Document Type


Date of Degree

Spring 2012

Degree Name

MS (Master of Science)

Degree In

Biomedical Engineering

First Advisor

Laura Frey Law


The development of localized muscle fatigue has classically been described by the nonlinear intensity - endurance time (ET) curve (Rohmert, 1960; El Ahrache et al., 2006). These empirical intensity-ET relationships have been well-documented and vary between joint regions. Xia and Frey Law (2008) previously proposed a three-compartment biophysical fatigue model, consisting of compartments (i.e. states) for active (MA), fatigued (MF), and resting (MR) muscle, to predict the decay and recovery of muscle force. However the model had yet to be validated for static or intermittent isometric tasks. The purpose of this thesis was to provide validation to the biophysical model.

The first goal of this thesis was to determine optimal model parameter values, fatigue (F) and recovery (R), which define the "flow rate" between muscle states and to evaluate the model's accuracy for estimating expected intensity - ET curves. Using a grid-search approach with modified Monte Carlo simulations, over 1 million F and R permutations were used to predict the maximum ET for sustained isometric tasks at 9 intensities ranging from 10 - 90% of maximum in 10% increments (over 9 million simulations total). Optimal F and R values ranged from 0.00589 (Fankle) and 0.0182 (Rankle) to 0.00058 (Fshoulder) and 0.00168 (Rshoulder) , reproducing the intensity-ET curves with low mean RMS errors: shoulder (2.7s), hand/grip (5.6s), knee (6.7s), trunk (9.3s), elbow (9.9s), and ankle (11.2s). Testing the model at different task intensities (15 - 95% maximum in 10% increments) produced slightly higher errors, but largely within the 95% prediction intervals expected for the intensity-ET curves. The second goal of this thesis was to conduct a meta-analysis of available percent torque decline data as a function of duty cycle and intensity from literature. For comparison across studies, decay in MVC (% decline) was extracted at a selected range of time points: 30, 60, 90, and 120 seconds across all joints (shoulder, hand/grip, knee, trunk, elbow, and ankle). Searches of the following databases were performed: PubMed, Cumulative Index to Nursing and Allied Health Literature (CINAHL), Web of Knowledge, and Google Scholar. The inclusion criteria included: studies with healthy human subjects, ages between 18-55 years old, intermittent tasks with force/torque data, a task time of at least 30 seconds, and published in English. Exclusion criteria included: dynamic contractions, simultaneous multi-joint testing (e.g. squat lifts), functional tasks, body/limb weight as primary resistance, and electrically stimulated contractions. The database search strategy resulted in a total of 2781 potential publications. Of these articles 44 met the required inclusion and exclusion criteria. Since there were so few publications that fit the required inclusion and exclusion criteria, static fatigue papers that were used in (Frey Law and Avin, 2010) meta-analysis and fit the inclusion requirements for this study were used to fill in points at the extreme of the surface (DC=1). Of the 194 publications that were used in the prior meta-analysis, only 3 fit the required inclusion and exclusion criteria for this analysis, for a total of 47 studies (torque decline was typically the limiting factor). From these 47 studies, empirical % decline models could be developed for the joint regions with 3 or more data points (ankle, knee, elbow, and hand/grip) and a general model for each of the 4 discrete time points. The total sample size for each joint ranged from 125 (elbow) to 306 (hand/grip). The total number of data points for each joint ranged from 28 (elbow) -to 68 (hand/grip) with a total of 193 data points extracted. The third goal of this thesis was to compare the empirical models developed from the meta-analysis to the predicted surfaces produced by the biophysical model. Each surface was compared to its empirical counterpart qualitatively and quantitatively. Qualitatively the predicted surfaces reasonable resembled the empirical models. Quantitative analysis was performed by calculating the mean RMS and relative errors between the surfaces. The predicted surfaces had reasonably low range of mean RMS errors across each time point: hand/grip (92.66-238s), knee (73.60-186.25s), elbow (23.62-96.31s), and ankle (34.02-129.63s). The quantitative analysis also showed that the percent of the data points found by the meta-analysis that fell within the predicted 95% confidence interval was reasonably high: 52%(hand/grip; 120s) to 100% (elbow; 60, 90, & 120s).

This thesis concluded that this three-compartment fatigue model can be used to accurately represent joint-specific static intensity-ET curves and 3D surfaces of percent torque decline as a function of intensity and duty cycle for short intermittent tasks (i.e. <120 seconds). While the intensity-ET curves are currently used for ergonomics analysis. The relative torque decline surfaces for intermittent tasks that were developed in this thesis provide further insight into what occurs at the muscle level (i.e. decline in muscle force production) during intermittent work cycles. This insight could provide a new method for developing rest-work cycles or job rotation cycles in industry.


Intermittent, Isometric, Mathmatical Modeling, Muscle Fatigue


x, 87 pages


Includes bibliographical references (pages 82-87).


Copyright 2012 John Maurice Looft