Linear and Nonlinear Smooth Orthogonal Decomposition to Reconstruct Local Fatigue Dynamics: A Comparison

Identifying physiological fatigue is important for the development of more robust training protocols, better energy supplements, and/or reduction of muscle injuries. Current fatigue measurement technologies are usually invasive and/or impractical, and may not be realizable in out of laboratory settings. A fatigue identification methodology that only uses motion kinematics measurements has a great potential for field applications. Phase space warping (PSW) features of motion kinematic time series analyzed through smooth orthogonal decomposition (SOD) have tracked individual muscle fatigue. In this paper, the performance of a standard SOD analysis is compared to its nonlinear extension using a new experimental data set. Ten healthy right-handed subjects (27 ± 2.8 years; 1.71 ± 0.10 m height; and 69.91 ± 18.26 kg body mass) perform a sawing motion by pushing a weighted handle back and forth until voluntary exhaustion. Three sets of joint kinematic angles are measured from the elbow, wrist and shoulder as well as surface Electromyography (EMG) from ten different muscle groups. A vector-valued feature time series is generated using PSW metrics estimated from movement kinematics. Dominant SOD coordinates of these features are extracted to track the individual muscle fatigue trends as indicated by mean and median frequencies of the corresponding EMG power spectra. Cross subject variability shows that considerably fewer nonlinear SOD coordinates are needed to track EMG-based fatigue markers, and that nonlinear SOD methodology captures fatigue dynamics in a lower-dimensional subspace than its linear counterpart.