# A model of a human neuromuscular system for small isometric tensions

## Abstract

A model is constructed of the motor units in the human first dorsal interosseus (FDI) muscle. Each motorneuron is simulated using a pseudo-steady-state model that omits the membrane capacity and the events underlying the action potential. Properties of individual twitches in the corresponding muscle units are based on the data of Milner-Brown et al. for the FDI, while the transduction between steady firing rate and percentage of maximum tension in a muscle unit is based on the work of Rack and Westbury on the cat soleus muscle. Since we are concerned only with small isometric tensions, we ignore effects due to muscle spindles and to recurrent inhibition. The model allows one to to determine, by simulation, the tension-time functions produced by different "programs" of input to an entire pool of 120 motorneurons. Thus, for example, in order to produce tension rising linearly with time, it suffices to deliver to each neuron in the pool a non-linearly rising conductance; the conductance can be the same for all neurons in the pool, but can NOT be scaled in proportion to the surface area of the respective neurons. The input may be delivered to any part of the neuron's dendritic tree, as long as the electrotonic distribution of input is the same for all the neurons. For a linearly rising force produced in this way, most of the motorneurons yield similar slopes for their frequency-force curves, as observed by Milner-Brown et al. To produce tensions greater than about 1 kg, mechanisms not included in this model must come into play, i.e. perhaps introduction of phasic motorneurons. The most important data needed to improve this model are sets of isometric frequency-force curves for muscle units of different twitch tensions. © 1977 Springer-Verlag.