DOI: 10.5061/dryad.326qs26
title: Data from: A comprehensive mathematical model of motor unit pool organization, surface electromyography and force generation

description: 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.
description: 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