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symmetries_travelling_waves

We illustrate the symmetries of travelling wave solutions to RD-models of cell growth.

https://github.com/johannesborgqvist/symmetries_travelling_waves

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Repository

We illustrate the symmetries of travelling wave solutions to RD-models of cell growth.

Basic Info
  • Host: GitHub
  • Owner: JohannesBorgqvist
  • Language: Jupyter Notebook
  • Default Branch: main
  • Size: 140 MB
Statistics
  • Stars: 0
  • Watchers: 1
  • Forks: 0
  • Open Issues: 0
  • Releases: 0
Created over 3 years ago · Last pushed almost 3 years ago
Metadata Files
Readme Citation

README.md

Model construction of travelling wave models of collective cell migration in two spatial dimensions using Lie symmetries

Date: 2023-01-03,
Written by: Johannes Borgqvist.
We illustrate the symmetries of travelling wave models of collective cell migration in two spatial dimensions. This repositry is an open--source repositry written in Python which contains two scripts:

  1. "plot_travelling_wave_symmetries.py",
  2. "cell_migration_FEM_simulation.py".

The first script plots the symmetries of three candidate models referred to as the exponential, logistic and generalised model. The second script simulates collective cell migration in two spatial dimensions by solving a PDE that was constructed based on Lie symmetries.

Solving the travelling wave ODEs for the three minimal models of collective cell migration

To generate the figure below, just run the script listed in the first bullet point above.

Travelling wave symmetries of models of collective cell migration

Simulating collective cell migration on the unit square

To generate a mesh, initial condition and lastly to solve a reaction-convection-diffusion PDE in two spatial dimensions of collective cell migration, run the script listed in the second bullet point above. This script solves the PDE using FEniCS. The easiest way to install FEniCS is by creating a conda environment using the provided yml-file called fenicsproject.yml. To install this environment (after conda has been installed), type

conda env create -f fenicsproject.yml

. Then, you can activate this environment which is called "fenicsproject" by using the command

conda activate fenicsproject

. After this, you should be able to run the FEM simulations of collective cell migration. To deactivate the environment, simply type

conda deactivate

. All figures are saved in the folder called Figures. The pvd files as well as the corresponding vtk files that are generated by FEniCS are saved in the Output folder and these can be looked at in ParaView.

FEM mesh of the unit square

Initial condition for the unit square

PDE simulations in two spatial dimensions of collective cell migration

Owner

  • Login: JohannesBorgqvist
  • Kind: user
  • Location: Oxford, UK
  • Company: Mathematical Institute, University of Oxford

I am a Post-Doc in Mathematical Biology. I model cell-migration using coupled system of PDEs of so called "reaction-diffusion" type.

Citation (CITATION.cff) 

cff-version: 1.2.0
message: "If you use this software, please cite it as below."
authors:
  - family-names: Borgqvist
    given-names: Johannes Gabriel
    orcid:  https://orcid.org/0000-0001-6441-2942
title: "Github repositry for symmetry based model construction of travelling wave models of collective cell migration in two spatial dimensions."
version: 1.0
doi: https://github.com/JohannesBorgqvist/symmetries_travelling_waves
date-released: 2023-01-10
preferred-citation:
  type: article
  authors:
  - family-names: "Borgqvist"
    given-names: "Johannes G."
    orcid: "https://orcid.org/0000-0001-6441-2942"
  doi: "https://github.com/JohannesBorgqvist/symmetries_travelling_waves"
  journal: "https://github.com/JohannesBorgqvist/symmetries_travelling_waves"
  month: 1
  start: 1 # First page number
  end: 10 # Last page number
  title: "Github repositry for symmetry based model construction of travelling wave models of collective cell migration in two spatial dimensions."
  issue: 1
  volume: 1
  year: 2023

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