Mathematical model that predicts the force-intensity and force-frequency relationships after spinal cord injuries

Jun Ding, Li Wei Chou, Trisha M. Kesar, Samuel C.K. Lee, Therese E. Johnston, Anthony S. Wexler, Stuart A. Binder-Macleod*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

21 Scopus citations


We have previously developed and tested a muscle model that predicts the effect of stimulation frequency on muscle force responses. The aim of this study was to enhance our isometric mathematical model to predict muscle forces in response to stimulation trains with a wide range of frequencies and intensities for the quadriceps femoris muscles of individuals with spinal cord injuries. Isometric forces were obtained experimentally from 10 individuals with spinal cord injuries (time after injury, 1.5-8 years) and then compared to forces predicted by the model. Our model predicted accurately the force-time integrals (FTI) and peak forces (PF) for stimulation trains of a wide range of frequencies (12.5-80 Hz) and intensities (150-600-μs pulse duration), and two different stimulation patterns (constant-frequency trains and doublet-frequency trains). The accurate predictions of our model indicate that our model, which now incorporates the effects of stimulation frequency, intensity, and pattern on muscle forces, can be used to design optimal customized stimulation strategies for spinal cord-injured patients.

Original languageEnglish
Pages (from-to)214-222
Number of pages9
JournalMuscle and Nerve
Issue number2
StatePublished - Aug 2007


  • Constant-frequency trains
  • Doublet-frequency trains
  • Force-time integral
  • Isometric forces
  • Mathematical muscle models
  • Paralyzed muscle
  • Peak force


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