Two-step, predictive, isometric force model tested on data from human and rat muscles

Jun Ding, Stuart A. Binder-Macleod, Anthony S. Wexler

Research output: Contribution to journalArticlepeer-review

39 Scopus citations


Functional electrical stimulation can assist paralyzed individuals to perform functional movements, but muscle fatigue is a major limitation to its practical use. An accurate and predictive mathematical model can facilitate the design of stimulation patterns that optimize aspects of the force transient while minimizing fatigue. Solution nonuniqueness, a major shortcoming in previous work, was overcome with a simpler model. The model was tested on data collected during isometric contractions of rat gastrocnemius muscles and human quadriceps femoris muscles under various physiological conditions. For each condition tested, parameter values were identified using the force response to one or two stimulation trains. The parameterized model was then used to predict forces in response to other stimulation patterns. The predicted forces closely matched the measured forces. The model was not sensitive to initial parameter estimates, demonstrating solution uniqueness. By predicting the force that develops in response to an arbitrary pattern of stimulation, we envision the present model helping identify optimal stimulation patterns for activation of skeletal muscle during functional electrical stimulation.

Original languageEnglish (US)
Pages (from-to)2176-2189
Number of pages14
JournalJournal of Applied Physiology
Issue number6
StatePublished - Dec 1998
Externally publishedYes


  • Catch-like property
  • Fatigue
  • Functional electrical stimulation
  • Mathematical model
  • Muscle length

ASJC Scopus subject areas

  • Physiology
  • Endocrinology
  • Orthopedics and Sports Medicine
  • Physical Therapy, Sports Therapy and Rehabilitation


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