Spinal Cord Neuronal Network Simulator for Muscle Control

Abstract

A simulator of a neuronal network of the spinal cord was developed based on mathematical models of motoneurons, Renshaw cells, synaptic noise, descending drives and muscle unit twitches.Methods: In its present version the simulator represents a pool of 272 motoneurons (MNs) and 68 Renshaw cells (RC). Simple MN models are used, based on a parallel association of a capacitance and conductances in series with battery elements, including a time-varying potassium conductance that is described by two exponentials. Other conductances in parallel are due to synaptic inputs from different afferent pathways, each described by an alpha function associated with a firing of a presynaptic neuron. All conductances are in series with their respective Nernst or reversal potential batteries Finally a lowpass synaptic noise current is injected. The model parameters were based on data from the literature on cat gastrocnemius muscle, representing the different dynamics of S, FR and FF type MNs. Each motor unit generates a twitch, according to an alpha function with parameters compatible with the parent MN type. There are two RC models: fixed burster and conductance-based. The simulator was developed in Visual C++ and has a user-friendly interface for changing the default parameter values. This allows, for example, for the choice of different standard deviations for each parameter of a given MN type, or alternatively, the same standard deviation for all parameters. The user can set the lowpass synaptic noise bandwidth and noise power, the type of afferent trains to the MN pool (either Poisson or truncated Gaussian interspike intervals), the twitch amplitude and time course for S, FR and FF type motor units. After each simulation run, the user can select the following graphs: spike times of MNs, RCs and descending drives; interspike interval histograms or membrane potential time course of selected MNs; developed muscle force as a function of time. For example, in a study on the difference between Poisson and Gaussian descending drives, the software would show a graph of the muscle force together with the spike trains of any subset of MNs, RCs and of the descending drives. The simulator is very user-friendly and reasonably fast and its results can also be exported to other programs such as Matlab for complementary processing.