Code for solving the KNP--EMI problem using a DG fem method.

All dependencies are listed in environment.yml. To create an environment with these dependencies use either conda or mamba and run

conda env create -f environment.yml

or

mamba env create -f environment.yml

Then call

conda activate KNP-EMI

# run MMS test in space
python run_MMS_space.py

# run MMS test in space
python run_MMS_time.py

# run simulation on idealized 2D geometry
python run_2D.py

# run simulation on idealized 3D geometry
python run_3D.py

# run simulation on realistic 3D geometry of rat neuron
python run_rat_neuron.py

• solver.py: class for PDE solver.

• membrane.py: class for membrane model (ODE stepping, functions for communication between PDE and ODE solver etc.).

• mm\_\*.py: spesification of membrane model (including all membrane parameters)

  • mm_hh.py: Hodkin Huxley model (with ODEs)
  • mm_leak.py: passive leak model (no ODEs)

• run_*.py: scripts for running various simulations. Contains PDE parameters (mesh, physical and numerical parameters)

  • run_MMS_space.py: MMS test in space
  • run_MMS_time.py: MMS test in time
  • run_2D.py: simulation with Hodkin Huxley dynamics in idealized 3D axons
  • run_3D.py: simulation with Hodkin Huxley dynamics in idealized 3D axons
  • run_rat_neuron.py: simulation with spatially varying membrane mechanisms in realistic 3D geometry

• make*mesh*\*.py: scripts for generating idealized 2D and 3D meshes

• make*mesh*\*.py: scripts for generating figures

The code assumes ECS cells are tagged with 0 and ICS cells are tagged with 1,2,3, ... and that all interior facets are tagged with 0. The membrane potential is defined as phi_i - phi_e (i.e. phi_1 - phi_2). Since we have marked cell in ECS with 0 and cells in ICS with 1 we have an interface normal pointing inwards. In general, normals will always point from lower to higher (e.g. from 0 -> 1)

The software is free: you can redistribute it and/or modify it under the terms of the GNU Lesser General Public License as published by the Free Software Foundation, either version 3 of the License, or (at your option) any later version.

Contact [email protected] for questions or to report issues with the software.