Effect of synchronization of firings of different motor unit types on the force variability in a model of the rat medial gastrocnemius muscle

Oscillations of muscle force, observed as physiological tremors, rely upon the synchronized firings of active motor units (MUs). This study aimed to investigate the effects of synchronizing the firings of three types of MUs on force development using a mathematical model of the rat medial gastrocnemius muscle. The model was designed based on the actual proportion and physiological properties of MUs and motoneurons innervating the muscle. The isometric muscle and MU forces were simulated by a model predicting non-synchronized firing of a pool of 57 MUs (including eight slow, 23 fast resistant to fatigue, and 26 fast fatigable) to ascertain a maximum excitatory signal when all MUs were recruited into the contraction. The mean firing frequency of each MU depended upon the twitch contraction time, whereas the recruitment order was determined according to increasing forces (the size principle). The synchronization of firings of individual MUs was simulated using four different modes and inducing the synchronization of firings within three time windows (± 2, ± 4, and ± 6 ms) for four different combinations of MUs. The synchronization was estimated using two parameters, the correlation coefficient and the cross-interval synchronization index. The four scenarios of synchronization increased the values of the root-mean-square, range, and maximum force in correlation with the increase of the time window. Greater synchronization index values resulted in higher root-mean-square, range, and maximum of force outcomes for all MU types as well as for the whole muscle output; however, the mean spectral frequency of the forces decreased, whereas the mean force remained nearly unchanged. The range of variability and the root-mean-square of forces were higher for fast MUs than for slow MUs; meanwhile, the relative values of these parameters were highest for slow MUs, indicating their important contribution to muscle tremor, especially during weak contractions. Author summary The synchronization of firings of motor units (MUs), the smallest functional elements of skeletal muscle increases fluctuations in muscle force, known as physiological tremor, which can disturb high-precision movements. In this study, we adopted a recently proposed muscle model consisting of MUs of three different types (fast fatigable, fast resistant to fatigue, and slow) to study four different scenarios of MU synchronization during a steady level of excitatory input to motoneurons. The discharge patterns were synchronized between pairs of MUs by shifting in time individual pulses, which occurred within a short time interval, and a degree of synchronization was then estimated. The increased synchronization index resulted in increased force variability for all MU types as well as for the whole muscle output; however, the mean force levels remained nearly unchanged, whereas the frequencies of the force oscillations were decreased. The absolute range of force variability was higher for fast than for slow MUs, indicating their dominant influence on muscle tremor at strong contractions, but the highest relative increase in force variability was observed for synchronized slow MUs, indicating their significant contribution to tremor during weak contractions, in which only slow MUs are active.