This tutorial is automatically generated from the file heart/test/tutorials/TestMonodomain3dExampleTutorial.hpp at revision 5e8c8d7218a9/git_repo. Note that the code is given in full at the bottom of the page.

3D monodomain example

In this tutorial we show how to run a 3D simulation using the monodomain equation. To go from monodomain to bidomain or vice versa is trivial, and for 2d to 3d is also very easy.

First include the headers, MonodomainProblem this time. 

#include <cxxtest/TestSuite.h>
#include "MonodomainProblem.hpp"
#include "LuoRudy1991.hpp"
#include "SimpleStimulus.hpp"
#include "TetrahedralMesh.hpp"
#include "PetscSetupAndFinalize.hpp"

Here we define a cell factory that gives stimuli to cells in the block 0<x<0.1, 0<y<0.1, 0<z<0.1. Note that it inherits from AbstractCardiacCellFactory<3> this time (not <2>). 

class BenchmarkCellFactory : public AbstractCardiacCellFactory<3> // <3> here
{
private:
    boost::shared_ptr<SimpleStimulus> mpStimulus;

public:
    BenchmarkCellFactory()
        : AbstractCardiacCellFactory<3>(), // <3> here as well!
          mpStimulus(new SimpleStimulus(-100000.0, 2))
    {
    }

    AbstractCardiacCell* CreateCardiacCellForTissueNode(Node<3>* pNode)
    {
        double x = pNode->rGetLocation()[0];
        double y = pNode->rGetLocation()[1];
        double z = pNode->rGetLocation()[2];

        if ((x<0.1+1e-6) && (y<0.1+1e-6) && (z<0.1+1e-6))
        {
            return new CellLuoRudy1991FromCellML(mpSolver, mpStimulus);
        }
        else
        {
            return new CellLuoRudy1991FromCellML(mpSolver, mpZeroStimulus);
        }
    }
};

Now define the test 

class TestMonodomain3dExampleTutorial : public CxxTest::TestSuite
{
public:
    void TestMonodomain3d()
    {

We will auto-generate a mesh this time, and pass it in, rather than provide a mesh file name. This is how to generate a cuboid mesh with a given spatial stepsize h.

Using a DistributedTetrahedralMesh is faster than TetrahedralMesh when running on multiple processes. However, it permutes the node ordering for output. Most of time time this won't matter, but later in this test we want to access specific node indices. One method of doing this is to ask HeartConfig to use the original node ordering for the output. 

        DistributedTetrahedralMesh<3,3> mesh;
        double h=0.02;
        mesh.ConstructRegularSlabMesh(h, 0.8 /*length*/, 0.3 /*width*/, 0.3 /*depth*/);
        HeartConfig::Instance()->SetOutputUsingOriginalNodeOrdering(true);

(In 2D the call is identical, but without the depth parameter).

Set the simulation duration, etc, and create an instance of the cell factory. One thing that should be noted for monodomain problems, the intracellular conductivity is used as the monodomain effective conductivity (not a harmonic mean of intra and extracellular conductivities). So if you want to alter the monodomain conductivity call HeartConfig::Instance()->SetIntracellularConductivities 

        HeartConfig::Instance()->SetSimulationDuration(5); //ms
        HeartConfig::Instance()->SetOutputDirectory("Monodomain3dExample");
        HeartConfig::Instance()->SetOutputFilenamePrefix("results");
        HeartConfig::Instance()->SetOdePdeAndPrintingTimeSteps(0.005, 0.01, 0.1);

        BenchmarkCellFactory cell_factory;

Now we declare the problem class, MonodomainProblem<3> instead of BidomainProblem<2>. The interface for both is the same. 

        MonodomainProblem<3> monodomain_problem( &cell_factory );

If a mesh-file-name hasn't been set using HeartConfig, we have to pass in a mesh using the SetMesh method (must be called before Initialise). 

        monodomain_problem.SetMesh(&mesh);

By default data for all nodes is output, but for big simulations, sometimes this might not be required, and the action potential only at certain nodes required. The following code shows how to output the results at the first, middle and last nodes, for example. (The output is written to the HDF5 file; regular visualisation output will be turned off. HDF5 files can be read using Matlab). We are not using this in this simulation however (hence the boolean being set to false). 

        bool partial_output = false;
        if (partial_output)
        {
            std::vector<unsigned> nodes_to_be_output;
            nodes_to_be_output.push_back(0);
            nodes_to_be_output.push_back((unsigned)round( (mesh.GetNumNodes()-1)/2 ));
            nodes_to_be_output.push_back(mesh.GetNumNodes()-1);
            monodomain_problem.SetOutputNodes(nodes_to_be_output);
        }

SetWriteInfo is a useful method that means that the min/max voltage is printed as the simulation runs (useful for verifying that cells are stimulated and the wave propagating, for example) 

        monodomain_problem.SetWriteInfo();

Finally, call Initialise and Solve as before 

        monodomain_problem.Initialise();
        monodomain_problem.Solve();

This part is just to check nothing has accidentally been changed in this example 

        ReplicatableVector voltage(monodomain_problem.GetSolution());
        TS_ASSERT_DELTA(voltage[0], 34.9032, 1e-2);
    }
};

Code

The full code is given below

File name TestMonodomain3dExampleTutorial.hpp

#include <cxxtest/TestSuite.h>
#include "MonodomainProblem.hpp"
#include "LuoRudy1991.hpp"
#include "SimpleStimulus.hpp"
#include "TetrahedralMesh.hpp"
#include "PetscSetupAndFinalize.hpp"

class BenchmarkCellFactory : public AbstractCardiacCellFactory<3> // <3> here
{
private:
    boost::shared_ptr<SimpleStimulus> mpStimulus;

public:
    BenchmarkCellFactory()
        : AbstractCardiacCellFactory<3>(), // <3> here as well!
          mpStimulus(new SimpleStimulus(-100000.0, 2))
    {
    }

    AbstractCardiacCell* CreateCardiacCellForTissueNode(Node<3>* pNode)
    {
        double x = pNode->rGetLocation()[0];
        double y = pNode->rGetLocation()[1];
        double z = pNode->rGetLocation()[2];

        if ((x<0.1+1e-6) && (y<0.1+1e-6) && (z<0.1+1e-6))
        {
            return new CellLuoRudy1991FromCellML(mpSolver, mpStimulus);
        }
        else
        {
            return new CellLuoRudy1991FromCellML(mpSolver, mpZeroStimulus);
        }
    }
};

class TestMonodomain3dExampleTutorial : public CxxTest::TestSuite
{
public:
    void TestMonodomain3d()
    {
        DistributedTetrahedralMesh<3,3> mesh;
        double h=0.02;
        mesh.ConstructRegularSlabMesh(h, 0.8 /*length*/, 0.3 /*width*/, 0.3 /*depth*/);
        HeartConfig::Instance()->SetOutputUsingOriginalNodeOrdering(true);
        HeartConfig::Instance()->SetSimulationDuration(5); //ms
        HeartConfig::Instance()->SetOutputDirectory("Monodomain3dExample");
        HeartConfig::Instance()->SetOutputFilenamePrefix("results");
        HeartConfig::Instance()->SetOdePdeAndPrintingTimeSteps(0.005, 0.01, 0.1);

        BenchmarkCellFactory cell_factory;

        MonodomainProblem<3> monodomain_problem( &cell_factory );

        monodomain_problem.SetMesh(&mesh);

        bool partial_output = false;
        if (partial_output)
        {
            std::vector<unsigned> nodes_to_be_output;
            nodes_to_be_output.push_back(0);
            nodes_to_be_output.push_back((unsigned)round( (mesh.GetNumNodes()-1)/2 ));
            nodes_to_be_output.push_back(mesh.GetNumNodes()-1);
            monodomain_problem.SetOutputNodes(nodes_to_be_output);
        }

        monodomain_problem.SetWriteInfo();

        monodomain_problem.Initialise();
        monodomain_problem.Solve();

        ReplicatableVector voltage(monodomain_problem.GetSolution());
        TS_ASSERT_DELTA(voltage[0], 34.9032, 1e-2);
    }
};