A Comprehensive Mathematical Model of Surface Electromyography and Force Generation

The purpose of this article is to provide a unified description of a comprehensive mathematical model of surface electromyographic (EMG) measurements and the corresponding force signal in skeletal muscles. The model comprises motor unit pool organization, recruitment and rate coding, intracellular action potential generation and the resulting EMG measurements, as well as the generated muscular force during voluntary isometric contractions. It consolidates and extends the results of several previous publications that proposed mathematical models for the individual model components. A parameterization of the electrical and mechanical components of the model is proposed that ensures a physiologically meaningful EMG-force relation in the simulated signals. Moreover, a novel nonlinear transformation of the excitation model input is proposed, which ensures that the model force output equals the desired target force. Finally, an alternative analytical formulation of the EMG model is proposed, which renders the physiological meaning of the model more clear and facilitates a mathematical proof that muscle fibers in this model at no point in time represent a net current source or sink. Neuromuscular physiology is a vibrant research field that has recently seen exciting advances. Many previous publications have focused on thorough analyses of particular aspects of neuromuscular physiology, yet an integration of the various novel findings into a single, comprehensive model is missing. A consistent description of a complete physiological model as presented here, including thorough justification of model component choices, will facilitate the use of these advanced models in future research. Results of a numerical simulation highlight the model's capability to reproduce many physiological effects observed in experimental measurements, and to produce realistic synthetic data that are useful for the validation of signal processing algorithms. The model is based on recent advances in the understanding of muscular physiology and hence also applicable for analyzing the influence of various physiological and measurement setup parameters on the measured force and EMG signals.