Abstract：
:Measures of local dynamic stability, such as the local divergence exponent (lambda*(s)) quantify how quickly small perturbations deviate from an attractor that defines the motion. When the governing equations of motion are unknown, an attractor can be reconstructed by defining an appropriate state space. However, state space definitions are not unique and accepted methods for defining state spaces have not been established for biomechanical studies. This study first determined how different state space definitions affected lambda*(s) for the Lorenz attractor, since exact theoretical values were known a priori. Values of lambda*(s) exhibited errors <10% for 7 of the 9 state spaces tested. State spaces containing redundant information performed the poorest. To examine these effects in a biomechanical context, 20 healthy subjects performed a repetitive sawing-like task for 5 min before and after fatigue. Local stability of pre- and post-fatigue shoulder movements was compared for 6 different state space definitions. Here, lambda*(s)decreased post-fatigue for all 6 state spaces. Differences were statistically significant for 3 of these state spaces. For state spaces defined using delay embedding, increasing the embedding dimension decreased lambda*(s) in both the Lorenz and experimental data. Overall, our findings suggest that direct numerical comparisons between studies that use different state space definitions should be made with caution. However, trends across experimental comparisons appear to persist. Biomechanical state spaces constructed using positions and velocities, or delay reconstruction of individual states, are likely to provide consistent results.
journal_name
J Biomechjournal_title
Journal of biomechanicsauthors
Gates DH,Dingwell JBdoi
10.1016/j.jbiomech.2009.03.015subject
Has Abstractpub_date
2009-06-19 00:00:00pages
1345-9issue
9eissn
0021-9290issn
1873-2380pii
S0021-9290(09)00153-5journal_volume
42pub_type
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