Abstract
The maximum Lyapunov exponent (MLE) has often been suggested as the prominent measure for evaluation of dynamic stability of locomotion in pathological and healthy population. Although the popularity of the MLE has increased in the last years, there is scarce information on the reliability of the method, especially during running. The purpose of the current study was, thus, to examine the reliability of the MLE during both walking and running. Sixteen participants walked and ran on a treadmill completing two measurement blocks (i.e., two trials per day for three consecutive days per block) separated by 2 months on average. Six different marker-sets on the trunk were analyzed. Intraday, interday and between blocks reliability was assessed using the intraclass correlation coefficient (ICC) and the root mean square difference (RMSD). The MLE was on average significantly higher (p < 0.001) in running (1.836 ± 0.080) compared to walking (1.386 ± 0.207). All marker-sets showed excellent ICCs (>0.90) during walking and mostly good ICCs (>0.75) during running. The RMSD ranged from 0.023 to 0.047 for walking and from 0.018 to 0.050 for running. The reliability was better when comparing MLE values between blocks (ICCs: 0.965–0.991 and 0.768–0.961; RMSD: 0.023–0.034 and 0.018–0.027 for walking and running respectively), and worse when considering trials of the same day (ICCs: 0.946–0.980 and 0.739–0.844; RMSD: 0.042–0.047 and 0.045–0.050 for walking and running respectively). Further, different marker-sets affect the reliability of the MLE in both walking and running. Our findings provide evidence that the assessment of dynamic stability using the MLE is reliable in both walking and running. More trials spread over more than 1 day should be considered in study designs with increased demands of accuracy independent of the locomotion condition.
Highlights
Stability is crucial for uninterrupted task execution in dynamic conditions such as locomotion and requires effective regulation by the CNS (Schöner and Kelso, 1988; Massion, 1992; Patla, 2003; Ting et al, 2009; Bohm et al, 2015)
Dynamic stability during gait refers to the ability of the system to maintain functional locomotion despite the presence of kinematic disturbances or control errors (England and Granata, 2007; Bruijn et al, 2013)
The maximum Lyapunov exponent (MLE) is based on the Lyapunov’s theory of dynamic stability, initially formulated to assess the sensitivity of a mechanical system to small perturbations and is often used to quantify how the patterns of gait kinematics change in response to small perturbations (Lyapunov, 1992; Ihlen et al, 2017)
Summary
Stability is crucial for uninterrupted task execution in dynamic conditions such as locomotion and requires effective regulation by the CNS (Schöner and Kelso, 1988; Massion, 1992; Patla, 2003; Ting et al, 2009; Bohm et al, 2015). One parameter to evaluate numerically the dynamic stability during locomotion is the maximum Lyapunov exponent (MLE) calculated using nonlinear time series analysis and has been adopted as a criterion for the occurrence of control errors (Dingwell and Cusumano, 2000; Buzzi et al, 2003; Bruijn et al, 2013, 2014). Based on the reported reliability between days (van Schooten et al, 2013; Reynard and Terrier, 2014), detection of differences after exercise or therapy-induced adaptations might not be feasible. There is no available information regarding intraday or between days reliability of the MLE during running
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