Background

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.

Method

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).

Results

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.

中文翻译：

---

通过运动频率含量在平衡板上验证平衡的踝关节模型

背景

脚踝策略模型（将人体建模为铰接在脚踝处的单个倒立摆）已使用了数十年，以研究人体直立姿势（UP）的动力学和稳定性。但是，每当考虑姿势干扰时，髋关节的贡献就至关重要。为了说明髋关节的贡献，最近在我们以前的工作中提出了围绕踝关节和髋关节旋转的双倒立摆（DIP）模型，但缺乏实验验证工作。

方法

在本研究中，研究了DIP模型是否能够再现实验观察到的平衡在柔顺表面上的青年和老年受试者的踝关节和髋关节运动学的频谱。通过傅立叶分析比较基于DIP模型和实验运动学，以获得其相应的振幅谱密度（ASD）函数。ASD功能的定量比较通过Bland-Altman（B＆A）分析和Pearson相关系数（PCC）完成。

结果

DIP模型可以重现脚踝和髋关节角度位置和速度的实验频谱的一部分，尤其是对于大于0.35 Hz的频率。此外，该模型捕获了实验ASD函数随频率增加的衰减行为。关于关节角速度，在老年受试者的髋关节中发现了基于模型的ASD和实验的ASD功能之间的最高PCC。B＆A分析表明，基于模型的ASD函数和实验性ASD函数之间的零差位于95％置信区间之间，尤其是对于关节角度位置结果。这些表明，DIP模型再现了实验观察到的频谱的一部分，这验证了该模型以研究人体直立姿势的动力学和稳定性。