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Research Papers

# Slow-Time Changes in Human EMG Muscle Fatigue States Are Fully Represented in Movement Kinematics

[+] Author and Article Information
Miao Song, David B. Segala

Nonlinear Dynamics Laboratory, Department of Mechanical Engineering and Applied Mechanics, University of Rhode Island, Kingston, RI 02881

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 Engineering and Applied Mechanics, University of Rhode Island, Kingston, RI 02881chelidze@egr.uri.edu

The generic definition of bifurcation is a sudden appearance of a qualitatively different solution for a nonlinear system as some parameter is varied. In our case slowly accumulating fatigue acts as a slowly varying parameter in a nonlinear system describing the movement kinematics. Overall, the changes in movement patterns are expected to be slowly varying but could also be rather sudden as fatigue accumulates. These changes might not conform to the true definition of bifurcations; however, long-time average statistics are still expected to vary discontinuously with any such sudden change in kinematics.

Here, the Katz–Servick fractal dimension, which indicates how completely a fractal fills a space (41), was used for simplicity of calculation. The focus here was on a measure that reflected the fractality of data, not an accurate estimates of fractal dimension.

$C(ϵ)$ reflects the probability that two points in phase space are within an $ϵ$ distance.

It is often recommended not to filter nonlinear time series using linear filters. However, in our case the cutoff frequency was set well beyond the observed bandwidth to attenuate high frequency noise.

Recall that our analysis looks at averaged measures of fast-time dynamics over intermediate-time scales to get to the slow-time dynamics of muscle fatigue

1

Corresponding author.

J Biomech Eng 131(2), 021004 (Dec 10, 2008) (11 pages) doi:10.1115/1.3005177 History: Received December 20, 2007; Revised September 02, 2008; Published December 10, 2008

## Abstract

The ability to identify physiologic fatigue and related changes in kinematics can provide an important tool for diagnosing fatigue-related injuries. This study examined an exhaustive cycling task to demonstrate how changes in movement kinematics and variability reflect underlying changes in local muscle states. Motion kinematics data were used to construct fatigue features. Their multivariate analysis, based on smooth orthogonal decomposition, was used to reconstruct physiological fatigue. Two different features composed of (1) standard statistical metrics (SSM), which were a collection of standard long-time measures, and (2) phase space warping (PSW)–based metrics, which characterized short-time variations in the phase space trajectories, were considered. Movement kinematics and surface electromyography (EMG) signals were measured from the lower extremities of seven highly trained cyclists as they cycled to voluntary exhaustion on a stationary bicycle. Mean and median frequencies from the EMG time series were computed to measure the local fatigue dynamics of individual muscles independent of the SSM- and PSW-based features, which were extracted solely from the kinematics data. A nonlinear analysis of kinematic features was shown to be essential for capturing full multidimensional fatigue dynamics. A four-dimensional fatigue manifold identified using a nonlinear PSW-based analysis of kinematics data was shown to adequately predict all EMG-based individual muscle fatigue trends. While SSM-based analyses showed similar dominant global fatigue trends, they failed to capture individual muscle activities in a low-dimensional manifold. Therefore, the nonlinear PSW-based analysis of strictly kinematic time series data directly predicted all of the local muscle fatigue trends in a low-dimensional systemic fatigue trajectory. These results provide the first direct quantitative link between changes in muscle fatigue dynamics and resulting changes in movement kinematics.

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## Figures

Figure 1

(a) Average power output (watts) and cadence (rpm) as a function of the percentage of the trial completed for each subject. Symbols represent the average across subjects. Error bars represent between-subject standard deviations. (b) Median frequency (MDF) results for the Vastus lateralis (VL) and biceps femoris (BF) muscles for a typical subject. Thin lines show original averaged median frequency values. Thick black lines show the boxcar filtered median frequencies. The thick straight lines represent linear regression lines computed from the original median frequency data. (c) Trunk lean and ankle angles for a typical subject. The thick straight lines represent linear regression lines.

Figure 2

SSM-based multivariate analyses comparing combined linear+nonlinear (-∗-) versus linear only (-○-) features ((a)–(d)) for subject 2 ankle time series with Y∊R30×24 and ((e)–(h)) for subject 6 hip. (a) and (e) show the first 25 SOVs. No significant differences due to nonlinearity are observed. (b)–(d) and (f)–(h) show the corresponding first three SOCs, computed within 30 disjoint windows extracted from the original time series. Differences in these mode shapes could be due to the addition of the nonlinear components. Similar results were obtained from all other subjects and time series analyzed.

Figure 3

PSW-based multivariate analyses comparing combined linear+nonlinear (-∗-) versus linear only (-○-) features ((a)–(d)) for subject 2 ankle time series and ((e)–(h)) for subject 6 hip. (a) and (e) show the first 25 SOVs. (b)–(d) and (f)–(h) show corresponding first three SOCs, computed within 60 disjoint windows extracted from the original time series. While the linear features exhibited only one dominant SOC, adding the nonlinear features revealed three (four) dominant SOCs. These differences demonstrate that the linear only feature vectors were not sufficient to fully capture all of the relevant variations in these ankle time series. Similar results were obtained from all other subjects and time series analyzed.

Figure 4

SSM-based (-∗-) and PSW-based (-○-) multivariate analyses ((a)–(d)) for subject 2 ankle time series with Y∊R30×24 and R30×20, respectively, and ((e)–(h)) for subject 6 hip. (a) and (e) show the first several SOVs, and (b)–(d) and (f)–(h) show corresponding first three SOCs, computed within 30 disjoint windows extracted from the original time series. Similar results were obtained from all other subjects and time series analyzed.

Figure 5

Projections of four SSM-based (thin solid lines) and PSW-based (thick solid lines) SOCs for subject 2 ankle angles onto the EMG median frequency (-○-). Similar results were obtained from all other subjects and time series analyzed and for tracking both mean and median frequency trends. Both methods generally capture the local muscular trends. However, in all cases PSW-based SOCs provided generically better fits for the same number of SOCs used.

Figure 6

Projections of four SSM-based (thin solid lines) and PSW-based (thick solid lines) SOCs for subject 6 hip angles onto the EMG median frequency (-○-). Similar results were obtained from all other subjects and time series analyzed and for tracking both mean and median frequency trends. Both methods generally capture the local muscular trends. However, in all cases PSW-based SOCs provided generically better fits for the same number of SOCs used.

Figure 7

R2 mean and standard deviations for ankle angle SSM-based fits (○) and PSW-based fits (●) to the EMG median frequency. Error bars are ±1 standard deviation. The PSW-based fits consistently outperformed the SSM-based fits.

Figure 8

R2 mean and standard deviations for hip angle SSM-based fits (○) and PSW-based fits (●) to EMG mean frequency. Error bars are ±1 standard deviation. The PSW-based fits consistently outperformed the SSM-based fits.

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