AbstractCardiacTissue.cpp

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*/
 
#include "AbstractCardiacTissue.hpp"
 
#include <boost/scoped_array.hpp>
 
#include "DistributedVector.hpp"
#include "AxisymmetricConductivityTensors.hpp"
#include "OrthotropicConductivityTensors.hpp"
#include "Exception.hpp"
#include "ChastePoint.hpp"
#include "AbstractChasteRegion.hpp"
#include "HeartEventHandler.hpp"
#include "PetscTools.hpp"
#include "PetscVecTools.hpp"
#include "AbstractCvodeCell.hpp"
#include "Warnings.hpp"
 
template <unsigned ELEMENT_DIM,unsigned SPACE_DIM>
AbstractCardiacTissue<ELEMENT_DIM,SPACE_DIM>::AbstractCardiacTissue(
            AbstractCardiacCellFactory<ELEMENT_DIM,SPACE_DIM>* pCellFactory,
            bool exchangeHalos)
    : mpMesh(pCellFactory->GetMesh()),
      mpDistributedVectorFactory(mpMesh->GetDistributedVectorFactory()),
      mpConductivityModifier(NULL),
      mHasPurkinje(false),
      mDoCacheReplication(true),
      mMeshUnarchived(false),
      mExchangeHalos(exchangeHalos)
{
    //This constructor is called from the Initialise() method of the CardiacProblem class
    assert(pCellFactory != NULL);
    assert(pCellFactory->GetMesh() != NULL);
 
    if (PetscTools::IsSequential())
    {
        //Remove the request for a halo exchange
        mExchangeHalos = false;
    }
 
    unsigned num_local_nodes = mpDistributedVectorFactory->GetLocalOwnership();
    bool process_has_no_nodes = (num_local_nodes == 0u);
    if (PetscTools::ReplicateBool(process_has_no_nodes))
    {
        /* If there are no nodes on a process then there is a potential for an error in preconditioning.
         * This is dangerous because the process without nodes may segfault and not propagate the error
         * to the other processes.  Therefore, to avoid deadlock, we share this potential for error between
         * processes and throw an exception.
         */
// LCOV_EXCL_START
        // This problem normally occurs on 3 or more processes, so we can't cover it - coverage only runs with 1 and 2 processes.
        EXCEPTION("No cells were assigned some process in AbstractCardiacTissue constructor. Advice: Make total number of processors no greater than number of nodes in the mesh");
// LCOV_EXCL_STOP
    }
    unsigned ownership_range_low = mpDistributedVectorFactory->GetLow();
    mCellsDistributed.resize(num_local_nodes);
 
    // Figure out if we're dealing with Purkinje
    auto* p_purkinje_cell_factory = dynamic_cast<AbstractPurkinjeCellFactory<ELEMENT_DIM,SPACE_DIM>*>(pCellFactory);
    if (p_purkinje_cell_factory)
    {
        mHasPurkinje = true;
        mPurkinjeCellsDistributed.resize(num_local_nodes);
    }
 
    // Set up cells
    try
    {
        for (unsigned local_index = 0; local_index < num_local_nodes; local_index++)
        {
            unsigned global_index = ownership_range_low + local_index;
            Node<SPACE_DIM>* p_node = mpMesh->GetNode(global_index);
            mCellsDistributed[local_index] = pCellFactory->CreateCardiacCellForNode(p_node);
            mCellsDistributed[local_index]->SetUsedInTissueSimulation();
 
            if (mHasPurkinje)
            {
                mPurkinjeCellsDistributed[local_index] = p_purkinje_cell_factory->CreatePurkinjeCellForNode(p_node, mCellsDistributed[local_index]);
                mPurkinjeCellsDistributed[local_index]->SetUsedInTissueSimulation();
            }
        }
 
        pCellFactory->FinaliseCellCreation(&mCellsDistributed,
                                           mpDistributedVectorFactory->GetLow(),
                                           mpDistributedVectorFactory->GetHigh());
        if (mHasPurkinje)
        {
            p_purkinje_cell_factory->FinalisePurkinjeCellCreation(&mPurkinjeCellsDistributed,
                                                                  mpDistributedVectorFactory->GetLow(),
                                                                  mpDistributedVectorFactory->GetHigh());
        }
    }
    catch (const Exception& e)
    {
        // This catch statement is quite tricky to cover, but it is actually done
        // in TestCardiacSimulation::TestMono1dSodiumBlockBySettingNamedParameter()
 
        // Errors thrown creating cells will often be process-specific
        PetscTools::ReplicateException(true);
 
        // Delete cells
        // Should really do this for other processes too, but this is all we need
        // to get memory testing to pass, and leaking when we're about to die isn't
        // that bad!
        for (std::vector<AbstractCardiacCellInterface*>::iterator cell_iterator = mCellsDistributed.begin();
             cell_iterator != mCellsDistributed.end();
             ++cell_iterator)
        {
            delete (*cell_iterator);
        }
 
        throw e;
    }
    PetscTools::ReplicateException(false);
 
    // Halo nodes (if required)
    SetUpHaloCells(pCellFactory);
 
    HeartEventHandler::BeginEvent(HeartEventHandler::COMMUNICATION);
    mIionicCacheReplicated.Resize( pCellFactory->GetNumberOfCells() );
    mIntracellularStimulusCacheReplicated.Resize( pCellFactory->GetNumberOfCells() );
 
    if (mHasPurkinje)
    {
        mPurkinjeIionicCacheReplicated.Resize( pCellFactory->GetNumberOfCells() );
        mPurkinjeIntracellularStimulusCacheReplicated.Resize( pCellFactory->GetNumberOfCells() );
    }
    HeartEventHandler::EndEvent(HeartEventHandler::COMMUNICATION);
 
    if (HeartConfig::Instance()->IsMeshProvided() && HeartConfig::Instance()->GetLoadMesh())
    {
        mFibreFilePathNoExtension = HeartConfig::Instance()->GetMeshName();
    }
    else
    {
        // As of r10671 fibre orientation can only be defined when loading a mesh from disc.
        mFibreFilePathNoExtension = "";
    }
    CreateIntracellularConductivityTensor();
}
 
// Constructor used for archiving
template <unsigned ELEMENT_DIM,unsigned SPACE_DIM>
AbstractCardiacTissue<ELEMENT_DIM,SPACE_DIM>::AbstractCardiacTissue(AbstractTetrahedralMesh<ELEMENT_DIM,SPACE_DIM>* pMesh)
    : mpMesh(pMesh),
      mpDistributedVectorFactory(mpMesh->GetDistributedVectorFactory()),
      mHasPurkinje(false),
      mDoCacheReplication(true),
      mMeshUnarchived(true),
      mExchangeHalos(false)
{
    mIionicCacheReplicated.Resize(mpDistributedVectorFactory->GetProblemSize());
    mIntracellularStimulusCacheReplicated.Resize(mpDistributedVectorFactory->GetProblemSize());
 
    mFibreFilePathNoExtension = ArchiveLocationInfo::GetArchiveDirectory() + ArchiveLocationInfo::GetMeshFilename();
    CreateIntracellularConductivityTensor();
}
 
template <unsigned ELEMENT_DIM,unsigned SPACE_DIM>
AbstractCardiacTissue<ELEMENT_DIM,SPACE_DIM>::~AbstractCardiacTissue()
{
    // Delete cells
    for (std::vector<AbstractCardiacCellInterface*>::iterator iter = mCellsDistributed.begin();
         iter != mCellsDistributed.end();
         ++iter)
    {
        delete (*iter);
    }
 
    // Delete cells for halo nodes
    for (std::vector<AbstractCardiacCellInterface*>::iterator iter = mHaloCellsDistributed.begin();
         iter != mHaloCellsDistributed.end();
         ++iter)
    {
        delete (*iter);
    }
 
    delete mpIntracellularConductivityTensors;
 
    // Delete Purkinje cells
    for (std::vector<AbstractCardiacCellInterface*>::iterator iter = mPurkinjeCellsDistributed.begin();
         iter != mPurkinjeCellsDistributed.end();
         ++iter)
    {
        delete (*iter);
    }
 
    // If the mesh was unarchived we need to free it explicitly.
    if (mMeshUnarchived)
    {
        delete mpMesh;
    }
}
 
 
template <unsigned ELEMENT_DIM,unsigned SPACE_DIM>
bool AbstractCardiacTissue<ELEMENT_DIM,SPACE_DIM>::HasPurkinje()
{
    return mHasPurkinje;
}
 
template <unsigned ELEMENT_DIM,unsigned SPACE_DIM>
void AbstractCardiacTissue<ELEMENT_DIM,SPACE_DIM>::CreateIntracellularConductivityTensor()
{
    HeartEventHandler::BeginEvent(HeartEventHandler::READ_MESH);
    mpConfig = HeartConfig::Instance();
 
    if (mpConfig->IsMeshProvided() && mpConfig->GetLoadMesh())
    {
        assert(mFibreFilePathNoExtension != "");
 
        switch (mpConfig->GetConductivityMedia())
        {
            case cp::media_type::Orthotropic:
            {
                mpIntracellularConductivityTensors = new OrthotropicConductivityTensors<ELEMENT_DIM,SPACE_DIM>;
                FileFinder ortho_file(mFibreFilePathNoExtension + ".ortho", RelativeTo::AbsoluteOrCwd);
                assert(ortho_file.Exists());
                mpIntracellularConductivityTensors->SetFibreOrientationFile(ortho_file);
                break;
            }
 
            case cp::media_type::Axisymmetric:
            {
                mpIntracellularConductivityTensors = new AxisymmetricConductivityTensors<ELEMENT_DIM,SPACE_DIM>;
                FileFinder axi_file(mFibreFilePathNoExtension + ".axi", RelativeTo::AbsoluteOrCwd);
                assert(axi_file.Exists());
                mpIntracellularConductivityTensors->SetFibreOrientationFile(axi_file);
                break;
            }
 
            case cp::media_type::NoFibreOrientation:
                mpIntracellularConductivityTensors = new OrthotropicConductivityTensors<ELEMENT_DIM,SPACE_DIM>;
                break;
 
            default:
                NEVER_REACHED;
        }
    }
    else // Slab defined in config file or SetMesh() called; no fibre orientation assumed
    {
        mpIntracellularConductivityTensors = new OrthotropicConductivityTensors<ELEMENT_DIM,SPACE_DIM>;
    }
 
    c_vector<double, SPACE_DIM> intra_conductivities;
    mpConfig->GetIntracellularConductivities(intra_conductivities);
 
    // this definition must be here (and not inside the if statement) because SetNonConstantConductivities() will keep
    // a pointer to it and we don't want it to go out of scope before Init() is called
    unsigned num_local_elements = mpMesh->GetNumLocalElements();
    std::vector<c_vector<double, SPACE_DIM> > hetero_intra_conductivities;
 
    if (mpConfig->GetConductivityHeterogeneitiesProvided())
    {
        try
        {
            assert(hetero_intra_conductivities.size()==0);
            hetero_intra_conductivities.resize(num_local_elements, intra_conductivities);
        }
        // LCOV_EXCL_START
        catch(std::bad_alloc &r_bad_alloc)
        {
            std::cout << "Failed to allocate std::vector of size " << num_local_elements << std::endl;
            PetscTools::ReplicateException(true);
            throw r_bad_alloc;
        }
        // LCOV_EXCL_STOP
 
        PetscTools::ReplicateException(false);
 
        std::vector<boost::shared_ptr<AbstractChasteRegion<SPACE_DIM> > > conductivities_heterogeneity_areas;
        std::vector< c_vector<double,3> > intra_h_conductivities;
        std::vector< c_vector<double,3> > extra_h_conductivities;
        HeartConfig::Instance()->GetConductivityHeterogeneities(conductivities_heterogeneity_areas,
                                                                intra_h_conductivities,
                                                                extra_h_conductivities);
 
        unsigned local_element_index = 0;
 
        for (typename AbstractTetrahedralMesh<ELEMENT_DIM,SPACE_DIM>::ElementIterator it = mpMesh->GetElementIteratorBegin();
             it != mpMesh->GetElementIteratorEnd();
             ++it)
        {
//            unsigned element_index = it->GetIndex();
            // if element centroid is contained in the region
            ChastePoint<SPACE_DIM> element_centroid(it->CalculateCentroid());
            for (unsigned region_index=0; region_index< conductivities_heterogeneity_areas.size(); region_index++)
            {
                if (conductivities_heterogeneity_areas[region_index]->DoesContain(element_centroid))
                {
                    //We don't use ublas vector assignment here, because we might be getting a subvector of a 3-vector
                    for (unsigned i=0; i<SPACE_DIM; i++)
                    {
                        hetero_intra_conductivities[local_element_index][i] = intra_h_conductivities[region_index][i];
                    }
                }
            }
            local_element_index++;
        }
 
        mpIntracellularConductivityTensors->SetNonConstantConductivities(&hetero_intra_conductivities);
    }
    else
    {
        mpIntracellularConductivityTensors->SetConstantConductivities(intra_conductivities);
    }
 
    mpIntracellularConductivityTensors->Init(this->mpMesh);
    HeartEventHandler::EndEvent(HeartEventHandler::READ_MESH);
}
 
 
template <unsigned ELEMENT_DIM,unsigned SPACE_DIM>
void AbstractCardiacTissue<ELEMENT_DIM,SPACE_DIM>::SetCacheReplication(bool doCacheReplication)
{
    mDoCacheReplication = doCacheReplication;
}
 
template <unsigned ELEMENT_DIM,unsigned SPACE_DIM>
bool AbstractCardiacTissue<ELEMENT_DIM,SPACE_DIM>::GetDoCacheReplication()
{
    return mDoCacheReplication;
}
 
template <unsigned ELEMENT_DIM,unsigned SPACE_DIM>
const c_matrix<double, SPACE_DIM, SPACE_DIM>& AbstractCardiacTissue<ELEMENT_DIM,SPACE_DIM>::rGetIntracellularConductivityTensor(unsigned elementIndex)
{
    assert( mpIntracellularConductivityTensors);
    if (mpConductivityModifier==NULL)
    {
        return (*mpIntracellularConductivityTensors)[elementIndex];
    }
    else
    {
        return mpConductivityModifier->rGetModifiedConductivityTensor(elementIndex, (*mpIntracellularConductivityTensors)[elementIndex], 0u);
    }
}
 
template <unsigned ELEMENT_DIM,unsigned SPACE_DIM>
const c_matrix<double, SPACE_DIM, SPACE_DIM>& AbstractCardiacTissue<ELEMENT_DIM,SPACE_DIM>::rGetExtracellularConductivityTensor(unsigned elementIndex)
{
     EXCEPTION("Monodomain tissues do not have extracellular conductivity tensors.");
}
 
template <unsigned ELEMENT_DIM,unsigned SPACE_DIM>
AbstractCardiacCellInterface* AbstractCardiacTissue<ELEMENT_DIM,SPACE_DIM>::GetCardiacCell( unsigned globalIndex )
{
    assert(mpDistributedVectorFactory->GetLow() <= globalIndex &&
           globalIndex < mpDistributedVectorFactory->GetHigh());
    return mCellsDistributed[globalIndex - mpDistributedVectorFactory->GetLow()];
}
 
template <unsigned ELEMENT_DIM,unsigned SPACE_DIM>
AbstractCardiacCellInterface* AbstractCardiacTissue<ELEMENT_DIM,SPACE_DIM>::GetPurkinjeCell( unsigned globalIndex )
{
    assert(mpDistributedVectorFactory->GetLow() <= globalIndex &&
           globalIndex < mpDistributedVectorFactory->GetHigh());
    EXCEPT_IF_NOT(mHasPurkinje);
    return mPurkinjeCellsDistributed[globalIndex - mpDistributedVectorFactory->GetLow()];
}
 
template <unsigned ELEMENT_DIM,unsigned SPACE_DIM>
AbstractCardiacCellInterface* AbstractCardiacTissue<ELEMENT_DIM,SPACE_DIM>::GetCardiacCellOrHaloCell( unsigned globalIndex )
{
    std::map<unsigned, unsigned>::const_iterator node_position;
    // First search the halo
    if ((node_position=mHaloGlobalToLocalIndexMap.find(globalIndex)) != mHaloGlobalToLocalIndexMap.end())
    {
        // Found a halo node
        return mHaloCellsDistributed[node_position->second];
    }
    // Then search the owned node
    if (mpDistributedVectorFactory->IsGlobalIndexLocal(globalIndex))
    {
        // Found an owned node
        return mCellsDistributed[globalIndex - mpDistributedVectorFactory->GetLow()];
    }
    // Not here
    EXCEPTION("Requested node/halo " << globalIndex << " does not belong to processor " << PetscTools::GetMyRank());
}
 
 
template <unsigned ELEMENT_DIM,unsigned SPACE_DIM>
void AbstractCardiacTissue<ELEMENT_DIM,SPACE_DIM>::CalculateHaloNodesFromNodeExchange()
{
    std::set<unsigned> halos_as_set;
    for (unsigned proc=0; proc<PetscTools::GetNumProcs(); proc++)
    {
        halos_as_set.insert(mNodesToReceivePerProcess[proc].begin(), mNodesToReceivePerProcess[proc].end());
    }
    mHaloNodes = std::vector<unsigned>(halos_as_set.begin(), halos_as_set.end());
    //PRINT_VECTOR(mHaloNodes);
}
 
 
template <unsigned ELEMENT_DIM,unsigned SPACE_DIM>
void AbstractCardiacTissue<ELEMENT_DIM,SPACE_DIM>::SetUpHaloCells(AbstractCardiacCellFactory<ELEMENT_DIM,SPACE_DIM>* pCellFactory)
{
    if (mExchangeHalos)
    {
        mpMesh->CalculateNodeExchange(mNodesToSendPerProcess, mNodesToReceivePerProcess);
        // Note that the following call will not work for a TetrahedralMesh which has
        // no concept of halo nodes.
        //mpMesh->GetHaloNodeIndices( mHaloNodes );
        CalculateHaloNodesFromNodeExchange();
        unsigned num_halo_nodes = mHaloNodes.size();
        mHaloCellsDistributed.resize( num_halo_nodes );
        for (unsigned local_index = 0; local_index < num_halo_nodes; local_index++)
        {
            unsigned global_index = mHaloNodes[local_index];
            // These are all halo nodes, so we use the "GetNodeOrHaloNode" variety of GetNode
            Node<SPACE_DIM>* p_node = mpMesh->GetNodeOrHaloNode(global_index);
            mHaloCellsDistributed[local_index] = pCellFactory->CreateCardiacCellForNode(p_node);
            mHaloCellsDistributed[local_index]->SetUsedInTissueSimulation();
            mHaloGlobalToLocalIndexMap[global_index] = local_index;
        }
        // No need to call FinaliseCellCreation() as halo node cardiac cells will
        // never be stimulated (their values are communicated from the process that
        // owns them).
    }
}
 
 
template <unsigned ELEMENT_DIM,unsigned SPACE_DIM>
void AbstractCardiacTissue<ELEMENT_DIM,SPACE_DIM>::SolveCellSystems(Vec existingSolution, double time, double nextTime, bool updateVoltage)
{
    if (mHasPurkinje)
    {
        // can't do Purkinje and operator splitting
        assert(!updateVoltage);
        // The code below assumes Purkinje is are monodomain, so the vector has two stripes.
        // The assert will fail the first time bidomain purkinje is coded - need to decide what
        // ordering the three stripes (V, V_purk, phi_e) are in
        assert(PetscVecTools::GetSize(existingSolution)==2*mpMesh->GetNumNodes());
    }
 
    HeartEventHandler::BeginEvent(HeartEventHandler::SOLVE_ODES);
 
    DistributedVector dist_solution = mpDistributedVectorFactory->CreateDistributedVector(existingSolution);
 
    // Solve cell models (except purkinje cell models)
    DistributedVector::Stripe voltage(dist_solution, 0);
    try
    {
        double voltage_before_update;
        for (DistributedVector::Iterator index = dist_solution.Begin();
             index != dist_solution.End();
             ++index)
        {
            voltage_before_update = voltage[index];
            mCellsDistributed[index.Local]->SetVoltage( voltage_before_update );
 
            // Added a try-catch here to provide more output to screen when an error occurs.
            try
            {
                if (!updateVoltage)
                {
                    // solve ODE system at this node.
                    // Note: Voltage is not being updated. The voltage is updated in the PDE solve.
#ifndef CHASTE_CVODE
                    mCellsDistributed[index.Local]->ComputeExceptVoltage(time, nextTime);
#else
                    // If CVODE is enabled, and this is a CVODE cell
                    // there's a chance we can recover this by doing a reset so put the above call in a try...catch.
                    try
                    {
                        mCellsDistributed[index.Local]->ComputeExceptVoltage(time, nextTime);
                    }
                    catch (Exception &e)
                    {
                        // Try an 'emergency' reset if this is a CVODE cell.
                        // See #2594 for why we think this may be necessary.
                        if (dynamic_cast<AbstractCvodeCell*>(mCellsDistributed[index.Local]))
                        {
                            // Reset the CVODE cell, this leads to a call to CVodeReInit.
                            static_cast<AbstractCvodeCell*>(mCellsDistributed[index.Local])->ResetSolver();
                            mCellsDistributed[index.Local]->ComputeExceptVoltage(time, nextTime);
                            WARNING("Global node " << index.Global << " had an ODE solving problem in t = [" << time <<
                                    ", " << nextTime << "] ms. This was fixed by a reset of CVODE, but may suggest PDE time"
                                    " step should be reduced, or CVODE tolerances relaxed.");
                        }
                        else
                        {
                            throw e;
                        }
                    }
#endif // CHASTE_CVODE
                }
                else
                {
                    // solve, including updating the voltage (for the operator-splitting implementation of the monodomain solver)
                    mCellsDistributed[index.Local]->SolveAndUpdateState(time, nextTime);
                    voltage[index] = mCellsDistributed[index.Local]->GetVoltage();
                }
            }
            catch (Exception &e)
            {
                std::cout << std::setprecision(16);
                std::cout << "Global node " << index.Global << " had problems with ODE solve between "
                        "t = " << time << " and " << nextTime << "ms.\n";
 
                std::cout << "Voltage at this node before solve was " << voltage_before_update << "mV\n"
                        "(this SHOULD NOT necessarily be the same as the one in the state variables,\n"
                        "which can be ignored and stay at the initial condition - the voltage is dictated by PDE instead of state variable.)\n";
 
                std::cout << "Stimulus current (NB converted to micro-Amps per cm^3) applied here is equal to:\n\t"
                    << mCellsDistributed[index.Local]->GetIntracellularStimulus(time) << " at t = " << time     << "ms,\n\t"
                    << mCellsDistributed[index.Local]->GetIntracellularStimulus(nextTime) << " at t = " << nextTime << "ms.\n";
 
                std::cout << "Cell model: " << dynamic_cast<AbstractUntemplatedParameterisedSystem*>(mCellsDistributed[index.Local])->GetSystemName() << "\n";
 
                std::cout << "All state variables are now:\n";
                std::vector<double> state_vars = mCellsDistributed[index.Local]->GetStdVecStateVariables();
                std::vector<std::string> state_var_names = mCellsDistributed[index.Local]->rGetStateVariableNames();
                for (unsigned i=0; i<state_vars.size(); i++)
                {
                    std::cout << "\t" << state_var_names[i] << "\t:\t" << state_vars[i] << "\n";
                }
                std::cout << std::flush;
 
                throw e;
            }
            // update the Iionic and stimulus caches
            UpdateCaches(index.Global, index.Local, nextTime);
        }
 
        if (updateVoltage)
        {
            dist_solution.Restore();
        }
    }
    catch (Exception &e)
    {
        PetscTools::ReplicateException(true);
        throw e;
    }
 
    // Solve purkinje cell models
    if (mHasPurkinje)
    {
        DistributedVector::Stripe purkinje_voltage(dist_solution, 1);
        try
        {
            for (DistributedVector::Iterator index = dist_solution.Begin();
                 index != dist_solution.End();
                 ++index)
            {
                // overwrite the voltage with the input value
                mPurkinjeCellsDistributed[index.Local]->SetVoltage( purkinje_voltage[index] );
 
                // solve
                // Note: Voltage is not being updated. The voltage is updated in the PDE solve.
                mPurkinjeCellsDistributed[index.Local]->ComputeExceptVoltage(time, nextTime);
 
                // update the Iionic and stimulus caches
                UpdatePurkinjeCaches(index.Global, index.Local, nextTime);
            }
        }
        // LCOV_EXCL_START
        catch (Exception& e)
        {
 
            NEVER_REACHED;
            PetscTools::ReplicateException(true);
            throw e;
        }
        // LCOV_EXCL_STOP
    }
 
    PetscTools::ReplicateException(false);
    HeartEventHandler::EndEvent(HeartEventHandler::SOLVE_ODES);
 
    // Communicate new state variable values to halo nodes
    if (mExchangeHalos)
    {
        assert(!mHasPurkinje);
 
        for ( unsigned rank_offset = 1; rank_offset < PetscTools::GetNumProcs(); rank_offset++ )
        {
            unsigned send_to      = (PetscTools::GetMyRank() + rank_offset) % (PetscTools::GetNumProcs());
            unsigned receive_from = (PetscTools::GetMyRank() + PetscTools::GetNumProcs()- rank_offset ) % (PetscTools::GetNumProcs());
 
            unsigned number_of_cells_to_send    = mNodesToSendPerProcess[send_to].size();
            unsigned number_of_cells_to_receive = mNodesToReceivePerProcess[receive_from].size();
 
            // Pack send buffer
            unsigned send_size = 0;
            for (unsigned i=0; i<number_of_cells_to_send; i++)
            {
                unsigned global_cell_index = mNodesToSendPerProcess[send_to][i];
                send_size += mCellsDistributed[global_cell_index - mpDistributedVectorFactory->GetLow()]->GetNumberOfStateVariables();
            }
 
            boost::scoped_array<double> send_data(new double[send_size]);
 
            unsigned send_index = 0;
            for (unsigned cell = 0; cell < number_of_cells_to_send; cell++)
            {
                unsigned global_cell_index = mNodesToSendPerProcess[send_to][cell];
                AbstractCardiacCellInterface* p_cell = mCellsDistributed[global_cell_index - mpDistributedVectorFactory->GetLow()];
                std::vector<double> cell_data = p_cell->GetStdVecStateVariables();
                const unsigned num_state_vars = p_cell->GetNumberOfStateVariables();
                for (unsigned state_variable = 0; state_variable < num_state_vars; state_variable++)
                {
                    send_data[send_index++] = cell_data[state_variable];
                }
            }
            // Receive buffer
            unsigned receive_size = 0;
            for (unsigned i=0; i<number_of_cells_to_receive; i++)
            {
                unsigned halo_cell_index = mHaloGlobalToLocalIndexMap[mNodesToReceivePerProcess[receive_from][i]];
                receive_size += mHaloCellsDistributed[halo_cell_index]->GetNumberOfStateVariables();
            }
 
            boost::scoped_array<double> receive_data(new double[receive_size]);
 
            // Send and receive
            int ret;
            MPI_Status status;
            ret = MPI_Sendrecv(send_data.get(), send_size,
                               MPI_DOUBLE,
                               send_to, 0,
                               receive_data.get(), receive_size,
                               MPI_DOUBLE,
                               receive_from, 0,
                               PETSC_COMM_WORLD, &status);
            UNUSED_OPT(ret);
            assert ( ret == MPI_SUCCESS);
 
            // Unpack
            unsigned receive_index = 0;
            for ( unsigned cell = 0; cell < number_of_cells_to_receive; cell++ )
            {
                AbstractCardiacCellInterface* p_cell = mHaloCellsDistributed[mHaloGlobalToLocalIndexMap[mNodesToReceivePerProcess[receive_from][cell]]];
                const unsigned number_of_state_variables = p_cell->GetNumberOfStateVariables();
 
                std::vector<double> cell_data(number_of_state_variables);
                for (unsigned state_variable = 0; state_variable < number_of_state_variables; state_variable++)
                {
                    cell_data[state_variable] = receive_data[receive_index++];
                }
                p_cell->SetStateVariables(cell_data);
            }
        }
    }
 
    HeartEventHandler::BeginEvent(HeartEventHandler::COMMUNICATION);
    if (mDoCacheReplication)
    {
        ReplicateCaches();
    }
    HeartEventHandler::EndEvent(HeartEventHandler::COMMUNICATION);
}
 
template <unsigned ELEMENT_DIM,unsigned SPACE_DIM>
ReplicatableVector& AbstractCardiacTissue<ELEMENT_DIM,SPACE_DIM>::rGetIionicCacheReplicated()
{
    return mIionicCacheReplicated;
}
 
template <unsigned ELEMENT_DIM,unsigned SPACE_DIM>
ReplicatableVector& AbstractCardiacTissue<ELEMENT_DIM,SPACE_DIM>::rGetIntracellularStimulusCacheReplicated()
{
    return mIntracellularStimulusCacheReplicated;
}
 
template <unsigned ELEMENT_DIM,unsigned SPACE_DIM>
ReplicatableVector& AbstractCardiacTissue<ELEMENT_DIM,SPACE_DIM>::rGetPurkinjeIionicCacheReplicated()
{
    EXCEPT_IF_NOT(mHasPurkinje);
    return mPurkinjeIionicCacheReplicated;
}
 
template <unsigned ELEMENT_DIM,unsigned SPACE_DIM>
ReplicatableVector& AbstractCardiacTissue<ELEMENT_DIM,SPACE_DIM>::rGetPurkinjeIntracellularStimulusCacheReplicated()
{
    EXCEPT_IF_NOT(mHasPurkinje);
    return mPurkinjeIntracellularStimulusCacheReplicated;
}
 
template <unsigned ELEMENT_DIM,unsigned SPACE_DIM>
void AbstractCardiacTissue<ELEMENT_DIM,SPACE_DIM>::UpdateCaches(unsigned globalIndex, unsigned localIndex, double nextTime)
{
    mIionicCacheReplicated[globalIndex] = mCellsDistributed[localIndex]->GetIIonic();
    mIntracellularStimulusCacheReplicated[globalIndex] = mCellsDistributed[localIndex]->GetIntracellularStimulus(nextTime);
}
 
template <unsigned ELEMENT_DIM,unsigned SPACE_DIM>
void AbstractCardiacTissue<ELEMENT_DIM,SPACE_DIM>::UpdatePurkinjeCaches(unsigned globalIndex, unsigned localIndex, double nextTime)
{
    assert(mHasPurkinje);
    mPurkinjeIionicCacheReplicated[globalIndex] = mPurkinjeCellsDistributed[localIndex]->GetIIonic();
    mPurkinjeIntracellularStimulusCacheReplicated[globalIndex] = mPurkinjeCellsDistributed[localIndex]->GetIntracellularStimulus(nextTime);
}
 
template <unsigned ELEMENT_DIM,unsigned SPACE_DIM>
void AbstractCardiacTissue<ELEMENT_DIM,SPACE_DIM>::ReplicateCaches()
{
    // ReplicateCaches only needed for SVI (and non-matrix based assembly which is no longer in code)
    // which is not implemented with Purkinje. See commented code below if introducing this.
    assert(!mHasPurkinje);
 
    mIionicCacheReplicated.Replicate(mpDistributedVectorFactory->GetLow(), mpDistributedVectorFactory->GetHigh());
    mIntracellularStimulusCacheReplicated.Replicate(mpDistributedVectorFactory->GetLow(), mpDistributedVectorFactory->GetHigh());
 
    //if (mHasPurkinje)
    //{
    //    mPurkinjeIionicCacheReplicated.Replicate(mpDistributedVectorFactory->GetLow(), mpDistributedVectorFactory->GetHigh());
    //    mPurkinjeIntracellularStimulusCacheReplicated.Replicate(mpDistributedVectorFactory->GetLow(), mpDistributedVectorFactory->GetHigh());
    //}
}
 
template <unsigned ELEMENT_DIM,unsigned SPACE_DIM>
const std::vector<AbstractCardiacCellInterface*>& AbstractCardiacTissue<ELEMENT_DIM,SPACE_DIM>::rGetCellsDistributed() const
{
    return mCellsDistributed;
}
 
template <unsigned ELEMENT_DIM,unsigned SPACE_DIM>
const std::vector<AbstractCardiacCellInterface*>& AbstractCardiacTissue<ELEMENT_DIM,SPACE_DIM>::rGetPurkinjeCellsDistributed() const
{
    EXCEPT_IF_NOT(mHasPurkinje);
    return mPurkinjeCellsDistributed;
}
 
template <unsigned ELEMENT_DIM,unsigned SPACE_DIM>
const AbstractTetrahedralMesh<ELEMENT_DIM,SPACE_DIM>* AbstractCardiacTissue<ELEMENT_DIM,SPACE_DIM>::pGetMesh() const
{
    return mpMesh;
}
 
template <unsigned ELEMENT_DIM,unsigned SPACE_DIM>
void AbstractCardiacTissue<ELEMENT_DIM,SPACE_DIM>::SetConductivityModifier(AbstractConductivityModifier<ELEMENT_DIM,SPACE_DIM>* pModifier)
{
    assert(pModifier!=NULL);
    assert(mpConductivityModifier==NULL); // shouldn't be called twice for example, or with two different modifiers (remove this assert
                                          // if for whatever reason want to be able to overwrite modifiers)
    mpConductivityModifier = pModifier;
}
 
// Explicit instantiation
template class AbstractCardiacTissue<1,1>;
template class AbstractCardiacTissue<1,2>;
template class AbstractCardiacTissue<1,3>;
template class AbstractCardiacTissue<2,2>;
template class AbstractCardiacTissue<3,3>;