Research Papers

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

[+] Author and Article Information
David B. Segala

Nonlinear Dynamics Laboratory, Department of Mechanical, Industrial and Systems Engineering, University of Rhode Island, Kingston, RI 02881

Deanna H. Gates

Department of Biomedical Engineering, University of Texas at Austin, Austin, TX 78712

Jonathan B. Dingwell

Nonlinear Biodynamics Laboratory, Department of Kinesiology and Health Education, University of Texas at Austin, Austin, TX 78712

David Chelidze1

Nonlinear Dynamics Laboratory, Department of Mechanical, Industrial and Systems Engineering, University of Rhode Island, Kingston, RI 02881chelidze@egr.uri.edu


Corresponding author.

J Biomech Eng 133(3), 031009 (Feb 08, 2011) (10 pages) doi:10.1115/1.4003320 History: Received July 14, 2010; Revised December 02, 2010; Posted December 22, 2010; Published February 08, 2011; Online February 08, 2011

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.

Copyright © 2011 by American Society of Mechanical Engineers
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Figure 3

Averaged MNF (darker line) and MDF (lighter line) for subject 6

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Figure 4

Left plots: first 15 dominant linear (red ○), quadratic (blue *), and cubic (green ◇) SOVs for subject 6 elbow flexion/extension (top), humeral plane angle (middle), and humeral elevation angle (bottom). The corresponding first four dominant linear (thick red line), quadratic (dashed blue line), and cubic (thin green line) SOCs for subject 6 elbow flexion/extension (plots on the right).

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Figure 6

Linear combinations of basic (thick red line), quadratic (dotted blue line), and cubic (thin green line) SOCs projections onto MNF (dashed black line) markers in a least squares sense for subject 6: (top plots) elbow flexion/extension angle (middle plots) humeral plane angle, and (bottom plots) humeral elevation angle

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Figure 5

Between subject variability in R2 values for MNF trends for linear (red ○), quadratic (blue *), and cubic (green ◇) SOCs. Error bars represent one standard deviation from the mean of R2. Elbow flexion/extension angle (top two rows), humeral plane angle (middle plots), and humeral elevation angle (bottom plots). Values on top of each plot indicate the number of SOCs needed to adequately track EMG trends.

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Figure 2

MNF (darker line) and MDF (lighter line) calculated over individual cycles of EMG data of subject 6

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Figure 1

Recorded raw EMG time series for subject 6




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