Neuromuscular physiology is a vibrant research field that has recently seen exciting advances. 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. In this article, we provide a unified description of a comprehensive mathematical model of surface electromyographic (EMG) measurements and the corresponding force signal in skeletal muscles, both consolidating and extending the results of previous studies regarding various components of the neuromuscular system. The model comprises motor unit (MU) 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. Mathematically, it consists of a large number of linear PDEs, ODEs, and various stochastic nonlinear relationships, some of which are solved analytically, others numerically. 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, in particular taking the continuous, size-dependent distribution of MU parameters into account. Moreover, we describe a novel nonlinear transformation of the common drive model input, which ensures that the model force output equals the desired target force. On a physiological level, this corresponds to adjusting the rate coding model to the force generating capabilities of the simulated muscle, while from a control theoretical point of view, this step is equivalent to an exact linearizing transformation of the controlled neuromuscular system. 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. 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.

Simulated EMG, force, and impulse train signalsSimulated muscle force, electromyography (EMG), and motor unit (MU) impulse train signals of a rectus abdominis muscle consisting of six simulated muscle bellies, each consisting of 50 motor units (MUs). The data are in the MATLAB .mat file format and can be imported, e.g., using GNU Octave.Simulation_data_rectus_abdominis_Petersen_Rostalski_2018.matData loading and plotting demo scriptMATLAB script file to demonstrate loading and plotting the data contained in "Simulation_data_rectus_abdominis_Petersen_Rostalski_2018.mat".plot_data.mSimulation configuration fileConfiguration file containing the definitions of all physiological and computational parameters required for running the simulation that generated the data contained in "Simulation_data_rectus_abdominis_Petersen_Rostalski_2018.mat". This is an R script file, to be executed using the R programming language and computing environment.Simulation_config_rectus_abdominis_Petersen_Rostalski_2018.rREADME