A model of the rat medial gastrocnemius muscle based on inputs to motoneurons and on an algorithm for prediction of the motor unit force

The muscle force is the sum of forces of multiple motor units (MUs), which have different contractile properties. During movements, MUs develop unfused tetani, which result from summation of twitch-shape responses to individual stimuli, which are variable in amplitude and duration. The aim of the study was to develop a realistic muscle model that would integrate previously developed models of MU contractions and an algorithm for the prediction of tetanic forces. The proposed model of rat medial gastrocnemius muscle is based on physiological data: excitability and tiring frequencies of motoneurons, contractile properties, and the number and proportion of MUs in the muscle. The MU twitches were modeled by a six-parameter analytical function. The excitability of motoneurons was modeled according to a distribution of their rheo-base currents measured experimentally. Processes of muscle force regulation were modeled according to a common drive hypothesis. The excitation signal to motoneurons was modeled by two form types: triangular and trapezoid. The discharge frequencies of MUs, calculated individually for each MU, corresponded to those recorded for rhythmic firing of motoneurons. The force of the muscle was calculated as the sum of all recruited MUs. Participation of the three types of MUs in the developed muscle force was presented at different levels of the excitation signal to motoneurons. The model appears highly realistic and open for input data from various skeletal muscles with different compositions of MU types. The results were compared with three other models with different distribution of the input parameters. NEW & NOTEWORTHY The proposed mathematical model of rat medial gastrocnemius muscle is highly realistic because it is based strictly on experimentally determined motor unit contractile parameters and motoneuron properties. It contains the actual number and proportion of motor units and takes into consideration their different contributions to the whole muscle force, depending on the level of the excitation signal. The model is open for input data from other muscles, and additional physiological parameters can also be included.