Comparison of Existing Methods for Characterizing Bi-Linear Natural Ankle Quasi-Stiffness

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.