BDF2 time stepping scheme

This directory contains an implementation of a numerical scheme for solving the Mori model in the zero flow limit with two three compartments (neurons, glial and ECS) and Na, K, Cl, Glu. Numerical scheme: BDF2 for time stepping, ESDIRK4 for ODE time stepping (can be altered in solve_BDF2.py) and a Strang or a Godenov splitting scheme.

Dependencies

To get the environment needed (all dependencies etc.) to run the code, download the docker container by running:

docker run -t -v $(pwd):/home/fenics -i quay.io/fenicsproject/stable
sudo apt-get update
sudo apt install texlive texlive-latex-extra texlive-fonts-recommended dvipng

Usage

The numerical experiments can be run:

python3 run_CSD_simulation.py

Files

• run_CSD_simulation.py
  Run different CSD scenarios (specifies in problems.py) and plot results

  • Output: generates time and space plots for all state variables, and calculates wave speed and duration.

• solver_BDF2.py
  Contains class for a FEM solver for the mori model. Numerical scheme: BDF2 for time stepping, ESDIRK4 for ODE time stepping (can be altered in solve_BDF2.py) and a Strang (solve_system_strange()) or Godenov splitting scheme (solve_system_godenov()).

• problem_base.py
  Contains class for problem base, specifying model parameters, initial conditions, membrane model (ODEs and/or algebraic expressions).

• problems.py
  Contains class for problems, specifying triggering mechanism (excitatory fluxes, drop of ECS K/Cl, or turning off Na/K/ATPase) and model parameteres (e.g. AQP4 and KIR knockouts)

• plotter.py
  Contains class for plotting.

License

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.

Community

Contact ada@simula.no for questions or to report issues with the software.