Department of Mechanical Engineering, University of Delaware, Luke Nigro 540 S College Ave, Newark, DE 19713.
Department of Kinesiology & Applied Physiology, University of Delaware, Newark, DE 19713; Biomechanics & Movement Science Interdisciplinary Program, University of Delaware, Newark, DE 19713.
J Biomech Eng. 2022 Nov 1;144(11). doi: 10.1115/1.4054798.
Natural ankle quasi-stiffness (NAS) is a mechanical property of the ankle joint during dynamic motion. NAS has been historically calculated as the average slope (linear regression) of the net ankle moment versus ankle angle during discrete phases of stance. However, recent work has shown that NAS is nonlinear during the stance phase. Specifically, during the loading phase of stance (∼10 to 60% of total stance), plantarflexion moment increases at an accelerating rate compared to dorsiflexion angle. Updated models have been developed to better capture this inherent nonlinearity. One type of model called bi-linear NAS (BL-NAS) divides the loading phase of stance into two subphases, called early loading (EL) and late loading (LL) NAS. Two papers, written by Crenna and Frigo (2011, "Dynamics of the Ankle Joint Analyzed Through Moment-Angle Loops During Human Walking: Gender and Age Effects," Hum. Mov. Sci., 30(6), pp. 1185-1198) and Shamaei et al. (2013, "Estimation of Quasi-Stiffness and Propulsive Work of the Human Ankle in the Stance Phase of Walking," PLoS One, 8(3), p. e59935), outline different BL-NAS models. Both models fit measured data better (lower root-mean-squared error (RMSE)) than standard single linear NAS (SL-NAS) models but have not been widely adopted, possibly because of methodological discrepancies and lack of applicability to physical devices at the time. This paper compares and contrasts these existing BL-NAS models and translates those findings to possible orthotic device designs. Results showed that both BL-NAS models had lower RMSE than SL-NAS, EL-NAS was not significantly different across walking speeds, and LL-NAS increased significantly at faster walking speeds. These improved models of NAS much better approximate natural human movement than commonly used SL-NAS models, and thus provide a basis to design ankle-foot devices with multiple stiffness properties to emulate and facilitate natural human motion.
自然踝关节准刚性（NAS）是踝关节在动态运动中的一种力学特性。NAS 历史上是通过在站立阶段的离散阶段中，将踝关节力矩与踝关节角度的净斜率（线性回归）来计算的。然而，最近的研究表明，NAS 在站立阶段是非线性的。具体来说，在站立的负重阶段（约占总站立时间的 10%至 60%）中，与背屈角度相比，跖屈力矩以加速的速度增加。已经开发了更新的模型来更好地捕捉这种固有的非线性。一种称为双线性 NAS（BL-NAS）的模型将站立的负重阶段分为两个子阶段，称为早期负重（EL）和晚期负重（LL）NAS。两篇论文，一篇由 Crenna 和 Frigo（2011 年，“通过人类行走时的力矩-角度环分析踝关节动力学：性别和年龄的影响”，人类运动科学，30(6)，第 1185-1198 页）和 Shamaei 等人（2013 年，“在行走的站立阶段估算人类踝关节的准刚性和推进功”，PLoS One，8(3)，第 e59935 页），概述了不同的 BL-NAS 模型。这两个模型都比标准的单一线性 NAS（SL-NAS）模型更能拟合测量数据（更低的均方根误差（RMSE）），但并未被广泛采用，可能是因为方法上的差异以及当时缺乏适用于物理设备的应用。本文比较和对比了这些现有的 BL-NAS 模型，并将这些发现转化为可能的矫形器设计。结果表明，与 SL-NAS 相比，两种 BL-NAS 模型的 RMSE 都更低，EL-NAS 在不同的步行速度下没有显著差异，而 LL-NAS 在更快的步行速度下显著增加。NAS 的这些改进模型比常用的 SL-NAS 模型更能准确地模拟自然的人类运动，因此为设计具有多个刚度特性的踝足装置提供了基础，以模拟和促进自然的人类运动。
