VertexBasedCellPopulation.cpp

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*/
 
#include "VertexBasedCellPopulation.hpp"
#include "Warnings.hpp"
#include "ShortAxisVertexBasedDivisionRule.hpp"
#include "StepSizeException.hpp"
#include "WildTypeCellMutationState.hpp"
#include "Cylindrical2dVertexMesh.hpp"
#include "SmartPointers.hpp"
#include "T2SwapCellKiller.hpp"
#include "ApoptoticCellProperty.hpp"
#include "CellPopulationElementWriter.hpp"
#include "VertexT1SwapLocationsWriter.hpp"
#include "VertexT2SwapLocationsWriter.hpp"
#include "VertexT3SwapLocationsWriter.hpp"
#include "VertexIntersectionSwapLocationsWriter.hpp"
#include "AbstractCellBasedSimulation.hpp"
 
template<unsigned DIM>
VertexBasedCellPopulation<DIM>::VertexBasedCellPopulation(MutableVertexMesh<DIM, DIM>& rMesh,
                                          std::vector<CellPtr>& rCells,
                                          bool deleteMesh,
                                          bool validate,
                                          const std::vector<unsigned> locationIndices)
    : AbstractOffLatticeCellPopulation<DIM>(rMesh, rCells, locationIndices),
      mDeleteMesh(deleteMesh),
      mOutputCellRearrangementLocations(true),
      mRestrictVertexMovement(true)
{
    mpMutableVertexMesh = static_cast<MutableVertexMesh<DIM, DIM>* >(&(this->mrMesh));
    mpVertexBasedDivisionRule.reset(new ShortAxisVertexBasedDivisionRule<DIM>());
 
    // If no location indices are specified, associate with elements from the mesh (assumed to be sequentially ordered).
    std::list<CellPtr>::iterator it = this->mCells.begin();
    for (unsigned i=0; it != this->mCells.end(); ++it, ++i)
    {
        unsigned index = locationIndices.empty() ? i : locationIndices[i]; // assume that the ordering matches
        AbstractCellPopulation<DIM, DIM>::AddCellUsingLocationIndex(index,*it);
    }
 
    // Check each element has only one cell attached
    if (validate)
    {
        Validate();
    }
 
    // If cells contain an SRN model, then we need to track mesh operations
    // and update SRNs accordingly. Here we assume the first cell is a representative of other cells
    if ((*this->mCells.begin())->HasSrnModel())
    {
        mPopulationSrn.SetVertexCellPopulation(this);
        mpMutableVertexMesh->SetMeshOperationTracking(true);
    }
}
 
template<unsigned DIM>
VertexBasedCellPopulation<DIM>::VertexBasedCellPopulation(MutableVertexMesh<DIM, DIM>& rMesh,
                                                          VertexBasedPopulationSrn<DIM>& rPopSrn)
    : AbstractOffLatticeCellPopulation<DIM>(rMesh),
      mDeleteMesh(true),
      mOutputCellRearrangementLocations(true),
      mRestrictVertexMovement(true),
      mPopulationSrn(rPopSrn)
{
    mpMutableVertexMesh = static_cast<MutableVertexMesh<DIM, DIM>* >(&(this->mrMesh));
    mPopulationSrn.SetVertexCellPopulation(this);
}
 
template<unsigned DIM>
VertexBasedCellPopulation<DIM>::~VertexBasedCellPopulation()
{
    if (mDeleteMesh)
    {
        delete &this->mrMesh;
    }
}
 
template<unsigned DIM>
double VertexBasedCellPopulation<DIM>::GetDampingConstant(unsigned nodeIndex)
{
    // Take the average of the cells containing this vertex
    double average_damping_constant = 0.0;
 
    std::set<unsigned> containing_elements = GetNode(nodeIndex)->rGetContainingElementIndices();
 
    unsigned num_containing_elements = containing_elements.size();
    if (num_containing_elements == 0)
    {
        EXCEPTION("At time " << SimulationTime::Instance()->GetTime() << ", Node " << nodeIndex << " is not contained in any elements, so GetDampingConstant() returns zero");
    }
 
    double temp = 1.0/((double) num_containing_elements);
    for (std::set<unsigned>::iterator iter = containing_elements.begin();
         iter != containing_elements.end();
         ++iter)
    {
        CellPtr p_cell = this->GetCellUsingLocationIndex(*iter);
        bool cell_is_wild_type = p_cell->GetMutationState()->IsType<WildTypeCellMutationState>();
 
        if (cell_is_wild_type)
        {
            average_damping_constant += this->GetDampingConstantNormal()*temp;
        }
        else
        {
            average_damping_constant += this->GetDampingConstantMutant()*temp;
        }
    }
 
    return average_damping_constant;
}
 
template<unsigned DIM>
MutableVertexMesh<DIM, DIM>& VertexBasedCellPopulation<DIM>::rGetMesh()
{
    return *mpMutableVertexMesh;
}
 
template<unsigned DIM>
const MutableVertexMesh<DIM, DIM>& VertexBasedCellPopulation<DIM>::rGetMesh() const
{
    return *mpMutableVertexMesh;
}
 
template<unsigned DIM>
VertexElement<DIM, DIM>* VertexBasedCellPopulation<DIM>::GetElement(unsigned elementIndex)
{
    return mpMutableVertexMesh->GetElement(elementIndex);
}
 
template<unsigned DIM>
unsigned VertexBasedCellPopulation<DIM>::GetNumNodes()
{
    return this->mrMesh.GetNumNodes();
}
 
template<unsigned DIM>
c_vector<double, DIM> VertexBasedCellPopulation<DIM>::GetLocationOfCellCentre(CellPtr pCell)
{
    return mpMutableVertexMesh->GetCentroidOfElement(this->mCellLocationMap[pCell.get()]);
}
 
template<unsigned DIM>
Node<DIM>* VertexBasedCellPopulation<DIM>::GetNode(unsigned index)
{
    return this->mrMesh.GetNode(index);
}
 
template<unsigned DIM>
std::set<unsigned> VertexBasedCellPopulation<DIM>::GetNeighbouringLocationIndices(CellPtr pCell)
{
    unsigned elem_index = this->GetLocationIndexUsingCell(pCell);
    return this->rGetMesh().GetNeighbouringElementIndices(elem_index);
}
 
template<unsigned DIM>
std::set<std::pair<unsigned, unsigned>>
VertexBasedCellPopulation<DIM>::GetNeighbouringEdgeIndices(CellPtr pCell, unsigned edgeLocalIndex)
{
    std::set<std::pair<unsigned, unsigned>> neighbours;
    auto cellLocationIndex = this->GetLocationIndexUsingCell(pCell);
    auto p_element = this->GetElement(cellLocationIndex);
    auto global_edge_index = p_element->GetEdgeGlobalIndex(edgeLocalIndex);
    auto neighbour_element_indices = p_element->GetNeighbouringElementAtEdgeIndex(edgeLocalIndex);
 
    // Normally there is only one neighbouring element
    for (auto neighbour_element_index : neighbour_element_indices)
    {
        auto p_neighbour_element = this->GetElement(neighbour_element_index);
 
        // Iterate over neighbouring element indices
        for (unsigned elem_index = 0; elem_index < p_neighbour_element->GetNumEdges(); elem_index++)
        {
            // If the neighbours edge matches EdgeLocalIndex
            if (p_neighbour_element->GetEdge(elem_index)->GetIndex() == global_edge_index)
            {
                neighbours.insert(std::pair<unsigned, unsigned>(neighbour_element_index, elem_index));
            }
        }
    }
 
    return neighbours;
}
 
template<unsigned DIM>
unsigned VertexBasedCellPopulation<DIM>::AddNode(Node<DIM>* pNewNode)
{
    return mpMutableVertexMesh->AddNode(pNewNode);
}
 
template<unsigned DIM>
void VertexBasedCellPopulation<DIM>::SetNode(unsigned nodeIndex, ChastePoint<DIM>& rNewLocation)
{
    mpMutableVertexMesh->SetNode(nodeIndex, rNewLocation);
}
 
template<unsigned DIM>
VertexElement<DIM, DIM>* VertexBasedCellPopulation<DIM>::GetElementCorrespondingToCell(CellPtr pCell)
{
    return mpMutableVertexMesh->GetElement(this->GetLocationIndexUsingCell(pCell));
}
 
template<unsigned DIM>
unsigned VertexBasedCellPopulation<DIM>::GetNumElements()
{
    return mpMutableVertexMesh->GetNumElements();
}
 
template<unsigned DIM>
CellPtr VertexBasedCellPopulation<DIM>::AddCell(CellPtr pNewCell, CellPtr pParentCell)
{
    // Get the element associated with this cell
    VertexElement<DIM, DIM>* p_element = GetElementCorrespondingToCell(pParentCell);
 
    // Get the orientation of division
    c_vector<double, DIM> division_vector = mpVertexBasedDivisionRule->CalculateCellDivisionVector(pParentCell, *this);
 
    // Divide the element
    unsigned new_element_index = mpMutableVertexMesh->DivideElementAlongGivenAxis(p_element, division_vector, true);
 
    // Associate the new cell with the element
    this->mCells.push_back(pNewCell);
 
    // Update location cell map
    CellPtr p_created_cell = this->mCells.back();
    this->SetCellUsingLocationIndex(new_element_index,p_created_cell);
    this->mCellLocationMap[p_created_cell.get()] = new_element_index;
 
    return p_created_cell;
}
 
template<unsigned DIM>
unsigned VertexBasedCellPopulation<DIM>::RemoveDeadCells()
{
    unsigned num_removed = 0;
 
    for (std::list<CellPtr>::iterator it = this->mCells.begin();
         it != this->mCells.end();
         )
    {
        if ((*it)->IsDead())
        {
            // Count the cell as dead
            num_removed++;
 
            // Remove the element from the mesh if it is not deleted yet
            if (!(this->GetElement(this->GetLocationIndexUsingCell((*it)))->IsDeleted()))
            {
                // This warning relies on the fact that there is only one other possibility for
                // vertex elements to be marked as deleted: a T2 swap
                WARN_ONCE_ONLY("A Cell is removed without performing a T2 swap. This could leave a void in the mesh.");
                mpMutableVertexMesh->DeleteElementPriorToReMesh(this->GetLocationIndexUsingCell((*it)));
            }
 
            // Delete the cell
            it = this->mCells.erase(it);
        }
        else
        {
            ++it;
        }
    }
    return num_removed;
}
 
template<unsigned DIM>
void VertexBasedCellPopulation<DIM>::CheckForStepSizeException(unsigned nodeIndex, c_vector<double,DIM>& rDisplacement, double dt)
{
    double length = norm_2(rDisplacement);
 
    /* There are two reasons to adjust movement in a vertex model:
     * - either the movement is large enough to cause a T2 swap,
     * - or the movement is too large (i.e. larger than AbsoluteMovementThreshold).
     *
     * In the first case we want to restrict movement but not throw an exception, just a warning.
     * In the second case we want to throw an exception which can be used by the adaptive timestepper.
     * This is handled in the parent class, which checks for movement above the AbsoluteMovementThreshold
     * and throws an exception. In this class we check for movement above half the CellRearrangementThreshold
     * and restrict movement if this is the case, but only throw an exception if movement is above the
     * AbsoluteMovementThreshold.
     */
 
    // Check for movement above the AbsoluteMovementThreshold first, and throw an exception if exceeded
    AbstractOffLatticeCellPopulation<DIM, DIM>::CheckForStepSizeException(nodeIndex, rDisplacement, dt);
 
    if (mRestrictVertexMovement)
    {
        if (length > 0.5*mpMutableVertexMesh->GetCellRearrangementThreshold())
        {
            // restrict the movement
            rDisplacement *= 0.5*mpMutableVertexMesh->GetCellRearrangementThreshold()/length;
 
            WARN_ONCE_ONLY("Vertices are moving more than half the CellRearrangementThreshold. This could cause elements to become inverted so the motion has been restricted. Use a smaller timestep to avoid these warnings.");
        }
    }
}
 
template<unsigned DIM>
bool VertexBasedCellPopulation<DIM>::IsCellAssociatedWithADeletedLocation(CellPtr pCell)
{
    return GetElementCorrespondingToCell(pCell)->IsDeleted();
}
 
template<unsigned DIM>
void VertexBasedCellPopulation<DIM>::Update(bool hasHadBirthsOrDeaths)
{
    VertexElementMap element_map(mpMutableVertexMesh->GetNumAllElements());
    mpMutableVertexMesh->ReMesh(element_map);
 
    if (!element_map.IsIdentityMap())
    {
        // Fix up the mappings between CellPtrs and VertexElements
        std::map<Cell*, unsigned> old_map = this->mCellLocationMap;
 
        this->mCellLocationMap.clear();
        this->mLocationCellMap.clear();
 
        for (std::list<CellPtr>::iterator cell_iter = this->mCells.begin();
             cell_iter != this->mCells.end();
             ++cell_iter)
        {
            // The cell vector should only ever contain living cells
            unsigned old_elem_index = old_map[(*cell_iter).get()];
            assert(!element_map.IsDeleted(old_elem_index));
 
            unsigned new_elem_index = element_map.GetNewIndex(old_elem_index);
            this->SetCellUsingLocationIndex(new_elem_index, *cell_iter);
        }
 
        // Check that each VertexElement has only one CellPtr associated with it in the updated cell population
        Validate();
    }
 
    if (this->GetNumAllCells()>0)
    {
        //First cell is representative of other cells
        bool EdgeModelOrNot = (*this->mCells.begin())->GetSrnModel()->HasEdgeModel();
 
        if (EdgeModelOrNot)
        {
            // Note that SRN initialisation in daughter cell is handled through Cell::Divide() method
            mPopulationSrn.UpdateSrnAfterBirthOrDeath(element_map);
        }
    }
 
    element_map.ResetToIdentity();
}
 
template<unsigned DIM>
void VertexBasedCellPopulation<DIM>::Validate()
{
    // Check each element has only one cell attached
    std::vector<unsigned> validated_element = std::vector<unsigned>(this->GetNumElements(), 0);
    for (typename AbstractCellPopulation<DIM>::Iterator cell_iter = this->Begin();
         cell_iter != this->End();
         ++cell_iter)
    {
        unsigned elem_index = this->GetLocationIndexUsingCell(*cell_iter);
        validated_element[elem_index]++;
    }
 
    for (unsigned i=0; i<validated_element.size(); i++)
    {
        if (validated_element[i] == 0)
        {
            EXCEPTION("At time " << SimulationTime::Instance()->GetTime() <<", Element " << i << " does not appear to have a cell associated with it");
        }
 
        if (validated_element[i] > 1)
        {
            // This should never be reached as you can only set one cell per element index
            EXCEPTION("At time " << SimulationTime::Instance()->GetTime() <<", Element " << i << " appears to have " << validated_element[i] << " cells associated with it");
        }
    }
}
 
template<unsigned DIM>
void VertexBasedCellPopulation<DIM>::AcceptPopulationWriter(boost::shared_ptr<AbstractCellPopulationWriter<DIM, DIM> > pPopulationWriter)
{
    pPopulationWriter->Visit(this);
}
 
template<unsigned DIM>
void VertexBasedCellPopulation<DIM>::AcceptPopulationCountWriter(boost::shared_ptr<AbstractCellPopulationCountWriter<DIM, DIM> > pPopulationCountWriter)
{
    pPopulationCountWriter->Visit(this);
}
 
template<unsigned DIM>
void VertexBasedCellPopulation<DIM>::AcceptPopulationEventWriter(boost::shared_ptr<AbstractCellPopulationEventWriter<DIM, DIM> > pPopulationEventWriter)
{
    pPopulationEventWriter->Visit(this);
}
 
template<unsigned DIM>
void VertexBasedCellPopulation<DIM>::AcceptCellWriter(boost::shared_ptr<AbstractCellWriter<DIM, DIM> > pCellWriter, CellPtr pCell)
{
    pCellWriter->VisitCell(pCell, this);
}
 
template<unsigned DIM>
unsigned VertexBasedCellPopulation<DIM>::GetRosetteRankOfCell(CellPtr pCell)
{
    // Get the vertex element index corresponding to this cell
    unsigned elem_index = this->GetLocationIndexUsingCell(pCell);
 
    // Get the element rosette rank from the vertex mesh
    unsigned rosette_rank = mpMutableVertexMesh->GetRosetteRankOfElement(elem_index);
 
    return rosette_rank;
}
 
template<unsigned DIM>
double VertexBasedCellPopulation<DIM>::GetVolumeOfCell(CellPtr pCell)
{
    // Get the vertex element index corresponding to this cell
    unsigned elem_index = this->GetLocationIndexUsingCell(pCell);
 
    // Get the cell's volume from the vertex mesh
    double cell_volume = mpMutableVertexMesh->GetVolumeOfElement(elem_index);
 
    return cell_volume;
}
 
template<unsigned DIM>
void VertexBasedCellPopulation<DIM>::WriteVtkResultsToFile(const std::string& rDirectory)
{
    unsigned num_cells = this->GetNumAllCells();
    if (num_cells>0)
    {
        auto cells = this->rGetCells();
        boost::shared_ptr<CellEdgeData> p_cell_edge_data = (*cells.begin())->GetCellEdgeData();
        //If edge SRNs are specified, then write vtk results into a mesh where quantities
        //associated with each edge are taken into account. We assume that the first cell is
        //representative of all cells.
        //Edge VTKs are also written if cells contain CellEdgeData
 
        //If cells contain edge data
        if (p_cell_edge_data->GetNumItems() != 0&&mWriteEdgeVtkResults)
        {
            this->WriteCellEdgeVtkResultsToFile(rDirectory);
            return;
        }
 
        //If cells don't contain edge data, output CellData only
        if (p_cell_edge_data->GetNumItems() == 0&&mWriteCellVtkResults)
        {
            this->WriteCellVtkResultsToFile(rDirectory);
        }
    }
}
 
template<unsigned DIM>
void VertexBasedCellPopulation<DIM>::WriteCellVtkResultsToFile(const std::string& rDirectory)
{
#ifdef CHASTE_VTK
 
    // Create mesh writer for VTK output
    VertexMeshWriter<DIM, DIM> mesh_writer(rDirectory, "results", false);
 
    // We avoid writing out CellData if the population is empty (i.e. no cells).
    unsigned num_cells = this->GetNumAllCells();
 
    if (num_cells > 0)
    {
        // Iterate over any cell writers that are present
        for (auto cell_writer_iter = this->mCellWriters.begin();
             cell_writer_iter != this->mCellWriters.end();
             ++cell_writer_iter)
        {
            // Create vector to store VTK cell data
            std::vector<double> vtk_cell_data(num_cells);
 
            // Iterate over vertex elements ///\todo #2512 - replace with loop over cells
            for (auto elem_iter = mpMutableVertexMesh->GetElementIteratorBegin();
                 elem_iter != mpMutableVertexMesh->GetElementIteratorEnd();
                 ++elem_iter)
            {
                // Get index of this element in the vertex mesh
                unsigned elem_index = elem_iter->GetIndex();
 
                // Get the cell corresponding to this element
                CellPtr p_cell = this->GetCellUsingLocationIndex(elem_index);
                assert(p_cell);
 
                // Populate the vector of VTK cell data
                vtk_cell_data[elem_index] = (*cell_writer_iter)->GetCellDataForVtkOutput(p_cell, this);
            }
 
            mesh_writer.AddCellData((*cell_writer_iter)->GetVtkCellDataName(), vtk_cell_data);
        }
 
        // When outputting any CellData, we assume that the first cell is representative of all cells
        unsigned num_cell_data_items = this->Begin()->GetCellData()->GetNumItems();
        std::vector<std::string> cell_data_names = this->Begin()->GetCellData()->GetKeys();
 
        std::vector<std::vector<double> > cell_data;
        for (unsigned var=0; var<num_cell_data_items; var++)
        {
            std::vector<double> cell_data_var(num_cells);
            cell_data.push_back(cell_data_var);
        }
 
        // Loop over vertex elements ///\todo #2512 - replace with loop over cells
        for (auto elem_iter = mpMutableVertexMesh->GetElementIteratorBegin();
                elem_iter != mpMutableVertexMesh->GetElementIteratorEnd();
                ++elem_iter)
        {
            // Get index of this element in the vertex mesh
            unsigned elem_index = elem_iter->GetIndex();
 
            // Get the cell corresponding to this element
            CellPtr p_cell = this->GetCellUsingLocationIndex(elem_index);
            assert(p_cell);
 
            for (unsigned var=0; var<num_cell_data_items; var++)
            {
                cell_data[var][elem_index] = p_cell->GetCellData()->GetItem(cell_data_names[var]);
            }
        }
        for (unsigned var=0; var<num_cell_data_items; var++)
        {
            mesh_writer.AddCellData(cell_data_names[var], cell_data[var]);
        }
    }
 
    unsigned num_timesteps = SimulationTime::Instance()->GetTimeStepsElapsed();
    std::stringstream time;
    time << num_timesteps;
 
    mesh_writer.WriteVtkUsingMesh(*mpMutableVertexMesh, time.str());
 
    *(this->mpVtkMetaFile) << "        <DataSet timestep=\"";
    *(this->mpVtkMetaFile) << num_timesteps;
    *(this->mpVtkMetaFile) << "\" group=\"\" part=\"0\" file=\"results_";
    *(this->mpVtkMetaFile) << num_timesteps;
    *(this->mpVtkMetaFile) << ".vtu\"/>\n";
 
#endif //CHASTE_VTK
}
 
template<unsigned DIM>
void VertexBasedCellPopulation<DIM>::WriteCellEdgeVtkResultsToFile(const std::string& rDirectory)
{
#ifdef CHASTE_VTK
    //Writes cell only data
    {
        // Create mesh writer for VTK output
        VertexMeshWriter<DIM, DIM> mesh_writer(rDirectory, "cell_results", false);
 
        // Iterate over any cell writers that are present
        unsigned num_cells = this->GetNumAllCells();
        for (typename std::vector<boost::shared_ptr<AbstractCellWriter<DIM, DIM> > >::iterator cell_writer_iter = this->mCellWriters.begin();
                cell_writer_iter != this->mCellWriters.end();
                ++cell_writer_iter)
        {
            // Create vector to store VTK cell data
            std::vector<double> vtk_cell_data(num_cells);
 
            // Iterate over vertex elements ///\todo #2512 - replace with loop over cells
            for (typename VertexMesh<DIM,DIM>::VertexElementIterator elem_iter = mpMutableVertexMesh->GetElementIteratorBegin();
                    elem_iter != mpMutableVertexMesh->GetElementIteratorEnd();
                    ++elem_iter)
            {
                // Get index of this element in the vertex mesh
                unsigned elem_index = elem_iter->GetIndex();
 
                // Get the cell corresponding to this element
                CellPtr p_cell = this->GetCellUsingLocationIndex(elem_index);
                assert(p_cell);
 
                // Populate the vector of VTK cell data
                vtk_cell_data[elem_index] = (*cell_writer_iter)->GetCellDataForVtkOutput(p_cell, this);
            }
 
            mesh_writer.AddCellData((*cell_writer_iter)->GetVtkCellDataName(), vtk_cell_data);
        }
 
        // When outputting any CellData, we assume that the first cell is representative of all cells
        unsigned num_cell_data_items = this->Begin()->GetCellData()->GetNumItems();
        std::vector<std::string> cell_data_names = this->Begin()->GetCellData()->GetKeys();
 
        std::vector<std::vector<double> > cell_data;
        for (unsigned var=0; var<num_cell_data_items; var++)
        {
            std::vector<double> cell_data_var(num_cells);
            cell_data.push_back(cell_data_var);
        }
 
        // Loop over vertex elements ///\todo #2512 - replace with loop over cells
        for (typename VertexMesh<DIM,DIM>::VertexElementIterator elem_iter = mpMutableVertexMesh->GetElementIteratorBegin();
                elem_iter != mpMutableVertexMesh->GetElementIteratorEnd();
                ++elem_iter)
        {
            // Get index of this element in the vertex mesh
            unsigned elem_index = elem_iter->GetIndex();
 
            // Get the cell corresponding to this element
            CellPtr p_cell = this->GetCellUsingLocationIndex(elem_index);
            assert(p_cell);
 
            for (unsigned var=0; var<num_cell_data_items; var++)
            {
                cell_data[var][elem_index] = p_cell->GetCellData()->GetItem(cell_data_names[var]);
            }
        }
        for (unsigned var=0; var<num_cell_data_items; var++)
        {
            mesh_writer.AddCellData(cell_data_names[var], cell_data[var]);
        }
 
        unsigned num_timesteps = SimulationTime::Instance()->GetTimeStepsElapsed();
        std::stringstream time;
        time << num_timesteps;
 
        mesh_writer.WriteVtkUsingMesh(*mpMutableVertexMesh, time.str());
 
        *(this->mpVtkMetaFile) << "        <DataSet timestep=\"";
        *(this->mpVtkMetaFile) << num_timesteps;
        *(this->mpVtkMetaFile) << "\" group=\"\" part=\"0\" file=\"cell_results_";
        *(this->mpVtkMetaFile) << num_timesteps;
        *(this->mpVtkMetaFile) << ".vtu\"/>\n";
    }
    // Create mesh writer for VTK output
    TrapezoidEdgeVertexMeshWriter<DIM, DIM> mesh_writer(rDirectory, "results", false);
    unsigned num_edges = 0;
 
    // Here elements are synonymous with cells
    const unsigned num_cells = this->GetNumElements();
    //Similarly as in TrapEdgeVerteMeshWriter, but instead of nodes
    //we fill edge arrays
    //The first value MUST be zero
    std::vector<unsigned> cell_offset_dist(num_cells);
    //The order of stored data is illustrated below:
    // [_____|_][____|_]
    //  ^^^^  ^
    // edge   cell interior
    for (unsigned i=1; i<num_cells; ++i)
    {
        cell_offset_dist[i] = cell_offset_dist[i-1]+this->GetElement(i-1)->GetNumEdges()+1;
        num_edges += this->GetElement(i)->GetNumEdges();
    }
    // Total number of edges
    num_edges += this->GetElement(0)->GetNumEdges();
 
    // Iterate over any cell writers that are present
    // The data that is written below is associated with the entire cell
    // E.g. the cell age. Thus, edges also share the same characteristic
    for (auto cell_writer : this->mCellWriters)
    {
        // Create vector to store VTK cell data
        std::vector<double> vtk_cell_data(num_edges+num_cells);
 
        // Iterate over vertex elements ///\todo #2512 - replace with loop over cells
        for (auto elem_iter = mpMutableVertexMesh->GetElementIteratorBegin();
             elem_iter != mpMutableVertexMesh->GetElementIteratorEnd();
             ++elem_iter)
        {
            // Get index of this element in the vertex mesh
            unsigned elem_index = elem_iter->GetIndex();
 
            // Get the cell corresponding to this element
            CellPtr p_cell = this->GetCellUsingLocationIndex(elem_index);
            assert(p_cell);
 
            // Write the same property in all the edges
            unsigned elem_num_edges = elem_iter->GetNumEdges();
 
            // Edge data
            for (unsigned e = 0; e < elem_num_edges; ++e)
            {
                // Populate the vector of VTK cell data
                vtk_cell_data[cell_offset_dist[elem_index]+e] = cell_writer->GetCellDataForVtkOutput(p_cell, this);
            }
            // Internal cell data
            vtk_cell_data[cell_offset_dist[elem_index]+elem_num_edges] = cell_writer->GetCellDataForVtkOutput(p_cell, this);
        }
        mesh_writer.AddCellData(cell_writer->GetVtkCellDataName(), vtk_cell_data);
    }
    // When outputting CellData and CellEdgeData, we assume that the first cell
    // and its edges are representative of the population
 
    // Get cell/edge data names
    const unsigned num_cell_data_items = this->Begin()->GetCellData()->GetNumItems();
    std::vector<std::string> cell_data_names = this->Begin()->GetCellData()->GetKeys();
 
    const unsigned num_edge_data_items = this->Begin()->GetCellEdgeData()->GetNumItems();
    std::vector<std::string> edge_data_names = this->Begin()->GetCellEdgeData()->GetKeys();
 
    // Total number of data items. Each data item (edge+interior) has its own value
    const unsigned num_data_items = num_edge_data_items + num_cell_data_items;
    std::vector<std::string> data_names(num_data_items);
    for (unsigned var=0; var<num_edge_data_items; ++var)
    {
        data_names[var] = edge_data_names[var];
    }
    for (unsigned var=num_edge_data_items; var<num_data_items; ++var)
    {
        data_names[var] = cell_data_names[var-num_edge_data_items];
    }
    std::vector<std::vector<double> > data_values(num_data_items,
                                                  std::vector<double>(num_edges + num_cells));
 
    // Writing CellEdgeData values to the edges of the cells
    // Loop over vertex elements ///\todo #2512 - replace with loop over cells
    for (auto elem_iter = mpMutableVertexMesh->GetElementIteratorBegin();
         elem_iter != mpMutableVertexMesh->GetElementIteratorEnd();
         ++elem_iter)
    {
        const unsigned elem_index = elem_iter->GetIndex();
        CellPtr p_cell = this->GetCellUsingLocationIndex(elem_index);
        assert(p_cell);
 
        // Edge data for interior data is set to zero.
        unsigned elem_num_edges = elem_iter->GetNumEdges();
        for (unsigned var = 0; var < num_edge_data_items; ++var)
        {
            // Write the same property in all the edges
            for (unsigned e = 0; e < elem_num_edges; ++e)
            {
                data_values[var][cell_offset_dist[elem_index]+e] = p_cell->GetCellEdgeData()->GetItem(data_names[var])[e];
            }
            // Cell interior is set to zero
            data_values[var][cell_offset_dist[elem_index]+elem_num_edges] = 0.0;
        }
    }
 
    // Writing CellData values to the interior of the cells
    // Loop over vertex elements ///\todo #2512 - replace with loop over cells
    for (auto elem_iter = mpMutableVertexMesh->GetElementIteratorBegin();
         elem_iter != mpMutableVertexMesh->GetElementIteratorEnd();
         ++elem_iter)
    {
        // Get index of this element in the vertex mesh
        unsigned elem_index = elem_iter->GetIndex();
        unsigned elem_num_edges = elem_iter->GetNumEdges();
 
        // Get the cell corresponding to this element
        CellPtr p_cell = this->GetCellUsingLocationIndex(elem_index);
        assert(p_cell);
 
        for (unsigned var = num_edge_data_items; var<num_data_items; ++var)
        {
            // Data in the edges are set to 0
            for (unsigned e = 0; e < elem_num_edges; ++e)
            {
                data_values[var][cell_offset_dist[elem_index]+e] = 0.0;
            }
            // Filling cell interior data
            data_values[var][cell_offset_dist[elem_index]+elem_num_edges] = p_cell->GetCellData()->GetItem(data_names[var]);
        }
    }
 
    for (unsigned var=0; var<num_data_items; var++)
    {
        mesh_writer.AddCellData(data_names[var], data_values[var]);
    }
 
    unsigned num_timesteps = SimulationTime::Instance()->GetTimeStepsElapsed();
    std::stringstream time;
    time << num_timesteps;
 
    mesh_writer.WriteVtkUsingMesh(*mpMutableVertexMesh, time.str());
 
    *(this->mpVtkMetaFile) << "        <DataSet timestep=\"";
    *(this->mpVtkMetaFile) << num_timesteps;
    *(this->mpVtkMetaFile) << "\" group=\"\" part=\"0\" file=\"results_";
    *(this->mpVtkMetaFile) << num_timesteps;
    *(this->mpVtkMetaFile) << ".vtu\"/>\n";
#endif //CHASTE_VTK
}
 
template<unsigned DIM>
void VertexBasedCellPopulation<DIM>::OpenWritersFiles(OutputFileHandler& rOutputFileHandler)
{
    if (this->mOutputResultsForChasteVisualizer)
    {
        if (!this-> template HasWriter<CellPopulationElementWriter>())
        {
            this-> template AddPopulationWriter<CellPopulationElementWriter>();
        }
    }
 
    if (mOutputCellRearrangementLocations)
    {
        if (!this-> template HasWriter<VertexT1SwapLocationsWriter>())
        {
            this-> template AddPopulationWriter<VertexT1SwapLocationsWriter>();
        }
        if (!this-> template HasWriter<VertexT2SwapLocationsWriter>())
        {
            this-> template AddPopulationWriter<VertexT2SwapLocationsWriter>();
        }
        if (!this-> template HasWriter<VertexT3SwapLocationsWriter>())
        {
            this-> template AddPopulationWriter<VertexT3SwapLocationsWriter>();
        }
        if (!this-> template HasWriter<VertexIntersectionSwapLocationsWriter>())
        {
            this-> template AddPopulationWriter<VertexIntersectionSwapLocationsWriter>();
        }
    }
 
    AbstractCellPopulation<DIM>::OpenWritersFiles(rOutputFileHandler);
}
 
template<unsigned DIM>
bool VertexBasedCellPopulation<DIM>::GetOutputCellRearrangementLocations()
{
    return mOutputCellRearrangementLocations;
}
 
template<unsigned DIM>
void VertexBasedCellPopulation<DIM>::SetOutputCellRearrangementLocations(bool outputCellRearrangementLocations)
{
    mOutputCellRearrangementLocations = outputCellRearrangementLocations;
}
 
template<unsigned DIM>
void VertexBasedCellPopulation<DIM>::OutputCellPopulationParameters(out_stream& rParamsFile)
{
    *rParamsFile << "\t\t<CellRearrangementThreshold>" << mpMutableVertexMesh->GetCellRearrangementThreshold() << "</CellRearrangementThreshold>\n";
    *rParamsFile << "\t\t<T2Threshold>" <<  mpMutableVertexMesh->GetT2Threshold() << "</T2Threshold>\n";
    *rParamsFile << "\t\t<CellRearrangementRatio>" << mpMutableVertexMesh->GetCellRearrangementRatio() << "</CellRearrangementRatio>\n";
    *rParamsFile << "\t\t<OutputCellRearrangementLocations>" << mOutputCellRearrangementLocations << "</OutputCellRearrangementLocations>\n";
 
    // Add the division rule parameters
    *rParamsFile << "\t\t<VertexBasedDivisionRule>\n";
    mpVertexBasedDivisionRule->OutputCellVertexBasedDivisionRuleInfo(rParamsFile);
    *rParamsFile << "\t\t</VertexBasedDivisionRule>\n";
 
    // Call method on direct parent class
    AbstractOffLatticeCellPopulation<DIM>::OutputCellPopulationParameters(rParamsFile);
}
 
template<unsigned DIM>
double VertexBasedCellPopulation<DIM>::GetWidth(const unsigned& rDimension)
{
    // Call GetWidth() on the mesh
    double width = this->mrMesh.GetWidth(rDimension);
 
    return width;
}
 
template<unsigned DIM>
std::set<unsigned> VertexBasedCellPopulation<DIM>::GetNeighbouringNodeIndices(unsigned index)
{
    return mpMutableVertexMesh->GetNeighbouringNodeIndices(index);
}
 
template<unsigned DIM>
boost::shared_ptr<AbstractVertexBasedDivisionRule<DIM> > VertexBasedCellPopulation<DIM>::GetVertexBasedDivisionRule()
{
    return mpVertexBasedDivisionRule;
}
 
template<unsigned DIM>
void VertexBasedCellPopulation<DIM>::SetVertexBasedDivisionRule(boost::shared_ptr<AbstractVertexBasedDivisionRule<DIM> > pVertexBasedDivisionRule)
{
    mpVertexBasedDivisionRule = pVertexBasedDivisionRule;
}
 
template<unsigned DIM>
TetrahedralMesh<DIM, DIM>* VertexBasedCellPopulation<DIM>::GetTetrahedralMeshForPdeModifier()
{
    // This method only works in 2D sequential
    if (DIM != 2)
    {
        EXCEPTION("This function is only valid in 2D"); // LCOV_EXCL_LINE
    }
    assert(PetscTools::IsSequential());
 
    unsigned num_vertex_nodes = mpMutableVertexMesh->GetNumNodes();
    unsigned num_vertex_elements = mpMutableVertexMesh->GetNumElements();
 
    std::string mesh_file_name = "mesh";
 
    // Get a unique temporary foldername
    std::stringstream pid;
    pid << getpid();
    OutputFileHandler output_file_handler("2D_temporary_tetrahedral_mesh_" + pid.str());
    std::string output_dir = output_file_handler.GetOutputDirectoryFullPath();
 
    // Compute the number of nodes in the TetrahedralMesh
    unsigned num_tetrahedral_nodes = num_vertex_nodes + num_vertex_elements;
 
    // Write node file
    out_stream p_node_file = output_file_handler.OpenOutputFile(mesh_file_name+".node");
    (*p_node_file) << std::scientific;
    (*p_node_file) << std::setprecision(20);
    (*p_node_file) << num_tetrahedral_nodes << "\t2\t0\t1" << std::endl;
 
    // Begin by writing each node in the VertexMesh
    for (unsigned node_index=0; node_index<num_vertex_nodes; node_index++)
    {
        Node<DIM>* p_node = mpMutableVertexMesh->GetNode(node_index);
 
        unsigned index = p_node->GetIndex();
        const c_vector<double, DIM>& r_location = p_node->rGetLocation();
        unsigned is_boundary_node = p_node->IsBoundaryNode() ? 1 : 0;
 
        (*p_node_file) << index << "\t" << r_location[0] << "\t" << r_location[1] << "\t" << is_boundary_node << std::endl;
    }
 
    // Now write an additional node at each VertexElement's centroid
    unsigned num_tetrahedral_elements = 0;
    for (unsigned vertex_elem_index=0; vertex_elem_index<num_vertex_elements; vertex_elem_index++)
    {
        unsigned index = num_vertex_nodes + vertex_elem_index;
 
        c_vector<double, DIM> location = mpMutableVertexMesh->GetCentroidOfElement(vertex_elem_index);
 
        // Any node located at a VertexElement's centroid will not be a boundary node
        unsigned is_boundary_node = 0;
        (*p_node_file) << index << "\t" << location[0] << "\t" << location[1] << "\t" << is_boundary_node << std::endl;
 
        // Also keep track of how many tetrahedral elements there will be
        num_tetrahedral_elements += mpMutableVertexMesh->GetElement(vertex_elem_index)->GetNumNodes();
    }
    p_node_file->close();
 
    // Write element file
    out_stream p_elem_file = output_file_handler.OpenOutputFile(mesh_file_name+".ele");
    (*p_elem_file) << std::scientific;
    (*p_elem_file) << num_tetrahedral_elements << "\t3\t0" << std::endl;
 
    std::set<std::pair<unsigned, unsigned> > tetrahedral_edges;
 
    unsigned tetrahedral_elem_index = 0;
    for (unsigned vertex_elem_index=0; vertex_elem_index<num_vertex_elements; vertex_elem_index++)
    {
        VertexElement<DIM, DIM>* p_vertex_element = mpMutableVertexMesh->GetElement(vertex_elem_index);
 
        // Iterate over nodes owned by this VertexElement
        unsigned num_nodes_in_vertex_element = p_vertex_element->GetNumNodes();
        for (unsigned local_index=0; local_index<num_nodes_in_vertex_element; local_index++)
        {
            unsigned node_0_index = p_vertex_element->GetNodeGlobalIndex(local_index);
            unsigned node_1_index = p_vertex_element->GetNodeGlobalIndex((local_index+1)%num_nodes_in_vertex_element);
            unsigned node_2_index = num_vertex_nodes + vertex_elem_index;
 
            (*p_elem_file) << tetrahedral_elem_index++ << "\t" << node_0_index << "\t" << node_1_index << "\t" << node_2_index << std::endl;
 
            // Add edges to the set if they are not already present
            std::pair<unsigned, unsigned> edge_0 = this->CreateOrderedPair(node_0_index, node_1_index);
            std::pair<unsigned, unsigned> edge_1 = this->CreateOrderedPair(node_1_index, node_2_index);
            std::pair<unsigned, unsigned> edge_2 = this->CreateOrderedPair(node_2_index, node_0_index);
 
            tetrahedral_edges.insert(edge_0);
            tetrahedral_edges.insert(edge_1);
            tetrahedral_edges.insert(edge_2);
        }
    }
    p_elem_file->close();
 
    // Write edge file
    out_stream p_edge_file = output_file_handler.OpenOutputFile(mesh_file_name+".edge");
    (*p_edge_file) << std::scientific;
    (*p_edge_file) << tetrahedral_edges.size() << "\t1" << std::endl;
 
    unsigned edge_index = 0;
    for (std::set<std::pair<unsigned, unsigned> >::iterator edge_iter = tetrahedral_edges.begin();
         edge_iter != tetrahedral_edges.end();
         ++edge_iter)
    {
        std::pair<unsigned, unsigned> this_edge = *edge_iter;
 
        // To be a boundary edge both nodes need to be boundary nodes.
        bool is_boundary_edge = false;
        if (this_edge.first  < mpMutableVertexMesh->GetNumNodes() &&
            this_edge.second  < mpMutableVertexMesh->GetNumNodes())
        {
            is_boundary_edge = (mpMutableVertexMesh->GetNode(this_edge.first)->IsBoundaryNode() &&
                                mpMutableVertexMesh->GetNode(this_edge.second)->IsBoundaryNode() );
        }
        unsigned is_boundary_edge_unsigned = is_boundary_edge ? 1 : 0;
 
        (*p_edge_file) << edge_index++ << "\t" << this_edge.first << "\t" << this_edge.second << "\t" << is_boundary_edge_unsigned << std::endl;
    }
    p_edge_file->close();
 
    // Having written the mesh to file, now construct it using TrianglesMeshReader
    TetrahedralMesh<DIM, DIM>* p_mesh = new TetrahedralMesh<DIM, DIM>;
 
    // Nested scope so reader is destroyed before we remove the temporary files
    {
        TrianglesMeshReader<DIM, DIM> mesh_reader(output_dir + mesh_file_name);
        p_mesh->ConstructFromMeshReader(mesh_reader);
    }
 
    // Delete the temporary files
    output_file_handler.FindFile("").Remove();
 
    // The original files have been deleted, it is better if the mesh object forgets about them
    p_mesh->SetMeshHasChangedSinceLoading();
 
    return p_mesh;
}
 
template<unsigned DIM>
std::vector< c_vector< double, DIM > > VertexBasedCellPopulation<DIM>::GetLocationsOfT2Swaps()
{
    return mLocationsOfT2Swaps;
}
 
template<unsigned DIM>
std::vector< unsigned > VertexBasedCellPopulation<DIM>::GetCellIdsOfT2Swaps()
{
    return mCellIdsOfT2Swaps;
}
 
template<unsigned DIM>
void VertexBasedCellPopulation<DIM>::AddLocationOfT2Swap(c_vector< double, DIM> locationOfT2Swap)
{
    mLocationsOfT2Swaps.push_back(locationOfT2Swap);
}
 
template<unsigned DIM>
void VertexBasedCellPopulation<DIM>::AddCellIdOfT2Swap(unsigned idOfT2Swap)
{
    mCellIdsOfT2Swaps.push_back(idOfT2Swap);
}
 
template<unsigned DIM>
void VertexBasedCellPopulation<DIM>::ClearLocationsAndCellIdsOfT2Swaps()
{
    mCellIdsOfT2Swaps.clear();
    mLocationsOfT2Swaps.clear();
}
 
template<unsigned DIM>
bool VertexBasedCellPopulation<DIM>::IsPdeNodeAssociatedWithNonApoptoticCell(unsigned pdeNodeIndex)
{
    bool non_apoptotic_cell_present = true;
 
    if (pdeNodeIndex < this->GetNumNodes())
    {
        std::set<unsigned> containing_element_indices = this->GetNode(pdeNodeIndex)->rGetContainingElementIndices();
 
        for (std::set<unsigned>::iterator iter = containing_element_indices.begin();
             iter != containing_element_indices.end();
             iter++)
        {
            if (this->GetCellUsingLocationIndex(*iter)->template HasCellProperty<ApoptoticCellProperty>() )
            {
                non_apoptotic_cell_present = false;
                break;
            }
        }
    }
    else
    {
        /*
         * This node of the tetrahedral finite element mesh is in the centre of the element of the
         * vertex-based cell population, so we can use an offset to compute which cell to interrogate.
         */
        non_apoptotic_cell_present = !(this->GetCellUsingLocationIndex(pdeNodeIndex - this->GetNumNodes())->template HasCellProperty<ApoptoticCellProperty>());
    }
 
    return non_apoptotic_cell_present;
}
 
template<unsigned DIM>
double VertexBasedCellPopulation<DIM>::GetCellDataItemAtPdeNode(
        unsigned pdeNodeIndex,
        std::string& rVariableName,
        bool dirichletBoundaryConditionApplies,
        double dirichletBoundaryValue)
{
    unsigned num_nodes = this->GetNumNodes();
    double value = 0.0;
 
    // Cells correspond to nodes in the centre of the vertex element; nodes on vertices have averaged values from containing cells
 
    if (pdeNodeIndex >= num_nodes)
    {
        // Offset to relate elements in vertex mesh to nodes in tetrahedral mesh
        assert(pdeNodeIndex-num_nodes < num_nodes);
 
        CellPtr p_cell = this->GetCellUsingLocationIndex(pdeNodeIndex - num_nodes);
        value = p_cell->GetCellData()->GetItem(rVariableName);
    }
    else
    {
        if (dirichletBoundaryConditionApplies)
        {
            // We need to impose the Dirichlet boundaries again here as not represented in cell data
            value = dirichletBoundaryValue;
        }
        else
        {
            assert(pdeNodeIndex < num_nodes);
            Node<DIM>* p_node = this->GetNode(pdeNodeIndex);
 
            // Average over data from containing elements (cells)
            std::set<unsigned> containing_elements = p_node->rGetContainingElementIndices();
            for (std::set<unsigned>::iterator index_iter = containing_elements.begin();
                 index_iter != containing_elements.end();
                 ++index_iter)
            {
                assert(*index_iter < num_nodes);
                CellPtr p_cell = this->GetCellUsingLocationIndex(*index_iter);
                value += p_cell->GetCellData()->GetItem(rVariableName);
            }
            value /= containing_elements.size();
        }
    }
 
    return value;
}
 
template<unsigned DIM>
double VertexBasedCellPopulation<DIM>::GetDefaultTimeStep()
{
    return 0.002;
}
 
template<unsigned DIM>
void VertexBasedCellPopulation<DIM>::WriteDataToVisualizerSetupFile(out_stream& pVizSetupFile)
{
    if (bool(dynamic_cast<Cylindrical2dVertexMesh*>(&(this->mrMesh))))
    {
        *pVizSetupFile << "MeshWidth\t" << this->GetWidth(0) << "\n";
    }
}
 
template<unsigned DIM>
void VertexBasedCellPopulation<DIM>::SimulationSetupHook(AbstractCellBasedSimulation<DIM, DIM>* pSimulation)
{
    MAKE_PTR_ARGS(T2SwapCellKiller<DIM>, p_t2_swap_cell_killer, (this));
    pSimulation->AddCellKiller(p_t2_swap_cell_killer);
}
 
 
template<unsigned DIM>
bool VertexBasedCellPopulation<DIM>::GetRestrictVertexMovementBoolean()
{
    return mRestrictVertexMovement;
}
 
template<unsigned DIM>
void VertexBasedCellPopulation<DIM>::SetRestrictVertexMovementBoolean(bool restrictMovement)
{
    mRestrictVertexMovement = restrictMovement;
}
 
template<unsigned DIM>
VertexBasedPopulationSrn<DIM>& VertexBasedCellPopulation<DIM>::rGetVertexBasedPopulationSrn()
{
    return mPopulationSrn;
}
 
template<unsigned DIM>
const VertexBasedPopulationSrn<DIM>& VertexBasedCellPopulation<DIM>::rGetVertexBasedPopulationSrn() const
{
    return mPopulationSrn;
}
 
template<unsigned DIM>
void VertexBasedCellPopulation<DIM>::SetWriteCellVtkResults(const bool new_val)
{
    mWriteCellVtkResults = new_val;
}
 
template<unsigned DIM>
void VertexBasedCellPopulation<DIM>::SetWriteEdgeVtkResults(const bool new_val)
{
    mWriteEdgeVtkResults = new_val;
}
 
// Explicit instantiation
template class VertexBasedCellPopulation<1>;
template class VertexBasedCellPopulation<2>;
template class VertexBasedCellPopulation<3>;
 
// Serialization for Boost >= 1.36
#include "SerializationExportWrapperForCpp.hpp"
EXPORT_TEMPLATE_CLASS_SAME_DIMS(VertexBasedCellPopulation)