Computer simulation of the steady-state input-output function of the cat medial gastrocnemius motoneuron pool

A pool of 100 simulated motor units was constructed in which the steady-state neural and mechanical properties of the units were very closely matched to the available experimental data for the cat medial gastrocnemius motoneuron pool and muscle. The resulting neural network generated quantitative predictions of whole system input-output functions based on the single unit data. The results of the simulations were compared with experimental data on normal motor system behavior in humans and animals. We considered only steady-state, isometric conditions. All motoneurons received equal proportions of the synaptic input, and no feedback loops were operative. Thus the intrinsic properties of the motor unit population alone determined the form of the system input-output function. Expressing the synaptic input in terms of effective synaptic current allowed the simulated motoneuron input-output functions to be specified by well-known firing rate-injected current relations. The motor unit forces were determined from standard motor unit force-frequency relations, and the system output at any input level was assumed to be the linear sum of the forces of the active motor units. The steady-state input-output function of the simulated motoneuron pool had a roughly sigmoidal shape that was quite different from those derived from previous recruitment models, which did not incorporate frequency modulation. Frequency modulation in combination with the skewed distribution of thresholds (low values much more frequent than high) restricted upward curvature to low input levels, whereas frequency modulation alone was responsible for the final gradual approach to the maximum force output. Sensitivity analyses were performed to assess the importance of several assumptions that were required to deal with gaps and uncertainties in the available experimental data. The shape of the input-output function was not critically dependent on any of these assumptions, including those specifying linear summation of inputs and outputs. A key assumption of the model was that systematic variance in motor unit properties was much more important than random variance for determining the input-output function. Addition of random variance via Monte Carlo techniques showed that this assumption was correct. These results suggest that the output of a motoneuron pool should be quite tolerant of random variance in the distribution of synaptic inputs and yet substantially altered by any systematic differences, such as unequal distribution of inputs among different motor unit types. The use of Monte Carlo techniques to reduce the level of covariance between the motor unit thresholds and forces to that reported in the experimental data resulted in simulated recruitment orders that were much more variable than those reported for hindlimb muscles of decerebrate cats. It is suggested that the distribution of effective synaptic current from homonymous Ia afferents within the motoneuron pool may significantly enhance the orderliness of motor unit recruitment. Uniform synaptic input to the model motoneuron pool resulted in considerable 'over-stimulation' of low-threshold motoneurons, that is, firing rates in excess of the fusion frequency of their muscle units. However, we found that marked frequency limiting of the low-threshold units could be obtained by introducing a modest degree of nonlinear summation to the processing of synaptic input. Moreover, this frequency limiting was accomplished with only subtle changes in the overall input-output function. The system gain was linearly related to total muscle force only at low force levels, as expected from the sigmoidal-shaped input-output function. This result implies that 'automatic gain compensation' of reflexes can only be attributed to the intrinsic properties of motor units if it too is restricted to low force levels.