CardiacElectroMechanicsProblem.cpp

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*/
 
#include "CardiacElectroMechanicsProblem.hpp"
 
#include "OutputFileHandler.hpp"
#include "ReplicatableVector.hpp"
#include "HeartConfig.hpp"
#include "LogFile.hpp"
#include "ChastePoint.hpp"
#include "Element.hpp"
#include "BoundaryConditionsContainer.hpp"
#include "AbstractDynamicLinearPdeSolver.hpp"
#include "TimeStepper.hpp"
#include "TrianglesMeshWriter.hpp"
#include "Hdf5ToMeshalyzerConverter.hpp"
#include "Hdf5ToCmguiConverter.hpp"
#include "MeshalyzerMeshWriter.hpp"
#include "PetscTools.hpp"
#include "ImplicitCardiacMechanicsSolver.hpp"
#include "ExplicitCardiacMechanicsSolver.hpp"
#include "CmguiDeformedSolutionsWriter.hpp"
#include "VoltageInterpolaterOntoMechanicsMesh.hpp"
#include "BidomainProblem.hpp"
 
 
template<unsigned DIM, unsigned ELEC_PROB_DIM>
void CardiacElectroMechanicsProblem<DIM,ELEC_PROB_DIM>::DetermineWatchedNodes()
{
    assert(mIsWatchedLocation);
 
    // find the nearest electrics mesh node
    double min_dist = DBL_MAX;
    unsigned node_index = UNSIGNED_UNSET;
    for (unsigned i=0; i<mpElectricsMesh->GetNumNodes(); i++)
    {
        double dist = norm_2(mWatchedLocation - mpElectricsMesh->GetNode(i)->rGetLocation());
        if (dist < min_dist)
        {
            min_dist = dist;
            node_index = i;
        }
    }
 
    // set up watched node, if close enough
    assert(node_index != UNSIGNED_UNSET); // should def have found something
    c_vector<double,DIM> pos = mpElectricsMesh->GetNode(node_index)->rGetLocation();
 
    if (min_dist > 1e-8)
    {
        // LCOV_EXCL_START
        std::cout << "ERROR: Could not find an electrics node very close to requested watched location - "
                  << "min distance was " << min_dist << " for node " << node_index
                  << " at location " << pos << std::flush;;
 
        //EXCEPTION("Could not find an electrics node very close to requested watched location");
        NEVER_REACHED;
        // LCOV_EXCL_STOP
    }
    else
    {
        LOG(2,"Chosen electrics node "<<node_index<<" at location " << pos << " to be watched");
        mWatchedElectricsNodeIndex = node_index;
    }
 
    // find nearest mechanics mesh
    min_dist = DBL_MAX;
    node_index = UNSIGNED_UNSET;
    c_vector<double,DIM> pos_at_min;
 
    for (unsigned i=0; i<mpMechanicsMesh->GetNumNodes(); i++)
    {
        c_vector<double,DIM> position = mpMechanicsMesh->GetNode(i)->rGetLocation();
 
        double dist = norm_2(position-mWatchedLocation);
 
        if (dist < min_dist)
        {
            min_dist = dist;
            node_index = i;
            pos_at_min = position;
        }
    }
 
    // set up watched node, if close enough
    assert(node_index != UNSIGNED_UNSET); // should def have found something
 
    if (min_dist > 1e-8)
    {
        // LCOV_EXCL_START
        std::cout << "ERROR: Could not find a mechanics node very close to requested watched location - "
                  << "min distance was " << min_dist << " for node " << node_index
                  << " at location " << pos_at_min;
 
        //EXCEPTION("Could not find a mechanics node very close to requested watched location");
        NEVER_REACHED;
        // LCOV_EXCL_STOP
    }
    else
    {
        LOG(2,"Chosen mechanics node "<<node_index<<" at location " << pos << " to be watched");
        mWatchedMechanicsNodeIndex = node_index;
    }
 
    OutputFileHandler handler(mOutputDirectory,false);
    mpWatchedLocationFile = handler.OpenOutputFile("watched.txt");
}
 
template<unsigned DIM, unsigned ELEC_PROB_DIM>
void CardiacElectroMechanicsProblem<DIM,ELEC_PROB_DIM>::WriteWatchedLocationData(double time, Vec voltage)
{
    assert(mIsWatchedLocation);
 
    std::vector<c_vector<double,DIM> >& deformed_position = mpMechanicsSolver->rGetDeformedPosition();
 
    ReplicatableVector voltage_replicated(voltage);
    double V = voltage_replicated[mWatchedElectricsNodeIndex];
 
    //     // Metadata is currently being added to CellML models and then this will be avoided by asking for Calcium.
    //    double Ca = mpElectricsProblem->GetMonodomainTissue()->GetCardiacCell(mWatchedElectricsNodeIndex)->GetIntracellularCalciumConcentration();
 
    *mpWatchedLocationFile << time << " ";
    for (unsigned i=0; i<DIM; i++)
    {
        *mpWatchedLocationFile << deformed_position[mWatchedMechanicsNodeIndex](i) << " ";
    }
    *mpWatchedLocationFile << V << "\n";
    mpWatchedLocationFile->flush();
}
 
template<unsigned DIM, unsigned ELEC_PROB_DIM>
c_matrix<double,DIM,DIM>& CardiacElectroMechanicsProblem<DIM,ELEC_PROB_DIM>::rCalculateModifiedConductivityTensor(unsigned elementIndex, const c_matrix<double,DIM,DIM>& rOriginalConductivity, unsigned domainIndex)
{
 
    // first get the deformation gradient for this electrics element
    unsigned containing_mechanics_elem = mpMeshPair->rGetCoarseElementsForFineElementCentroids()[elementIndex];
    c_matrix<double,DIM,DIM>& r_deformation_gradient = mDeformationGradientsForEachMechanicsElement[containing_mechanics_elem];
 
    // compute sigma_def = F^{-1} sigma_undef F^{-T}
    c_matrix<double,DIM,DIM> inv_F = Inverse(r_deformation_gradient);
    mModifiedConductivityTensor = prod(inv_F, rOriginalConductivity);
    mModifiedConductivityTensor = prod(mModifiedConductivityTensor, trans(inv_F));
 
    return mModifiedConductivityTensor;
}
 
 
template<unsigned DIM, unsigned PROBLEM_DIM>
class CreateElectricsProblem
{
public:
    static AbstractCardiacProblem<DIM, DIM, PROBLEM_DIM>* Create(ElectricsProblemType problemType,
                                                                 AbstractCardiacCellFactory<DIM>* pCellFactory);
};
 
template<unsigned DIM>
class CreateElectricsProblem<DIM, 1u>
{
public:
    static AbstractCardiacProblem<DIM, DIM, 1u>* Create(ElectricsProblemType problemType,
                                                        AbstractCardiacCellFactory<DIM>* pCellFactory)
    {
        if (problemType == MONODOMAIN)
        {
            return new MonodomainProblem<DIM>(pCellFactory);
        }
        EXCEPTION("The second template parameter should be 2 when a bidomain problem is chosen");
    }
};
 
template<unsigned DIM>
class CreateElectricsProblem<DIM, 2u>
{
public:
    static AbstractCardiacProblem<DIM, DIM, 2u>* Create(ElectricsProblemType problemType,
                                                        AbstractCardiacCellFactory<DIM>* pCellFactory)
    {
        if (problemType == BIDOMAIN)
        {
            return new BidomainProblem<DIM>(pCellFactory, false);//false-> no bath
        }
        if (problemType == BIDOMAIN_WITH_BATH)
        {
            return new BidomainProblem<DIM>(pCellFactory, true);// true-> bath
        }
        EXCEPTION("The second template parameter should be 1 when a monodomain problem is chosen");
    }
};
 
 
template<unsigned DIM, unsigned ELEC_PROB_DIM>
CardiacElectroMechanicsProblem<DIM,ELEC_PROB_DIM>::CardiacElectroMechanicsProblem(
            CompressibilityType compressibilityType,
            ElectricsProblemType electricsProblemType,
            TetrahedralMesh<DIM,DIM>* pElectricsMesh,
            QuadraticMesh<DIM>* pMechanicsMesh,
            AbstractCardiacCellFactory<DIM>* pCellFactory,
            ElectroMechanicsProblemDefinition<DIM>* pProblemDefinition,
            std::string outputDirectory)
      : mCompressibilityType(compressibilityType),
        mpCardiacMechSolver(NULL),
        mpMechanicsSolver(NULL),
        mpElectricsMesh(pElectricsMesh),
        mpMechanicsMesh(pMechanicsMesh),
        mpProblemDefinition(pProblemDefinition),
        mHasBath(false),
        mpMeshPair(NULL),
        mNoElectricsOutput(false),
        mIsWatchedLocation(false),
        mWatchedElectricsNodeIndex(UNSIGNED_UNSET),
        mWatchedMechanicsNodeIndex(UNSIGNED_UNSET),
        mNumTimestepsToOutputDeformationGradientsAndStress(UNSIGNED_UNSET)
{
    // Do some initial set up...
    // However, NOTE, we don't use either the passed in meshes or the problem_definition.
    // These pointers are allowed to be NULL, in case a child constructor wants to set
    // them up (eg CardiacElectroMechProbRegularGeom).
    // The meshes and problem_defn are used for the first time in Initialise().
 
 
    // Start-up mechanics event handler..
    MechanicsEventHandler::Reset();
    MechanicsEventHandler::BeginEvent(MechanicsEventHandler::ALL);
    // disable the electric event handler, because we use a problem class but
    // don't call Solve, so we would have to worry about starting and ending any
    // events in AbstractCardiacProblem::Solve() (esp. calling EndEvent(EVERYTHING))
    // if we didn't disable it.
    HeartEventHandler::Disable();
 
    assert(HeartConfig::Instance()->GetSimulationDuration()>0.0);
    assert(HeartConfig::Instance()->GetPdeTimeStep()>0.0);
 
    // Create the monodomain problem.
    // **NOTE** WE ONLY USE THIS TO: set up the cells, get an initial condition
    // (voltage) vector, and get a solver. We won't ever call Solve on the cardiac problem class
    assert(pCellFactory != NULL);
    mpElectricsProblem = CreateElectricsProblem<DIM,ELEC_PROB_DIM>::Create(electricsProblemType, pCellFactory);
 
    if (electricsProblemType == BIDOMAIN_WITH_BATH)
    {
        mHasBath = true;
    }
    // check whether output is required
    mWriteOutput = (outputDirectory!="");
    if (mWriteOutput)
    {
        mOutputDirectory = outputDirectory;
        // create the directory
        OutputFileHandler handler(mOutputDirectory);
        mDeformationOutputDirectory = mOutputDirectory + "/deformation";
        HeartConfig::Instance()->SetOutputDirectory(mOutputDirectory + "/electrics");
        HeartConfig::Instance()->SetOutputFilenamePrefix("voltage");
    }
    else
    {
        mDeformationOutputDirectory = "";
    }
 
//    mpImpactRegion=NULL;
}
 
template<unsigned DIM, unsigned ELEC_PROB_DIM>
CardiacElectroMechanicsProblem<DIM,ELEC_PROB_DIM>::~CardiacElectroMechanicsProblem()
{
    // NOTE if SetWatchedLocation but not Initialise has been called, mpWatchedLocationFile
    // will be uninitialised and using it will cause a seg fault. Hence the mpMechanicsMesh!=NULL
    // it is true if Initialise has been called.
    if (mIsWatchedLocation && mpMechanicsMesh)
    {
        mpWatchedLocationFile->close();
    }
 
    delete mpElectricsProblem;
    delete mpCardiacMechSolver;
    delete mpMeshPair;
 
    LogFile::Close();
}
 
template<unsigned DIM, unsigned ELEC_PROB_DIM>
void CardiacElectroMechanicsProblem<DIM,ELEC_PROB_DIM>::Initialise()
{
    assert(mpElectricsMesh!=NULL);
    assert(mpMechanicsMesh!=NULL);
    assert(mpProblemDefinition!=NULL);
    assert(mpCardiacMechSolver==NULL);
 
    mNumElecTimestepsPerMechTimestep = (unsigned) floor((mpProblemDefinition->GetMechanicsSolveTimestep()/HeartConfig::Instance()->GetPdeTimeStep())+0.5);
    if (fabs(mNumElecTimestepsPerMechTimestep*HeartConfig::Instance()->GetPdeTimeStep() - mpProblemDefinition->GetMechanicsSolveTimestep()) > 1e-6)
    {
        EXCEPTION("Electrics PDE timestep does not divide mechanics solve timestep");
    }
 
    // Create the Logfile (note we have to do this after the output dir has been
    // created, else the log file might get cleaned away
    std::string log_dir = mOutputDirectory; // just the TESTOUTPUT dir if mOutputDir="";
    LogFile::Instance()->Set(2, mOutputDirectory);
    LogFile::Instance()->WriteHeader("Electromechanics");
    LOG(2, DIM << "d Implicit CardiacElectroMechanics Simulation:");
    LOG(2, "End time = " << HeartConfig::Instance()->GetSimulationDuration() << ", electrics time step = " << HeartConfig::Instance()->GetPdeTimeStep() << ", mechanics timestep = " << mpProblemDefinition->GetMechanicsSolveTimestep() << "\n");
    LOG(2, "Contraction model ode timestep " << mpProblemDefinition->GetContractionModelOdeTimestep());
    LOG(2, "Output is written to " << mOutputDirectory << "/[deformation/electrics]");
 
    LOG(2, "Electrics mesh has " << mpElectricsMesh->GetNumNodes() << " nodes");
    LOG(2, "Mechanics mesh has " << mpMechanicsMesh->GetNumNodes() << " nodes");
 
    LOG(2, "Initialising..");
 
 
    if (mIsWatchedLocation)
    {
        DetermineWatchedNodes();
    }
 
    // initialise electrics problem
    mpElectricsProblem->SetMesh(mpElectricsMesh);
    mpElectricsProblem->Initialise();
 
    if (mCompressibilityType==INCOMPRESSIBLE)
    {
        switch(mpProblemDefinition->GetSolverType())
        {
            case EXPLICIT:
                mpCardiacMechSolver = new ExplicitCardiacMechanicsSolver<IncompressibleNonlinearElasticitySolver<DIM>,DIM>(
                                        *mpMechanicsMesh,*mpProblemDefinition,mDeformationOutputDirectory);
                break;
            case IMPLICIT:
                mpCardiacMechSolver = new ImplicitCardiacMechanicsSolver<IncompressibleNonlinearElasticitySolver<DIM>,DIM>(
                                        *mpMechanicsMesh,*mpProblemDefinition,mDeformationOutputDirectory);
                break;
            default:
                NEVER_REACHED;
        }
    }
    else
    {
        // repeat above with Compressible solver rather than incompressible -
        // not the neatest but avoids having to template this class.
        switch(mpProblemDefinition->GetSolverType())
        {
            case EXPLICIT:
                mpCardiacMechSolver = new ExplicitCardiacMechanicsSolver<CompressibleNonlinearElasticitySolver<DIM>,DIM>(
                                        *mpMechanicsMesh,*mpProblemDefinition,mDeformationOutputDirectory);
                break;
            case IMPLICIT:
                mpCardiacMechSolver = new ImplicitCardiacMechanicsSolver<CompressibleNonlinearElasticitySolver<DIM>,DIM>(
                                        *mpMechanicsMesh,*mpProblemDefinition,mDeformationOutputDirectory);
                break;
            default:
                NEVER_REACHED;
        }
    }
 
 
    mpMechanicsSolver = dynamic_cast<AbstractNonlinearElasticitySolver<DIM>*>(mpCardiacMechSolver);
    assert(mpMechanicsSolver);
 
    // set up mesh pair and determine the fine mesh elements and corresponding weights for each
    // quadrature point in the coarse mesh
    mpMeshPair = new FineCoarseMeshPair<DIM>(*mpElectricsMesh, *mpMechanicsMesh);
    mpMeshPair->SetUpBoxesOnFineMesh();
    mpMeshPair->ComputeFineElementsAndWeightsForCoarseQuadPoints(*(mpCardiacMechSolver->GetQuadratureRule()), false);
    mpMeshPair->DeleteFineBoxCollection();
 
    mpCardiacMechSolver->SetFineCoarseMeshPair(mpMeshPair);
    mpCardiacMechSolver->Initialise();
 
    unsigned num_quad_points = mpCardiacMechSolver->GetTotalNumQuadPoints();
    mInterpolatedCalciumConcs.assign(num_quad_points, 0.0);
    mInterpolatedVoltages.assign(num_quad_points, 0.0);
 
    if (mpProblemDefinition->ReadFibreSheetDirectionsFromFile())
    {
       mpCardiacMechSolver->SetVariableFibreSheetDirections(mpProblemDefinition->GetFibreSheetDirectionsFile(),
                                                            mpProblemDefinition->GetFibreSheetDirectionsDefinedPerQuadraturePoint());
    }
 
 
    if (mpProblemDefinition->GetDeformationAffectsConductivity() || mpProblemDefinition->GetDeformationAffectsCellModels())
    {
        mpMeshPair->SetUpBoxesOnCoarseMesh();
    }
 
 
    if (mpProblemDefinition->GetDeformationAffectsCellModels() || mpProblemDefinition->GetDeformationAffectsConductivity())
    {
        // initialise the stretches saved for each mechanics element
        mStretchesForEachMechanicsElement.resize(mpMechanicsMesh->GetNumElements(), 1.0);
 
        // initialise the store of the F in each mechanics element (one constant value of F) in each
        mDeformationGradientsForEachMechanicsElement.resize(mpMechanicsMesh->GetNumElements(),identity_matrix<double>(DIM));
    }
 
 
    if (mpProblemDefinition->GetDeformationAffectsCellModels())
    {
        // compute the coarse elements which contain each fine node -- for transferring stretch from
        // mechanics solve electrics cell models
        mpMeshPair->ComputeCoarseElementsForFineNodes(false);
 
    }
 
    if (mpProblemDefinition->GetDeformationAffectsConductivity())
    {
        // compute the coarse elements which contain each fine element centroid -- for transferring F from
        // mechanics solve to electrics mesh elements
        mpMeshPair->ComputeCoarseElementsForFineElementCentroids(false);
 
        // tell the abstract tissue class that the conductivities need to be modified, passing in this class
        // (which is of type AbstractConductivityModifier)
        mpElectricsProblem->GetTissue()->SetConductivityModifier(this);
    }
 
    if (mWriteOutput)
    {
        TrianglesMeshWriter<DIM,DIM> mesh_writer(mOutputDirectory,"electrics_mesh",false);
        mesh_writer.WriteFilesUsingMesh(*mpElectricsMesh);
    }
}
 
template<unsigned DIM, unsigned ELEC_PROB_DIM>
void CardiacElectroMechanicsProblem<DIM,ELEC_PROB_DIM>::Solve()
{
    // initialise the meshes and mechanics solver
    if (mpCardiacMechSolver==NULL)
    {
        Initialise();
    }
 
    bool verbose_during_solve = (    mpProblemDefinition->GetVerboseDuringSolve()
                                  || CommandLineArguments::Instance()->OptionExists("-mech_verbose")
                                  || CommandLineArguments::Instance()->OptionExists("-mech_very_verbose"));
 
 
    mpProblemDefinition->Validate();
 
    boost::shared_ptr<BoundaryConditionsContainer<DIM,DIM,ELEC_PROB_DIM> > p_bcc(new BoundaryConditionsContainer<DIM,DIM,ELEC_PROB_DIM>);
    p_bcc->DefineZeroNeumannOnMeshBoundary(mpElectricsMesh, 0);
    mpElectricsProblem->SetBoundaryConditionsContainer(p_bcc);
 
    // get an electrics solver from the problem. Note that we don't call
    // Solve() on the CardiacProblem class, we do the looping here.
    AbstractDynamicLinearPdeSolver<DIM,DIM,ELEC_PROB_DIM>* p_electrics_solver
       = mpElectricsProblem->CreateSolver();
 
    // set up initial voltage etc
    Vec electrics_solution=NULL; //This will be set and used later
    Vec calcium_data= mpElectricsMesh->GetDistributedVectorFactory()->CreateVec();
    Vec initial_voltage = mpElectricsProblem->CreateInitialCondition();
 
    // write the initial position
    unsigned counter = 0;
 
    TimeStepper stepper(0.0, HeartConfig::Instance()->GetSimulationDuration(), mpProblemDefinition->GetMechanicsSolveTimestep());
 
    CmguiDeformedSolutionsWriter<DIM>* p_cmgui_writer = NULL;
 
    std::vector<std::string> variable_names;
 
    if (mWriteOutput)
    {
        mpMechanicsSolver->SetWriteOutput();
        mpMechanicsSolver->WriteCurrentSpatialSolution("undeformed","nodes");
 
        p_cmgui_writer = new CmguiDeformedSolutionsWriter<DIM>(mOutputDirectory+"/deformation/cmgui",
                                                               "solution",
                                                               *(this->mpMechanicsMesh),
                                                               WRITE_QUADRATIC_MESH);
        variable_names.push_back("V");
        if (ELEC_PROB_DIM==2)
        {
            variable_names.push_back("Phi_e");
            if (mHasBath==true)
            {
                std::vector<std::string> regions;
                regions.push_back("tissue");
                regions.push_back("bath");
                p_cmgui_writer->SetRegionNames(regions);
            }
        }
        p_cmgui_writer->SetAdditionalFieldNames(variable_names);
        p_cmgui_writer->WriteInitialMesh("undeformed");
    }
 
 
    LOG(2, "\nSolving for initial deformation");
    // LCOV_EXCL_START
    if (verbose_during_solve)
    {
        std::cout << "\n\n ** Solving for initial deformation\n";
    }
    // LCOV_EXCL_STOP
 
    mpMechanicsSolver->SetWriteOutput(false);
 
    mpMechanicsSolver->SetCurrentTime(0.0);
    MechanicsEventHandler::BeginEvent(MechanicsEventHandler::ALL_MECH);
 
    mpMechanicsSolver->SetIncludeActiveTension(false);
    if (mNumTimestepsToOutputDeformationGradientsAndStress!=UNSIGNED_UNSET)
    {
        mpMechanicsSolver->SetComputeAverageStressPerElementDuringSolve(true);
    }
 
    unsigned total_newton_iters = 0;
    for (unsigned index=1; index<=mpProblemDefinition->GetNumIncrementsForInitialDeformation(); index++)
    {
        // LCOV_EXCL_START
        if (verbose_during_solve)
        {
            std::cout << "    Increment " << index << " of " << mpProblemDefinition->GetNumIncrementsForInitialDeformation() << "\n";
        }
        // LCOV_EXCL_STOP
 
        if (mpProblemDefinition->GetTractionBoundaryConditionType()==PRESSURE_ON_DEFORMED)
        {
            mpProblemDefinition->SetPressureScaling(((double)index)/mpProblemDefinition->GetNumIncrementsForInitialDeformation());
        }
        mpMechanicsSolver->Solve();
 
        total_newton_iters += mpMechanicsSolver->GetNumNewtonIterations();
    }
 
    mpMechanicsSolver->SetIncludeActiveTension(true);
    MechanicsEventHandler::EndEvent(MechanicsEventHandler::ALL_MECH);
    LOG(2, "    Number of newton iterations = " << total_newton_iters);
 
 
    unsigned mech_writer_counter = 0;
 
    if (mWriteOutput)
    {
        LOG(2, "  Writing output");
        mpMechanicsSolver->SetWriteOutput();
        mpMechanicsSolver->WriteCurrentSpatialSolution("solution","nodes",mech_writer_counter);
        p_cmgui_writer->WriteDeformationPositions(rGetDeformedPosition(), mech_writer_counter);
 
        if (!mNoElectricsOutput)
        {
            // the writer inside monodomain problem uses the printing timestep
            // inside HeartConfig to estimate total number of timesteps, so make
            // sure this is set to what we will use.
            HeartConfig::Instance()->SetPrintingTimeStep(mpProblemDefinition->GetMechanicsSolveTimestep());
 
            // When we consider archiving these simulations we will need to get a bool back from the following
            // command to decide whether or not the file is being extended, and hence whether to write the
            // initial conditions into the .h5 file.
            mpElectricsProblem->InitialiseWriter();
            mpElectricsProblem->WriteOneStep(stepper.GetTime(), initial_voltage);
        }
 
        if (mIsWatchedLocation)
        {
            WriteWatchedLocationData(stepper.GetTime(), initial_voltage);
        }
 
        if (mNumTimestepsToOutputDeformationGradientsAndStress!=UNSIGNED_UNSET)
        {
            mpMechanicsSolver->WriteCurrentStrains(DEFORMATION_GRADIENT_F,"deformation_gradient",mech_writer_counter);
            mpMechanicsSolver->WriteCurrentAverageElementStresses("second_PK",mech_writer_counter);
        }
    }
 
 
    PrepareForSolve();
 
//    std::vector<double> current_solution_previous_time_step = mpMechanicsSolver->rGetCurrentSolution();
//    std::vector<double> current_solution_second_last_time_step = mpMechanicsSolver->rGetCurrentSolution();
//    bool first_step = true;
 
 
    // reset this to false, may be reset again below
    mpMechanicsSolver->SetComputeAverageStressPerElementDuringSolve(false);
 
    while (!stepper.IsTimeAtEnd())
    {
        LOG(2, "\nCurrent time = " << stepper.GetTime());
        // LCOV_EXCL_START
        if (verbose_during_solve)
        {
            // also output time to screen as newton solve information will be output
            std::cout << "\n\n ** Current time = " << stepper.GetTime() << "\n";
        }
        // LCOV_EXCL_STOP
 
        if (mpProblemDefinition->GetDeformationAffectsCellModels() || mpProblemDefinition->GetDeformationAffectsConductivity())
        {
            //  Determine the stretch and deformation gradient on each element.
            //
            //  If mpProblemDefinition->GetDeformationAffectsCellModels()==true:
            //  Stretch will be passed to the cell models.
            //
            //  If mpProblemDefinition->GetDeformationAffectsConductivity()==true:
            //  The deformation gradient needs to be set up but does not need to be passed to the tissue
            //  so that F is used to compute the conductivity. Instead this is
            //  done through the line "mpElectricsProblem->GetMonodomainTissue()->SetConductivityModifier(this);" line above, which means
            //  rCalculateModifiedConductivityTensor() will be called on this class by the tissue, which then uses the F
 
            mpCardiacMechSolver->ComputeDeformationGradientAndStretchInEachElement(mDeformationGradientsForEachMechanicsElement, mStretchesForEachMechanicsElement);
        }
 
        if (mpProblemDefinition->GetDeformationAffectsCellModels())
        {
            //  Set the stretches on each of the cell models
            for (unsigned global_index = mpElectricsMesh->GetDistributedVectorFactory()->GetLow();
                         global_index < mpElectricsMesh->GetDistributedVectorFactory()->GetHigh();
                         global_index++)
            {
                unsigned containing_elem = mpMeshPair->rGetCoarseElementsForFineNodes()[global_index];
                double stretch = mStretchesForEachMechanicsElement[containing_elem];
                mpElectricsProblem->GetTissue()->GetCardiacCell(global_index)->SetStretch(stretch);
            }
        }
 
        p_electrics_solver->SetTimeStep(HeartConfig::Instance()->GetPdeTimeStep());
 
        LOG(2, "  Solving electrics");
        MechanicsEventHandler::BeginEvent(MechanicsEventHandler::NON_MECH);
        for (unsigned i=0; i<mNumElecTimestepsPerMechTimestep; i++)
        {
            double current_time = stepper.GetTime() + i*HeartConfig::Instance()->GetPdeTimeStep();
            double next_time = stepper.GetTime() + (i+1)*HeartConfig::Instance()->GetPdeTimeStep();
 
            // solve the electrics
            p_electrics_solver->SetTimes(current_time, next_time);
            p_electrics_solver->SetInitialCondition( initial_voltage );
 
            electrics_solution = p_electrics_solver->Solve();
 
            PetscReal min_voltage, max_voltage;
            VecMax(electrics_solution,PETSC_NULL,&max_voltage); //the second param is where the index would be returned
            VecMin(electrics_solution,PETSC_NULL,&min_voltage);
            if (i==0)
            {
                LOG(2, "  minimum and maximum voltage is " << min_voltage <<", "<<max_voltage);
            }
            else if (i==1)
            {
                LOG(2, "  ..");
            }
 
            PetscTools::Destroy(initial_voltage);
            initial_voltage = electrics_solution;
        }
 
        if (mpProblemDefinition->GetDeformationAffectsConductivity())
        {
            p_electrics_solver->SetMatrixIsNotAssembled();
        }
 
 
 
        // compute Ca_I at each quad point (by interpolation, using the info on which
        // electrics element the quad point is in. Then set Ca_I on the mechanics solver
        LOG(2, "  Interpolating Ca_I and voltage");
 
        //Collect the distributed calcium data into one Vec to be later replicated
        for (unsigned node_index = 0; node_index<mpElectricsMesh->GetNumNodes(); node_index++)
        {
            if (mpElectricsMesh->GetDistributedVectorFactory()->IsGlobalIndexLocal(node_index))
            {
                double calcium_value = mpElectricsProblem->GetTissue()->GetCardiacCell(node_index)->GetIntracellularCalciumConcentration();
                VecSetValue(calcium_data, node_index ,calcium_value, INSERT_VALUES);
            }
        }
        PetscTools::Barrier();//not sure this is needed
 
        //Replicate electrics solution and calcium (replication is inside this constructor of ReplicatableVector)
        ReplicatableVector electrics_solution_repl(electrics_solution);//size=(number of electrics nodes)*ELEC_PROB_DIM
        ReplicatableVector calcium_repl(calcium_data);//size = number of electrics nodes
 
        //interpolate values onto mechanics mesh
        for (unsigned i=0; i<mpMeshPair->rGetElementsAndWeights().size(); i++)
        {
            double interpolated_CaI = 0;
            double interpolated_voltage = 0;
 
            Element<DIM,DIM>& element = *(mpElectricsMesh->GetElement(mpMeshPair->rGetElementsAndWeights()[i].ElementNum));
 
            for (unsigned node_index = 0; node_index<element.GetNumNodes(); node_index++)
            {
                unsigned global_index = element.GetNodeGlobalIndex(node_index);
                double CaI_at_node =  calcium_repl[global_index];
                interpolated_CaI += CaI_at_node*mpMeshPair->rGetElementsAndWeights()[i].Weights(node_index);
                //the following line assumes interleaved solution for ELEC_PROB_DIM>1 (e.g, [Vm_0, phi_e_0, Vm1, phi_e_1...])
                interpolated_voltage += electrics_solution_repl[global_index*ELEC_PROB_DIM]*mpMeshPair->rGetElementsAndWeights()[i].Weights(node_index);
            }
 
            assert(i<mInterpolatedCalciumConcs.size());
            assert(i<mInterpolatedVoltages.size());
            mInterpolatedCalciumConcs[i] = interpolated_CaI;
            mInterpolatedVoltages[i] = interpolated_voltage;
        }
 
        LOG(2, "  Setting Ca_I. max value = " << Max(mInterpolatedCalciumConcs));
 
        // NOTE IF NHS: HERE WE SHOULD PERHAPS CHECK WHETHER THE CELL MODELS HAVE Ca_Trop
        // AND UPDATE FROM NHS TO CELL_MODEL, BUT NOT SURE HOW TO DO THIS.. (esp for implicit)
 
        // set [Ca], V, t
        mpCardiacMechSolver->SetCalciumAndVoltage(mInterpolatedCalciumConcs, mInterpolatedVoltages);
        MechanicsEventHandler::EndEvent(MechanicsEventHandler::NON_MECH);
 
 
        LOG(2, "  Solving mechanics ");
        mpMechanicsSolver->SetWriteOutput(false);
 
        // make sure the mechanics solver knows the current time (in case
        // the traction say is time-dependent).
        mpMechanicsSolver->SetCurrentTime(stepper.GetTime());
 
        // see if we will need to output stresses at the end of this timestep
        if (mNumTimestepsToOutputDeformationGradientsAndStress!=UNSIGNED_UNSET
            && (counter+1)%mNumTimestepsToOutputDeformationGradientsAndStress == 0)
        {
            mpMechanicsSolver->SetComputeAverageStressPerElementDuringSolve(true);
        }
 
//        for (unsigned i=0; i<mpMechanicsSolver->rGetCurrentSolution().size(); i++)
//        {
//            double current = mpMechanicsSolver->rGetCurrentSolution()[i];
//            double previous = current_solution_previous_time_step[i];
//            double second_last = current_solution_second_last_time_step[i];
//            //double guess = 2*current - previous;
//            double guess = 3*current - 3*previous + second_last;
//
//            if (!first_step)
//            {
//                current_solution_second_last_time_step[i] = current_solution_previous_time_step[i];
//            }
//            current_solution_previous_time_step[i] = mpMechanicsSolver->rGetCurrentSolution()[i];
//            mpMechanicsSolver->rGetCurrentSolution()[i] = guess;
//        }
//        first_step = false;
 
        MechanicsEventHandler::BeginEvent(MechanicsEventHandler::ALL_MECH);
        mpCardiacMechSolver->Solve(stepper.GetTime(), stepper.GetNextTime(), mpProblemDefinition->GetContractionModelOdeTimestep());
        MechanicsEventHandler::EndEvent(MechanicsEventHandler::ALL_MECH);
 
        LOG(2, "    Number of newton iterations = " << mpMechanicsSolver->GetNumNewtonIterations());
 
         // update the current time
        stepper.AdvanceOneTimeStep();
        counter++;
 
 
        MechanicsEventHandler::BeginEvent(MechanicsEventHandler::OUTPUT);
        if (mWriteOutput && (counter%WRITE_EVERY_NTH_TIME==0))
        {
            LOG(2, "  Writing output");
            // write deformed position
            mech_writer_counter++;
            mpMechanicsSolver->SetWriteOutput();
            mpMechanicsSolver->WriteCurrentSpatialSolution("solution","nodes",mech_writer_counter);
 
            p_cmgui_writer->WriteDeformationPositions(rGetDeformedPosition(), counter);
 
            if (!mNoElectricsOutput)
            {
                mpElectricsProblem->mpWriter->AdvanceAlongUnlimitedDimension();
                mpElectricsProblem->WriteOneStep(stepper.GetTime(), electrics_solution);
            }
 
            if (mIsWatchedLocation)
            {
                WriteWatchedLocationData(stepper.GetTime(), electrics_solution);
            }
            OnEndOfTimeStep(counter);
 
            if (mNumTimestepsToOutputDeformationGradientsAndStress!=UNSIGNED_UNSET && counter%mNumTimestepsToOutputDeformationGradientsAndStress==0)
            {
                mpMechanicsSolver->WriteCurrentStrains(DEFORMATION_GRADIENT_F,"deformation_gradient",mech_writer_counter);
                mpMechanicsSolver->WriteCurrentAverageElementStresses("second_PK",mech_writer_counter);
            }
            mpMechanicsSolver->SetComputeAverageStressPerElementDuringSolve(false);
        }
        MechanicsEventHandler::EndEvent(MechanicsEventHandler::OUTPUT);
 
        // write the total elapsed time..
        LogFile::Instance()->WriteElapsedTime("  ");
    }
 
    if ((mWriteOutput) && (!mNoElectricsOutput))
    {
        HeartConfig::Instance()->Reset();
        mpElectricsProblem->mpWriter->Close();
        delete mpElectricsProblem->mpWriter;
 
        std::string input_dir = mOutputDirectory+"/electrics";
 
        // Convert simulation data to meshalyzer format - commented
        std::string config_directory = HeartConfig::Instance()->GetOutputDirectory();
        HeartConfig::Instance()->SetOutputDirectory(input_dir);
 
//      Hdf5ToMeshalyzerConverter<DIM,DIM> meshalyzer_converter(FileFinder(input_dir, RelativeTo::ChasteTestOutput),
//                                                              "voltage", mpElectricsMesh,
//                                                                HeartConfig::Instance()->GetOutputUsingOriginalNodeOrdering(),
//                                                                HeartConfig::Instance()->GetVisualizerOutputPrecision() );
 
        // convert output to CMGUI format
        Hdf5ToCmguiConverter<DIM,DIM> cmgui_converter(FileFinder(input_dir, RelativeTo::ChasteTestOutput),
                                                      "voltage", mpElectricsMesh, mHasBath,
                                                      HeartConfig::Instance()->GetVisualizerOutputPrecision());
 
        // Write mesh in a suitable form for meshalyzer
        //std::string output_directory =  mOutputDirectory + "/electrics/output";
        // Write the mesh
        //MeshalyzerMeshWriter<DIM,DIM> mesh_writer(output_directory, "mesh", false);
        //mesh_writer.WriteFilesUsingMesh(*mpElectricsMesh);
        // Write the parameters out
        //HeartConfig::Instance()->Write();
 
        // interpolate the electrical data onto the mechanics mesh nodes and write CMGUI...
        // Note: this calculates the data on ALL nodes of the mechanics mesh (incl internal,
        // non-vertex ones), which won't be used if linear CMGUI visualisation
        // of the mechanics solution is used.
        VoltageInterpolaterOntoMechanicsMesh<DIM> converter(*mpElectricsMesh,*mpMechanicsMesh,variable_names,input_dir,"voltage");
 
        // reset to the default value
        HeartConfig::Instance()->SetOutputDirectory(config_directory);
    }
 
    if (p_cmgui_writer)
    {
        if (mNoElectricsOutput)
        {
            p_cmgui_writer->WriteCmguiScript("","undeformed");
        }
        else
        {
            p_cmgui_writer->WriteCmguiScript("../../electrics/cmgui_output/voltage_mechanics_mesh","undeformed");
        }
        delete p_cmgui_writer;
    }
    PetscTools::Destroy(electrics_solution);
    PetscTools::Destroy(calcium_data);
    delete p_electrics_solver;
 
    MechanicsEventHandler::EndEvent(MechanicsEventHandler::ALL);
}
 
template<unsigned DIM, unsigned ELEC_PROB_DIM>
double CardiacElectroMechanicsProblem<DIM,ELEC_PROB_DIM>::Max(std::vector<double>& vec)
{
    double max = -1e200;
    for (unsigned i=0; i<vec.size(); i++)
    {
        if (vec[i]>max) max=vec[i];
    }
    return max;
}
 
template<unsigned DIM, unsigned ELEC_PROB_DIM>
void CardiacElectroMechanicsProblem<DIM,ELEC_PROB_DIM>::SetNoElectricsOutput()
{
    mNoElectricsOutput = true;
}
 
template<unsigned DIM, unsigned ELEC_PROB_DIM>
void CardiacElectroMechanicsProblem<DIM,ELEC_PROB_DIM>::SetWatchedPosition(c_vector<double,DIM> watchedLocation)
{
    mIsWatchedLocation = true;
    mWatchedLocation = watchedLocation;
}
 
template<unsigned DIM, unsigned ELEC_PROB_DIM>
void CardiacElectroMechanicsProblem<DIM,ELEC_PROB_DIM>::SetOutputDeformationGradientsAndStress(double timeStep)
{
    mNumTimestepsToOutputDeformationGradientsAndStress = (unsigned) floor((timeStep/mpProblemDefinition->GetMechanicsSolveTimestep())+0.5);
    if (fabs(mNumTimestepsToOutputDeformationGradientsAndStress*mpProblemDefinition->GetMechanicsSolveTimestep() - timeStep) > 1e-6)
    {
        EXCEPTION("Timestep provided for SetOutputDeformationGradientsAndStress() is not a multiple of mechanics solve timestep");
    }
}
 
template<unsigned DIM, unsigned ELEC_PROB_DIM>
std::vector<c_vector<double,DIM> >& CardiacElectroMechanicsProblem<DIM,ELEC_PROB_DIM>::rGetDeformedPosition()
{
    return mpMechanicsSolver->rGetDeformedPosition();
}
 
// Explicit instantiation
 
//note: 1d incompressible material doesn't make sense
template class CardiacElectroMechanicsProblem<2,1>;
template class CardiacElectroMechanicsProblem<3,1>;
template class CardiacElectroMechanicsProblem<2,2>;
template class CardiacElectroMechanicsProblem<3,2>;