MeshBasedCellPopulation.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 "MeshBasedCellPopulation.hpp"
#include "CellwiseData.hpp"
#include "TrianglesMeshWriter.hpp"
#include "VtkMeshWriter.hpp"
#include "CellBasedEventHandler.hpp"
#include "ApoptoticCellProperty.hpp"
#include "Cylindrical2dMesh.hpp"
#include "NodesOnlyMesh.hpp"


template<unsigned DIM>
MeshBasedCellPopulation<DIM>::MeshBasedCellPopulation(MutableMesh<DIM, DIM>& rMesh,
                                      std::vector<CellPtr>& rCells,
                                      const std::vector<unsigned> locationIndices,
                                      bool deleteMesh,
                                      bool validate)
    : AbstractCentreBasedCellPopulation<DIM>(rCells, locationIndices),
      mrMesh(rMesh),
      mpVoronoiTessellation(NULL),
      mDeleteMesh(deleteMesh),
      mUseAreaBasedDampingConstant(false),
      mAreaBasedDampingConstantParameter(0.1),
      mOutputVoronoiData(false),
      mOutputCellPopulationVolumes(false),
      mWriteVtkAsPoints(false)
{
    // This must always be true
    assert(this->mCells.size() <= mrMesh.GetNumNodes());

    this->mCellPopulationContainsMesh = true;

    if (validate)
    {
        Validate();
    }
}

template<unsigned DIM>
MeshBasedCellPopulation<DIM>::MeshBasedCellPopulation(MutableMesh<DIM, DIM>& rMesh)
    : mrMesh(rMesh)
{
    this->mCellPopulationContainsMesh = true;
    mpVoronoiTessellation = NULL;
    mDeleteMesh = true;
}

template<unsigned DIM>
MeshBasedCellPopulation<DIM>::~MeshBasedCellPopulation()
{
    delete mpVoronoiTessellation;

    if (mDeleteMesh)
    {
        delete &mrMesh;
    }
}

template<unsigned DIM>
bool MeshBasedCellPopulation<DIM>::UseAreaBasedDampingConstant()
{
    return mUseAreaBasedDampingConstant;
}

template<unsigned DIM>
void MeshBasedCellPopulation<DIM>::SetAreaBasedDampingConstant(bool useAreaBasedDampingConstant)
{
    assert(DIM==2);
    mUseAreaBasedDampingConstant = useAreaBasedDampingConstant;
}

template<unsigned DIM>
unsigned MeshBasedCellPopulation<DIM>::AddNode(Node<DIM>* pNewNode)
{
    return mrMesh.AddNode(pNewNode);
}

template<unsigned DIM>
void MeshBasedCellPopulation<DIM>::SetNode(unsigned nodeIndex, ChastePoint<DIM>& rNewLocation)
{
    mrMesh.SetNode(nodeIndex, rNewLocation, false);
}

template<unsigned DIM>
double MeshBasedCellPopulation<DIM>::GetDampingConstant(unsigned nodeIndex)
{
    double damping_multiplier = AbstractCentreBasedCellPopulation<DIM>::GetDampingConstant(nodeIndex);

    if (mUseAreaBasedDampingConstant)
    {
        assert(DIM==2);

        double rest_length = 1.0;
        double d0 = mAreaBasedDampingConstantParameter;

        double d1 = 2.0*(1.0 - d0)/(sqrt(3)*rest_length*rest_length);

        double area_cell = GetVolumeOfVoronoiElement(nodeIndex);

        assert(area_cell < 1000);

        damping_multiplier = d0 + area_cell*d1;
    }

    return damping_multiplier;
}

template<unsigned DIM>
void MeshBasedCellPopulation<DIM>::Validate()
{
    std::vector<bool> validated_node = std::vector<bool>(this->GetNumNodes(), false);

    for (typename AbstractCellPopulation<DIM>::Iterator cell_iter=this->Begin(); cell_iter!=this->End(); ++cell_iter)
    {
        unsigned node_index = GetLocationIndexUsingCell(*cell_iter);
        validated_node[node_index] = true;
    }

    for (unsigned i=0; i<validated_node.size(); i++)
    {
        if (!validated_node[i])
        {
            std::stringstream ss;
            ss << "Node " << i << " does not appear to have a cell associated with it";
            EXCEPTION(ss.str());
        }
    }
}

template<unsigned DIM>
MutableMesh<DIM, DIM>& MeshBasedCellPopulation<DIM>::rGetMesh()
{
    return mrMesh;
}

template<unsigned DIM>
const MutableMesh<DIM, DIM>& MeshBasedCellPopulation<DIM>::rGetMesh() const
{
    return mrMesh;
}

template<unsigned DIM>
unsigned MeshBasedCellPopulation<DIM>::RemoveDeadCells()
{
    unsigned num_removed = 0;
    for (std::list<CellPtr>::iterator it = this->mCells.begin();
         it != this->mCells.end();
         ++it)
    {
        if ((*it)->IsDead())
        {
            // Check if this cell is in a marked spring
            std::vector<const std::pair<CellPtr,CellPtr>*> pairs_to_remove; // Pairs that must be purged
            for (std::set<std::pair<CellPtr,CellPtr> >::iterator it1 = mMarkedSprings.begin();
                 it1 != mMarkedSprings.end();
                 ++it1)
            {
                const std::pair<CellPtr,CellPtr>& r_pair = *it1;

                for (unsigned i=0; i<2; i++)
                {
                    CellPtr p_cell = (i==0 ? r_pair.first : r_pair.second);

                    if (p_cell == *it)
                    {
                        // Remember to purge this spring
                        pairs_to_remove.push_back(&r_pair);
                        break;
                    }
                }
            }

            // Purge any marked springs that contained this cell
            for (std::vector<const std::pair<CellPtr,CellPtr>* >::iterator pair_it = pairs_to_remove.begin();
                 pair_it != pairs_to_remove.end();
                 ++pair_it)
            {
                mMarkedSprings.erase(**pair_it);
            }

            // Remove the node from the mesh
            num_removed++;
            mrMesh.DeleteNodePriorToReMesh(this->mCellLocationMap[(*it).get()]);

            // Update mappings between cells and location indices
            unsigned location_index_of_removed_node = this->mCellLocationMap[(*it).get()];
            this->mCellLocationMap.erase((*it).get());
            this->mLocationCellMap.erase(location_index_of_removed_node);

            // Update vector of cells
            it = this->mCells.erase(it);
            --it;
        }
    }

    return num_removed;
}


template<unsigned DIM>
void MeshBasedCellPopulation<DIM>::Update(bool hasHadBirthsOrDeaths)
{
    NodeMap map(mrMesh.GetNumAllNodes());
    mrMesh.ReMesh(map);

    if (!map.IsIdentityMap())
    {
        UpdateGhostNodesAfterReMesh(map);

        // Update the mappings between cells and location indices
        std::map<Cell*, unsigned> old_map = this->mCellLocationMap;

        // Remove any dead pointers from the maps (needed to avoid archiving errors)
        this->mLocationCellMap.clear();
        this->mCellLocationMap.clear();

        for (std::list<CellPtr>::iterator it = this->mCells.begin();
             it != this->mCells.end();
             ++it)
        {
            unsigned old_node_index = old_map[(*it).get()];

            // This shouldn't ever happen, as the cell vector only contains living cells
            assert(!map.IsDeleted(old_node_index));

            unsigned new_node_index = map.GetNewIndex(old_node_index);
            this->mLocationCellMap[new_node_index] = *it;
            this->mCellLocationMap[(*it).get()] = new_node_index;
        }

        this->Validate();
    }

    // Purge any marked springs that are no longer springs
    std::vector<const std::pair<CellPtr,CellPtr>*> springs_to_remove;
    for (std::set<std::pair<CellPtr,CellPtr> >::iterator spring_it = mMarkedSprings.begin();
         spring_it != mMarkedSprings.end();
         ++spring_it)
    {
        CellPtr p_cell_1 = spring_it->first;
        CellPtr p_cell_2 = spring_it->second;
        Node<DIM>* p_node_1 = this->GetNodeCorrespondingToCell(p_cell_1);
        Node<DIM>* p_node_2 = this->GetNodeCorrespondingToCell(p_cell_2);

        bool joined = false;

        // For each element containing node1, if it also contains node2 then the cells are joined
        std::set<unsigned> node2_elements = p_node_2->rGetContainingElementIndices();
        for (typename Node<DIM>::ContainingElementIterator elem_iter = p_node_1->ContainingElementsBegin();
             elem_iter != p_node_1->ContainingElementsEnd();
             ++elem_iter)
        {
            if (node2_elements.find(*elem_iter) != node2_elements.end())
            {
                joined = true;
                break;
            }
        }

        // If no longer joined, remove this spring from the set
        if (!joined)
        {
            springs_to_remove.push_back(&(*spring_it));
        }
    }

    // Remove any springs necessary
    for (std::vector<const std::pair<CellPtr,CellPtr>* >::iterator spring_it = springs_to_remove.begin();
         spring_it != springs_to_remove.end();
         ++spring_it)
    {
        mMarkedSprings.erase(**spring_it);
    }

    // Tessellate if needed
    if (DIM==2 || DIM==3)
    {
        CellBasedEventHandler::BeginEvent(CellBasedEventHandler::TESSELLATION);
        if (mUseAreaBasedDampingConstant || mOutputVoronoiData || mOutputCellPopulationVolumes || this->mOutputCellVolumes)
        {
            CreateVoronoiTessellation();
        }
        CellBasedEventHandler::EndEvent(CellBasedEventHandler::TESSELLATION);
    }

    mrMesh.SetMeshHasChangedSinceLoading();
}

template<unsigned DIM>
Node<DIM>* MeshBasedCellPopulation<DIM>::GetNode(unsigned index)
{
    return mrMesh.GetNode(index);
}

template<unsigned DIM>
unsigned MeshBasedCellPopulation<DIM>::GetNumNodes()
{
    return mrMesh.GetNumAllNodes();
}

template<unsigned DIM>
void MeshBasedCellPopulation<DIM>::UpdateGhostNodesAfterReMesh(NodeMap& rMap)
{
}

template<unsigned DIM>
CellPtr MeshBasedCellPopulation<DIM>::AddCell(CellPtr pNewCell, const c_vector<double,DIM>& rCellDivisionVector, CellPtr pParentCell)
{
    assert(pNewCell);
    assert(pParentCell);

    // Add new cell to cell population
    CellPtr p_created_cell = AbstractCentreBasedCellPopulation<DIM>::AddCell(pNewCell, rCellDivisionVector, pParentCell);
    assert(p_created_cell == pNewCell);

    // Mark spring between parent cell and new cell
    std::pair<CellPtr,CellPtr> cell_pair = CreateCellPair(pParentCell, p_created_cell);
    MarkSpring(cell_pair);

    // Return pointer to new cell
    return p_created_cell;
}

//                             Output methods                               //

template<unsigned DIM>
void MeshBasedCellPopulation<DIM>::CreateOutputFiles(const std::string& rDirectory, bool cleanOutputDirectory)
{
    AbstractCentreBasedCellPopulation<DIM>::CreateOutputFiles(rDirectory, cleanOutputDirectory);

    OutputFileHandler output_file_handler(rDirectory, cleanOutputDirectory);
    mpVizElementsFile = output_file_handler.OpenOutputFile("results.vizelements");

    if (mOutputVoronoiData)
    {
        mpVoronoiFile = output_file_handler.OpenOutputFile("voronoi.dat");
    }
    if (mOutputCellPopulationVolumes)
    {
        mpCellPopulationVolumesFile = output_file_handler.OpenOutputFile("cellpopulationareas.dat");
    }
    if (this->mOutputCellVolumes)
    {
        mpCellVolumesFile = output_file_handler.OpenOutputFile("cellareas.dat");
    }
}

template<unsigned DIM>
void MeshBasedCellPopulation<DIM>::CloseOutputFiles()
{
    AbstractCentreBasedCellPopulation<DIM>::CloseOutputFiles();

    mpVizElementsFile->close();

    if (mOutputVoronoiData)
    {
        mpVoronoiFile->close();
    }
    if (mOutputCellPopulationVolumes)
    {
        mpCellPopulationVolumesFile->close();
    }
    if (this->mOutputCellVolumes)
    {
        mpCellVolumesFile->close();
    }
}

template<unsigned DIM>
void MeshBasedCellPopulation<DIM>::WriteResultsToFiles()
{
    AbstractCentreBasedCellPopulation<DIM>::WriteResultsToFiles();

    // Write element data to file
    *mpVizElementsFile << SimulationTime::Instance()->GetTime() << "\t";

    for (typename MutableMesh<DIM,DIM>::ElementIterator elem_iter = mrMesh.GetElementIteratorBegin();
         elem_iter != mrMesh.GetElementIteratorEnd();
         ++elem_iter)
    {
        bool element_contains_dead_cells_or_deleted_nodes = false;

        // Hack that covers the case where the element contains a node that is associated with a cell that has just been killed (#1129)
        for (unsigned i=0; i<DIM+1; i++)
        {
            unsigned node_index = elem_iter->GetNodeGlobalIndex(i);

            if (this->GetNode(node_index)->IsDeleted())
            {
                element_contains_dead_cells_or_deleted_nodes = true;
                break;
            }
            else if (this->mLocationCellMap[node_index])
            {
                if (this->mLocationCellMap[node_index]->IsDead())
                {
                    element_contains_dead_cells_or_deleted_nodes = true;
                    break;
                }
            }
        }
        if (!element_contains_dead_cells_or_deleted_nodes)
        {
            for (unsigned i=0; i<DIM+1; i++)
            {
                *mpVizElementsFile << elem_iter->GetNodeGlobalIndex(i) << " ";
            }
        }
    }
    *mpVizElementsFile << "\n";

    if (mpVoronoiTessellation != NULL)
    {
        if (mOutputVoronoiData)
        {
            WriteVoronoiResultsToFile();
        }
        if (mOutputCellPopulationVolumes)
        {
            WriteCellPopulationVolumeResultsToFile();
        }
        if (this->mOutputCellVolumes)
        {
            WriteCellVolumeResultsToFile();
        }
    }
}

template<unsigned DIM>
void MeshBasedCellPopulation<DIM>::WriteVtkResultsToFile()
{
#ifdef CHASTE_VTK
    // Write time to file
    std::stringstream time;
    time << SimulationTime::Instance()->GetTimeStepsElapsed();

    unsigned num_points = GetNumNodes();
    if (!mWriteVtkAsPoints && (mpVoronoiTessellation != NULL))
    {
        num_points = mpVoronoiTessellation->GetNumElements();
    }

    std::vector<double> cell_types(num_points);
    std::vector<double> cell_ancestors(num_points);
    std::vector<double> cell_mutation_states(num_points);
    std::vector<double> cell_ages(num_points);
    std::vector<double> cell_cycle_phases(num_points);
    std::vector<std::vector<double> > cellwise_data;

    if (CellwiseData<DIM>::Instance()->IsSetUp())
    {
        CellwiseData<DIM>* p_data = CellwiseData<DIM>::Instance();
        for (unsigned var=0; var<p_data->GetNumVariables(); var++)
        {
            std::vector<double> cellwise_data_var(num_points);
            cellwise_data.push_back(cellwise_data_var);
        }
    }

    if (mWriteVtkAsPoints)
    {
        VtkMeshWriter<DIM, DIM> mesh_writer(this->mDirPath, "results_"+time.str(), false);
    
        // Loop over cells
        for (typename AbstractCellPopulation<DIM>::Iterator cell_iter = this->Begin();
             cell_iter != this->End();
             ++cell_iter)
        {
            // Get the node index corresponding to this cell
            unsigned node_index = this->GetLocationIndexUsingCell(*cell_iter);
    
            // Get this cell-cycle model
            AbstractCellCycleModel* p_model = cell_iter->GetCellCycleModel();

            if (this->mOutputCellAncestors)
            {
                double ancestor_index = (cell_iter->GetAncestor() == UNSIGNED_UNSET) ? (-1.0) : (double)cell_iter->GetAncestor();
                cell_ancestors[node_index] = ancestor_index;
            }
            if (this->mOutputCellProliferativeTypes)
            {
                cell_types[node_index] = p_model->GetCellProliferativeType();
            }
            if (this->mOutputCellMutationStates)
            {
                cell_mutation_states[node_index] = cell_iter->GetMutationState()->GetColour();
            }
            if (this->mOutputCellAges)
            {
                cell_ages[node_index] = cell_iter->GetAge();
            }
            if (this->mOutputCellCyclePhases)
            {
                cell_cycle_phases[node_index] = p_model->GetCurrentCellCyclePhase();
            }
            if (CellwiseData<DIM>::Instance()->IsSetUp())
            {
                CellwiseData<DIM>* p_data = CellwiseData<DIM>::Instance();
                for (unsigned var=0; var<p_data->GetNumVariables(); var++)
                {
                    cellwise_data[var][node_index] = p_data->GetValue(*cell_iter, var);
                }
            }
        }

        if (this->mOutputCellProliferativeTypes)
        {
            mesh_writer.AddPointData("Cell types", cell_types);
        }
        if (this->mOutputCellAncestors)
        {
            mesh_writer.AddPointData("Ancestors", cell_ancestors);
        }
        if (this->mOutputCellMutationStates)
        {
            mesh_writer.AddPointData("Mutation states", cell_mutation_states);
        }
        if (this->mOutputCellAges)
        {
            mesh_writer.AddPointData("Ages", cell_ages);
        }
        if (this->mOutputCellCyclePhases)
        {
            mesh_writer.AddPointData("Cycle phases", cell_cycle_phases);
        }
        if (CellwiseData<DIM>::Instance()->IsSetUp())
        {
            for (unsigned var=0; var<cellwise_data.size(); var++)
            {
                std::stringstream data_name;
                data_name << "Cellwise data " << var;
                std::vector<double> cellwise_data_var = cellwise_data[var];
                mesh_writer.AddPointData(data_name.str(), cellwise_data_var);
            }
        }

        {
            // Make a copy of the nodes in a disposable mesh for writing
            std::vector<Node<DIM>* > nodes;
            for (unsigned index=0; index<mrMesh.GetNumNodes(); index++)
            {
                Node<DIM>* p_node = mrMesh.GetNode(index);
                nodes.push_back(p_node);
            }
            
            NodesOnlyMesh<DIM> mesh;
            mesh.ConstructNodesWithoutMesh(nodes);
            mesh_writer.WriteFilesUsingMesh(mesh);
        }

        *(this->mpVtkMetaFile) << "        <DataSet timestep=\"";
        *(this->mpVtkMetaFile) << SimulationTime::Instance()->GetTimeStepsElapsed();
        *(this->mpVtkMetaFile) << "\" group=\"\" part=\"0\" file=\"results_";
        *(this->mpVtkMetaFile) << SimulationTime::Instance()->GetTimeStepsElapsed();
        *(this->mpVtkMetaFile) << ".vtu\"/>\n";
    }
    else if (mpVoronoiTessellation != NULL)
    {
        VertexMeshWriter<DIM, DIM> mesh_writer(this->mDirPath, "results", false);
        std::vector<double> cell_volumes(num_points);
    
        // Loop over elements of mpVoronoiTessellation
        for (typename VertexMesh<DIM,DIM>::VertexElementIterator elem_iter = mpVoronoiTessellation->GetElementIteratorBegin();
             elem_iter != mpVoronoiTessellation->GetElementIteratorEnd();
             ++elem_iter)
        {
            // Get index of this element in mpVoronoiTessellation
            unsigned elem_index = elem_iter->GetIndex();
    
            // Get the index of the corresponding node in mrMesh
            unsigned node_index = mpVoronoiTessellation->GetDelaunayNodeIndexCorrespondingToVoronoiElementIndex(elem_index);
    
            // There should be no ghost nodes
            assert(!this->IsGhostNode(node_index));
    
            // Get the cell corresponding to this element
            CellPtr p_cell = this->mLocationCellMap[node_index];

            // Get this cell-cycle model
            AbstractCellCycleModel* p_model = p_cell->GetCellCycleModel();
    
            if (this->mOutputCellAncestors)
            {
                double ancestor_index = (p_cell->GetAncestor() == UNSIGNED_UNSET) ? (-1.0) : (double)p_cell->GetAncestor();
                cell_ancestors[elem_index] = ancestor_index;
            }
            if (this->mOutputCellProliferativeTypes)
            {
                cell_types[elem_index] = p_model->GetCellProliferativeType();
            }
            if (this->mOutputCellMutationStates)
            {
                cell_mutation_states[elem_index] = p_cell->GetMutationState()->GetColour();
            }
            if (this->mOutputCellAges)
            {
                cell_ages[elem_index] = p_cell->GetAge();
            }
            if (this->mOutputCellCyclePhases)
            {
                cell_cycle_phases[elem_index] = p_model->GetCurrentCellCyclePhase();
            }
            if (this->mOutputCellVolumes)
            {
                cell_volumes[elem_index] = mpVoronoiTessellation->GetVolumeOfElement(elem_index);
            }
            if (CellwiseData<DIM>::Instance()->IsSetUp())
            {
                CellwiseData<DIM>* p_data = CellwiseData<DIM>::Instance();
                for (unsigned var=0; var<p_data->GetNumVariables(); var++)
                {
                    cellwise_data[var][elem_index] = p_data->GetValue(p_cell, var);
                }
            }
        }
    
        if (this->mOutputCellProliferativeTypes)
        {
            mesh_writer.AddCellData("Cell types", cell_types);
        }
        if (this->mOutputCellAncestors)
        {
            mesh_writer.AddCellData("Ancestors", cell_ancestors);
        }
        if (this->mOutputCellMutationStates)
        {
            mesh_writer.AddCellData("Mutation states", cell_mutation_states);
        }
        if (this->mOutputCellAges)
        {
            mesh_writer.AddCellData("Ages", cell_ages);
        }
        if (this->mOutputCellCyclePhases)
        {
            mesh_writer.AddCellData("Cycle phases", cell_cycle_phases);
        }
        if (this->mOutputCellVolumes)
        {
            mesh_writer.AddCellData("Cell volumes", cell_volumes);
        }
        if (CellwiseData<DIM>::Instance()->IsSetUp())
        {
            for (unsigned var=0; var<cellwise_data.size(); var++)
            {
                std::stringstream data_name;
                data_name << "Cellwise data " << var;
                std::vector<double> cellwise_data_var = cellwise_data[var];
                mesh_writer.AddCellData(data_name.str(), cellwise_data_var);
            }
        }
    
        mesh_writer.WriteVtkUsingMesh(*mpVoronoiTessellation, time.str());
        *(this->mpVtkMetaFile) << "        <DataSet timestep=\"";
        *(this->mpVtkMetaFile) << SimulationTime::Instance()->GetTimeStepsElapsed();
        *(this->mpVtkMetaFile) << "\" group=\"\" part=\"0\" file=\"results_";
        *(this->mpVtkMetaFile) << SimulationTime::Instance()->GetTimeStepsElapsed();
        *(this->mpVtkMetaFile) << ".vtu\"/>\n";
    }
#endif //CHASTE_VTK
}

template<unsigned DIM>
void MeshBasedCellPopulation<DIM>::WriteVoronoiResultsToFile()
{
    assert(DIM==2 || DIM==3);

    // Write time to file
    *mpVoronoiFile << SimulationTime::Instance()->GetTime() << " ";

    // Loop over elements of mpVoronoiTessellation
    for (typename VertexMesh<DIM,DIM>::VertexElementIterator elem_iter = mpVoronoiTessellation->GetElementIteratorBegin();
         elem_iter != mpVoronoiTessellation->GetElementIteratorEnd();
         ++elem_iter)
    {
        // Get index of this element in mpVoronoiTessellation
        unsigned elem_index = elem_iter->GetIndex();

        // Get the index of the corresponding node in mrMesh
        unsigned node_index = mpVoronoiTessellation->GetDelaunayNodeIndexCorrespondingToVoronoiElementIndex(elem_index);

        // Write node index and location to file
        *mpVoronoiFile << node_index << " ";
        c_vector<double, DIM> node_location = this->GetNode(node_index)->rGetLocation();
        for (unsigned i=0; i<DIM; i++)
        {
            *mpVoronoiFile << node_location[i] << " ";
        }

        double cell_volume = mpVoronoiTessellation->GetVolumeOfElement(elem_index);
        double cell_surface_area = mpVoronoiTessellation->GetSurfaceAreaOfElement(elem_index);
        *mpVoronoiFile << cell_volume << " " << cell_surface_area << " ";
    }
    *mpVoronoiFile << "\n";
}

template<unsigned DIM>
void MeshBasedCellPopulation<DIM>::WriteCellPopulationVolumeResultsToFile()
{
    assert(DIM==2 || DIM==3);

    // Write time to file
    *mpCellPopulationVolumesFile << SimulationTime::Instance()->GetTime() << " ";

    // Don't use the Voronoi tessellation to calculate the total area of the mesh because it gives huge areas for boundary cells
    double total_area = mrMesh.GetVolume();
    double apoptotic_area = 0.0;

    // Loop over elements of mpVoronoiTessellation
    for (typename VertexMesh<DIM,DIM>::VertexElementIterator elem_iter = mpVoronoiTessellation->GetElementIteratorBegin();
         elem_iter != mpVoronoiTessellation->GetElementIteratorEnd();
         ++elem_iter)
    {
        // Get index of this element in mpVoronoiTessellation
        unsigned elem_index = elem_iter->GetIndex();

        // Get the index of the corresponding node in mrMesh
        unsigned node_index = mpVoronoiTessellation->GetDelaunayNodeIndexCorrespondingToVoronoiElementIndex(elem_index);

        // Discount ghost nodes
        if (!this->IsGhostNode(node_index))
        {
            // Get the cell corresponding to this node
            CellPtr p_cell =  this->mLocationCellMap[node_index];

            // Only bother calculating the area/volume of apoptotic cells
            bool cell_is_apoptotic = p_cell->HasCellProperty<ApoptoticCellProperty>();
            if (cell_is_apoptotic)
            {
                double cell_volume = mpVoronoiTessellation->GetVolumeOfElement(elem_index);
                apoptotic_area += cell_volume;
            }
        }
    }
    *mpCellPopulationVolumesFile << total_area << " " << apoptotic_area << "\n";
}

template<unsigned DIM>
void MeshBasedCellPopulation<DIM>::WriteCellVolumeResultsToFile()
{
    assert(DIM==2 || DIM==3);

     // Write time to file
    *mpCellVolumesFile << SimulationTime::Instance()->GetTime() << " ";

    // Loop over elements of mpVoronoiTessellation
    for (typename VertexMesh<DIM,DIM>::VertexElementIterator elem_iter = mpVoronoiTessellation->GetElementIteratorBegin();
         elem_iter != mpVoronoiTessellation->GetElementIteratorEnd();
         ++elem_iter)
    {
        // Get index of this element in mpVoronoiTessellation
        unsigned elem_index = elem_iter->GetIndex();

        // Get the index of the corresponding node in mrMesh
        unsigned node_index = mpVoronoiTessellation->GetDelaunayNodeIndexCorrespondingToVoronoiElementIndex(elem_index);

        // Discount ghost nodes
        if (!this->IsGhostNode(node_index))
        {
            // Write node index to file
            *mpCellVolumesFile << node_index << " ";

            // Get the cell corresponding to this node
            CellPtr p_cell =  this->mLocationCellMap[node_index];

            // Write cell ID to file
            unsigned cell_index = p_cell->GetCellId();
            *mpCellVolumesFile << cell_index << " ";

            // Write node location to file
            c_vector<double, DIM> node_location = this->GetNode(node_index)->rGetLocation();
            for (unsigned i=0; i<DIM; i++)
            {
                *mpCellVolumesFile << node_location[i] << " ";
            }

            // Write cell volume (in 3D) or area (in 2D) to file
            double cell_volume = mpVoronoiTessellation->GetVolumeOfElement(elem_index);
            *mpCellVolumesFile << cell_volume << " ";
        }
    }
    *mpCellVolumesFile << "\n";
}

template<unsigned DIM>
void MeshBasedCellPopulation<DIM>::SetWriteVtkAsPoints(bool writeVtkAsPoints)
{
    mWriteVtkAsPoints = writeVtkAsPoints;
}

template<unsigned DIM>
bool MeshBasedCellPopulation<DIM>::GetWriteVtkAsPoints()
{
    return mWriteVtkAsPoints;
}

//                          Spring iterator class                           //

template<unsigned DIM>
Node<DIM>* MeshBasedCellPopulation<DIM>::SpringIterator::GetNodeA()
{
    return mEdgeIter.GetNodeA();
}

template<unsigned DIM>
Node<DIM>* MeshBasedCellPopulation<DIM>::SpringIterator::GetNodeB()
{
    return mEdgeIter.GetNodeB();
}

template<unsigned DIM>
CellPtr MeshBasedCellPopulation<DIM>::SpringIterator::GetCellA()
{
    assert((*this) != mrCellPopulation.SpringsEnd());
    return mrCellPopulation.GetCellUsingLocationIndex(mEdgeIter.GetNodeA()->GetIndex());
}

template<unsigned DIM>
CellPtr MeshBasedCellPopulation<DIM>::SpringIterator::GetCellB()
{
    assert((*this) != mrCellPopulation.SpringsEnd());
    return mrCellPopulation.GetCellUsingLocationIndex(mEdgeIter.GetNodeB()->GetIndex());
}

template<unsigned DIM>
bool MeshBasedCellPopulation<DIM>::SpringIterator::operator!=(const MeshBasedCellPopulation<DIM>::SpringIterator& rOther)
{
    return (mEdgeIter != rOther.mEdgeIter);
}

template<unsigned DIM>
typename MeshBasedCellPopulation<DIM>::SpringIterator& MeshBasedCellPopulation<DIM>::SpringIterator::operator++()
{
    bool edge_is_ghost = false;

    do
    {
        ++mEdgeIter;
        if (*this != mrCellPopulation.SpringsEnd())
        {
            bool a_is_ghost = mrCellPopulation.IsGhostNode(mEdgeIter.GetNodeA()->GetIndex());
            bool b_is_ghost = mrCellPopulation.IsGhostNode(mEdgeIter.GetNodeB()->GetIndex());

            edge_is_ghost = (a_is_ghost || b_is_ghost);
        }
    }
    while (*this!=mrCellPopulation.SpringsEnd() && edge_is_ghost);

    return (*this);
}

template<unsigned DIM>
MeshBasedCellPopulation<DIM>::SpringIterator::SpringIterator(
            MeshBasedCellPopulation<DIM>& rCellPopulation,
            typename MutableMesh<DIM,DIM>::EdgeIterator edgeIter)
    : mrCellPopulation(rCellPopulation),
      mEdgeIter(edgeIter)
{
    if (mEdgeIter!=mrCellPopulation.mrMesh.EdgesEnd())
    {
        bool a_is_ghost = mrCellPopulation.IsGhostNode(mEdgeIter.GetNodeA()->GetIndex());
        bool b_is_ghost = mrCellPopulation.IsGhostNode(mEdgeIter.GetNodeB()->GetIndex());

        if (a_is_ghost || b_is_ghost)
        {
            ++(*this);
        }
    }
}

template<unsigned DIM>
typename MeshBasedCellPopulation<DIM>::SpringIterator MeshBasedCellPopulation<DIM>::SpringsBegin()
{
    return SpringIterator(*this, mrMesh.EdgesBegin());
}

template<unsigned DIM>
typename MeshBasedCellPopulation<DIM>::SpringIterator MeshBasedCellPopulation<DIM>::SpringsEnd()
{
    return SpringIterator(*this, mrMesh.EdgesEnd());
}

template<>
void MeshBasedCellPopulation<2>::CreateVoronoiTessellation()
{
    delete mpVoronoiTessellation;

    // Check if the mesh associated with this cell population is periodic
    bool is_mesh_periodic = false;
    if (dynamic_cast<Cylindrical2dMesh*>(&mrMesh))
    {
        is_mesh_periodic = true;
    }

    mpVoronoiTessellation = new VertexMesh<2, 2>(mrMesh, is_mesh_periodic);
}

template<>
void MeshBasedCellPopulation<3>::CreateVoronoiTessellation()
{
    delete mpVoronoiTessellation;
    mpVoronoiTessellation = new VertexMesh<3, 3>(mrMesh);
}

template<>
void MeshBasedCellPopulation<1>::CreateVoronoiTessellation()
{
    // No 1D Voronoi tessellation
    NEVER_REACHED;
}

template<unsigned DIM>
VertexMesh<DIM, DIM>* MeshBasedCellPopulation<DIM>::GetVoronoiTessellation()
{
    assert(mpVoronoiTessellation!=NULL);
    return mpVoronoiTessellation;
}

template<unsigned DIM>
double MeshBasedCellPopulation<DIM>::GetVolumeOfVoronoiElement(unsigned index)
{
    unsigned element_index = mpVoronoiTessellation->GetVoronoiElementIndexCorrespondingToDelaunayNodeIndex(index);
    double volume = mpVoronoiTessellation->GetVolumeOfElement(element_index);
    return volume;
}

template<unsigned DIM>
double MeshBasedCellPopulation<DIM>::GetSurfaceAreaOfVoronoiElement(unsigned index)
{
    unsigned element_index = mpVoronoiTessellation->GetVoronoiElementIndexCorrespondingToDelaunayNodeIndex(index);
    double surface_area = mpVoronoiTessellation->GetSurfaceAreaOfElement(element_index);
    return surface_area;
}

template<unsigned DIM>
double MeshBasedCellPopulation<DIM>::GetVoronoiEdgeLength(unsigned index1, unsigned index2)
{
    unsigned element_index1 = mpVoronoiTessellation->GetVoronoiElementIndexCorrespondingToDelaunayNodeIndex(index1);
    unsigned element_index2 = mpVoronoiTessellation->GetVoronoiElementIndexCorrespondingToDelaunayNodeIndex(index2);
    double edge_length = mpVoronoiTessellation->GetEdgeLength(element_index1, element_index2);
    return edge_length;
}

template<unsigned DIM>
void MeshBasedCellPopulation<DIM>::CheckCellPointers()
{
    bool res = true;
    for (std::list<CellPtr>::iterator it=this->mCells.begin();
         it!=this->mCells.end();
         ++it)
    {
        CellPtr p_cell = *it;
        assert(p_cell);
        AbstractCellCycleModel* p_model = p_cell->GetCellCycleModel();
        assert(p_model);

        // Check cell exists in cell population
        unsigned node_index = this->mCellLocationMap[p_cell.get()];
        std::cout << "Cell at node " << node_index << " addr " << p_cell << std::endl << std::flush;
        CellPtr p_cell_in_cell_population = this->GetCellUsingLocationIndex(node_index);
#define COVERAGE_IGNORE //Debugging code.  Shouldn't fail under normal conditions
        if (p_cell_in_cell_population != p_cell)
        {
            std::cout << "  Mismatch with cell population" << std::endl << std::flush;
            res = false;
        }

        // Check model links back to cell
        if (p_model->GetCell() != p_cell)
        {
            std::cout << "  Mismatch with cycle model" << std::endl << std::flush;
            res = false;
        }
    }
    assert(res);
#undef COVERAGE_IGNORE

    res = true;
    for (std::set<std::pair<CellPtr,CellPtr> >::iterator it1 = mMarkedSprings.begin();
         it1 != mMarkedSprings.end();
         ++it1)
    {
        const std::pair<CellPtr,CellPtr>& r_pair = *it1;

        for (unsigned i=0; i<2; i++)
        {
            CellPtr p_cell = (i==0 ? r_pair.first : r_pair.second);

            assert(p_cell);
            AbstractCellCycleModel* p_model = p_cell->GetCellCycleModel();
            assert(p_model);
            unsigned node_index = this->mCellLocationMap[p_cell.get()];
            std::cout << "Cell at node " << node_index << " addr " << p_cell << std::endl << std::flush;

#define COVERAGE_IGNORE //Debugging code.  Shouldn't fail under normal conditions
            // Check cell is alive
            if (p_cell->IsDead())
            {
                std::cout << "  Cell is dead" << std::endl << std::flush;
                res = false;
            }

            // Check cell exists in cell population
            CellPtr p_cell_in_cell_population = this->GetCellUsingLocationIndex(node_index);
            if (p_cell_in_cell_population != p_cell)
            {
                std::cout << "  Mismatch with cell population" << std::endl << std::flush;
                res = false;
            }

            // Check model links back to cell
            if (p_model->GetCell() != p_cell)
            {
                std::cout << "  Mismatch with cycle model" << std::endl << std::flush;
                res = false;
            }
        }
#undef COVERAGE_IGNORE
    }
    assert(res);
}

template<unsigned DIM>
std::pair<CellPtr,CellPtr> MeshBasedCellPopulation<DIM>::CreateCellPair(CellPtr pCell1, CellPtr pCell2)
{
    assert(pCell1);
    assert(pCell2);

    std::pair<CellPtr,CellPtr> cell_pair;

    if (pCell1->GetCellId() < pCell2->GetCellId())
    {
        cell_pair.first = pCell1;
        cell_pair.second = pCell2;
    }
    else
    {
        cell_pair.first = pCell2;
        cell_pair.second = pCell1;
    }
    return cell_pair;
}

template<unsigned DIM>
bool MeshBasedCellPopulation<DIM>::IsMarkedSpring(const std::pair<CellPtr,CellPtr>& rCellPair)
{
    // the pair should be ordered like this (CreateCellPair will ensure this)
    assert(rCellPair.first->GetCellId() < rCellPair.second->GetCellId());

    return mMarkedSprings.find(rCellPair) != mMarkedSprings.end();
}

template<unsigned DIM>
void MeshBasedCellPopulation<DIM>::MarkSpring(std::pair<CellPtr,CellPtr>& rCellPair)
{
    // the pair should be ordered like this (CreateCellPair will ensure this)
    assert(rCellPair.first->GetCellId() < rCellPair.second->GetCellId());

    mMarkedSprings.insert(rCellPair);
}

template<unsigned DIM>
void MeshBasedCellPopulation<DIM>::UnmarkSpring(std::pair<CellPtr,CellPtr>& rCellPair)
{
    // the pair should be ordered like this (CreateCellPair will ensure this)
    assert(rCellPair.first->GetCellId() < rCellPair.second->GetCellId());

    mMarkedSprings.erase(rCellPair);
}

template<unsigned DIM>
double MeshBasedCellPopulation<DIM>::GetAreaBasedDampingConstantParameter()
{
    return mAreaBasedDampingConstantParameter;
}

template<unsigned DIM>
void MeshBasedCellPopulation<DIM>::SetAreaBasedDampingConstantParameter(double areaBasedDampingConstantParameter)
{
    assert(areaBasedDampingConstantParameter >= 0.0);
    mAreaBasedDampingConstantParameter = areaBasedDampingConstantParameter;
}

template<unsigned DIM>
bool MeshBasedCellPopulation<DIM>::GetOutputVoronoiData()
{
    return mOutputVoronoiData;
}

template<unsigned DIM>
void MeshBasedCellPopulation<DIM>::SetOutputVoronoiData(bool outputVoronoiData)
{
    mOutputVoronoiData = outputVoronoiData;
}

template<unsigned DIM>
bool MeshBasedCellPopulation<DIM>::GetOutputCellPopulationVolumes()
{
    return mOutputCellPopulationVolumes;
}

template<unsigned DIM>
void MeshBasedCellPopulation<DIM>::SetOutputCellPopulationVolumes(bool outputCellPopulationVolumes)
{
    mOutputCellPopulationVolumes = outputCellPopulationVolumes;
}

template<unsigned DIM>
void MeshBasedCellPopulation<DIM>::OutputCellPopulationParameters(out_stream& rParamsFile)
{
    *rParamsFile << "\t\t<UseAreaBasedDampingConstant>" << mUseAreaBasedDampingConstant << "</UseAreaBasedDampingConstant> \n";
    *rParamsFile << "\t\t<AreaBasedDampingConstantParameter>" <<  mAreaBasedDampingConstantParameter << "</AreaBasedDampingConstantParameter> \n";
    *rParamsFile << "\t\t<OutputVoronoiData>" <<  mOutputVoronoiData << "</OutputVoronoiData> \n";
    *rParamsFile << "\t\t<OutputCellPopulationVolumes>" << mOutputCellPopulationVolumes << "</OutputCellPopulationVolumes> \n";

    // Call method on direct parent class
    AbstractCentreBasedCellPopulation<DIM>::OutputCellPopulationParameters(rParamsFile);
}

template<unsigned DIM>
double MeshBasedCellPopulation<DIM>::GetWidth(const unsigned& rDimension)
{
    // Call GetWidth() on the mesh
    double width = mrMesh.GetWidth(rDimension);
    return width;
}

// Explicit instantiation

template class MeshBasedCellPopulation<1>;
template class MeshBasedCellPopulation<2>;
template class MeshBasedCellPopulation<3>;

// Serialization for Boost >= 1.36
#include "SerializationExportWrapperForCpp.hpp"
EXPORT_TEMPLATE_CLASS_SAME_DIMS(MeshBasedCellPopulation)

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