Application of the LaGrange polynomial in skeletal muscle fatigue analysis

David Gabriel, David Proctor, Dean Engle, Sreekumaran Nair, Janet Vittone, Kai Nan An

Research output: Contribution to journalArticlepeer-review

4 Scopus citations


The percentage of decrement in torque and the number of serial contractions are mutually exclusive methodological controls in the study of muscular fatigue. This paper examines the feasibility of using the LaGrange polynomial in the analysis of voluntary muscular fatigue patterns. Twenty-one men (ages 20-60 years) reported to the orthopedic biomechanics laboratory on 2 days separated by 4 months. During both sessions, participants completed three maximal isokinelic (180 deg·s-1) contractions of the knee extensors to serve as baseline, before starting the fatigue protocol. The fatigue protocol consisted of serial contractions until a 50% strength decrement was reached. The LaGrange polynomial was first used to interpolate the individual fatigue pattern for each participant into 15 data points (trials). Data analysis was then conducted on these 15 data points, lntraclass correlation analysis of variance showed that the reliability of baseline torque was very good (.93). Baseline torque, the average of three trials, exhibited a 5.4 Nm (6%) increase from the first to second test session (p <. 05). The mean level of torque, average of the 15-point fatigue pattern, also increased 7.5 Nm (15%) on the second test session (p <. 05). The classic torque deficit for the first trial of a fatigue series was preserved by the interpolation method. Serial contractions resulted in an average decrease in torque of 29.5 Nm (50%)from the first to last trial (p <. 05). The interpolation method also retained the linear and quadratic trend components commonly observed for isometric and isokinetic fatigue patterns. The two trend components accounted for 94.7% of the total trial variance. It was concluded that the LaGrange polynomial used to interpolate fatigue patterns to fewer data points was successful.

Original languageEnglish (US)
Pages (from-to)168-174
Number of pages7
JournalResearch Quarterly for Exercise and Sport
Issue number2
StatePublished - 2002

All Science Journal Classification (ASJC) codes

  • Physical Therapy, Sports Therapy and Rehabilitation
  • Orthopedics and Sports Medicine
  • Nephrology


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