SHM-Conduction

This repository contains a modular model of the human cardiac conduction system written in Modelica as well as an extension of this model that introduces a trigger for premature ventricular contractions (PVCs). It is based on the Seidel-Herzel Model (SHM) of the human baroreflex that was first published by Henrik Seidel in his PhD thesis [1].

The monolithic version of the conduction system model is based on a previous translation of the whole SHM from C to Modelica [2]. This modular version and the PVC extension where developed as an example how a language that is modular, hybrid (supporting multiple formalisms), human-readable, open-source, declarative, and graphical can facilitate model reuse. This will be discussed in detail in an upcoming paper of our research group [3].

Project structure

The main parts of this project can be found in the following files:

• SHMConduction/package.mo contains a full description of the models in this project.
• SHMConduction/Components/MonolithicConduction.mo contains the monolithic version of the contraction model.
• SHMConduction/Components/ModularConduction.mo is the main file for the modular version binding all submodules together.
• SHMConduction/Components/PVC/ModularConductionX.mo is the main file for the extended modular version with PVCs.
• SHMConduction/Examples/ModularExample.mo contains a simulation example that compares MonolithicConduction.mo with ModularConduction.mo.
• SHMConduction/Examples/PVCExample.mo contains a simulation example that tests the PVC extension for plausibility.

Reproduction of plots from the paper

If you want to reproduce the plots in [3], you can alternatively use OMEdit (the IDE of OpenModelica), or the Julia script.

OMEdit

To reproduce the plots with OMEdit you have to use the following steps:

1. Download and install OpenModelica.
2. Clone this repository with Git or download a ZIP file of the current master branch and extract it with an archive manager of your choice.
3. Start OMEdit and open the folder SHMConduction with "File" → "Load Library".

For Figure 2:

• Open the model SHMConduction.Examples.ModularExample (select from "Libraries Browser" on the left hand side with a double click).
• Simulate the model with "Simulation" → "Simulate".
• In the "Variables Browser" on the right hand side select the variables monC.T_cont and modC.T.

For Figure 4:

• Open the model SHMConduction.Examples.PVCExample (select from "Libraries Browser" on the left hand side with a double click).
• Navigate to the "Text View" () in the gray bar under the tab PVCExample.
• Change the value of the parameter with_sinus either to true to produce Figure 4a or to false for Figure 4b.
• Simulate the model with "Simulation" → "Simulate".
• In the "Variables Browser" on the right hand side select the variable con.T.

Julia script

Using the Julia script in scripts/unittests.jl requires additional software, but eliminates the need to interact with OMEdit and allows you to use a plotting library or tool of your choice.

To reproduce the plots you have to use the following steps:

1. Download and install OpenModelica.
2. Download and install Julia.
3. Clone this repository with Git or download a ZIP file of the current master branch and extract it with an archive manager of your choice.
4. Run the following commands in a terminal from the repository folder:

• julia --project=. -e 'ENV["PYTHON"]=""; using Pkg; Pkg.instantiate()'
• julia scripts/unittests.jl

5. This should create the folder out with the following result files:

• SHMConduction.Examples.ModularExample_res.csv contains the data for Figure 2 in the columns time, monC.T_cont and modC.T.
• SHMConduction.Examples.PVCExample_res.csv contains the data for Figure 4a in the columns time and con.T.
• PVCNoSinus_res.csv contains the data for Figure 4b in the columns time and con.T

6. Produce the plots with a plotting tool or library of your choice or use the already existing Python script in scripts/plot_mc_compare.py which will write the plots as PDF files in to the out folder. To run the Python script use the following commands:

• python -m pip install -r requirements.txt
• python scripts/plot_mc_compare.py

Publication

The models in this repository are described in the following article:

C. Schölzel, V. Blesius, G. Ernst, and A. Dominik, “Characteristics of mathematical modeling languages that facilitate model reuse in systems biology: a software engineering perspective,” npj Syst Biol Appl, vol. 7, no. 1, p. 27, 2021, doi: 10.1038/s41540-021-00182-w.

References

[1] H. Seidel, “Nonlinear dynamics of physiological rhythms,” PhD thesis, Technische Universität Berlin, Berlin, Germany, 1997.

[2] C. Schölzel, A. Goesmann, G. Ernst, and A. Dominik, “Modeling biology in Modelica: The human baroreflex,” in Proceedings of the 11th International Modelica Conference, Versailles, France, 2015, pp. 367–376.

[3] C. Schölzel, V. Blesius, G. Ernst, and A. Dominik, “Characteristics of mathematical modeling languages that facilitate model reuse in systems biology: A software engineering perspective,” bioRxiv, preprint 10.1101/2019.12.16.875260v6, 2021. doi: 10.1101/2019.12.16.875260.