CardiacElectroMechanicsProblem.cpp

/*

Copyright (C) University of Oxford, 2005-2011

University of Oxford means the Chancellor, Masters and Scholars of the
University of Oxford, having an administrative office at Wellington
Square, Oxford OX1 2JD, UK.

This file is part of Chaste.

Chaste is free software: you can redistribute it and/or modify it
under the terms of the GNU Lesser General Public License as published
by the Free Software Foundation, either version 2.1 of the License, or
(at your option) any later version.

Chaste is distributed in the hope that it will be useful, but WITHOUT
ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
FITNESS FOR A PARTICULAR PURPOSE.  See the GNU Lesser General Public
License for more details. The offer of Chaste under the terms of the
License is subject to the License being interpreted in accordance with
English Law and subject to any action against the University of Oxford
being under the jurisdiction of the English Courts.

You should have received a copy of the GNU Lesser General Public License
along with Chaste. If not, see <http://www.gnu.org/licenses/>.

*/

#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 "QuadraturePointsGroup.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"


template<unsigned DIM>
void CardiacElectroMechanicsProblem<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)
    {
        #define COVERAGE_IGNORE
        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;
        #undef COVERAGE_IGNORE
    }
    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)
    {
        #define COVERAGE_IGNORE
        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;
        #undef COVERAGE_IGNORE
    }
    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>
void CardiacElectroMechanicsProblem<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 = mpMonodomainProblem->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>
c_matrix<double,DIM,DIM>& CardiacElectroMechanicsProblem<DIM>::rGetModifiedConductivityTensor(unsigned elementIndex, const c_matrix<double,DIM,DIM>& rOriginalConductivity)
{
    if(mLastModifiedConductivity.first==elementIndex)
    {
        // if already computed on this electrics element, just return conductivity
        return mLastModifiedConductivity.second;
    }
    else
    {
        // new element, need to compute conductivity

        // 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);
        mLastModifiedConductivity.second = prod(inv_F, rOriginalConductivity);
        mLastModifiedConductivity.second = prod(mLastModifiedConductivity.second, trans(inv_F));

        // save the current element and return the tensor
        mLastModifiedConductivity.first = elementIndex;
        return mLastModifiedConductivity.second;
    }
}


//
//
//template<unsigned DIM>
//void CardiacElectroMechanicsProblem<DIM>::SetImpactRegion(std::vector<BoundaryElement<DIM-1,DIM>*>& rImpactRegion)
//{
//    assert(mpImpactRegion == NULL);
//    mpImpactRegion = &rImpactRegion;
//}
//
//template<unsigned DIM>
//void CardiacElectroMechanicsProblem<DIM>::ApplyImpactTractions(double time)
//{
//    if(mpImpactRegion==NULL)
//    {
//        return;
//    }
//
//    double start_time = 10;
//    double end_time = 20;
//    double magnitude = 1.5;
//    unsigned direction = 1;
//
//    c_vector<double,DIM> traction = zero_vector<double>(DIM);
//    if( (time>=start_time) && (time<=end_time) )
//    {
//        traction(direction) = magnitude;
//    }
//    mImpactTractions.clear();
//    mImpactTractions.resize(mpImpactRegion->size(), traction);
//    mpCardiacMechSolver->SetSurfaceTractionBoundaryConditions(*mpImpactRegion, mImpactTractions);
//}

template<unsigned DIM>
CardiacElectroMechanicsProblem<DIM>::CardiacElectroMechanicsProblem(
            CompressibilityType compressibilityType,
            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),
        mpMeshPair(NULL),
        mNoElectricsOutput(false),
        mIsWatchedLocation(false),
        mWatchedElectricsNodeIndex(UNSIGNED_UNSET),
        mWatchedMechanicsNodeIndex(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 an solver. We won't ever call solve on the MonodomainProblem
    assert(pCellFactory != NULL);
    mpMonodomainProblem = new MonodomainProblem<DIM>(pCellFactory);

    // 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 = "";
    }

    mLastModifiedConductivity.first = UNSIGNED_UNSET; //important

//    mpImpactRegion=NULL;
}

template<unsigned DIM>
CardiacElectroMechanicsProblem<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 mpMonodomainProblem;
    delete mpCardiacMechSolver;
    delete mpMeshPair;

    LogFile::Close();
}

template<unsigned DIM>
void CardiacElectroMechanicsProblem<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 monodomain problem
    mpMonodomainProblem->SetMesh(mpElectricsMesh);
    mpMonodomainProblem->Initialise();


    if(mCompressibilityType==INCOMPRESSIBLE)
    {
        // NOTE: if adding to this, do below as well for compressible option.
        switch(mpProblemDefinition->GetContractionModel())
        {
            case NASH2004:
                // Create an EXPLICIT, INCOMPRESSIBLE solver
                mpCardiacMechSolver = new ExplicitCardiacMechanicsSolver<IncompressibleNonlinearElasticitySolver<DIM>,DIM>(
                        mpProblemDefinition->GetContractionModel(),*mpMechanicsMesh,*mpProblemDefinition,mDeformationOutputDirectory);
            break;

            case KERCHOFFS2003:
            case NHS:
                // Create an IMPLICIT, INCOMPRESSIBLE solver
                mpCardiacMechSolver = new ImplicitCardiacMechanicsSolver<IncompressibleNonlinearElasticitySolver<DIM>,DIM>(
                        mpProblemDefinition->GetContractionModel(),*mpMechanicsMesh,*mpProblemDefinition,mDeformationOutputDirectory);
            break;
            default:
                EXCEPTION("Invalid contraction model, options are: NASH2004, KERCHOFFS2003 or NHS");
        }
    }
    else
    {
        // repeat above with Compressible solver rather than incompressible - not the neatest but avoids having to template
        // this class.
        switch(mpProblemDefinition->GetContractionModel())
        {
            case NASH2004:
                // Create an EXPLICIT, COMPRESSIBLE solver
                mpCardiacMechSolver = new ExplicitCardiacMechanicsSolver<CompressibleNonlinearElasticitySolver<DIM>,DIM>(
                        mpProblemDefinition->GetContractionModel(),*mpMechanicsMesh,*mpProblemDefinition,mDeformationOutputDirectory);
            break;

            case KERCHOFFS2003:
            case NHS:
                // Create an IMPLICIT, COMPRESSIBLE solver
                mpCardiacMechSolver = new ImplicitCardiacMechanicsSolver<CompressibleNonlinearElasticitySolver<DIM>,DIM>(
                        mpProblemDefinition->GetContractionModel(),*mpMechanicsMesh,*mpProblemDefinition,mDeformationOutputDirectory);
            break;
            default:
                EXCEPTION("Invalid contraction model, options are: NASH2004, KERCHOFFS2003 or NHS");
        }
    }

    mpMechanicsSolver = dynamic_cast<AbstractNonlinearElasticitySolver<DIM>*>(mpCardiacMechSolver);
    assert(mpMechanicsSolver);

    if(mpProblemDefinition->ReadFibreSheetDirectionsFromFile())
    {
       mpCardiacMechSolver->SetVariableFibreSheetDirections(mpProblemDefinition->GetFibreSheetDirectionsFile(),
                                                            mpProblemDefinition->GetFibreSheetDirectionsDefinedPerQuadraturePoint());
    }

    // 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();



    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)
        mpMonodomainProblem->GetMonodomainTissue()->SetConductivityModifier(this);
    }

    if(mWriteOutput)
    {
        TrianglesMeshWriter<DIM,DIM> mesh_writer(mOutputDirectory,"electrics_mesh",false);
        mesh_writer.WriteFilesUsingMesh(*mpElectricsMesh);
    }
}

template<unsigned DIM>
void CardiacElectroMechanicsProblem<DIM>::Solve()
{
    // initialise the meshes and mechanics solver
    if(mpCardiacMechSolver==NULL)
    {
        Initialise();
    }

    mpProblemDefinition->Validate();

    boost::shared_ptr<BoundaryConditionsContainer<DIM,DIM,1> > p_bcc(new BoundaryConditionsContainer<DIM,DIM,1>);
    p_bcc->DefineZeroNeumannOnMeshBoundary(mpElectricsMesh, 0);
    mpMonodomainProblem->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,1>* p_electrics_solver
       = mpMonodomainProblem->CreateSolver();

    // set up initial voltage etc
    Vec voltage=NULL; //This will be set and used later
    Vec initial_voltage = mpMonodomainProblem->CreateInitialCondition();

    unsigned num_quad_points = mpCardiacMechSolver->GetTotalNumQuadPoints();
    std::vector<double> interpolated_calcium_concs(num_quad_points, 0.0);
    std::vector<double> interpolated_voltages(num_quad_points, 0.0);

    // write the initial position
    unsigned counter = 0;

    TimeStepper stepper(0.0, HeartConfig::Instance()->GetSimulationDuration(), mpProblemDefinition->GetMechanicsSolveTimestep());

    CmguiDeformedSolutionsWriter<DIM>* p_cmgui_writer = NULL;

    unsigned mech_writer_counter = 0;
    if (mWriteOutput)
    {
        mpMechanicsSolver->SetWriteOutput();
        mpMechanicsSolver->WriteCurrentDeformation("solution",mech_writer_counter);

        p_cmgui_writer = new CmguiDeformedSolutionsWriter<DIM>(mOutputDirectory+"/deformation/cmgui",
                                                               "solution",
                                                               *(this->mpMechanicsMesh),
                                                               WRITE_QUADRATIC_MESH);
        std::vector<std::string> fields;
        fields.push_back("V");
        p_cmgui_writer->SetAdditionalFieldNames(fields);
        p_cmgui_writer->WriteInitialMesh();


        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());
            mpMonodomainProblem->InitialiseWriter();
            mpMonodomainProblem->WriteOneStep(stepper.GetTime(), initial_voltage);
        }

        if(mIsWatchedLocation)
        {
            WriteWatchedLocationData(stepper.GetTime(), initial_voltage);
        }
    }

    PrepareForSolve();

    while (!stepper.IsTimeAtEnd())
    {
        LOG(2, "\nCurrent time = " << stepper.GetTime());
        #ifdef MECH_VERBOSE // defined in AbstractNonlinearElasticitySolver
        // also output time to screen as newton solve information will be output
        std::cout << "\n\n ** Current time = " << stepper.GetTime() << "\n";
        #endif

        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 "mpMonodomainProblem->GetMonodomainTissue()->SetConductivityModifier(this);" line above, which means
            //  rGetModifiedConductivityTensor() 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];
                mpMonodomainProblem->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 );

            voltage = p_electrics_solver->Solve();

            PetscReal min_voltage, max_voltage;
            VecMax(voltage,PETSC_NULL,&max_voltage); //the second param is where the index would be returned
            VecMin(voltage,PETSC_NULL,&min_voltage);
            if(i==0)
            {
                LOG(2, "  minimum and maximum voltage is " << min_voltage <<", "<<max_voltage);
            }
            else if(i==1)
            {
                LOG(2, "  ..");
            }

            VecDestroy(initial_voltage);
            initial_voltage = voltage;
        }

        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");

        ReplicatableVector voltage_repl(voltage);

        // collect all the calcium concentrations (from the cells, which are
        // distributed) in one (replicated) vector
        ReplicatableVector calcium_repl(mpElectricsMesh->GetNumNodes());
        PetscInt lo, hi;
        VecGetOwnershipRange(voltage, &lo, &hi);
        for(int index=lo; index<hi; index++)
        {
            calcium_repl[index] = mpMonodomainProblem->GetTissue()->GetCardiacCell(index)->GetIntracellularCalciumConcentration();
        }
        PetscTools::Barrier();
        calcium_repl.Replicate(lo,hi);


        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_node_index = element.GetNodeGlobalIndex(node_index);
                double CaI_at_node =  calcium_repl[global_node_index];
                interpolated_CaI += CaI_at_node*mpMeshPair->rGetElementsAndWeights()[i].Weights(node_index);
                interpolated_voltage += voltage_repl[global_node_index]*mpMeshPair->rGetElementsAndWeights()[i].Weights(node_index);
            }

            interpolated_calcium_concs[i] = interpolated_CaI;
            interpolated_voltages[i] = interpolated_voltage;
        }

        LOG(2, "  Setting Ca_I. max value = " << Max(interpolated_calcium_concs));

        // 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(interpolated_calcium_concs, interpolated_voltages);
        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());

//        ApplyImpactTractions(stepper.GetTime());

        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->WriteCurrentDeformation("solution",mech_writer_counter);

            p_cmgui_writer->WriteDeformationPositions(rGetDeformedPosition(), counter);

            if(!mNoElectricsOutput)
            {
                mpMonodomainProblem->mpWriter->AdvanceAlongUnlimitedDimension();
                mpMonodomainProblem->WriteOneStep(stepper.GetTime(), voltage);
            }

            if(mIsWatchedLocation)
            {
                WriteWatchedLocationData(stepper.GetTime(), voltage);
            }
            OnEndOfTimeStep(counter);
        }
        MechanicsEventHandler::EndEvent(MechanicsEventHandler::OUTPUT);

        // write the total elapsed time..
        LogFile::Instance()->WriteElapsedTime("  ");
    }



    if ((mWriteOutput) && (!mNoElectricsOutput))
    {
        HeartConfig::Instance()->Reset();
        mpMonodomainProblem->mpWriter->Close();
        delete mpMonodomainProblem->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(input_dir, "voltage", mpElectricsMesh);

        // convert output to CMGUI format
        Hdf5ToCmguiConverter<DIM,DIM> cmgui_converter(input_dir,"voltage",mpElectricsMesh);

        // 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> cnverter(*mpElectricsMesh,*mpMechanicsMesh,input_dir,"voltage");

        // reset to the default value
        HeartConfig::Instance()->SetOutputDirectory(config_directory);
    }

    if(p_cmgui_writer)
    {
        if(mNoElectricsOutput)
        {
            p_cmgui_writer->WriteCmguiScript();
        }
        else
        {
            p_cmgui_writer->WriteCmguiScript("../../electrics/cmgui_output/voltage_mechanics_mesh");
        }
        delete p_cmgui_writer;
    }
    VecDestroy(voltage);
    delete p_electrics_solver;

    MechanicsEventHandler::EndEvent(MechanicsEventHandler::ALL);
}



template<unsigned DIM>
double CardiacElectroMechanicsProblem<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>
void CardiacElectroMechanicsProblem<DIM>::SetNoElectricsOutput()
{
    mNoElectricsOutput = true;
}

template<unsigned DIM>
void CardiacElectroMechanicsProblem<DIM>::SetWatchedPosition(c_vector<double,DIM> watchedLocation)
{
    mIsWatchedLocation = true;
    mWatchedLocation = watchedLocation;
}


template<unsigned DIM>
std::vector<c_vector<double,DIM> >& CardiacElectroMechanicsProblem<DIM>::rGetDeformedPosition()
{
    return mpMechanicsSolver->rGetDeformedPosition();
}




// Explicit instantiation

//note: 1d incompressible material doesn't make sense
template class CardiacElectroMechanicsProblem<2>;
template class CardiacElectroMechanicsProblem<3>;