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

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-mus 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.