A mathematical model that predicts skeletal muscle force

This study demonstrates the validity of a mathematical model that predicts the force generated by rat skeletal muscles during brief subtetanic and tetanic isometric contractions. The model consists of three coupled differential equations (ODEs). The first two equations represent the calcium dynamics and the third equation represents force dynamics. The model parameters were identified from brief trains of regularly spaces pulses [constant-frequency trains (CFTs)] that produce subtetanic muscle responses. Using these parameters, the model was able to predict isometric forces from other stimulation patterns. For the gastrocnemius muscles predictions were made for responses to CFTs with interpulse intervals (IPI's) ranging from 10 to 50 ms and variable-frequency trains (VFT's), where the initial IPI=10 ms and the remaining IPIs were identical to those used for the CFTs. For the soleus muscles predictions were made for 10-100-ms CFTs. The shape of the predicted responses closely match the experimental data. Comparisons between experimental and modeled force-time integrals, peak forces, and time-to-peak also suggest excellent agreement between the model and the experiment data. Many physiological parameters predicted by the model agree with values obtained independently by others. In conclusion, the model accurately predicts isometric forces generated by rat gastrocnemius and soleus muscles produced by brief stimulation trains.