Description

This package implements the 1D blood flow equations using the finite element framework FEniCS. The package provides tools for modelling blood flow through a network of arteries by solving a 1D approximation of the cross-sectional area and flow rate of each artery. FEniCS is a finite element framework that is being increasingly used in cardiovascular modelling. To the best of our knowledge, no easy-to-use open-source implementation of the 1D blood flow equations currently exists within the FEniCS framework. Most commonly, the 1D blood flow equations have previously been implemented using finite difference methods. In addition to providing tools for modelling artery networks and computing blood flow, this package may serve as a reference for others who intend to use FEniCS for vascular modelling. In a more general framework, the package may also be used as an example of how to solve equations in conservation form on multiple domains with shared boundary conditions. A simulation is based on the parameter (.cfg) file provided by the user. The file consists of parameters for the geometry of the artery network, as well as intrinsic parameters for each artery. The user is also able to specify parameters for the solver, and output parameters. Flow through the artery network is driven by flow at the inlet of the root artery provided by the user. The main part of the package is the class Artery_Network, which provides methods for describing the geometry of the network of arteries, meshing the arteries, computing boundary conditions, and solving the governing equations for cross-sectional area and flow rate. Each artery is defined by the Artery class. The boundary conditions are defined within the Artery class and evaluated in the Artery_Network class. The module provides tools for running simulations, interpreting output and visualising data. An example run-file is set up to read parameters from a config (.cfg) file and to run the necessary functions from Artery_Network in the right order, and thus generating an output folder containing the solution to the 1D blood flow equations. Functions related to the manipulation and interpretation of output are provided in the file utils.py, while post-processing functions that create the appropriate figures from the solutions are provided in postprocess.py.