EMI High-Order Operator-Splitting

This repository serves as a research environment for studying the application of high-order operator-splitting methods to the cardiac EMI (Extracellular–Membrane–Intracellular) model.

📂 Repository Structure

The repository is organized into the following key components:

🔹 Experiment Scripts

File	Description
exp1_single_circular_cell.py	Simulates a single circular cell.
exp2_two_semicircular_cells.py	Simulates two coupled semicircular cells.
exp3_n_2D_idealized_cell.py	Simulates an n×m grid of cells using the FHN or tTP cell model.
exp4_channelopathy.py	Simulates a 2×1 configuration of cells with the tTP model under Brugada and LQT1 syndromes.

🔹 Meshes

The meshes/ folder contains .geo files for generating meshes required for the experiments. To generate a mesh, use the following command:

gmsh -2 <file_name>.geo -o <output_file_name>.msh

🔹 Results

The results/ directory contains scripts for post-processing and visualization. Due to the large size of the output data, please request access by contacting carlos.ballesteros@usask.ca.

Once you have the data, you can use the following scripts:

File	Description
MRMS_exp<n>.py	Computes and exports MRMS error data to an Excel file.
take_plot_data_exp4.py	Extracts voltage data for plotting from experiment 4.
plot_data_exp4.py	Generates plots from the extracted data.

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🛠 Requirements

The following dependencies are required to run the simulations:

• gmsh
• firedrake
• irksome
• pythOS

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🏗 Installation

You can install the dependencies manually, but for convenience, the repository includes container.def, a definition file for building a container using Apptainer (formerly Singularity) with Ubuntu Linux.

🔹 Building the Container

Run the following command to build the container:

singularity build container.sif container.def

Once built, the container.sif file will be available for execution.

🔹 Running the Container

To launch the container, use the following command:

apptainer shell --writable-tmpfs --bind ./:/container --bind <path-to-repo>/EMI-HighOrder-OperatorSplitting:<path-to-repo>/EMI-HighOrder-OperatorSplitting container.sif

Replace <path-to-repo> with the actual path to your repository.

🔹 Inside the Container

Once inside, navigate to the container directory:

cd /container

Then, activate the Firedrake virtual environment:

source /opt/firedrake/bin/activate

You're now ready to run simulations and process results!

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