Readme

Eike Petersen 7/16/2021

semgsim

This is the R package that implements the comprehensive sEMG/force simulation model described in Petersen and Rostalski (2019): “A Comprehensive Mathematical Model of Motor Unit Pool Organization, Surface Electromyography and Force Generation”, https://doi.org/10.3389/fphys.2019.00176. All details regarding the model can be found there. (The paper is openly accessible.)

The package implements the simulation of one or multiple muscles consisting of a number of motor units (MUs). Both electromyographic as well as force responses of all MUs are simulated, and particular care is taken to obtain a realistic EMG-force relationship of both individual MUs and the whole muscle. Once a muscle model is set up, arbitrary contractions can be simulated by specifying a desired muscle force trajectory. Impulse trains of each individual MU are then simulated, and the resulting force and EMG signals (at an arbitrary number of electrodes) are calculated.

Please keep in mind that this is a one-person academic project. Contributions of any kind are very welcome, but I can currently not provide a lot of support myself due to time constraints. I’ll do my best to answer any questions and provide any support I can, though!

Setup

To run, first install the package and all required dependencies. I always install using

install.packages("devtools")
library(devtools)
install("semgsim")

A very simple integration test can then be performed like this:

library(semgsim)
results <- simulate_muscle("semgsim/config/integration.r", deterministic=TRUE, num_cores=3)

That runs a simple demo simulation of a muscle with just three motor units. The call to simulate_muscle should take several minutes up to an hour to complete, but should fail early if something does not work.

The top-level function simulate_muscle automatically performs all intermediate steps required to perform a simulation, including: * Constructing a muscle model object (or multiple of them, if more than one muscle are simulated). * Setting up the motor unit pool of each muscle, including force generating capabilities, action potential shapes and amplitudes, and rate coding and recruitment properties of each MU * Calculating the surface EMG and force twitch responses of each MU * Simulating the desired contraction by calculating an impulse train of each involved MU and then obtaining the resulting force and EMG signals as the sums of the contributions of all individual MUs.

A more complex example can be run using the config file abdominals.r, which simulates the rectus abdominis superior muscles and the transversus abdominis muscles. You can also implement your own muscles and simulations by setting up appropriate config files. (See the various examples in the config directory.)

Simulation diagnostics and plots

The package also implements various plotting functions to analyze the results of a simulation run. In the following, we will assume that the “abdominals.r” config has been run before, like this:

library(semgsim)
results <- simulate_muscle("config/abdominals.r", deterministic=TRUE, num_cores=3, out_file = "simout/abdominals.RDS")

First, load the simulation result. Notice that the simulated rectus abdominis superior consists of six individual muscles (the six “bellies”, three left and three right) and we have a right and a left transversus muscle. Therefore, we have a total of eight muscles in this simulation.

results <- readRDS("simout/abdominals.RDS")

Before we look at plots, let us look at a very basic numerical summary of two of the simulated muscles:

summarize_muscles(results, muscles=c(1, 7))

## [1] "--------- MUSCLE 1------------"
## [1] "Number of MUs: 50"
## [1] "Number of fibers (total): 28422"
## [1] "Number of fibers per MU (avg, min-max range): 568.4 [29 - 1628]"
## [1] "MU recruitment thresholds (avg, min-max range): 0.19 [0.00 - 0.58]"
## [1] "MU cut-off ratios (avg, min-max range): 0.06 [0.00 - 0.56]"
## [1] "--------- MUSCLE 7------------"
## [1] "Number of MUs: 100"
## [1] "Number of fibers (total): 52761"
## [1] "Number of fibers per MU (avg, min-max range): 527.6 [39 - 1436]"
## [1] "MU recruitment thresholds (avg, min-max range): 0.17 [0.00 - 0.56]"
## [1] "MU cut-off ratios (avg, min-max range): 0.12 [0.00 - 0.64]"

Plotting muscle properties

The package includes quite a few functions that visualize internal properties of the generated muscle model.

To assess the geometry of the simulated model, plot_geometry plots the simulated muscle fibers from three different perspectives, indicating skin/fat/muscle tissue layers using different background colors. Innervation zones and fibers ends are indicated using markers. Electrode locations and IDs are also shown. As you can see, the geometrical model and its visualization are not the most sophisticated parts of this package…

plot_geometry(results)

We can also look at the force and EMG twitches generated by a single activation of different MUs.

plot_force_twitches(results$MUs, MUs_to_plot=c(1,11,21,31,41,50), muscle=1)

plot_firing_responses(results, MUs=c(1, 11, 21, 31, 41, 50), muscles=1, electrodes=1)

Various electrical and mechanical properties of the MUs are inter-related following the size principle. To analyze the properties of the MU pool, we can look at the relationship between different properties to assess whether the distribution is realistic.

plot_electromechanical_properties(results$MUs, muscles=1)

plot_exp_rel(results$MUs, muscle=1)

The activation thresholds (in terms of the generated muscle force) above which each MU is activated, as well as the firing rates at which it fires, can also be shown.

plot_firing_rate_funcs(results, MUs=c(1, 11, 21, 31, 41, 50), muscles=1)

Overall we can see that the model generates a continuum of MUs with different properties that range from “slow, small, weak, recruited early” (small MU IDs in the model) to “fast, large, strong, recruited late” (large MU IDs in the model). (Some previous authors have modeled a small number of discrete MU classes or types instead of a continuous distribution. We do not believe this to be accurate, cf. the discussion and references provided in our paper.)

Plotting simulation results

Next, let us look at the simulated force and EMG contributions of all simulated muscles. Muscles 3 and 6 (the lowest rectus “bellies” on both sides) do not generate strong EMG signals at either electrode pair because of the large distance. Muscles 7 and 8 are the left and right transversus muscles, which generate similar contributions to electrode pair one, whereas the contribution to the second pair is of course much more pronounced in the muscle above which the electrode pair is placed (cf. the geometry plot above).

plot_muscle_contribs(results$muscle_contribs)

We can also plot the impulse trains, i.e., the instants at which individual MUs are activated (value X means that there are X firing events for this MU within one sampling period):

plot_impulse_trains(results, MUs=c(1, 11, 21, 31, 41, 50), tlims=c(0, 5))

Moving on from the contributions of the individual muscles to (single-)differential sEMG measurements, we can look at, e.g., the differences of electrode pairs 1-2 and 3-4. (“electrode_confs” is a list of electrode weights.)

plot_surface_potentials(results$surface_potentials, electrodes=c(1,2,3,4), electrode_confs = list(c(1, -1, 0, 0), c(0, 0, 1, -1)))

Using both plot_muscle_contribs and plot_surface_potentials, we can also look at the RMS envelope, the Fourier spectrum and the amplitude distribution of the signals (here shown only for plot_surface_potentials):

plot_surface_potentials(results$surface_potentials, analysis="rms", electrodes=c(1,2,3,4), electrode_confs = list(c(1, -1, 0, 0), c(0, 0, 1, -1)))

plot_surface_potentials(results$surface_potentials, analysis="fourier", electrodes=c(1,2,3,4), electrode_confs = list(c(1, -1, 0, 0), c(0, 0, 1, -1)))

plot_surface_potentials(results$surface_potentials, analysis="density", electrodes=c(1,2,3,4), electrode_confs = list(c(1, -1, 0, 0), c(0, 0, 1, -1)))

Data export

The most important elements of the simulation results can be easily exported using export_to_mat(results, "target_file.mat") or export_to_csv(results, "target_file.csv").

Customization

The easiest way of running a simulation is by calling simulate_muscle, as demonstrated above. This automatically performs all intermediate steps, including: * Constructing a muscle model object (or multiple of them, if more than one muscle are simulated). * Setting up the motor unit pool of each muscle, including force generating capabilities, action potential shapes and amplitudes, and rate coding and recruitment properties of each MU * Calculating the surface EMG and force twitch responses of each MU * Simulating the desired contraction by calculating an impulse train of each involved MU and then obtaining the resulting force and EMG signals as the sums of the contributions of all individual MUs.

All of these steps can also be performed individually, however: see the implementation of the simulate_muscle function for details on how to perform this (essentially by passing the muscle object through a chain of function calls). In particular, it is possible to set up one or multiple muscle objects using setup_muscles (computationally very cheap), calculate the resulting surface EMG twitch responses using calculate_semg_TFs (computationally rather expensive), and then store the resulting muscle object for future usage. This muscle object can then be reloaded very quickly and be used to simulate a desired muscle force trajectory using simulate_model without having to re-calculate all the muscle properties.

The computational effort required to perform a simulation roughly depends on two factors: a) The number of muscle fiber - electrode pairs for which transfer functions need to be computed. This obviously scales with the product “num_fibers * num_electrodes”. b) The number of time steps to simulate.

The function simulate_model implements the simulation of a complete contraction, following a prescribed muscle force activation level. Currently, there is no easily callable method implemented for simulating just a single time step. If this is desired, see the implementation of the “simulate_model” function for pointers on how this can be implemented.

Current Limitations

• Effects due to peripheral fatigue are not included in the model.
• Effects due to dynamic changes of geometry (muscle shortening & thickening, etc.) are not included in the model.
• The geometrical model of Farina and Rainoldi (1999) which is implemented here is very limited and - depending on the particular muscle to be modeled - may be far from reality: fibers are following straight lines parallel to a planar skin surface, and they do not deform during contractions. For limb muscles, Farina et al. have later derived a circular volume conduction model that could be easily plugged into the simulator if someone would be willing to implement it.
• Physiological force control is neither modeled nor simulated. The model simply describes the muscle’s response to an input activation signal that corresponds to a particular output force level. For simulating responses to rapid stimuli or target tracking, a force controller model should be used to control the input to the simulation model.
• Measurement noise is not included in the simulated data, but can obviously easily be added to the resulting signals.
• (For the included simulation of respiratory mechanics: many of the physiological parameters are not known in the literature and have been estimated rather crudely. Note also that for this application, the assumed geometrical model is definitely quite far from reality.)

The code is reasonably modular, and modifications or improvements of individual model components can likely be implemented and integrated with the rest of the simulator with reasonable effort.

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Eike Petersen, Institute for Electrical Enginnering in Medicine (IME), Universität zu Lübeck. 2015-2021. Contributions by Marcus Eger, Drägerwerk AG & Co KGaA.