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A model for studying cardiac muscle fibrillation

In this project, we reproduce the model developed in the article [1]. The model allows us to study the effects of applying external electrical signals to various drivers of the heart rate - the centers that excite heart contractions.

An external signal in the form of alternating current of varying amplitude, frequency, and duration of use can cause reversible and irreversible signal conduction blockages, atrial fibrillation, and ventricular fibrillation.

The model can become the basis for creating a hardware electronic simulator useful for educational purposes and for debugging coupled systems.

Description of the model

In addition to the external signal source, there are two types of subsystems in the circuit: rhythm drivers and models of depolarization and repolarization processes.

image.png

The model of each of the three pacemakers (sinoatrial, atrioventricular node, and Gis bundle) are modified Van der Pol oscillators.:

where indicates the parameters related to each of the three rhythm directors (SA, AV and HP), and indicates the coefficient of influence of each driver on the system (, and In the model, this system occurs in three blocks with different parameters, but with the same structure.

image.png

Depolarization and repolarization processes are modeled using the Fitzhugh—Nagumo model equations.:

where is the index indicates the parameters related to different components of the cardiogram (P, T, Ta waves and the QRS complex).

image.png

Depending on the direction of improvement of the model, which will be interesting for the reader to develop, subsystems of the same type could be packaged in masked blocks and only their parameters changed, or presented in text form. But the proposed model is simple enough to reproduce based on illustrations, and also allows you to generate code with the least effort.

Launching the model

Let's run the model and study the ECG of the cardiac system when applying a signal with an angular frequency of 300 rad/s for a duration of 1.5 seconds, starting at t = 5 c.

In [ ]: 
engee.open("$(@__DIR__)/ecg_external.engee")
data = engee.run("ecg_external")
Out[0]:
SimulationResult(
    "ECG" => WorkspaceArray{Float64}("ecg_external/ECG")
,
    "Pacemakers" => WorkspaceArray{Vector{Float64}}("ecg_external/Pacemakers")

)
In [ ]: 
ECG = collect(data["ECG"] )
Pacemakers = collect(data["Pacemakers"])

plot(
    plot( Pacemakers.time, hcat(Pacemakers.value...)', label=["SA" "AV" "HP"] ),
    plot( ECG.time, ECG.value, label=false, c=:black ),
    layout=(2,1)
)
Out[0]:

According to this model, applying such an alternating current to three heart rate drivers simultaneously creates a reversible disorder.

Conclusion

The presented model, for all its simplified nature, allows us to study the influence of external signals on the heart rate.

It is best to start all further work by studying the original article [1].

Bibliography

[1] Ryzhii M., Ryzhii E. Simulink heart model for simulation of the effect of external signals //2016 IEEE Conference on Computational Intelligence in Bioinformatics and Computational Biology (CIBCB). – IEEE, 2016. – pp. 1-5.

Blocks used in example