Local state space temporal fluctuations: a methodology to reveal changes during a fatiguing repetitive task

The effect of muscular fatigue on temporal and spectral features of muscle activities and motor performance, i.e., kinematics and kinetics, has been studied. It is of value to quantify fatigue related kinematic changes in biomechanics and sport sciences using simple measurements of joint angles. In this work, a new approach was introduced to extract kinematic changes from 2D phase portraits to study the fatigue adaptation patterns of subjects performing elbow repetitive movement. This new methodology was used to test the effect of load and repetition rate on the temporal changes of an elbow phase portrait during a dynamic iso-inertial fatiguing task. The local flow variation concept, which quantifies the trajectory shifts in the state space, was used to track the kinematic changes of an elbow repetitive fatiguing task in four conditions (two loads and two repetition rates). Temporal kinematic changes due to muscular fatigue were measured as regional curves for various regions of the phase portrait and were also expressed as a single curve to describe the total drift behavior of trajectories due to fatigue. Finally, the effect of load and repetition rate on the complexity of kinematic changes, measured by permutation entropy, was tested using analysis of variance with repeated measure design. Statistical analysis showed that kinematic changes fluctuated more (showed more complexity) under higher loads (p=0.014), but did not differ under high and low repetition rates (p=0.583). Using the proposed method, new features for complexity of kinematic changes could be obtained from phase portraits. The local changes of trajectories in epochs of time reflected the temporal kinematic changes in various regions of the phase portrait, which can be used for qualitative and quantitative assessment of fatigue adaptation of subjects and evaluation of the influence of task conditions (e.g., load and repetition rate) on kinematic changes.