Bidomain With Bath

This tutorial is automatically generated from TestBidomainWithBathTutorial.hpp at revision 9ccbb9cb6db8. Note that the code is given in full at the bottom of the page.

An example showing how to run a bidomain simulation for tissue contained in a perfusing bath

In this tutorial we show how the changes the need to be made when running a simulation of cardiac tissue contained in a bath.

The usual headers are included

#include <cxxtest/TestSuite.h>
#include "BidomainProblem.hpp"
#include "PlaneStimulusCellFactory.hpp"

Cell models can be solved using a specialised (for cardiac cell models) Backward Euler implementation, with again the code being automatically generated from the cellml files. Backward Euler allows greater ODE timesteps to be used. For cellml models provided with Chaste, using Backward Euler is trivial: just change the .hpp included as follows, and the class name as below.

#include "LuoRudy1991BackwardEulerOpt.hpp"
#include "PetscSetupAndFinalize.hpp"

This test will show how to load a mesh in the test and pass it into the problem, for which the following includes are needed

#include "DistributedTetrahedralMesh.hpp"
#include "TrianglesMeshReader.hpp"

This header is needed for the sqrt function.

#include <cmath>

Define the test

class TestBidomainWithBathTutorial : public CxxTest::TestSuite
{
public: // Tests should be public!

    void TestWithBathAndElectrodes()
    {

First, set the end time and output info. In this simulation we’ll explicitly read the mesh, alter it, then pass it to the problem class, so we don’t set the mesh file name.

        HeartConfig::Instance()->SetSimulationDuration(3.0);  //ms
        HeartConfig::Instance()->SetOutputDirectory("BidomainTutorialWithBath");
        HeartConfig::Instance()->SetOutputFilenamePrefix("results");

Bath problems seem to require decreased ODE timesteps.

        HeartConfig::Instance()->SetOdeTimeStep(0.001);  //ms

Use the PlaneStimulusCellFactory to define a set of Luo-Rudy cells. We pass the stimulus magnitude as 0.0 as we don’t want any stimulated cells.

        PlaneStimulusCellFactory<CellLuoRudy1991FromCellMLBackwardEulerOpt,2> cell_factory(0.0);

Now, we load up a rectangular mesh (in triangle/tetgen format), done as follows, using TrianglesMeshReader. Note that we use a distributed mesh, so the data is shared among processes if run in parallel.

        TrianglesMeshReader<2,2> reader("mesh/test/data/2D_0_to_1mm_400_elements");
        DistributedTetrahedralMesh<2,2> mesh;
        mesh.ConstructFromMeshReader(reader);

In most simulations there is one valid tissue identifier and one valid bath identifier (for elements). One of these can be assigned to an element with

mesh.GetElement(i)->SetAttribute(HeartRegionCode::GetValidTissueId());
mesh.GetElement(i)->SetAttribute(HeartRegionCode::GetValidBathId());

If we want heterogeneous conductivities outside the heart (for example for torso and blood) then we will need different identifiers:

        std::set<unsigned> tissue_ids;
        static unsigned tissue_id=0;
        tissue_ids.insert(tissue_id);

        std::set<unsigned> bath_ids;
        static unsigned bath_id1=1;
        bath_ids.insert(bath_id1);
        static unsigned bath_id2=2;
        bath_ids.insert(bath_id2);

        HeartConfig::Instance()->SetTissueAndBathIdentifiers(tissue_ids, bath_ids);

In bath problems, each element has an attribute which must be set to 0 (cardiac tissue) or 1 (bath). This can be done by having an extra column in the element file (see the file formats documentation, or for example mesh/test/data/1D_0_to_1_10_elements_with_two_attributes.ele, and note that the header in this file has 1 at the end to indicate that the file defines an attribute for each element). We have read in a mesh without this type of information set up, so we set it up manually, by looping over elements and setting those more than 2mm from the centre as bath elements (by default, the others are cardiac elements).

        for (AbstractTetrahedralMesh<2,2>::ElementIterator iter = mesh.GetElementIteratorBegin();
             iter != mesh.GetElementIteratorEnd();
             ++iter)
        {
            double x = iter->CalculateCentroid()[0];
            double y = iter->CalculateCentroid()[1];
            if (sqrt((x-0.05)*(x-0.05) + (y-0.05)*(y-0.05)) > 0.02)
            {
                if (y<0.05)
                {
                    //Outside circle on the bottom
                    iter->SetAttribute(bath_id1);
                }
                else
                {
                    //Outside circle on the top
                    iter->SetAttribute(bath_id2);
                }
            }
            else
            {
                //IDs default to 0, but we want to be safe
                iter->SetAttribute(tissue_id);
            }
        }

Since we have modified the mesh by setting element attributes, we need to inform Chaste of this fact. If we do not, problems will arise when checkpointing, since the code that saves the simulation state will assume that it can just reuse the original mesh files, and thus won’t save the new element attributes.

(Some mesh modifications, that use methods on the mesh class directly, will automatically record that the mesh has been modified. Since we’re just modifying elements, this information isn’t propagated at present.)

        mesh.SetMeshHasChangedSinceLoading();

The external conductivity can set two ways:

the default conductivity in the bath is set with SetBathConductivity(double)
heterogeneous overides can be set with SetBathMultipleConductivities(std::map<unsigned, double> )

        HeartConfig::Instance()->SetBathConductivity(7.0);  //bath_id1 tags will take the default value (actually 7.0 is the default)
        std::map<unsigned, double> multiple_bath_conductivities;
        multiple_bath_conductivities[bath_id2] = 6.5;  // mS/cm

        HeartConfig::Instance()->SetBathMultipleConductivities(multiple_bath_conductivities);

Now we define the electrodes. First define the magnitude of the electrodes (ie the magnitude of the boundary extracellular stimulus), and the duration it lasts for. Currently, electrodes switch on at time 0 and have constant magnitude until they are switched off. (Note that this test has a small range of magnitudes that will work, perhaps because the electrodes are close to the tissue).

        // For default conductivities and explicit cell model -1e4 is under threshold, -1.4e4 too high - crashes the cell model
        // For heterogeneous conductivities as given, -1e4 is under threshold
        double magnitude = -14.0e3; // uA/cm^2
        double start_time = 0.0;
        double duration = 1; //ms

Electrodes work in two ways: the first electrode applies an input flux, and the opposite electrode can either be grounded or apply an equal and opposite flux (ie an output flux). The false here indicates the second electrode is not grounded, ie has an equal and opposite flux. The “0” indicates that the electrodes should be applied to the bounding surfaces in the x-direction (1 would be $y$-direction, 2 the $z$-direction), which are $X=0.0$ and $X=0.1$ in the given mesh. (This explains why the full mesh ought to be rectangular/cuboid - the nodes on $x=xmin$ and $x=xmax$ ought to be form two surfaces of equal area.

        HeartConfig::Instance()->SetElectrodeParameters(false, 0, magnitude, start_time, duration);

Now create the problem class, using the cell factory and passing in true as the second argument to indicate we are solving a bath problem..

        BidomainProblem<2> bidomain_problem( &cell_factory, true );

..set the mesh and electrodes..

        bidomain_problem.SetMesh(&mesh);

..and solve as before.

        bidomain_problem.Initialise();
        bidomain_problem.Solve();

The results can be visualised as before. Note: The voltage is only defined at cardiac nodes (a node contained in ‘‘any’’ cardiac element), but for visualisation and computation a ‘fake’ value of ZERO is given for the voltage at bath nodes.

Finally, we can check that an AP was induced in any of the cardiac cells. We use a ReplicatableVector as before, and make sure we only check the voltage at cardiac cells.

        Vec solution = bidomain_problem.GetSolution(); // the Vs and phi_e's, as a PetSc vector
        ReplicatableVector solution_repl(solution);

        bool ap_triggered = false;
        for (AbstractTetrahedralMesh<2,2>::NodeIterator iter = mesh.GetNodeIteratorBegin();
             iter != mesh.GetNodeIteratorEnd();
             ++iter)
        {
            if (HeartRegionCode::IsRegionTissue( iter->GetRegion() ))
            {
                if (solution_repl[2*iter->GetIndex()] > 0.0) // 2*i, ie the voltage for this node (would be 2*i+1 for phi_e for this node)
                {
                    ap_triggered = true;
                }
            }
        }
        TS_ASSERT(ap_triggered);
    }
};

Full code

#include <cxxtest/TestSuite.h>
#include "BidomainProblem.hpp"
#include "PlaneStimulusCellFactory.hpp"

#include "LuoRudy1991BackwardEulerOpt.hpp"
#include "PetscSetupAndFinalize.hpp"
#include "DistributedTetrahedralMesh.hpp"
#include "TrianglesMeshReader.hpp"
#include <cmath>

class TestBidomainWithBathTutorial : public CxxTest::TestSuite
{
public: // Tests should be public!

    void TestWithBathAndElectrodes()
    {
        HeartConfig::Instance()->SetSimulationDuration(3.0);  //ms
        HeartConfig::Instance()->SetOutputDirectory("BidomainTutorialWithBath");
        HeartConfig::Instance()->SetOutputFilenamePrefix("results");

        HeartConfig::Instance()->SetOdeTimeStep(0.001);  //ms

        PlaneStimulusCellFactory<CellLuoRudy1991FromCellMLBackwardEulerOpt,2> cell_factory(0.0);

        TrianglesMeshReader<2,2> reader("mesh/test/data/2D_0_to_1mm_400_elements");
        DistributedTetrahedralMesh<2,2> mesh;
        mesh.ConstructFromMeshReader(reader);

        std::set<unsigned> tissue_ids;
        static unsigned tissue_id=0;
        tissue_ids.insert(tissue_id);

        std::set<unsigned> bath_ids;
        static unsigned bath_id1=1;
        bath_ids.insert(bath_id1);
        static unsigned bath_id2=2;
        bath_ids.insert(bath_id2);

        HeartConfig::Instance()->SetTissueAndBathIdentifiers(tissue_ids, bath_ids);

        for (AbstractTetrahedralMesh<2,2>::ElementIterator iter = mesh.GetElementIteratorBegin();
             iter != mesh.GetElementIteratorEnd();
             ++iter)
        {
            double x = iter->CalculateCentroid()[0];
            double y = iter->CalculateCentroid()[1];
            if (sqrt((x-0.05)*(x-0.05) + (y-0.05)*(y-0.05)) > 0.02)
            {
                if (y<0.05)
                {
                    //Outside circle on the bottom
                    iter->SetAttribute(bath_id1);
                }
                else
                {
                    //Outside circle on the top
                    iter->SetAttribute(bath_id2);
                }
            }
            else
            {
                //IDs default to 0, but we want to be safe
                iter->SetAttribute(tissue_id);
            }
        }

        mesh.SetMeshHasChangedSinceLoading();

        HeartConfig::Instance()->SetBathConductivity(7.0);  //bath_id1 tags will take the default value (actually 7.0 is the default)
        std::map<unsigned, double> multiple_bath_conductivities;
        multiple_bath_conductivities[bath_id2] = 6.5;  // mS/cm

        HeartConfig::Instance()->SetBathMultipleConductivities(multiple_bath_conductivities);

        // For default conductivities and explicit cell model -1e4 is under threshold, -1.4e4 too high - crashes the cell model
        // For heterogeneous conductivities as given, -1e4 is under threshold
        double magnitude = -14.0e3; // uA/cm^2
        double start_time = 0.0;
        double duration = 1; //ms

        HeartConfig::Instance()->SetElectrodeParameters(false, 0, magnitude, start_time, duration);

        BidomainProblem<2> bidomain_problem( &cell_factory, true );

        bidomain_problem.SetMesh(&mesh);

        bidomain_problem.Initialise();
        bidomain_problem.Solve();

        Vec solution = bidomain_problem.GetSolution(); // the Vs and phi_e's, as a PetSc vector
        ReplicatableVector solution_repl(solution);

        bool ap_triggered = false;
        for (AbstractTetrahedralMesh<2,2>::NodeIterator iter = mesh.GetNodeIteratorBegin();
             iter != mesh.GetNodeIteratorEnd();
             ++iter)
        {
            if (HeartRegionCode::IsRegionTissue( iter->GetRegion() ))
            {
                if (solution_repl[2*iter->GetIndex()] > 0.0) // 2*i, ie the voltage for this node (would be 2*i+1 for phi_e for this node)
                {
                    ap_triggered = true;
                }
            }
        }
        TS_ASSERT(ap_triggered);
    }
};

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An example showing how to run a bidomain simulation for tissue contained in a perfusing bath#

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Full code