Solve the monodomain equation using Finite Volume Method.

The project is divided in 4 parts.

• Skeleton_Mesh
• Mesh_Generator
• Pk-Noble
• Pk-LiRudy

• PURPOSE: Build the skeleton for the network mesh.
• INPUT: Length of the fiber
• INPUT: Number of fibers leaving a bifurcation
• INPUT: Type of network
• INPUT: Name of the output file
• The output file is using the .vtk extension.
• To visualize the structure open the output file using Paraview
• There are 3 types of network that could be generated:
  • Fiber with a bifurcation at the endpoints (Type 1);
  • Fiber with iterative growth (Type 2);
  • Fiber with iterative growth and angle control (Type 3).
• For the Type 2 and 3 network the maximum number of iterations and angle control can be adjusted by the variables MAX_ITER and ANG, respectevely.

Build and execute

$ make
$ ./skeletonMesh <xMax> <biff> <type> <out_VTK_file>

Example

$ ./skeletonMesh 1.0 2 3 example.vtk

This example will build a network of type 3 with two segments leaving each bifurcation and a fiber length of 1cm.

• PURPOSE: Build the mesh network that will be used to solve FVM. The mesh is constructed by providing a type of cell, which is size of the space discretization.
• INPUT: network generated by the SkeletonMesh program must be provided.
• INPUT: type of the cell that make up the fiber
  • pig = 68 um
  • dog = 164 um
  • test1 = 75 um
  • test2 = 100 um
  • test3 = 125 um
  • test4 = 150 um
  • test5 = 175 um
  • test6 = 200 um
• The output file must defined with the extension ".msh".
• The syntax of the ".msh" file is defined as

Build and execute

$ make
$ ./meshGenerator example.vtk example.msh

• These flags are turned on by editing the Makefile.
• -DDIAMETER: Activate the variable diameter length of the Purkinje cells between each growing iteration (for Experiment 4 and 5).

• PURPOSE: Solve the monodomain equation using the Noble celullar model from 1962 (https://www.ncbi.nlm.nih.gov/pmc/articles/PMC1359535/pdf/jphysiol01248-0130.pdf)
• INPUT: Type of the solution
  • -t: SteadyState
  • -s: Solver
• INPUT: Size of the time discretization
• INPUT: Maximum simulation time
• INPUT: Mesh file generated by the MeshGenerator (use the extension ".msh")
• INPUT: SteadyState filename (use the extension ".sst")
• INPUT: Plot filename (use extension ".plt")
• INPUT: Gamma parameter (for the PMJ simulations)
• INPUT: Diameter of the Purkinje cell

• To run this program the Eigen library version 3.3.4 must be installed.
• To install the Eigen library follow these steps:
  1. Download the version 3.3.4 library at: http://bitbucket.org/eigen/eigen/get/3.3.4.tar.gz
  2. Extract the ".zip" file to a folder
  3. On that folder do the following

  $ mkdir build; cd build
  $ cmake ..
  $ make
  $ make install

• The CMake plataform should be also be installed to proper build the Eigen library.
• To install the CMake plataform just execute

$ sudo apt-get install cmake; sudo apt-get upgrade

• These flags are turned on by editing the Makefile.
• -DOUTPUT: Activate the visual output on the terminal screen
• -DVTK: Activate the writing of the ".vtk" files, enabling the visualization of the simulation on Paraview. Files are written on the folder ./VTK
• -DDIAMETER: Activate the variable diameter length of the Purkinje cells between each growing iteration (for Experiment 4 and 5).
• -DPMJ: Activate the PMJs.

• PURPOSE: Solve the monodomain equation using the Li and Rudy celullar model from 2011 (http://circres.ahajournals.org/content/109/1/71.long)
• INPUT: Type of the solution
  • -t: SteadyState
  • -s: Solver
• INPUT: Size of the time discretization
• INPUT: Maximum simulation time
• INPUT: Mesh file generated by the MeshGenerator (use the extension ".msh")
• INPUT: SteadyState filename (use the extension ".sst")
• INPUT: Plot filename (use extension ".plt")
• INPUT: Gamma parameter (for the PMJ simulations)
• INPUT: Diameter of the Purkinje cell

• To run this program the Eigen library version 3.3.4 must be installed.
• To install the Eigen library follow these steps:
  1. Download the version 3.3.4 library at: http://bitbucket.org/eigen/eigen/get/3.3.4.tar.gz
  2. Extract the ".zip" file to a folder
  3. On that folder do the following

  $ mkdir build; cd build
  $ cmake ..
  $ make
  $ make install

• The CMake plataform should be also be installed to proper build the Eigen library.
• To install the CMake plataform just execute

$ sudo apt-get install cmake; sudo apt-get upgrade

• These flags are turned on by editing the Makefile.
• -DOUTPUT: Activate the visual output on the terminal screen
• -DVTK: Activate the writing of the ".vtk" files, enabling the visualization of the simulation on Paraview. Files are written on the folder ./VTK
• -DDIAMETER: Activate the variable diameter length of the Purkinje cells between each growing iteration (for Experiment 4 and 5).
• -DPMJ: Activate the PMJs.

• There are additional codes used in this project:
  1. Python scripts to build the figures
  2. A graph network reader/parser for VTK files
  3. A network visualizer

• It is possible to run each experiment by just executing the following shell script locate on the folder of each celullar model.
• Example of how to execute the Experiment 3 simulations:

  $ ./genExp3.sh --sst; ./genExp3.sh --solver

• This will first execute the steady state simulation for the range of parameters defined on the header of the script.
• Store the output files with the state variables of all control volumes on the SteadyState folder
• And then execute the solver simulation
• The output files are then stored on the Results folder