fenics-stubs

Setup Tool for Unified Biophysical Simulations

STUBS is a biophysical simulation library that provides a level of abstraction to models, making it easier for users to develop, share, and simulate their mathematical models. STUBS is highly suited for building systems biology models and simulating them as deterministic partial differential equations [PDEs] in realistic geometries using the Finite Element Method [FEM] - the integration of additional physics such as electro-diffusion or stochasticity may come in future updates. Systems biology models are converted by STUBS into the appropriate systems of reaction-diffusion PDEs with proper boundary conditions. FEniCS is a core dependency of STUBS which handles the assembly of finite element matrices as well as solving the resultant linear algebra systems.

Installation

!!! IMPORTANT !!!

Although FEniCS is a core dependency, because it has many different versions (2019.1, development, FEniCSx, etc.), is quite large, and is complicated to build, it is not packaged with STUBS by default. The recommended way to use STUBS is to create a container from one of the official FEniCS docker images and to pip install STUBS from within the container.

# create a container from the official fenics docker image
jgl:~$ docker run -ti --init quay.io/fenicsproject/dev
# pip install stubs from within the container
fenics:~$ pip install stubs

Dependencies

• STUBS uses FEniCS to assemble finite element matrices as well as solve the resultant linear algebra systems.
• STUBS uses pandas as an intermediate data structure to help organize and process models.
• STUBS uses Pint for unit tracking and conversions.
• STUBS uses matplotlib to automatically generate plots of min/mean/max (integrated over space) concentrations over time, as well as plots showing solver convergence.
• STUBS uses sympy to allow users to input custom reactions and also to determine the appopriate solution techniques (e.g. testing for non-linearities).
• STUBS uses numpy and scipy for general array manipulations and basic calculations.
• STUBS uses tabulate to make pretty ASCII tables.
• STUBS uses termcolor for pretty terminal output so that simulations are more satisfying to watch.

Functionality

STUBS is equipped to handle:

• Reaction-diffusion with any number of species, reactions, and compartments.
• Reaction-diffusion with boundary conditions between coupled sub-volumes and sub-surfaces (defined by marker values in the .xml file).
• Reaction-diffusion in non-manifold meshes (experimental).
• Conversion of units at run-time via Pint so that models can be specified in whatever units are most natural/convenient to the user.
• Specification of a time-dependent function either algebraically or from data (STUBS will numerically integrate the data points at each time-step).
• Customized reaction equations (e.g. irreversible Hill equation).

STUBS does not handle (it is possible to implement these features but would require a lot of work - contact author if interested):

• Problems with coupled-physics spanning more than two dimensions. For example you may solve a problem with many 3d sub-volumes coupled to many 2d sub-surfaces, or a problem with many 2d "sub-volumes" coupled to many 1d "sub-surfaces" but a problem with 3d physics can't be coupled to a problem with 1d physics.
• Sub-volumes embedded within sub-volumes (i.e. from any point inside the interior sub-volume, one must traverse two surfaces to get to the exterior of the full mesh)

Nomenclature

Because STUBS methods are viable in both 3 dimensional and 2 dimensional geometries we use the following nomenclature to define various functions in the code.

Cell : The element of the highest geometric dimension (e.g. "cell" refers to a tetrahedra in 3d, but a triangle in 2d). Facet : The element of dimenion n-1 if n is the highest geometric dimension. Volume mesh : A set of elements of the highest geometric dimension. Surface mesh : A set of elements of dimension n-1 if n is the highest geometric dimension.

"Cell" and "Volume" are used interchangeably (e.g. a volume mesh is a collection of cells). "Facet" and "Surface" are used interchangeably.

License

STUBS is free software: 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.

STUBS is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more details.

You should have received a copy of the GNU Lesser General Public License along with STUBS. If not, see http://www.gnu.org/licenses/.

Acknowledgements

Thanks to Christopher Lee, Yuan Gao, and William Xu for their valuable input and contributions to STUBS.