A Simple Integrated Mathematical Model of Neuromuscular Activation

Abstract

In the present work, we propose a new integrated mathematical model of neuromuscular activation. It combines the Izhikevich model of neural activity with the Williams model of calcium activity inside the muscle cell and a Hill-type model for the resultant muscle force. The coupling is done using a heuristic approach. The aim is to construct a simple model, which has biophysically meaningful parameters and is applicable to the study of neuromuscular diseases. Then, we study numerically the properties of the model solutions with respect to the main parameters. To that end, we study the effect of various firing patterns of the motoneuron, variations in the properties of the end-plate as well as the rates, corresponding to the calcium dynamics inside the muscle cell.