficient (PCC).

The DIP model can reproduce part of the experimental frequency spectrum of the ankle and hip joint angle position and velocity, especially for frequencies larger than 0.35 Hz. Moreover, the model captures the decaying behavior of the experimental ASD functions as frequency increases. With respect to joint angle velocities, the highest PCC between model-based and experimental ASD functions is found for the hip joint of elderly subjects. The B&A analysis shows that the zero-difference between model-based and experimental ASD functions lies between the 95 % confidence interval, especially for the joint angle position results. These suggest that the DIP model reproduces part of the experimentally observed frequency spectrum, which validates the model to study the dynamics and stability of the human upright posture.