Nonlinear Smooth Orthogonal Decomposition of Kinematic Features of Sawing Reconstructs Muscle Fatigue Evolution as Indicated by Electromyography

Abstract

Tracking or predicting physiological fatigue is important for developing more robust training protocols and better energy supplements and/or reducing muscle injuries. Current methodologies are usually impractical and/or invasive and may not be realizable outside of laboratory settings. It was recently demonstrated that smooth orthogonal decomposition (SOD) of phase space warping (PSW) features of motion kinematics can identify fatigue in individual muscle groups. We hypothesize that a nonlinear extension of SOD will identify more optimal fatigue coordinates and provide a lower-dimensional reconstruction of local fatigue dynamics than the linear SOD. Both linear and nonlinear SODs were applied to PSW features estimated from measured kinematics to reconstruct muscle fatigue dynamics in subjects performing a sawing motion. Ten healthy young right-handed subjects pushed a weighted handle back and forth until voluntary exhaustion. Three sets of joint kinematic angles were measured from the right upper extremity in addition to surface electromyography (EMG) recordings. The SOD coordinates of kinematic PSW features were compared against independently measured fatigue markers (i.e., mean and median EMG spectrum frequencies of individual muscle groups). This comparison was based on a least-squares linear fit of a fixed number of the dominant SOD coordinates to the appropriate local fatigue markers. Between subject variability showed that at most four to five nonlinear SOD coordinates were needed to reconstruct fatigue in local muscle groups, while on average 15 coordinates were needed for the linear SOD. Thus, the nonlinear coordinates provided a one-order-of-magnitude improvement over the linear ones.

A System-Based Approach to Monitoring the Performance of a Human Neuromusculoskeletal System

“…In addition, negative JFI trends for GHNE and WF were significant for all but one subject, while negative trends for the JFIs of EF were significant for all but three subjects. These prevalent downward trends are commensurate with the slow fatigue dynamics noted by Dingwell et al, (2007) and Segala et al (2011).…”

“…On the other hand, temporal changes in neuronal excitation frequency are highly important for NMS function because the very nature of neural communication with muscles can be characterized by both amplitude and frequency modulation (Keynes et al, 2010). Furthermore, monitoring the NMS system performance has been approached from a purely symptomatic perspective, relying on tracking the behavior of either the EMG signatures (Dingwell, Napolitano and Chelidze, 2007), or joint kinematic trajectories (Segala, Gates, Dingwell and Chelidze, 2011), independently. A system-based approach to monitoring the NMS system based on dynamic models relating EMG signals with joint kinematic variables has not yet been posed.…”

Toward a unified interpretation of the “proper”/“smooth” orthogonal decompositions and “state variable”/“dynamic mode” decompositions with application to fluid dynamics

“…The idea of SOD was first explored by Chatterjee et al 15 and later formalized by Chelidze and Zhou 3 in the context of nonlinear vibrations, who provided a thorough treatment, including computational details and its many beneficial properties. [7][8][9][10] Again, the current work will simply highlight key aspects of the method. SOD considers the constrained maximization problem max ψ s…”

On the Inclusion of Time Derivatives of State Variables for Parametric Model Order Reduction for a Beam on a Nonlinear Foundation

“…Rezaee et al [25] used SOD to derive the modal parameters of a vehicle suspension system. In the biomechanics community, SOD was used to extract smooth trends from multivariate biomechanical data to determine fatigue markers instead of medical techniques that require invasive physiological measurements [26]. SOD was first introduced into the fluids community by Kuehl et al [27], which extracted a slowly varying Rossby wave in measured ocean currents using SOD when POD was unable to do so.…”